Citation
Motion control of a citrus-picking robot

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Title:
Motion control of a citrus-picking robot
Series Title:
Motion control of a citrus-picking robot
Creator:
Pool, Thomas Alan,
Place of Publication:
Gainesville FL
Publisher:
University of Florida
Publication Date:

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Subjects / Keywords:
Control loops ( jstor )
Fruits ( jstor )
Hydraulics ( jstor )
Kinetics ( jstor )
Pixels ( jstor )
Robots ( jstor )
Servomotors ( jstor )
Signals ( jstor )
Sliding ( jstor )
Velocity ( jstor )
City of Gainesville ( local )

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University of Florida
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University of Florida
Rights Management:
Copyright Thomas Alan Pool. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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030484770 ( alephbibnum )
21085429 ( oclc )

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Full Text











MOTION CONTROL OF A CITRUS-PICKING ROBOT


By

THOMAS ALAN POOL

















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1989















ACKNOWLEDGEMENTS


The author wishes to express sincere appreciation to Dr. Roy C. Harrell, his major

advisor and friend, for guidance and assistance provided during the graduate program. For the

enormous amounts of time Dr. Harrell invested reviewing this dissertation, the author is

especially grateful.

Thanks are also due to the professors who graciously gave of their time to serve on the

graduate committee: Dr. Keith Doty, Dr. John Staudhammer, Dr. Robert Peart, and Dr. Carl

Crane. These men provided necessary excitement and instruction for making the author capable

of completing this project.

Mr. Ralph Hoffman provided some very necessary assistance with the tests which are

described within this dissertation. He was always available with an encouraging word, never

even once refusing to assist with even the most mundane chores. For all of this, the author is

grateful.

Mr. Phil Adsit, a fellow graduate student, assisted with many of the programming

tasks which were undertaken in this work. He gave much-needed encouragement and advice as

he worked so closely with the author. Much appreciation is extended to Mr. P.

Financial assistance was awarded to the author in the form of a fellowship under the

USDA Food and Agricultural Sciences National Needs Graduate Fellowships Grants Program.

For this assistance, the author is also grateful.

Funding for the citrus picking robot was provided by Agricultural Industrial

Development, SpA, Catania, Italy.

Most importantly, the author expresses sincere thanks to his parents, Mr. and Mrs.

William H. Pool, for their encouragement and support during this project. Their leadership

and guidance proved invaluable to the completion of this work.

ii














TABLE OF CONTENTS

page

ACKNOW LEDGEM ENTS ............................................................ ........................... ii

LIST OF TABLES ....................................................................................................... vi

LIST OF FIGURES ..................................................................................................... vii

ABSTRACT ............................................................................................................... xiii

CHAPTERS

1 INTRODUCTION ........................................................... ........................... 1

2 OBJECTIVES OF RESEARCH .................................................. .................... 6

3 REVIEW OF LITERATURE ................................................................................. 9

Previous Robotics in Tree Fruit Harvest ........................................... ............. 9
Robot Kinem atics Background............................................ ....................... 14
Controls Background ......................................................... .......................... 16
Performance Specifications ................................................... ....................... 20

4 DESIGN OF THE FLORIDA CITRUS-PICKING ROBOT ................................... 21

M echanical Design .......................................................... ........................... 21
Control Computer ........................................................... ............................ 25
Hardware ............................................................... .............................. 25
Video system .......................................................... ........................ 26
Ultrasonics .......................................................... ............................ 27
Analog to digital converters .................................................... ............. 27
Parallel I/O signals .................................................. ...................... 28
Servo mechanisms .................................................... ...................... 28
Software ........................................................... .................................... 29
Picking M echanism ........................................................... ........................... 31
Construction ................................................................................................ 31
Fruit Sensor Package ..................................................................................... 33
CCD camera ......................................................... .......................... 33
Ultrasonic range sensor ................................................ .................... 34
Lights ............................................................. ................................ 35
Hydraulic Actuation ....................................................... ............................ 36
Position Sensors ......................................... ................ .................................. 37
Velocity Sensors ............................................................ ............................. 42





iii









page

5 ROBOT KINEM ATIC M ODEL ................................................ ..................... 45

M anipulator Kinem atics ............................................................................ 45
Im aging Kinematics ......................................................................................... 49
Vision-Servo Kinem atics .................................................................................. 50

6 ROBOT OPEN-LOOP DYNAM ICS ............................................. ................. 55

Background .......................................... ................. ...................................... 55
Param eter Estim ation ........................................................ .......................... 58
Results and Discussion.................................................................................... 64

7 PERFORM ANCE CRITERIA ..................................................... ................... 75

Background ................................................................................................... 75
Characteristics of Fruit M otion ................................................ .................... 76
Picking Envelope Definition .................................................. ...................... 78
Velocity Control Requirem ents ....................................................................... 82
Position Control Requirem ents ............................................................................. 84
Vision Control Requirements .................................................. ...................... 85
Summ ary of Performance Criteria ................................................................... .... 88

8 CONTROLLER SELECTION AND IMPLEMENTATION ................................... 90

Controller Selection ............................................................... 90
Control System Discretization .......................................................... ............ ...... 93
Controller Im plem entation .............................................................................. 97
Velocity Controllers ..................................................... ......................... 97
Position Controllers............................. ................. .................................. 99
Position Controller With Velocity Control Minor Loop ................................. 101
Vision Controllers ........................................................................................ 103
Controller Tuning ................................................................................................ 107
Velocity Controller Tuning ............................................................................ 110
Position Controller Tuning ............................................................................. 113
Position Controller with Velocity Control Minor Loop Tuning ........................ 115
Vision Controller Tuning................................................................................ 116
Sum mary ....................................................................................................... 118

9 RESULTS AND DISCUSSION ............................................................................ 120

Velocity Controller Performance ........................................................................ 120
Position Controller Performance .......................................................................... 127
Vision Controller Performance ............................................................................ 131
Dynam ic Perform ance................................................................................... 131
Static Perform ance................................................................................... 133
Overall Controller Perform ance....................... ............. ........................ 137
Perform ance in the Search Routine................................................................. 137
Performance During the Pick Cycle ............................................................... 140









page

10 SUM M ARY AND CONCLUSIONS ................................................................ 150

Sum m ary ....................................................................................................... 150
Conclusions ................................................................................... .... ............ 152

REFERENCES ........................................................................................................... 155

BIOGRAPHICAL SKETCH ........................................................................................ 157















LIST OF TABLES


Table page

4.1. Servo amplifier and servo valve characteristics. ........................................... 29

4.2. Conversion factors for changing A/D information to actual positions and
velocities of the robot's joints. .................................................................... 44

5.1. Link parameters for the orange-picking robot. .................................................... 48

5.2. Range of motion for the joint parameters of the orange-picking robot. ............... 49

6.1. Experimentally determined steady-state gains, damping ratios, and hydraulic
natural frequencies of joint 0 in relation to position of joint 2 and direction of
m option ............................................................................................................... 62

6.2. Experimentally determined steady-state gains, damping ratios, and hydraulic
natural frequencies of joint 1 in relation to position of joint 2 and direction of
m option ............................................................................................................... 64

6.3. Steady-state gains, hydraulic damping ratios, and hydraulic natural
frequencies as determined by analysis of the step test responses .......................... 65

7.1. Range of positions of a fruit's centroid to guarantee a successful pick ................... 82

7.2. Values read by vision system corresponding to the established picking
envelope. ...................................................................................................... 82

7.3. Summary of performance criteria for the velocity,position, and vision control
algorithm s. ................................................................................................... 89

8.1. Velocity control variables as used for the velocity controllers as shown in
Figure 8.6. ............................................................... ................................... 99

8.2. Position control variables as used in Figures 8.10, 8.11 and 8.12. ............................ 101

8.3. Position control variables as used in Figures 8.14 and 8.15. .................................... 103

8.4. Vision control variables as used in Figures 8.17 and 8.18. ...................................... 107

8.5. Final velocity controller parameters for joints 0, 1, and 2. ..................................... 112

8.6. Final position controller parameters for joints 0 and 1. ........................................ 114

8.7. Final vision controller parameters for joints 0 and 1. ........................................... 118

8.8. Final determined values for all controller parameters. ........................................ 119

vi















LIST OF FIGURES


Figure page

1.1. The Florida Laboratory. ............................................................................ 2

3.1. Kinematic link frames as attached to the links of a manipulator (Paul, 1981). ..... 15

4.1. The three degree-of-freedom orange-picking robot. ......................................... 22

4.2. Base support stand of the robot. ................................................................... 23

4.3. Outer link of the robot. ............................................................................... 24

4.4. The inner link ............................................................................................... 25

4.5. The sliding link .......................................................................................... .. 26

4.6. I/O hardware architecture of the control computer. ......................................... 27

4.7. Organization of the robot programming environment. ......................................... 30

4.8. Cutaway side view of the picking mechanism showing the position of the
ultrasonic transducer, the color CCD camera, and the lights. .............................. 32

4.9. Top view of the picking mechanism showing the drive linkage and the lever
arm for actuating the rotating lip mechanism. ................................... .......... 32

4.10. Picking mechanism actuation assembly. ......................................... ........... 33

4.11. Front view of the picking mechanism showing the color CCD camera, ultrasonic
transducer, and the four lights. .................................................................. 34

4.12. Horizontal field of view of the color CCD camera and lens combination in the
vertical plane. ........................................................... ................................ 35

4.13. Vertical field of view of the color CCD camera and lens combination in the
horizontal plane. ......................................................... .............................. 35

4.14. Circuit diagram of hydraulic power unit. ........................................ .......... 36

4.15. Circuit diagram of hydraulic actuators for joints 0 and 1 ..................................... 37

4.16 Circuit diagram of hydraulic motor actualtor for joint 2. .................................... 37

4.17. Circuit diagram of picking mechanism lip actuator. ........................................ 38

4.18. Circuit diagram of the position sensing potentiometers. ..................................... 39

vii









Figure page

4.19. Relationship between position of joint 0 and the A/D value of the position of
joint 0. ................................................................................................................. 40

4.20. Relationship between position of joint 1 and the A/D value of the position of
joint 1. ........................................................................................................... 41

4.21. Relationship between position of joint 2 and the A/D value of the position of
joint 2. ................................................................................................................ 42

4.22. Circuit diagram of the tachometers. ............................................................ 43

5.1. Kinematic frames of the three degree-of-freedom robot. .................................... 46

5.2. Kinematic frames as assigned to the links of the robot. ..................................... 47

5.3. Lens imaging geometry. ............................................................................... 50

5.4. Coordinate frame representation of the camera frame and the fruit position
with respect to the base frame. ................................................................... 52

6.1. Open-loop hydraulic servo system. ..................................................................... 56

6.2. Reduced block diagram of the open-loop system. .......................................... 56

6.3. Block diagram of the open-loop system with external torque load ...................... 58

6.4. Typical response of joint 0 of the orange-picking robot to a step input of 1200
D/A bits with joint 2 centered in the Hooke joint. ............................................... 61

6.5. Typical response joint 1 of the orange-picking robot to a step input of -500 D/A
bits with joint 2 centered in the Hooke Joint. .................................... ........... 63

6.6. Typical response of joint 2 of the orange-picking robot to a step input of 750 D/A
bits. ................................................................................................................... 65

6.7. Responses of joint 0 to a step input: (a) actual, (b) simulated.
h = 32.95 rad/sec, Sh = 0.30, Kv = 0.036 (deg/sec)/(D/A word) ........................... 69

6.8. Responses of joint 0 to a step input: (a) actual, (b) simulated.
h = 17.36 rad/sec, 0h = 0.16, Kv = 0.032 (deg/sec)/(D/A word) ........................... 70

6.9. Responses of joint 0 to a step input: (a) actual, (b) simulated.
h = 16.54 rad/sec, h = 0.31, Kv = 0.044 (deg/sec)/(D/A word) ............................. 71

6.10. Responses of joint 1 to a step input: (a) actual, (b) simulated.
= 31.87 rad/sec, 8h = 0.17, K, = 0.055 (deg/sec)/(D/A word) ........................... 72

6.11. Responses of joint 1 to a step input: (a) actual, (b) simulated.
h = 22.02 rad/sec, h = 0.31, Kv = 0.056 (deg/sec)/(D/A word) ........................... 73

6.12. Responses of joint 1 to a step input: (a) actual, (b) simulated.
(O = 21.47 rad/sec, 8h = 0.22, Kv = 0.056 (deg/sec)/(D/A word) ........................... 74

viii









Figure page

7.1. Typical observations of the motion of fruit swinging from the canopy of a tree
indicating the peak-to-peak magnitude of the fruit for various periods of
oscillation. ............................................................... .................................. 77

7.2. Apparatus for determining the picking envelope of the robot's end-effector. ......... 78

7.3. Picking range of the end-effector in the vertical plane located on the centerline
of axis 2. ........................................................................................................ 80

7.4. Picking range of the end-effector in the vertical plane located 1 cm from the
centerline of axis 2. ........................................................ ............................. 80

7.5. Picking range of the end-effector in the vertical plane located 2 cm from the
centerline of axis 2. ........................................................ ............................. 81

7.6. Relationship between the amplitude of a fruit and the amplitude of its image
on the camera image plane. ..................................... .................................... 86

7.7. Maximum allowable phase lag as a function of amplitude ratio, ar/af, as
described in equation 7-3. Maximum allowable error = 47 pixels (2 cm). Case I:
af = 50 cm (1077 pixels). Case II: af = 12.5 cm (269 pixels) ................................. 88

8.1. Bode diagram of the open-loop velocity control system. ..................................... 91

8.2. Bode diagram of the open-loop position control system. ..................................... 92

8.3. Simulated responses of continuous-time and discrete domain controllers and the
percent error differences.
Kc = -15.00, Td = 3.7, and ri = 1.0 Kc = 4.00, rd = 0.02, and i = 0.01
(a) continuous-time domain controller (d) continuous-time domain controller
(b) discrete controller (e) discrete controller
(c) percent error (f) percent error ................................ 96

8.4. Subroutine to calculate coefficients of the discretized controller from the
continuous domain parameters. .................................................................... 97

8.5. Block diagram of the velocity control loop. ........................................................ 98

8.6. Implementation of the Lag-Lead velocity controllers as found in the software
environment. Note: change O's in the variables to 1's or 2's for joint 1 or 2. ........... 98

8.9. Block diagram of the position control feedback loop for joints 0 and 1 .................. 100

8.10. Position error calculation for joints 0 and 1 from ERRORCAL:C subroutine ........... 100

8.11. Position control subroutine for joint 0. .................................................................. 100

8.12. Position control subroutine for joint 1. .................................................................. 100

8.13. Block diagram of the position control feedback loop with velocity feedback in a
m inor loop. ......................................................................................................... 102









Figure page

8.14. Position error calculation for joint 2 as accomplished in the ERRORCAL:C
routine. .............................................................................................................. 102

8.15. Major loop position control subroutine for joint 2. ................................................ 103

8.16. Block diagram of a vision control loop. .............................................................. 104

8.17. Vision gain implementation scheme. .................................................................. 105

8.18. Vision error calculations as performed in ERRORCAL:C routine. ........................ 106

8.19. Vision control subroutine. ...................... ............................................................... 106

8.20. Bode diagram of a controlled second-order system indicating the effects changes
in the lag tim e constant, Ti .................................................................................. 108

8.21. Bode diagram of a controlled second-order system indicating the effects changes
in the lead time constant, d. .............................................................. 108

8.22. Bode diagram of a controlled second-order system indicating the effects changes
in the controller gain, K ............................................. ..................................... 109

8.23. Generalized open-loop Bode diagram of a lag-lead compensated velocity
control system ............................................................................................... 111

8.24. Bode diagram of an open-loop compensated position control system. ................... 114

8.25. Open-loop Bode diagram for joint 0 vision system indicating the gain
requirements for picking worst case fruit motions. ............................................... 117

9.1. Typical closed-loop response of joint 0 to an alternating step input of
16.3 deg/sec, joint 2 extended. ............................................................................ 121

9.2. Typical closed-loop response of joint 0 to an alternating step input of
39.1 deg/sec, joint 2 positioned at its mid location. ........................................... 122

9.3. Typical closed-loop response of joint 0 to an alternating step input of
48.8 deg/sec, joint 2 retracted. ........................................................................... 122

9.4. Typical closed-loop response of joint 1 to an alternating step input of
32.6 deg/sec, joint 2 retracted. ........................................................................... 122

9.5. Typical closed-loop response of joint 1 to an alternating step input of
32.6 deg/sec, joint 2 extended. ............................................................................ 124

9.6. Typical closed-loop response of joint 1 to an alternating step input of
32.6 deg/sec, joint 2 centered in the support. ..................................................... 125

9.7. Typical closed-loop response of joint 2 to step inputs of 34.8 cm/sec .................... 126

9.8. Typical closed-loop response of joint 2 to an alternating step input of
104.4 cm /sec. ............................................................................................... 126

x









Figure page

9.9. Typical closed-loop response of joint 0 to a step change in the position setpoint
of +51.8 deg. .................................................................................................. 128

9.10. Worst case closed-loop response of joint 0 to a step change in the position
setpoint of -51.8 deg with joint 2 extended. ......................................................... 128

9.11. Typical closed-loop response of joint 1 to a step change in the position setpoint
of +23.8 deg. .................................................................................................. 129

9.12. Worst case closed-loop response of joint 1 to a step change in the position
setpoint of -23.8 deg with joint 2 extended. ......................................................... 130

9.13. Typical closed-loop response of joint 2 to a step change in the position setpoint
of 43.8 cm ......................................................................................... ........... 131

9.14. Worst case closed-loop response of joint 2 to a step change in the position
setpoint of 43.8 cm ......................................................................................... 131

9.15. Closed-loop magnitude and phase plots for joint 0 vision control system:
Kc = 4.0 (D/A word)/pixel Kp = 2.27 pixels/(D/A word)
Ti= 0.02 sec = 0.18
Td =0.01 sec h = 17 rad/sec ......................... 133

9.16. Closed-loop magnitude and phase plots for joint 1 vision control system:
Kc = 4.0 (D/A word)/pixel Kp = 3.85 pixels/(D/A word)
Ti =0.02 sec 8 = 0.18
d = 0.01 sec h = 22 rad/sec ......................... 134

9.17. Pickable fruit motions as determined from the closed-loop response of the
manipulator along with the fruit motions determined to exist in the grove........... 135

9.18. Closed-loop vision system response of joint 0 to a setpoint of 200 pixels with the
beginning fruit location of 50 pixels in the vertical direction in the image
plane ........................................................................................................... 136

9.19. Closed-loop vision system response of joint 1 to a setpoint of 192 pixels with a
beginning fruit location of 37 pixels in the horizontal direction in the image
plane. ................................................................................................................ 136

9.20. Plot of position and position setpoint of joint 0 during a typical fruit search
routine. .............................................................................................................. 138

9.21. Plot of velocity and velocity setpoint of joint 0 during a typical fruit search
routine ......................................................................................................... 138

9.22. Plot of position and position setpoint of joint 1 during a typical fruit search
routine. ............................................................................................................. 139

9.23. Plot of velocity and velocity setpoint of joint 0 during a typical fruit search
routine. .............................................................................................................. 139

9.24. Control modes and position and velocity of joint 2 during a typical pick cycle ....... 141

xi









Figure page

9.25. Position of joints 0 and 1 and locations of the furit during a typical pick. cycle....... 142

9.26. Controller responses to large fruit motions using the wait state. ........................... 144

9.27. Control modes and joint 0 and 1 positions during a pick cycle with large fruit
motion which required use of the wait state. ..................................................... 145

9.28. Pick cycle aborted because of a collision during the fruit approach routine. ........... 148















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

MOTION CONTROL OF A CITRUS-PICKING ROBOT

By

Thomas Alan Pool

May, 1989



Chairman: Dr. Roy C. Harrell
Major Department: Agricultural Engineering

This work focused on the design and implementation of motion control strategies for a

citrus-picking robot. These control strategies were used by an intelligence base for the robot

which required precise control of the individual joints based on information from velocity,

position, and vision sensors. The type of controller that was used at any instant was determined

by this intelligence base, which called the applicable controller and supplied it with

setpoints.

Initially, the design of the hydraulically actuated, three degree-of-freedom,

spherical coordinate arm was presented. The picking mechanism housed the vision and

ultrasonic sensors, which provided real-time end of the arm fruit position sensing and a rotating

lip for removing the fruit from the tree. From the known dimensions of the robot, a kinematic

model was derived. This model provided a basis upon which the position of the joints could be

related to the information detected by vision sensor. Dynamic models of the robot joints were

experimentally determined for use in designing and tuning the joint controllers. Lag-lead

compensators were chosen for their ability to improve a system's steady state performance

while improving the response rate by increasing the system bandwidth. These controllers were

discretized and programmed into the software environment of the robot.

xiii










The performance of the robot was assessed by its suitability for the specified task.

Thus, typical fruit motions were investigated. Also, a picking envelope was established which

defined the volume with respect to the end-effector in which a fruit must be located to be

picked. These characteristics were used to relate the task of picking citrus fruit to performance

requirements for each of the robot's joint motion controllers.

The controllers achieved acceptable robot performance during a normal pick cycle.

Tests of the velocity and position controllers for all of the joints showed that these controllers

met or exceeded the established requirements. The vision controllers achieved success when

subjected to fruit with slower motions. For large, fast fruit motions, however, the robot was

required to wait for the fruit to slow before a successful pick attempt was achieved.















CHAPTER 1
INTRODUCTION


Traditionally, the harvest of citrus fruit has been a labor-intensive operation. Much of

this manual labor in America has been provided in the form of seasonal farm workers who were

actually illegal aliens from Mexico and other Latin-American countries (Martin, 1983). Martin

also observed that even with the illegal work force the turnover was very high. In fact,

maintaining a work force of 20 workers has required that some farmers hire as many as 200

workers in a month's time. Another challenge that farmers have been faced with is the rising

cost of harvest. In the United States, Martin noted that the farmer paid 20 percent of the fruit

price for harvesting. In comparison with other countries, the U.S. farm worker wages are 5

times that of Greece and 10 times that of Mexico. Therefore, U.S. farmers start out behind in

the competition for the world market. After identifying these problems, researchers have

turned their attention toward the mechanization of the harvest process. Several mechanical

harvesters such as tree shakers and blowers have been designed and built, only to find that

these attempts caused damage to the fruit trees. These non-selective harvesters also proved

detrimental to future yields from the Valencia orange which is harvested after the immature

fruit for the following season have already formed (Coppock, 1984). Damage and removal of

the small, unripe fruit reduced the following year's production. The conclusions of many of the

researchers was that individual and selective harvest of the fruit would be most desirable.

In 1984, researchers at the University of Florida began an investigation of the physical

and economic feasibility of picking citrus fruit with a robotic mechanism. Initially, a

commercially available robot was acquired for this purpose. A spherical coordinate

manipulator was chosen which allowed for ease of vision-servoing-controlling the motion of

the robot joints based on fruit position as determined by a camera. This spherical coordinate










(RRP: revolute, revolute, prismatic) configuration consisted of two revolute or rotary joints with

axes of rotation intersecting at a right angle and a prismatic or sliding joint. These first two

joints allowed the distal end of the robot to be "pointed" while the third joint provided the

capability for extension. A computer was interfaced with the robot's controller and the

manipulator was used to demonstrate the vision-servoing concept by picking artificial fruit

from a simulated canopy. Successes with the laboratory robot prompted the construction of a

more portable field robot which could be tested in actual grove settings.

The ideas for the Florida Laboratory (Figure 1.1) sprung forth. The Florida Laboratory

was constructed as a trailer package which could be towed behind a truck to groves around the

state of Florida. Basic construction of the lab consisted of an enclosed front section with an open

flat bed to the rear. The enclosed section sheltered the environment-sensitive hardware, such

as the control computer and electrical connections, and provided a comfortable working area for

the operators. Two software development stations were provided in this control room. The


Figure 1.1. The Florida Laboratory.


r--~YB: A










hydraulically actuated manipulator was mounted on the rear, flatbed portion of the lab. A 15

kW electric generator furnished electricity for the hydraulic power unit, the control computer,

and other hardware used in the development of software for the grove model robot. Visual

access to the robot was furnished by three windows mounted on the rear and picking side of the

control room.

The robot was a three degree-of-freedom, spherical-coordinate geometry arm.

Actuation of the joints was accomplished through the use of servo-hydraulic drives consisting

of servo amplifiers, servo valves, and actuators. For the first two joints, rotary actuators were

used to generate the revolute motion about intersecting horizontal and vertical axes. The third

joint, a sliding joint, was actuated by a hydraulic motor through a rack and pinion drive. The

revolute motion of the first two joints provided the robot with the ability to point toward a

fruit, and the prismatic or sliding joint provided the ability to reach toward the targeted fruit.

A picking mechanism was attached to the end of the arm and enclosed the color CCD camera

and ultrasonic ranging transducer which were used for fruit detection. Also, a rotating lip was

attached to the picking mechanism which was used to grasp the fruit and remove it from the

tree. The motion of the joints was determined by an intelligence base which used the

information from the position and velocity sensors on the joints as well as the fruit sensors to

establish desired actions of the manipulator.

The intelligence for the robot was built around a concept of states or modes of operation

in which decisions were made based on the available information from the sensors. The

intelligence base was developed and programmed for the orange-picking robot by Adsit (1989).

The heart of the intelligence base was a state network which provided robot command

decisions through sensing, action, and reasoning agents. Sensing agents were used to quantify

the robot's work environment and the robot's status. Reasoning agents made decisions in regard

to the information from the sensing agents. Action agents caused motion of the robot to alter the

work environment or the sensor's perception of the work environment. These agents were linked

together by a common database with result fields, parameter fields, and activate fields. The










result fields held the results from an agent's operation. Parameter fields specified the criteria

for accomplishing a task. Activate fields contained flags which induced or terminated an

action. The information contained in these fields was compared to models which characterized

significant events which occurred during the picking operation. The results of this comparison

were used to cause the execution to move from one command state to another.

The execution of a pick cycle included stepping through the state network in a logical

manner which resulted in removing a fruit from a tree. Each pick cycle began with the robot in

its home configuration and concluded by dropping the fruit while in this same configuration.

Before any joint motion was specified, the vision sensors were checked for the presence of fruit.

If no fruit were found in the field of view, a search pattern was initialized. When a fruit was

detected, an approach state was activated which actuated the revolute joints to align the arm

with the fruit (vision-servoing). While this vision-servoing operation continued, the sliding

joint was activated to extend to the targeted fruit. When the picking mechanism was

positioned so that the fruit could be captured, robot motion was stopped, and the fruit was

girdled by the rotating lip of the picking mechanism. The sliding joint was then retracted to its

home position. Once the sliding joint reached its home position, both revolute joints were

returned to their home locations, and the fruit was released from the picking mechanism. This

pick cycle was repeated until no more fruit were detected by the fruit sensors.

This picking operation required control of the motion of the joints based on velocity,

position, and vision information. When the robot was requested to search the tree canopy for a
)
fruit, the revolute joints were instructed to move with constant velocity. When a fruit was

detected, the motion of these two joints was changed to cause the targeted fruit to be positioned

in the center of the image of the camera. Thus, the motion of these two joints was also to be

altered by the commands of the vision system. Since the actual distance between the end-

effector and the targeted fruit was not known, the slider was directed to proceed at a constant

velocity until proximity with the fruit was detected by the ultrasonic system. As the fruit was

being girdled by the rotating lip, all three of the joints were required to remain stationary at










their present positions. For the slider to be retracted from the canopy at a constant velocity,

the revolute joints were to hold their positions. The instruction to go to the home location was

provided in the form of positions for each of the joints.

Thus, three modes of control were necessary for the orange-picking robot. First, each of

the joints was to be moved at a constant velocity by a velocity controller. Second, to cause the

joints to go to specified positions, position controllers were needed. Third, vision controllers

were required to change the position of the revolute joints to point the end-effector toward a

targeted fruit. The development of these three motion control strategies was the overall goal

of this work. The accomplishment of this goal would provide controllers which would take

setpoints from the intelligence base and accomplish the desired result in a smooth and accurate

manner.















CHAPTER 2
OBJECTIVES OF RESEARCH


The main objective of this work was to develop motion control strategies for the orange-

picking robot. This objective was divided into the following specific areas:

1. develop a kinematic model for the orange-picking robot;

2. derive an open-loop dynamic model for each robot joint;

3. define performance criteria necessary for picking citrus fruit;

4. develop and implement control strategies to provide acceptable robot performance; and

5. test and evaluate the performance of the robot.

Algorithms were necessary for controlling the robot, based on desired positions and

velocities of the joints of the manipulator and based on fruit position related to the end of the

robot. These motion control algorithms were to be called from the robot intelligence base to

cause the manipulator to move in a specified manner. The control algorithms were to be links

between the software environment, the manipulator, and the manipulator's workspace, with

the ultimate task of removing fruit from the canopy of an orange tree. Because the algorithms

were to be used with a digital computer, they were required to operate in the discrete domain.

Only a minimum of computational complexity was to be permitted because real-time control

was necessary to enable the robot to pick moving fruit.

A kinematic model was necessary to describe the geometric relationship between the

joints and links of the robot. This model was to provide an understanding of the motion of the

manipulator links for specified changes in joint positions. Ultimately, the kinematic model

was to be used for determining the relationship between the position of the robot's end-effector

and the position of a targeted fruit. This relationship provided a basis upon which functions

for the vision control system gains could be derived.










An open-loop dynamic model for each robot joint was to be derived for use in selecting

control systems for the manipulator. These dynamic models would provide insight into the

response characteristics of the manipulator's joints, which could be used for tuning the

controllers and thus to achieve desired responses from the joints. The open-loop response of

each joint to different step input signals was to be evaluated for use in determining open-loop

dynamic models. The dynamic models were to be used as plants in closed-loop systems for

selecting and tuning the controllers. Once established, these dynamic models were to be

verified by comparison of the actual response of the joints with the simulated response of the

determined dynamic models.

Final performance of the robot was to be defined by critical performance criteria. These

performance criteria were to be determined from observations of fruit motion in the tree's

canopy and other pick-cycle motion requirements. Along with the robot's ability to track the

motion of fruit in the canopy of the tree, the robot would be required to position the picking

mechanism such that the rotating lip would be able to remove the located fruit from the tree.

The manipulator was also to be required to move through a fruit-locating search pattern with

rapid though smooth actions. These criteria were to be used for designing and evaluating the

strategies and algorithms which were developed for controlling the orange-picking robot.

Based on the information from the kinematic and dynamic models and the performance

criteria, position, velocity, and vision control strategies for the manipulator were to be

developed. These control strategies were to be the basis upon which robot-control algorithms

were to be developed. The algorithms were to be incorporated into a robot-programming

environment which contained intelligence for the orange-picking robot. From the programming

environment, the algorithms could be called when necessary to accomplish a desired motion of

the manipulator.

Once implemented, the performance of each of the motion-control strategies was to be

evaluated. Assessment of the controllers would involve designing tests which would

demonstrate the ability or lack of ability of the controllers to meet the specified performance






8


criteria. First, the controllers would be tested on an individual basis. Finally, the response of

the controllers while operating in the intelligence base would be evaluated for the ability to

control the joint motions of the manipulator during the actual picking operation.















CHAPTER 3
REVIEW OF LITERATURE


Previous Robotics in Tree Fruit Harvest

Researchers have long noticed the necessity for automated harvest of tree fruit. Many

of these researchers have investigated the use of mechanical components. The need for a

proficient citrus harvester that would individually remove the fruit from the tree was

perceived early (Schertz and Brown, 1968). Schertz and Brown pointed out that any method of

mechanical harvest should inflict only minimal damage to the fruit and tree. They observed

that leaf removal of over 25 percent have corresponding yield decreases for the subsequent year.

However, defoliation of up to 25 percent did not provide an indication of reducing the yield.

These men realized that an advantage of individual fruit harvest over mass fruit removal

could be a reduction in damage to the fruit and to the tree. This method would also have less

impact on the succeeding year's production. Although many researchers have indicated the

need for robotic fruit harvesters and presented their ideas, the technology for making it

achievable has developed only within the last decade.

Pejsa and Orrock (1984) studied potential applications of robotics to agricultural

operations. In their work, some of the sensing and control requirements for intelligent robot

systems in agriculture and especially in orange harvesting were presented. These sensing

requirements included the use of vision for detecting the presence of fruit and its location in two-

dimensions. Range and proximity sensing were deemed necessary for determining the third

dimension of the fruit's location and for collision avoidance. These researchers proposed the

use of force and tactile sensors for reporting the status of the end-effector's grasp of the fruit.

Pejsa and Orrock pointed out that a major effort would be necessary to integrate the sensing

functions with the mechanical functions required to pick tree fruit. They stated that most










industrial robots provided greater accuracy and more degrees of freedom than would be required

of a fruit harvester. Thus, a task-specific robot could be designed for the purpose of fruit

picking. A closed-loop system would be needed that could tie the sensing functions with the

arm motion controllers.

Some of the earliest work in the development of the technology was conducted by

Parrish and Goksel (1977). These men studied the feasibility of analyzing the work space of

the robot by use of machine vision. In their study, a black-and-white video camera was used to

detect the fruit, which were represented by blobs in the two-dimensional picture array. By

analyzing their perimeters, the larger blobs which contained overlapping fruit were

successfully divided into separate fruit. The location of the fruit centroids were determined in

the two-dimensional picture array. Trajectories were calculated from the camera lens center to

the positions of the detected fruit centroids. The mechanical arm was driven to follow these

trajectories toward the fruit. When contact with a fruit was detected by a touch sensor, the

motion of the robot was halted. As fruit removal was not in the scope of this work, a successful

picking attempt was recorded when contact with the fruit was detected. In this work, a scene

was analyzed and one trajectory was calculated for each fruit in the scene. The arm was driven

until all of the trajectories were exhausted. Then, a new scene was analyzed, and the operation

was repeated. Although this system was quite elementary, the concepts and the feasibility of

robotically harvesting tree fruit were inspired. These concepts have been used as a motivation

for many of the later attempts.

Grand d'Esnon (1984 and 1985) developed an apple picker which used similar ideas for

the detection of fruit. This manipulator was a cylindrical coordinate robot (PRP, prismatic in

the first joint, revolute in the second, and prismatic in the third). Using the vision system to

determine the fruit's position in two coordinates, the robot was pointed towards the fruit by

raising the arm along a vertical prismatic joint and then pivoting around a vertical axis. This

motion relied on the concept that the fruit did not move between the time that the image was

acquired and the picking tool reached the fruit. In a later attempt, Grand d'Esnon et al. (1987)










developed a fruit picker which consisted of five revolute joints. The first two joints provided

the robot with the pointing ability while the remaining three joints formed an elbow for

extending the end-effector towards a targeted fruit. Operation of the robot again involved

acquiring an image and then adjusting the joints of the robot to align the end-effector with the

camera's line of sight. After the arm was pointed toward the fruit, the joints were moved to

extend the end-effector toward the determined location of the fruit. Again, the robot had no

ability to change its trajectory with the motion of the targeted fruit. In both attempts, the

robot was directed to follow the vector from the camera lens center to the determined position of

the fruit. Forward motion of the robots was continued until contact with a fruit was detected.

Grand d'Esnon et al. reported the removal of 50 percent of the fruit in a hedge at a rate of one

fruit every 4 seconds.

Tutle (1984) developed an idea for an image-controlled robot for harvesting tree fruit.

For his imaginary robot, Tutle proposed the use of a photo-diode-based camera and the

appropriate filters and lighting for detecting the fruit in the canopy of the tree. After the

location of a fruit was determined, the camera was to be displaced so that the arm could be

moved to align with the optical sensor's line of sight towards a detected fruit. Once aligned

with the fruit, the severance module would be extended towards the fruit. The severance

module would contain a second optical sensor that Tutle called a 'seeker' sensor, which

consisted of a four-element photovoltaic detector. The idea behind use of this sensor included

oscillating the severance module until equal light, supposedly reflected from a fruit, was

detected by each of the four elements. This action was intended to align the severance module

with the fruit and adjust for any fruit motion that might have occurred before the robot reached

the fruit. Response from this seeker sensor would also be a signal to slow the forward motion of

the arm. Tactile sensors in the severance module would indicate that a fruit had been scooped

into the module and that forward motion of the arm should be stopped. The fruit would then be

grasped by the severance module, which would twist the fruit while the arm was retracted to

remove the fruit from the tree branch. Since an operational model of this idea was not










constructed, its successfulness could not be evaluated. Also, the control problems were only

assumed and never actually encountered.

The application of robotics in fruit harvesting has also been investigated by

researchers at the Laboratory of Agricultural Machinery in Kyoto, Japan (Kawamura et al.,

1985; Kawamura et al., 1986). This work involved the design of a five degree-of-freedom

manipulator for picking tomatoes and oranges. A global color vision system was employed for

the detection of fruit. The camera was mounted on a vertical support and could be moved up or

down the support. An image was acquired with the camera in one location and then the camera

was moved for acquisition of a second image. The two images were analyzed and the centroids

of the fruit in the image were determined. The three-dimensional positions of the fruit were

calculated from the two-dimensional images by triangulation. A trajectory to each of the fruits

and the robot joint angles required to follow the desired path to a fruit were calculated. As the

arm approached the calculated position of the fruit, the speed of the joints was slowed. When

the hand reached the calculated position of the fruit, the fruit was gripped and severed from

its supporting stem. Three-fingered flexible hands were built for use with the manipulator

(Kawamura et al., 1987). These hands provided gripping forces similar to those of a human

hand while picking tomatoes and oranges. Image processing and joint motion calculations were

rather extensive, causing the picking time for one fruit to be approximately 20 sec.

Harrell et al. (1985) examined the concept of real-time vision-servoing for controlling

the manipulator during the picking process. This work involved the use of a commercially

available spherical coordinate (RRP) robot. A small black-and-white camera was mounted in

the end-effector of the robot and aligned with the axis of the prismatic joint. With this

configuration, a fruit whose image was centered in the camera's image plane was directly in

front of the end-effector. Thus, the end-effector could be extended towards the fruit. Since the

vision-servoing was kept active during the picking process, any motions of the fruit could be

followed by making changes in the two revolute joints. In this first generation, signals from the

control computer were sent directly to the electric robot controller for serving the positions of










the joints. In the controlled environment of a laboratory, this vision-servoing method was

proven to have potential for control of a grove model robot.

Tests in the grove, however, indicated that the black-and-white camera could classify

light reflections from the soil as fruit. Therefore, the use of color vision was investigated

(Slaughter et al., 1986; Slaughter, 1987; Slaughter and Harrell, 1987). In his work, a scheme

was developed which segmented the image into fruit and background regions based on the color

of each pixel. From this image, the centroid of each fruit's image could be determined for use in

adjusting the joints of the robot to point towards the fruit. Since the image was processed in

real-time, the robot could be controlled to track the dynamic motion of the targeted fruit.

In a joint project between researchers at the University of Florida and AID of Italy, two

robots were designed and constructed as prototypes for future work aimed at a commercially

produced tree-fruit-picking robot (Harrell and Levi, 1988). The AID robot relied on electrical

servo controllers to position the joints to point the arm towards the fruit. A global vision system

was used to determine the location of the fruit throughout the picking sequence. The Florida

robot further developed the previous concepts while implementing the vision system of

Slaughter. A hydraulically actuated robot was designed and constructed with a spherical

coordinate architecture (RRP).

For this prototype, a controller was not available. Even if a controller were available,

the exclusive use of point-to-point joint positioning would not have provided the desired

flexibility. The robot motion was to be formulated based on velocity and vision requirements as

well. An intelligence base for the robot was designed and programmed (Adsit, 1989). This

intelligence base added a requirement for fast and accurate control of the joints of the robot

based on velocity, position, and vision setpoints. The design and implementation of these

controllers is the scope of this work.










Robot Kinematics Background

Craig (1986) describes kinematics as the science of motion, ignoring the forces which

cause the motion. Kinematics deals with the variable joint coordinates as they relate to the

position and orientation of the end-effector. Because the relationships between the joints of a

manipulator can be quite complex, the study of robot kinematics deals with the coordinate

frames that describe the kinematic relationships. Any robot manipulator is made up of links

and joints. Most joints are grouped into one of two categories with one degree-of-freedom:

revolute or hinged joints and prismatic or sliding joints. The links of the manipulator are

usually rigid and define the relationship between the joints. The common normal distance, an,

between the axes of two consecutive joints and the twist angle, an, characterize a robot link (see

Figure 3.1). The twist angle is defined as the angle between the consecutive axes in a plane

perpendicular to an. For this work, the Denavit-Hartenberg (1955) notation will be used as

applied by Paul (1981).

The relationships between coordinate frames are expressed as products of rotation and

translation transformations. Homogeneous transformations which represent rotations of one

coordinate frame about the x, y, and z axes of a reference coordinate frame by angles 0 are

represented by the following 4 x 4 matrices:



Rot(x,e) =
0 sin cose 0




Rot(y,) 0 1 0
sin 0 cos E 0
0 and (3-2)


Rot(, sine cos 0 0
Rot(z,6) =
0 0 1 0
S 0 0 1 (3-3)














Joint n-1

) 0-, Link n-1


Link n-2


Joint n
8n


Joint n+1

on.l


Link n


Figure 3.1. Kinematic link frames as attached to the links of a manipulator (Paul, 1981).


A translational homogeneous transformation of one coordinate frame with respect to another by

a vector, ai + bj + ck, is described by

S10 0 a
Trans(a,b,c) = 1 c

.0 0 0 1. (3-4)

The general relationship between two successive frames (the coordinate frame of link n

and the coordinate frame of link n-1, see Figure 3.1) is expressed as the product of two rotation

transformations and two translation transformations. This relationship is referred to as a

general A matrix (Paul, 1981)

"-'An = Rot(zn-l,On) Trans(0,0,dn) Trans(a,,0,0) Rot (xn,an) (3-5)

where n-An = relationship between frame n-1 and n,

Rot(zn.i,9) = rotation transformation about zn.-, an angle On,

Trans(0,0,dn) translation along zn-, a distance dn,










Trans(an,0,0) a translation along rotated Xn.1 = xn a length an, and

Rot(xn,a) = rotation about x,, the twist angle cn.

By multiplying these rotation and translation matrices, the general A matrix for any two

successive links is calculated as

cos sin 8 cos a sin 0 sin a a cos 8
n-1n sin cos cos a -cos sin a a sin
0 sina cos a d
0 0 0 1 (3-6)
(3-6)

In this work, the term frames refers to the coordinate frames assigned to the links of the

manipulator. Coordinate frames represent a three-dimensional space by three orthonormal

vectors; X, Y, and Z. The origin of each frame is located at the intersection of these vectors.

When referring to these vectors, a trailing subscript will be used to identify the frame in

concern. Links are the physical components which make up the manipulator. The motion of the

links is accomplished by the joints. A joint can be rotational revolutee) or translational

(prismatic). The coordinate frames are fixed to the links, and homogeneous transformations are

used to relate the position and orientation of the frames. A joint axis is the vector about which

joint motion takes place. Link coordinate frames are assigned such that the frame's Z axis

defines the vector about which joint motion occurs. Joint motion will be either around or along

the respective Z axis.


Controls Background

The use of a Bode plot, in which the frequency response of a system can be analyzed,

enables the control system designer to evaluate closed-loop system characteristics based on

knowledge of the open-loop system. A controller can then be designed to achieve the desired

system characteristics. Palm (1983) presented some of the basic considerations used in the

frequency-response methods of control system design. First, the cosed-loop system's steady-

state error can be minimized by maintaining a high, open-loop gain in the low-frequency range.

Second, a slope of -1 in the gain curve near the crossover frequency will help to provide an










adequate phase margin. The crossover frequency is the frequency at which the open-loop gain

of the system is unity (0 db). Third, a small gain at higher frequencies will help to attenuate

the effects of noise or mechanical vibrations. All of these characteristics proved to be

applicable to the controller design for the orange-picking robot. Thus, controllers were desired

which provided flexibility to shape the phase and gain curves to achieve the necessary phase

and gain margins.

Lag and lead compensators furnish this flexibility by providing the ability to adjust

the phase and gain in a wide variety of frequencies. When tuned properly, a lag-lead

compensator improves the steady-state performance while also improving the transient

response (Palm, 1983; Ogata, 1970). The lag-lead compensator is represented by the transfer

function

HP s) Kc rdS+ 1
Hp (S)=
Tis+l (3-7)

where s = Laplace operator (sec-1)

Kc = controller gain (appropriate units),

dra lead time constant (sec), and

zi lag time constant (sec).

The design of the controllers involves the placement of the controller gain and the pole and zero

of the controller so that an acceptable response is achieved while meeting the steady-state

requirements. The open-loop system gain can be increased by increasing the controller gain, Kc.

The use of the lag-lead compensator increases the order of the system by one in between the lag

and lead factors. In other words, the addition of the lag or lead compensator causes an

attenuation of the system response between the frequencies of the lag and lead factors (1/zi and

1/Td). Thus, the value of Ti determines the frequency at which this attenuation takes place

while the value of rd determines the frequency at which the attenuation is canceled. The slope

of the gain curve is decreased by 1 between the lag and lead factors.










The applications of control theory to hydraulic systems were presented by Merritt

(1967) and supported by Gibson and Tuteur (1958), Johnson (1977), and McCloy and Martin

(1980). Merritt presented the background necessary for determining the dynamic characteristics

of many hydraulic systems. He demonstrated the methods for deriving the characteristic

equations for each of the system components. Then, he pointed out that the closed-loop response

of a system is limited by the response of the slowest element. Thus, the selection of the

components should take into consideration the hydraulic natural frequency by choosing

actuators that are capable of the desired system response. By choosing system components with

fast response rates (i.e., large natural frequencies), the response rate of the actuator and load

combination is left as the performance-limiting factor of the system. Merritt noted that after

choosing fast control components a normal position control hydraulic servo can be reduced to a

second-order system with an integration. Thus, the position servo system is represented by

2
Gp(s) = Koh 2
s + 28h(hS + (Oh (3-8)

where s = Laplace operator (secr')

Kp = position system gain (appropriate units),

Oh = system natural frequency (rad/sec), and

Sh = system damping ratio (unitless).

A normal velocity control servo can be reduced to a second-order system as in the following

transfer function:

2
G, (s) Kv(Oh
s +28h(hS + (Oh (3-9)

where s = Laplace operator (sec-1)

K, = velocity system gain (appropriate units),

(Oh system natural frequency (rad/sec), and

Sh = system damping ratio (unitless).










Fast components should have a natural frequency of 10 times or greater than the natural

frequency of the actuator and load. Merritt also indicated that the stability of the servo

system can be determined by the position of the resonant peak which occurs near the hydraulic

natural frequency of the second-order system on the Bode magnitude plot. The loop gain at the

resonant peak must be less than unity for stability. Merritt also noted that the lag-lead

controller usually provides acceptable results for both position and velocity control servos. He

demonstrated that the use of velocity minor feedback loops could be used to reduce errors which

result from drift and load friction.

Merritt summarized hydraulic servo design as follows. A power element which will

meet the basic considerations of the load and response is selected. The other components of the

loop are sized to provide the best accuracy and response under the limitations of the power

element. A controller is selected to give the highest possible gain and crossover frequency

while maintaining stability. The only way to achieve a faster response from the system is to

choose a faster power element. These methods of hydraulic controller design along with the

frequency-response design techniques were used for the selection and design of tuners for this

work.

According to Merritt, all real systems are nonlinear to some extent. However, no general

nonlinear theory exists for design of controllers for these nonlinear systems. But, techniques are

available for this design based on the familiar linear techniques. The most widely used

method is to assume that the nonlinearities are small and that the system is linear. In the case

of the orange-picking robot, the nonlinearities that would cause limit cycles or instabilities

were negligible in the range of operation. The deadband caused by imperfect valve

characteristics and the backlash and hysteresis were minimized by dithering the output signal

from the servo amplifiers. The saturation possibilities which would also cause nonlinear

performance were eliminated by limiting the controller outputs. This nonlinearity was

handled within the intelligence base of the robot. Thus, the effects caused by the










nonlinearities of the hydraulic servo systems were considered negligible allowing the design of

controllers based on common linear techniques as previously described.


Performance Specifications

According to Lau et al. (1988), a robot's performance is measured by its ability to

perform a task. Performance measurements are those general operating characteristics that are

important for determining the robot's suitability for a given task. The performance for

industrial robots is usually specified in terms of accuracy, repeatability, positioning resolution,

and speed. These measurements were also defined by Ranky and Wodzinski (1988), who also

presented very precise methods for determining each of them.

These performance measurements prove sufficient for industrial robots which operate in

a structured environment. However, in the unpredictable environment found in agricultural

operations, these methods of performance evaluation have little significance. The ultimate

performance measurement is that of determining the robot's suitability for its intended

operation. Because the location of each fruit in the tree is different, the accuracy and

repeatability of the robot were not pertinent. Performance requirements and evaluation

methods for robots which operate in unstructured environments are much more difficult to

assess. Evaluation of the control strategies for the citrus-picking robot made evident the need

for performance criteria for this specific task.















CHAPTER 4
DESIGN OF THE FLORIDA CITRUS-PICKING ROBOT


An overview of the design of the orange-picking robot, developed by Harrell et al.

(1988), is presented in this chapter. The physical specifications of each part of the robot are

described in the first section along with the position and orientation of the kinematic

coordinate frames as they relate to each physical component. The second section contains a

description of the computer hardware and software designed to control the robot. In the third

section, an illustration of the picking mechanism is introduced showing the configuration of the

components of the fruit sensor package. Hydraulic actuation of the robot is described in the

fourth section of the chapter. Finally, sensing mechanisms for position and velocity of the robot

joints are described in the fifth and sixth sections.


Mechanical Design

A brief description of the physical components that make up the orange-picking robot

are presented in this section. The parts are described along with their relationship to one

another. Also, presented in this section are the axes about which the motion of the robot is

accomplished. These axes of rotation form the Z axes of three-dimensional kinematic frames

which will be presented in a later chapter. The position and orientation of the kinematic

frames as related to the physical components are presented here as an aid in understanding the

kinematics chapter which follows.

The orange-picking robot (Figure 4.1) was built as four major parts: base stand, outer

link, inner link, and sliding tube. The base of the robot was bolted to the flat bed of the

laboratory trailer and acted as a stand to support the other components (Figure 4.2). The first

coordinate frame, frame 0, of the kinematic model was assigned to the base link as shown in the

figure. On the base, the outer link was supported by flange bearings which allowed the outer

21














Outer Link
Joint 0
Servo Drive


Servo Drive Nylon Rack
Inner Link -
Iero rive 1 Base Support
Joint 1 : *J
Servo Drive


Figure 4.1. The three degree-of-freedom orange-picking robot.


link to rotate about a horizontal axis (Zo). Similarly, the inner link was mounted inside of the

outer frame and provided rotation about a vertical axis (Z2). The inner link included a bearing

assembly which supported the sliding tube and provided linear motion along the Z axis of the

inner link (Z2). The picking mechanism of the robot which held the sensor package was

mounted on the end of the sliding tube.

The outer link (Figure 4.3) was fabricated from rectangular steel stock and reinforced at

the corners for increased rigidity. Two solid-steel cylindrical-shaped shafts were mounted on

either side of the outer link. The outer link was mounted to the support stand by a pair of

bearings which connected between these mounting shafts and the vertical members of the base

stand. Coordinate frame 1 of the kinematic model was assigned to the outer link. The center

line of the two shafts were coincident with the Zo axis of coordinate frame 0 allowing the outer

link and coordinate frame 1 to rotate about Zo by an amount O1. Connected to these shafts were a

rotary actuator used for rotating the axis through its motion, a tachometer, and a








































Figure 4.2. Base support stand of the robot.


potentiometer. Motion of the outer link was mechanically limited by two chains to

approximately 39 degrees in either direction from vertical. These chains were connected

between the lower member of the outer link and the cross member of the supporting structure.

The inner link (Figure 4.4) was constructed in two pieces and mounted inside of the outer

link in much the same way as the outer link was mounted to the support. This inner link was

also constructed of rectangular steel with reinforcements at the covers for added rigidity.

Solid steel cylindrical mounting shafts were fastened to the top and bottom of the link allowing

the inner link to rotate about the vertical axis of the outer link, Z1. This link was actuated by a

rotary actuator mounted to the bottom of the outer link and connected to the bottom shaft of the

inner link. The motion of this link was measured by the joint variable 82. Coordinate frame 2














S, Mechanical
Stop

!, -, 0o I
S50 cm z
30 cm


7/ 10.1 cm

S50cm

18.25 cm

Figure 4.3. Outer link of the robot.


was assigned to the inner link and positioned so that its origin was coincident with the origin of

the first two coordinate frames. The vertical axis of this link was always at a right angle to

the horizontal axis of the outer link, resulting in a Hooke joint. Inside of the two part inner link

casing, a split steel pipe was welded as a bushing housing which supported the sliding link.

The two part construction of the inner link allowed shims to be added or removed from between

the two sections to adjust for wear in the nylon slider bushings. The motion of the inner link was

mechanically limited to approximately 30 degrees in either direction from center by

mechanical stops welded to the outer link.

The sliding joint of axis 2 (Figure 4.5) was constructed from a high grade aluminum tube.

Sliding joint motion was accomplished by a rack and pinion drive actuated by a hydraulic

motor. A 1.5 cm square nylon rack was attached to a flat surface machined on the lower side of

the aluminum tube. A 10 pitch, 3.81 cm diameter pinion gear was incorporated into the lower

section of the inner link assembly and meshed with the rack for actuation of joint 2. The Z2 axis

was coincident with the centerline of the tube and intersected with Zo and Z1 at their





















35.5


z1, Y2


z2

20.3 cm

Figure 4.4. The inner link.


intersection point. The motion of the sliding tube was mechanically limited by end caps which

were mounted on either end of the tube. One end cap was welded to the forward or distal end of

the tube and used for mounting the end-effector. The other end cap was bolted to the rear or

proximal end of the tube. These end caps and mechanical stops bolted to the inner link limited

the linear motion of the tube, the joint variable d3, to approximately 1.31 meters.


Control Computer

In this section, the hardware and software used for controlling the robot is introduced.

Components of the computer hardware are presented in systems as they relate to controlling the

robot. A very brief description of the elaborate software environment is also presented here.

Hardware

The control computer for the orange-picking robot was a VME-bussed system with a

Mizar 7120 CPU card. The Mizar card utilized a 12.5 MHZ Motorola MC68020 processor and 1










1 163.5 cm



12 cm T--- 11.2 cm


end-cap actuation end-cap
rack

Figure 4.5. The sliding link.


MB of RAM. The hardware architecture for the control computer is diagrammed in Figure 4.6.

Mass storage for the computer was provided by a 20 MB hard drive and a 1 MB floppy drive

which were connected to the VME bus. The computer was equipped with three serial ports. The

main system console was connected to the computer through one serial port, while a second port

was wired to a remote connector for connecting a terminal outside of the control room of the

trailer. An Apple Macintosh Plus system, with 2 MB of RAM, a 20 MB hard disk, and a printer,

was used as a printer/plotter station and was connected to the VME bus by way of the third

serial port.

Video system. The video system was composed of the CCD camera, the FOR-A color

decoder, three Datacube VVG-128 video frame grabbers, and a Sony RGB video monitor. The

NTSC output signal from the camera was converted into separate red, green, and blue video

signals by the color decoder. The three Datacube frame grabbers provided the ability to

digitize, store, display, and process full color video images in real-time. The red, green, and

blue signals from the decoder were acquired simultaneously by the frame grabbers at a 60 HZ

rate. The signal for each primary color was quantified with 5 bit resolution based on the

intensity of the signal at each pixel. These acquired video data, ranging in value from 0 to 31,

were stored in memory as three, 384 x 244 pixel arrays, one for each primary color signal. The

red frame grabber also generated a hardware interrupt on the VME bus with each vertical

blanking period. This interrupt was used to synchronize all of the real-time activities. Video



































- VMEBUS
EXTERNAL CONNECTIONS


Figure 4.6. I/O hardware architecture of the control computer.


output from all three frame grabbers was displayed on the RGB monitor in the control room of

the Florida Lab.

Ultrasonics. The electronic circuitry for the Ocean Motion ultrasonic ranging transducer

provided a TTL pulse with width proportional to the time required for the ultrasonic burst to

echo from an object. A counter-timer module was used to quantify the duration of the TTL pulses

generated by the ultrasonic ranging unit. Output from the counter-timer was a digital value

which represented the distance from the picking mechanism to the targeted fruit. The counter-

timer was mounted on a card that plugged directly to the VME bus.

Analog to digital converters. Seven analog-to-digital (A/D) converters were used in

the hardware to convert analog voltage signals from the position, velocity, and temperature

sensors to digital values. Six A/D converters were used for the position and velocity sensors as










described in the position and velocity sensing sections. The seventh A/D converter was

connected to a type "T" thermocouple panel meter for monitoring the temperature of the

hydraulic fluid during operation. All of the A/D converters represented an input voltage

ranging from -5 volts to +5 volts with a value ranging from 0 to 4095. The A/D converters were

plugged directly to the VME bus of the control computer.

Parallel I/O signals. Control of components which required a signal depicting either on

or off operation was accomplished by the addition of a parallel card and an Opto-22 switching

panel. The parallel port of the card was connected to the Opto-22 panel. The Opto-22 panel

allowed the addition of either input or output modules. The output modules acted as electronic

relays for switching other components based on the signal from the corresponding pin of the

parallel port. Output modules were used to switch 120 VAC for the picking mechanism lights,

the solenoids of the picking mechanism actuator, and the main hydraulic dump valve. Input

modules were added to the card to sense the status of the hydraulic dump valve and the servo

amplifiers. A 5 VDC input module was used to sense the position of push button safety switches

which were located at various strategic locations in the lab and connected in series to one

another. Signals from the input modules were routed to the appropriate pins of the parallel

card.

Servo mechanisms. Joint motion of the manipulator was accomplished by two

hydraulic rotary actuators and a hydraulic motor. Hydraulic fluid flow to these actuators was

controlled by servo valves. The rate of fluid flow through a servo valve was proportional to

the amount of current passing through the coil of the valve. Three Vickers EM-D-20 servo

amplifier modules were used to adapt the output voltage from the control computer to a coil

current usable by the servo valves. The output voltages from the computer were generated by

three 12-bit digital-to-analog (D/A) converters. Gains for the servo amplifiers were adjusted

to produce the maximum coil current to each of the valves at the maximum output voltage of

2.5 volts from the D/A converters as listed in Table 4.1. The bandwidth characteristics for the

servo amplifiers and servo valves are also presented in Table 4.1.











Table 4.1. Servo amplifier and servo valve characteristics.

D/A ---- Servo Amplifiers ------
Output Gain Bandwidth
Toint (volts) (ma/volt) (rad/sec) (HZ)
0 2.5 80 1885 300
1 2.5 80 1885 300
2 2.5 16.8 1885 300

--------------- Servo Valves -----------
Max. Coil
Current Bandwidth
Joint Type (ma) (rad/sec) (HZ)
0 Pegasus 200 377 60
1 Pegasus 200 377 60
2 Sundstrand 42 189 30
note: Gain = Max. Coil Current / (D/A Output)


Software

The software environment for controlling the robot was written to run in a multi-user

PDOS operating system. The control system was organized into groups of sensing, action, and

control agents as presented in Figure 4.7. These agents exchanged information through a

dynamic database by way of result, parameter, and activate fields. The result fields stored

data which resulted from an agent's operation. Instructions for accomplishing an agent's

desired task were indicated in parameter fields. The ability to activate or deactivate certain

agents was included in activate fields within the database.

Sensing agents were those devices through which the work environment of the robot

and the robot states were quantified. Data from the sensing agents were filtered by fourth order

Integral of Time-multiplied Absolute Error (ITAE) data filters before their storage in the

database. The work environment or the sensors' perception of the work environment were

affected by the action agents. Control agents were used to direct the action agents to cause the

robot to move to a desired state. A desired robot state was characterized by setpoints which

were stored in the database and used by the control agents. For decreased calculation time, the

setpoints were specified in units compatible with the result fields rather than physical

measurements. An error calculator was used to compute the difference between the actual robot











WORK ENVIRONMENT





ACTION SENSING
AGENTS AGENTS

MODELSk
MOD S .. SUPERVISOR

CONOL DATA BASE
AGENTS --USER
SSHELLS
STATE I
NETWORK D
ERROR LOGGER
CALCULATOR

Figure 4.7. Organization of the robot programming environment.


state as perceived by the sensing agents and the desired robot state as prescribed by the control

agents in the setpoint fields. Results from the error calculator were also stored in the database

for used by the control agents.

Models characterized significant features and events within the work environment

through functional relationships which mapped sensing agent results and other system

information to boolean results. These models characterized certain conditions based on

information from the database. The models then returned boolean values to the database to be

used by the state network for directing the intelligence of the robot. The intelligence base for

picking fruit was programmed in the state network. This intelligence gave the robot the

ability to recognize and respond to events that commonly occurred during picking. The state

network mapped elements from the modeled response set to robot reactions through states

linked together by logical exit conditions. Each state in the network defined a different

modeled response or robot reaction. The responsibility of the state network was to cause the










robot to take the appropriate action to achieve its goal. The supervisor was responsible for the

orderly execution of the various system agents based on the intelligence programmed into the

state network. The connection between the developer and the database was accomplished

through user shells. These user shells were also the path for retrieving important database

information which was saved by a data-logger at a 60 HZ rate. Explicit details of this robot

programming environment can be found in Adsit (1989).


Picking Mechanism

In this section, the physical design of the picking mechanism is discussed. The

technique for mounting the picking mechanism on the sliding tube is presented along with the

method of mounting its actuation cylinder. The arrangement of fruit sensors and lights

incorporated in the end-effector are presented.

Construction

A picking mechanism (Figures 4.8 and 4.9) was developed with a rotating lip for

removing the fruit from the tree. The rotating lip of the picking mechanism was actuated so

that it encircled the fruit, impinging the stem of the fruit between the upper surface of the end-

effector and the rotating lip. Once the fruit was collected, the stem was broken as the end-

effector was retracted from the canopy of the tree. The detached fruit was secured with an

elastic collection sock as the end-effector was retracted and then dropped onto the ground or

into a collection bin.

The picking mechanism was constructed from a hollow aluminum cylinder (13 cm OD, 12

cm ID, 45 cm long). To aid in the ability of the end-effector to penetrate the canopy of a citrus

tree, its front end was machined on the top and bottom at an angle of approximately 34 degrees

from the centerline. A plastic collection scoop was added to the top of the picking mechanism

to aid in collection of the fruit as the rotating lip girdled it. The rotating lip was mounted to

the end-effector by shafts on either end which rotated in brass bushings. The lip was

constructed from spring steel formed into a slight oval profile. On the outer end of the shafts












Picking
Mechanism


Lights


Rear Drive
Sprocket


Tube
Centerline

Lens
Center


Rotating
Lip


Lens
Optical
Center


Figure 4.8. Cutaway side view of the picking mechanism showing the position of the
ultrasonic transducer, the color CCD camera, and the lights.




Rotating Lip
(Extended Position) Collection Sock
Bushing Bushing


Front Drive
Sprocket Front Drive
Sprocket

Collection Sp Picking Mechanism
Housing

Drive Chain Drive Chain

Lever Arm -- Rear Shaft
Bushing Bushing


Rear Drive
Sprocket Rear Drive
Sprocket

Cotter Key Adjustable
ILL Linkage


Figure 4.9. Top view of the picking mechanism showing the drive linkage and the lever arm
for actuating the rotating lip mechanism.


I










were mounted sprockets which were driven by a 25 pitch chain and a larger set of sprockets

providing a 3:1 drive ratio. The rear drive shaft, holding the larger set of sprockets, was

turned by a 5 cm long lever arm which converted the linear motion of the actuating cylinder to

rotary motion of the drive sprockets (Figure 4.10). A square aluminum linkage was connected

between the actuating cylinder and the lever arm. On the rear end of the sliding tube, the end

cap was bolted to the tube and used for mounting the actuator for the rotating lip picking

mechanism. On the forward end of the tube, an end cap was welded for mounting the end-

effector. Kinematic coordinate frame 3 was assigned to the end-effector (see Figure 4.1).

Fruit Sensor Package

The sensor package for locating the fruit in the canopy of the tree was mounted inside of

the tube of the picking mechanism (Figure 4.11). The sensor package included a color CCD

camera, an ultrasonic ranging transducer, and four small light sources and provided the real-

time three-dimensional position sensing between the end of the arm and a fruit in the

manipulator's workspace.

CCD camera. A Sony DXC-101 color CCD video camera with an 8 mm fixed focal length

and automatic aperture control lens was employed for detecting the fruit in the canopy of the

tree. The camera was mounted in the picking mechanism so that the optical axis of its lens was

approximately 25 mm below and parallel to the Z axis of the tube. The sensing element of the

camera was an 8.8 mm x 6.6 mm Charge Coupled Device (CCD) array. The CCD array was


Picking
Mechanism


Figure 4.10. Picking mechanism actuation assembly.











Bulb Lights
Retainer Ultrasonic

Lip Drive Lip Drive
Sprocket Sprocket

Light
Light
Plexiglas
Protector Color Camera
Collection Sock
Shield RotatingLip

Figure 4.11. Front view of the picking mechanism showing the color CCD camera, ultrasonic
transducer, and the four lights.


composed of a usable array of 384 pixels horizontally and 488 lines vertically. Since each

image corresponded to an acquired field, virtual resolution was reduced to 244 rows, with each

image using alternating even and odd rows. The image in the even rows (0,2,4,...) was processed

while a new image was being acquired in the odd rows (1,3,5,...). Integrated with the 8 mm

fixed focal length of the lens, the CCD gave the camera a field of view of 22.4 vertically and

28.80 horizontally as shown in Figures 4.12 and 4.13. The opening in the iris of the lens was

controlled by the control computer and based on the brightness of the targeted fruit (see

Slaughter, 1987). The NTSC color video information from the camera was decoded into red-

green-blue (RGB) format by a FOR.A, DEC-100 RGB color decoder. The video information was

processed by the control computer to obtain two-dimensional fruit-position data in real time (60

HZ).

Ultrasonic range sensor. The third dimension of the fruit, the distance from the picking

mechanism to the targeted fruit, was obtained by an Ocean Motion ultrasonic ranging

transducer. This transducer was equipped with a focusing horn to minimize reflection of the

ultrasonic burst from objects other than the targeted fruit. The transducer was positioned in the

picking mechanism above the camera and angled 10 degrees below the optical axis of the

camera so that the axis of the camera and the axis of the transducer intersected approximately

30 cm in front of the picking mechanism. The electronics provided with the ultrasonic ranging

transducer produced a TTL pulse with width proportional to the distance of the fruit from the










Camera Lens


Image Array


Figure 4.12. Horizontal field of view of the color CCD camera and lens combination in the
vertical plane.





8.8 mm Camera Lens




28.8*

28.8. Z4



8 mm
Image Array


Figure 4.13. Vertical field of view of the color CCD camera and lens combination in the
horizontal plane.


picking mechanism. This signal was quantified by a counter-timer module in the control

computer.

Lights. Four small flashlights were used as supplemental light sources. These lights

were needed to illuminate a targeted fruit as the arm was extended to the fruit and the picking

mechanism shaded the ambient light from the fruit. A pair of AA size flashlights were

secured on either side of the camera and powered by a separate 5 volt power supply.










Hydraulic Actuation

Joint motion was accomplished by hydraulic actuators controlled by servo valves. A

pressure compensated hydraulic power unit (Figure 4.14) provided hydraulic power to the

actuators. A 1 liter accumulator, charged to 7000 kPa, was added to help maintain constant

hydraulic pressure. Bird-Johnson SS-2-100 rotary actuators were utilized for actuating joints 0

and 1 (Figure 4.15). These actuators had splined shafts which interlaced with the splines that

were machined into the steel spindles that served as mounts for the outer and inner links.

Control of the fluid flow to these two actuators was achieved by Pegasus 3.8 liter-per-minute

(1.0 GPM), 120 series servo valves. The servo valves were connected to the actuators with

hydraulic manifolds which provided cross port pressure relief. Motion of the prismatic joint 2

was performed by a Hartmann HT-5 hydraulic motor (Figure 4.16) which was mounted to the

inner link of the robot. This motor was connected to the drive shaft of the pinion gear by a

Lovejoy coupling. It was controlled by a 18.9 liter-per-minute (5.0 GPM) Sundstrand MCV 103A



Charged to 6900 kPa
Lip Actuator
Axis2
Axis 1
Axis 0

Pressure Manifold
Return Manifold Type 'T'
Thermocouple

0 |Axis2
5 micronT Preset at Axis 1
filter 17000 kPa A-- is 0

o10 micron filter

14000 kPa Weeage
Weepage
3.7 kW Motor drain lin.. To Hartmann
1750 rpm -- case drain
1750 rpm O SM -M---. I I case drain


Figure 4.14. Circuit diagram of hydraulic power unit.










Bird-Johnson
SS-2-100 rotary
actuator


Hartmann
HTF-5
Relief valves Manifold hydraulic
set at Block motor
21000 kPa Assembly









servo valve servo valve

SFrom Pressure
To Return From Pressure Manifold
Manifold Manifold ToReturn
Manifold

Figure 4.15. Circuit diagram of hydraulic Figure 4.16. Circuit diagram of hydraulic
actuators for joints 0 and 1. motor actuator for joint 2.


series servo valve. The Sundstrand valve was mounted to the motor by a manifold block that

also provided for a case drain to the motor. Actuation of the rotating-lip picking mechanism

(Figure 4.17) was accomplished with a double-acting hydraulic cylinder (Allenair, 3500 kPa,

2.22 cm bore x 5.08 cm stroke) which was controlled by a 3-way solenoid valve energized by 120

volt AC current. Two solid-state relays were utilized to control the AC current. A pressure

reducing valve was used to reduce the hydraulic pressure to 3500 kPa for the actuating cylinder.


Position Sensors

The kinematics of the robot manipulator was developed with the understanding that

the position of each of the joints would be known. Control of the manipulator was based on the

ability to calculate the difference in the actual position from the desired position of each joint.

Rotary potentiometers were used to sense the actual position of each joint at any given time

(Figure 4.18).

The position of each of the joints of the robot was sensed by 2k ohm potentiometers

directly connected to the actuators. For joints 0 and 1, Spectrol single turn potentiometers were











Allenair double acting
hydraulic cylinder
2.22 cm bore
5.08 cm stroke







3-way solenoid valve



STo Return
SManifold


Pressure reducing
valve set to 3400 kPa

L ---J



From Pressure
Manifold

Figure 4.17. Circuit diagram of picking mechanism lip actuator.


chosen for their high precision and linearity. In both cases, the potentiometer body was

mounted to a plate which was attached to the actuator. The shaft of the potentiometer was

connected directly to the back side of the moving shaft of the actuator. A voltage was applied

across each of the potentiometers. The voltage across the wiper of the potentiometer was

proportional to the angular position of the rotary actuator and thus the position of the axis.

This voltage drop was quantified by a 12-bit, 5 volts analog-to-digital (A/D) converter.

On joint 0, the potentiometer was required to relate a total motion of approximately 78

degrees to a voltage ranging between -5 volts and +5 volts. The potentiometer was supplied

with +5 volts to the positive side and -12 volts to the negative side creating a voltage

difference of 17 volts across the 360 degrees of the single turn potentiometer. The result was a

resolution of approximately 19 bits per degree of rotation of the potentiometer wiper shaft

(0.0520/bit). A summary of the range of motion for joint 0 and the A/D bits read for some critical

positions is presented in Figure 4.19.










Pot + Supply
Pot Supply
Pot + Return


Pot Return


Toint 0
variable:
potentiometer:
+ supply:
supply:
Toint 1
variable:
potentiometer:
+ supply:
supply:
Toint 2
variable:
potentiometer:
+ supply:
supply:


PO
Spectrol, 2K, Single turn, 132-0-0-202
+5 V
-12 V

P1
Spectrol, 2K, Single turn, 132-0-0-202
+12 V
-12 V

P2
Bourns, 2K, Ten turn, 536
+5 V
GND


Figure 4.18. Circuit diagram of the position sensing potentiometers.


The potentiometer on joint 1 converted a total motion of approximately 46 degrees to a

voltage that could be used by the A/D converter. Because of the smaller motion of joint 1, a

larger voltage drop across the potentiometer was needed to increase the resolution. The

positive side of the potentiometer was connected to a +12 volts supply while the negative side

was connected to a -12 volts supply. This 24 volt difference across the 360 degrees of the

potentiometer resulted in a change of approximately 3.15 volts through the joint's 46 degree

range of motion. For this joint, the resolution was approximately 27 bits per degree or 0.037

degree per bit. The summary of the range of motion and the critical positions for joint 1 is

presented in Figure 4.20.

For determining the position of the sliding joint of the robot, a Bourns 10 turn, 2k ohm

potentiometer was used. In order to move the full length of the tube, the sliding joint actuator

















A/D bits 3072 Position of
\-38.7 Joint 0




3819 down



Position of Computer
joint 0 A/D Value Description
+38.7' 2324 upper mechanical limit
+34.6' 2400 low
+29.3' 2500 min
-1.6' 3100 home
-32.7' 3700 max
-37.8' 3800 high
-38.7' 3819 lower mechanical limit


Figure 4.19. Relationship between position of joint 0 and the A/D value of the position of
joint 0.


was required to make almost 11 complete revolutions. For measuring the position of the tube

with the Bourns potentiometer, a gear reduction was necessary to keep the motion within the

allowable 10 turns. This potentiometer was connected to the shaft of the Hartmann motor by

way of a small set of miter gears with a drive ratio of 2/3 turn of the potentiometer per

revolution of the motor. The 2:3 gear reduction caused the potentiometer to turn 7.3 revolutions

over the entire length of the tube. The positive supply voltage of this potentiometer was

connected to a +5 volts source while the negative supply was tied to ground. Again, a 12-bit

A/D converter was used to convert the analog voltage to a digital value that could be used by

the control computer. This set-up yielded a resolution of approximately 11 bits per centimeter

























Position of Joint 1


Position of Computer
Toint 1 A/D Value Description
67.0' 2518 left mechanical limit
69.9" 2600 low
73.5' 2700 min
88.7' 3125 home
103.8' 3550 max
107.4" 3650 high
113.0' 3807 right mechanical limit


Figure 4.20. Relationship between position of joint 1 and the A/D value of the position of
joint 1.


of linear travel (0.088 cm per A/D bit). A range of motion summary for joint 2 is presented in

Figure 4.21.

Even though the calculations for the resolution of the position sensors show high

sensitivity, other components also effect the precision of the measured positions. Variations in

the power supply for the entire Florida Laboratory influence the output voltage from the

voltage supply to the potentiometers. These fluctuations along with noise in the connections to

and from the potentiometers add error to the signals from the position sensors. Due to these and

other factors effecting the accuracy of the measurements, the accuracy of the revolute joint

position sensors was assumed to be limited to 05 degree. Likewise, the assumed accuracy of

the prismatic joint was limited to 0.5 cm. These limitations seemed necessary but did not










Picking
Mechanism-
Picking r Pivot for Joint 0 Actuator
Mechanism -




I I i I
A B


---- Robot Support



Actual Position Computer
A (cm) B (cm) A/D Value Position
131.5 0 2321 fully extended (to stop)
129.0 2.5 2350 low
124.5 7.0 2400 min
54.5 77.0 3200 home
10.5 121.0 3700 max
2.0 129.5 3800 high
0 131.5 3821 fully retracted (to stop)


Figure 4.21. Relationship between position of joint 2 and the A/D value of the position of
joint 2.


significantly reduce the ability to control the position of the orange-picking manipulator. A

summary of the conversion factors for converting A/D values to actual positions of the joints is

presented in Table 4.2.


Velocity Sensors

Effective control of the robot required a direct reading of the velocity of each joint. The

velocity of the joints was monitored by the use of DC tachometers (Figure 4.22) mounted to the

actuator or linkage of each of the joints. The voltage output from each of the tachometers was

quantified by 12-bit A/D converters with an input range of 5 volts. This range gave a digital

resolution of 409.6 bits per input volt from each of the tachometers.











Tachometer +




Tachometer -


Toint 0
variable:
tachometer:
output:
drive ratio:
filter gain:
Toint 1
variable:
tachometer:
output:
drive ratio:
filter gain:
Toint 2
variable:
tachometer:
output:
drive ratio:
filter gain:


V0
Servo-Tek SU-780D-1
45 volts per 1000 RPM
1:1
10

V1
Servo-Tek SU-780D-1
45 volts per 1000 RPM
1:1
10

V2
Servo-Tek SA-740A-2
7.0 volts per 1000 RPM
1:1
5


Figure 4.22. Circuit diagram of the tachometers.


For joints 0 and 1, Servo-Tek D series tachometers were chosen (Figure 4.22). The shaft

of each tachometer was directly connected to the mounting shaft of the link so that any motion

of the link created a voltage across the tachometer. Using 12-bit A/D converters and a software

filter with a gain of 10, the resulting resolution of the tachometers was 30.7 bits per degree per

second (0.033 degrees per second per bit). The velocity of the sliding tube was determined by a

Servo-Tek model SA-740A-2 tachometer. The 740A tachometer was mounted on the back side of

the Hartmann motor but connected to the motor's shaft through the 1:1 miter gear. This

mounting arrangement allowed the linear velocity of the sliding joint to be measured by the

angular velocity of the tachometer. A 12-bit A/D converter and a software filter with a gain of

5 were used to quantify the tachometer voltage. The resolution of the velocity sensor for the







44


sliding tube was 71.9 bits per cm per second (0.014 cm per second per bit). A full summary of the

velocity conversion factors is presented in Table 4.2.


Table 4.2. Conversion factors for changing A/D information to actual positions and velocities
of the robot's joints.

Conversion Factors
Toint Position Velocity
0 0.052 deg/bit 0.033 (deg/sec) / bit
1 0.037 deg/bit 0.033 (deg/sec) / bit
2 0.088 cm/bit 0.014 (cm/sec) / bit















CHAPTER 5
ROBOT KINEMATIC MODEL


The kinematic relationships between the joints and links of the robot are presented in

this section. In the field of robotics, homogeneous transformations are used to describe the

position and orientation of one link coordinate system with respect to another one. By

describing the position and orientation of a coordinate frame which is assigned to a link of the

manipulator, the homogeneous transformation describes the position and orientation of the link

itself. According to Paul's method (1981), the product of these homogeneous transformations

(called a T matrix) will be used to calculate the position values of each joint necessary to place

the final coordinate frame (corresponding to the robot camera) at a given position and

orientation in the robot's workspace. The inverse of this T matrix will be useful in calculating

the position and orientation of the camera coordinate frame when given the joint variable

positions. A vector will be defined to relate the position of the centroid of a fruit in the camera

coordinate frame. The T matrix will then be used to relate the position of the fruit to the origin

of the base frame of the manipulator. A similar kinematic relationship will be used to relate

the position of a fruit in the robot's workspace to the position of the fruit's image in the

imaging array of the CCD camera. After establishing this relationship, the information will

be used to present the change in position of the fruit in the imaging array for small changes in

the joint angles of the robot. The vision-servoing gains will be established for adjusting the

gains of the vision control system based on the position of the fruit and position of the robot joint

angles.


Manipulator Kinematics

The citrus-picking robot consisted of three joints which were numbered 0, 1, and 2. Joints

0 and 1 were revolute with intersecting and perpendicular axes of rotation (Zo and Z1,

45










respectively). Joint 2 was prismatic which slid about its Z2 axis that passed through the

intersection of axes 0 and 1. A robot with this order and configuration of the joints and links is

referred to as a spherical-coordinate manipulator.

The order of assignment of the coordinate frames on the orange-picking robot is

presented in Figures 5.1 and 5.2. The first coordinate frame (frame 0, labeled Xo, Y and Z )

was assigned to the stationary base of the robot. Frame 1 was attached to the outer link and

positioned to rotate about Zo an angle 81. The third frame (frame 2) was designated to the inner

moving link (link 2) of the robot and allowed to rotate 82 about Z1. The final coordinate frame

(frame 3) was assigned to the sliding tube of the robot and fixed to have linear motion along

axis Z2 which was coincident with Z3. This final frame was positioned in the end-effector of

the robot so that its origin corresponded with the optical lens center of the robot camera. This

arrangement caused the final coordinate frame of the manipulator and the camera's coordinate

frame to be coincident.

For the orange-picking robot, the joint parameters were specified as variables for

rotation and translation about the axes of motion and as constants to establish the fixed



frame 0

Yo, Z, Y2





frameframe 2 frame 3,






camera frame
Xo/, X ^^





frame 2 frame 3,
camera frame


Figure 5.1. Kinematic frames of the three degree-of-freedom robot.










Yo, Z1,


Outer Link


Sliding Tube


Z2 X3, Xc

Z3, Z,

Base \ Z31 Zc
Y1 Camera
Frame



Inner Link

d Base


Figure 5.2. Kinematic frames as assigned to the links of the robot.


relationships between the successive coordinate frames. The joint variables and geometry

constants for the orange-picking robot are listed in Table 5.1. Based on these parameters, the

following A matrices were determined

C, 0 -S, 0
0A S1 0 C1 0
0 -1 0 0
0001
0 0 0 1 (5-1)


C2 0 S2 0
12 S2 0 -C2 0
A2
0 1 0 0
0 1001 and (5-2)
0001
,and (5-2)









Table 5.1. Link parameters for the orange-picking robot.

Axis of Joint
Link Motion Variable a d a a
1 Zo 81 81 0 0 -900
2 Z12 4 0 0 900
3 Z2 d3 0 d3 0 0



01000
1 0 0 0
2A3 0 1 0 0
0 0 1 da
0 0 0 1 (5-3)

where Si = sin Oi, Ci = cos Oi, and d3 is the distance along Z2 from the axis of rotation Z1 to the

origin of frame 3. Multiplying these A matrices, the position and orientation of the image

plane of the manipulator's vision system with respect to the base was established as T3:

C1 C2 -S, C1S2 C1S2d3
T 1 2 SlC2 C1 S1S2 S1S2d3
T3= A2 A3 -S2 0 C2 C2d3

0 0 0 1 (5-4)

The orientation of Z3 with respect to the robot base frame (frame 0) was determined by the 3 x 3

matrix in the upper left-hand corer of T3. The three column vectors of the 3 x 3 matrix, from

left to right, defined the direction of the X3, Y3, and Z3 axes, respectively. The fourth column

vector of the T3 matrix defined the position of the origin of the camera frame (frame 3). Due to

the configuration of the manipulator, this position vector, [ C1S2d3 S1S2d3 C2d3 1 ]T, was

always colinear with the Z3 = [ C1S2 S1S2 C2 1 T vector of the camera frame.

Due to the importance of these position vectors in establishing the imaging and vision-

servoing kinematics, it was also important to understand the configuration of the robot for the

possible values of the joint variables. First, let all of the joint variables be equal to 0. In this

case, all of the coordinate frames of the robot had a common point as their origins. Frames 0, 2,

and 3 were completely coincident with common X, Y, and Z vectors. Frame 1, on the other hand,

was positioned so that X1 and Xo, Y1 and -Zo, and Z1 and Yo were coincident. As a result, if all of










the variables could be set to 0, the robot would be configured so that the outer link would be

parallel with the supports of the base. The inner link would be positioned at a right angle to

the outer link so that the sliding tube would point through the actuated mounting shaft of the

outer link. The sliding tube would be retracted so that the axis of the inner link would pass

through the lens of the camera in the end-effector.

However, the action of the orange-picking robot was limited by the mechanical stops

on each of the joints. In addition, these mechanical stops restricted the boundaries of the

individual parameters which governed the motion of the coordinate frames. The range of

motion for each of the joint variables is shown in Table 5.2. These ranges of motion for each joint

defined the working envelope of the orange-picking robot.


Table 5.2. Range of motion for the joint parameters of the orange-picking robot.

Range
Parameter Minimum Maximum
91 -390 +390
92 +670 +1130
d3 +51.0 cm +182.5 cm


Imaging Kinematics

Vision-servoing of the robot required that the relationship between actual position of a

fruit and the position of the fruit's image in the imaging array of the camera be established

(see Figure 5.3). For this derivation, the position of the fruit was defined by a vector, pc = [ x y

z 1 ]T, from the origin of the camera coordinate frame to the centroid of the fruit. The position

of the fruit's image was defined by another vector, pi = [ xi i zi 1 ]T, from the camera coordinate

frame to the centroid of the fruit's image in the imaging array.

The CCD imaging array of the camera was parallel to the X-Y plane of the camera

frame and positioned in the negative Z direction from the origin of the frame the distance of

the focal length of the lens, zi = -f. The position of a fruit's projection in the image plane, pi,

was related to Pc, its actual position, by


Pi = Tp pc


(5-5)










YC

XC
^y 4 x,





SOC z Z

Lens




Figure 5.3. Lens imaging geometry.


where

-/ 0 0 0
'z
0 J/ 0 0
T= z
0 0 -f/
0001
(5-6)

pc =[ x y z 1 F,and

pi= x, yi zi 1 F.

Calculating xi and yi, the relationship between the actual position of the fruit and the position

of the fruit's projection on the image plane was established,

xi = x (-f/z), and

yi = y (-f/z)

A change in the fruit's position in the camera frame resulted in a position change of the image

in the image array scaled by the -f/z factor.


Vision-Servo Kinematics

In the end-effector of the robot, the camera was mounted in such a way that its optical

axis was coincident with Z3. The later addition of the ultrasonic ranging horn required that the










position of the camera be lowered by a small amount. This amount was very small and

considered negligible in the further derivation of the vision geometry. The camera was

assumed to be positioned so that the center of its lens was at the origin of frame 3. Therefore,

the coordinate frame of the camera was the same as frame 3.

The relationship between the position of the fruit in the camera frame, Pc, and the

position of its image on the imaging array, pi, was important in formulating the effects of

changes in the position of the manipulator's joints on the position of the image. To vision-servo

the robot, it was necessary to develop closed-form solutions that related changes in 81 and 82 to

changes in xi and yi. These relationships were referred to as vision gains and expressed as

K -dyi
=d8 and (5-7)

dxi
Kvx=
d22. (5-8)

Because the position of the fruit was assumed to remain the same regardless of the

configuration of the robot, it became necessary to define the position of the fruit with respect to

the stationary base frame (see Figure 5.4). Using the T3 matrix to specify the position of the

fruit in the coordinates of the base frame, po, was established as


Po= T3Pc. (5-9)

Utilizing this relationship, the position of the fruit in the camera coordinate frame was

determined to be

-1
Pc= T3 Po. (5-10)

Substituting pc into equation 5-5, the position of the fruit's projection in the image array, pi, was

found


-1
Pi= TT3 PO.


(5-11)




























Figure 5.4. Coordinate frame representation of the camera frame and the fruit position with
respect to the base frame.


where

C1C2 S1C2 -S2 0
-1 -S Ci 0 0
C1S2 S1S2 C2 -d3
0 0 0 and (5-12)

po- the position of the fruit in the base frame coordinates.

The derivation of the vision gains began by assuming the manipulator was initially

aligned with a fruit which was located at some position po in the base frame coordinates and

some distance z from the camera. The joints of the manipulator were located at some position

81, e2, and d3 when the fruit was aligned. This arrangement caused the fruit to lie along Zc at a

radial distance (d3 + z) from the origin of the base frame. Therefore, po was expressed as

p (d3+z)C1 S2
P (d3+z)S1S2
(d3+ z)C2
1 (5-13)


Substituting equation 5-13 into equation 5-11 and solving for pi,









-1

Pi=TpT 3o= .f

(5-14)

xi and yi were found to be 0 as expected for the aligned position of the fruit. Also as expected, zi

was found to be the negative value of the focal length of the camera and lens (zi = -f).

Assuming that the manipulator position was changed to some position (e1 + dO1, 82 + d%2, d3) by

rotating joints 1 and 2 by some very small increments de1 and d82, the position of the fruit in the

image array was offset from the center by incremental amounts dxi and dyi. Because of the

increments were very small, the second order terms of d81 and d@2 were assumed to be 0. Also,

for small dEi, sin(di) dOi and cos(d)i) = 1. Solving equation 5-11 with the new T3-1 (equation

5-12) for pi yielded

d f de2(d3+z)
z and (5-15)

f dOe S2(d3+z)
dyi=
z (5-16)

Solving for the vision gains resulted in

vxf + 1
K=f z ( and (5-17)


K Y=f S2 d3+1
f +1). (5-18)

The vision gains were approximately proportional to d3 and inversely proportional to z.

Therefore, during a pick cycle, as the picking mechanism was extended toward the targeted

fruit, smaller motions of the two revolute joints were required to compensate for misalignment of

the robot with the targeted fruit. Additionally, Kvy was proportional to the sine of 02. This

term indicated that smaller adjustments in e) were required to compensate for the misalignment

of the robot and the fruit as the position of 02 moved to greater distances from 90.

Another important indication from this kinematic analysis of the relationships among

the position of the joints of the robot, the position of the camera frame, and the position of the







54


fruit was that the vision-servo problem was geometrically decoupled. In other words, changes

in 81 did not affect xi, and changes in 02 did not affect yi. This decoupling was indicated by the

absence of a dO1 term in equation 5-15 and the absence of a de2 term in equation 5-16. The

geometry contributed to the decoupling effect allowing the two-dimensional vision control

problem to be treated as separate problems, greatly simplifying the development of the control

algorithms.















CHAPTER 6
ROBOT OPEN-LOOP DYNAMICS


In this chapter, the open-loop dynamic models of the robot are presented. The joint

components of a generic electrohydraulic servo system and their interaction are discussed first.

The mathematical form of each of the components is presented. The open-loop model is then

reduced to a representative model which approximates the dynamic response of a servo system

and can be used for selecting and tuning control algorithms. Open-loop step tests of the robot

joints are then presented and used to estimate model parameters. Simulated responses to step

inputs are compared to the responses of the actual joints to step inputs for model and parameter

verification.


Background

Merritt (1967) discusses the design of control systems for electrohydraulic servo

mechanisms. He derives a mathematical model for each of the components of the generic

electrohydraulic servo system. An open-loop servo system (Figure 6.1) includes servo amplifier

dynamics, servo valve dynamics, external torque load dynamics, and actuator and load

dynamics. In his presentation, Merritt points out that the servo amplifier, servo valve, and no-

load system all respond as second-order systems. Merritt discusses the selection of components

of the servo system stressing the fact that the bandwidth of the servo amplifiers and servo

valves should be higher than that of the selected actuators. By choosing fast servo amplifiers

and valves, their dynamics can be reduced to a single gain as in Figure 6.2. In this case, the

open-loop transfer function for the velocity control servo system of each joint of the orange-

picking robot is approximated as a second-order system:











inD/A C Servo Amp Servo Valve Load ac o et
converter I Dynamics I Dynamics |- Load Tach | Converte--1-

Figure 6.1. Open-loop hydraulic servo system.



D/A
word liter deg
t(bits) g-7-"v-"vtq Servo Amp/ [iec Actuator and _sec ----v-olts -bits
Signal Converter Sero ADnas aValve ad Converter| Signal

Figure 6.2. Reduced block diagram of the open-loop system.


2
Au(s) = Kv- -
2 2
s +28h(OhS + (Oh (6-1)


where Au(s) = open-loop transfer function ((deg/sec)/(D/A word)),

s s Laplacian operator (sec-),

Kv = open-loop gain of the system ((deg/sec)/(D/A word)),

(h open-loop hydraulic natural frequency (rad/sec), and

6h = open-loop damping ratio dimensionlesss).

In this system, the open-loop gain includes the gains of the D/A converter, the servo amp/servo

valve combination, and the actuator and load dynamics.

The hydraulic natural frequency and the damping ratio are functions of parameters of

the fluid and the mechanical components of the controlled system and can generally be

approximated as

4 eDm
Wh= V
VVt t (6-2)


8h e(6-3)Pe
Dm V V (6-3)










where: pe = bulk modulus of hydraulic fluid (N/m2),

Dm volumetric displacement of rotary actuator or motor (ml/rad),

Vt total compressed volume of fluid (ml),

Jt M total inertia of load and actuator (N m sec2), and

Kce a servo valve flow-pressure coefficient (ml/sec/N/m2).

Each of these parameters can vary during operation. However, by keeping the temperature of

the hydraulic fluid constant during operation of a servo hydraulic system, the bulk modulus (Pe)

of the fluid can be considered constant. As rotary actuators and motors rotate, the volume of

fluid in one chamber decreases while the volume in another chamber increases. Since the total

volume of fluid in the actuators and motors changes only very small amounts due to pressure

differential during operation, the volumetric displacement (Dm) can also considered to be

constant. Likewise, if the total compressed volume of fluid (Vi) in the system changes only very

small amounts if any during operation, it can be considered constant. Because the quantities, 3e,

Dm, and Vt, are fairly constant, they cause only minor changes in the values of oh and 8h during

operation of the servo hydraulic system.

Another important effect on the performance of an electrohydraulic servo system is the

external torque load on the output shaft of the actuator as shown in the block diagram of Figure

6.3. External loads on the system must be accounted for in the derivation of the open-loop

transfer function. In the case of the orange-picking robot, this external load was altered by the

position of the joints 0 and 2. When the sliding joint was moved from a balanced position, an

external torque was added to joint 0 actuator. This torque was proportional to the position of

joint 2 with positive and negative maximum values occurring when the tube was extended or

retracted, respectively. When joint 0 was moved from a horizontal position, an external load

was induced on the motor which actuated joint 2 by the pull of gravity on the sliding tube. This

load was greatest when joint 0 was positioned to its maximum or minimum rotation. Each of

these loads affected the operation of the robot.










External
Torque Load
TL External
Torque Load
N.m Dynamics

D/A
word liter deg
Signal CoG + Dynami Converter Signal

Figure 6.3. Block diagram of the open-loop system with external torque load.


During critical performance times for the citrus-picking robot, the tube was already

extended toward the fruit. During these periods, motion of the sliding tube was so small that

changes in the torque load caused by its changing motion were considered negligible. Therefore,

the dynamics of the external torque on joint 0 were also considered constant. Similarly, changes

in position of the sliding tube were required only during occasions in which motion of joint 0 was

very small or nonexistent. As the end-effector was extended toward a targeted fruit, the

position of joint 0 was controlled by the vision system to follow the small vertical motion of the

fruit. This vertical fruit motion was very small and resulted in very small and negligible

position changes in joint 0. While joint 2 was being retracted from the tree, joints 0 and 1 were

held practically motionless to prevent manipulator damage caused by collisions with large

limbs or other obstacles. Therefore, the external touque load on joint 2 due to changes in the joint

0 position was also constant during the motion of joint 2. In other words, the external torque

loads that affected joint 2 could be considered constant during any operation of the sliding joint.


Parameter Estimation

In the general case, the actuator and load dynamics is the limiting factor for the

response of a servo system. As Merritt points out, servo amplifiers and valves should have

faster response rates than the actuator and load combinations. In this case, the dynamic

response characteristics of the servo amplifiers and servo valves can be neglected. In the case of

the orange-picking robot, servo amplifiers and servo valves were chosen with this criteria in

mind. All three of the servo amplifiers had bandwidths of 1885 rad/sec (300 HZ) (Table 4.1).










Also, servo valves with bandwidths of 377 rad/sec (60 HZ) for joints 0 and 1 and 189 rad/sec (30

HZ) for joint 2 were used. Equation 6-2 was used to approximate the hydraulic natural

frequencies for the joints of the robot. For the revolute joints, the maximum natural frequency

was estimated to be approximately 28 rad/sec which was classified as slow when compared to

the response rate of the actuators. Assuming that the sliding tube was a simple mass for the

motor actuator, a natural frequency of 67 rad/sec was estimated. Not included in this

estimation was the decrease in the response of the slider which developed as a result of the

friction in the bearing. Therefore, the response of the chosen actuator for joint 2 was adequate to

be considered fast enough to be neglected in the further analysis.

Theoretically, the steady-state gains, hydraulic natural frequencies, and damping

ratios could have been calculated from the known characteristics of the manipulator.

However, for the orange-picking robot, such parameters as link mass and mass moment of

inertia as well as some hydraulic fluid characteristics which affected the actuator and load

dynamics were unknown. Also, flow characteristics of the servo valves were undeterminable.

Therefore, the steady-state gain, hydraulic natural frequency, and hydraulic damping ratio

for each joint were determined experimentally. The experimental tests consisted of actuating

each joint by stepping the reference voltage to the servo amplifier and measuring the joint

response. These open-loop tests were conducted on each joint individually. For each joint, the

computer was programmed to signal the servo amplifier to send a current to the servo valve

holding it opened for a given amount of time while the computer recorded the velocity and

position of the joint as it moved. A routine was added to the user interface of the robot control

program to obtain a description of the step from the user and send the appropriate control signal

to the D/A board. The step was maintained until the joint reached a constant velocity or the

position of the joint reached a specified maximum or minimum. The valve was then closed to

stop the action and bring the joint to rest.

Typical graphs for step test results are shown in Figures 6.4, 6.5, and 6.6 for joints 0, 1,

and 2, respectively. Information from the graphs was used to estimate the gain, the hydraulic










natural frequency and the hydraulic damping ratio for each joint. The steady-state gain of a

joint was the ratio of the achieved steady-state velocity to the input value. The gain for each

joint was determined as

K Vout
K,-
V*P (6-4)

where: Kv a steady-state gain ((deg/sec)/(D/A word)),

Vout steady-state output velocity (deg/sec), and

Vsp = velocity control signal (D/A word).

The damping ratio was approximated with (Palm, 1983):



In ln(os) )2
Sh= ( I
2
1+ (In (os))
-IC ) (6-5)

where: 5h hydraulic damping ratio dimensionlesss), and
V max-V
os overshoot (decimal value) Vmax
V sa

The hydraulic natural frequency was approximated with (Palm, 1983)



tPv l- (6-6)

where oh = hydraulic natural frequency (rad/sec),

kh = damping ratio dimensionlesss), and

tp = time to peak (sec).

A typical response of joint 0 of the orange-picking robot to a step input is shown in

Figure 6.4. The response signals from the A/D converters were converted from the bit values as

used by the control computer to deg/sec by the conversion factor 0.033 (deg/sec)/bit from Table

4.2. For a step input to the actuator of 1200 D/A bits, the joint started from a velocity of 0

deg/sec (0 A/D bits) and peaked at a velocity of 65 deg/sec (1980 A/D bits) before returning to

an average steady-state velocity of 46 deg/sec (1400 A/D bits). Thus, the steady-state gain for







61


80

60-

40-

I 20



-20-

40 l i i i --- i i .
0 15 30 45 60 75 90 105 120
Time (1/60 sec)

1500

10


so-


0 15 30 45 60 75 90 105 120
Time (1/60 sec)

Figure 6.4. Typical response of joint 0 of the orange-picking robot to a step input of 1200 D/A
bits with joint 2 centered in the Hooke joint.


this system was calculated using equation 6-4 as approximately 0.038 (deg/sec)/(D/A word).

These values represent an overshoot of 19 deg/sec (580 A/D bits) which corresponds to 41

percent. Using this measured overshoot in equation 6-5, a damping ratio of 0.27 was calculated.

The time to peak was determined by finding the number of counter ticks required for the

velocity of the joint to reach its maximum and dividing by the scale factor, 60 ticks per sec. In

this case, the joint reached its maximum velocity in 10 counter ticks or 0.17 sec. This value along

with the already determined damping ratio was used in equation 6-6 to find the hydraulic

natural frequency of the joint of 20 rad/sec or 3.1 HZ.

Open-loop step tests were conducted on joint 0 for different directions of motion and

different positions of joint 2. The tests were conducted with the tube extended, in the center of

its working range, and retracted. Repetitions of the tests included step inputs that caused the

end-effector to be moved down from a raised position and up from a lowered position, or in









response to positive and negative steps. The results of the repetitions were averaged. The

average steady-state gains, hydraulic natural frequencies, and damping ratios are presented in

Table 6.1.

A typical response of joint 1 of the robot to a step input of -500 D/A bits is shown in

Figure 6.5. This step caused the joint to move the end-effector of the robot from left to right.

The step input was initialized at 1/2 sec (30 counter timer ticks). The joint which began from a

velocity of approximately 0 deg/sec (0 A/D bits) responded to the input by reaching a peak

velocity of -38 deg/sec (-1150 A/D bits) before returning to an average steady-state velocity of

-28 deg/sec (-850 A/D bits). The values for this step test represent an overshoot of -10 deg/sec

(-300 A/D bits) or 35 percent of the steady-state velocity. Joint 1 reached its maximum or peak

velocity in 7 counter timer ticks or 0.12 sec. Using these values in equations 6-4, 6-5, and 6-6, the

hydraulic natural frequency and damping ratio of joint 1 were found to be 28 rad/sec (4.5 HZ)

and 0.32, respectively. The steady-state gain, Kv, for joint 1 was found to be

0.056 (deg/sec)/(D/A word).

For step test response of joint 1, the position of joint 0 was held constant while joint 1

was free to respond to the step input from the control computer. These tests included both

positive and negative step inputs from the computer resulting in horizontal motions of the end-

effector. The test was also conducted in repetition for joint 2 in the retracted, centered, and


Table 6.1. Experimentally determined steady-state gains, damping ratios, and hydraulic
natural frequencies of joint 0 in relation to position of joint 2 and direction of
motion.

steady-state
joint 0 gain hydraulic hydraulic natural
position direction (deg/sec) damping frequency
of joint 2 of motion (D/A word) ratio rad/sec HZ
retracted down 0.035 0.30 33 5.2
up 0.042 021 22 3.4
centered down 0.033 0.18 17 2.8
up 0.038 0.26 20 3.1
extended down 0.044 0.31 17 2.8
up 0.040 0.34 27 4.3

















-10

S-20-

-30

-40
0 15 30 45 60 75 90 105 120
Time (1/60 sec)



"a 0

| | -200-

400-


0 15 30 45 60 75 90 105 120
Time (1/60 sec)

Figure 6.5. Typical response joint 1 of the orange-picking robot to a step input of -500 D/A bits
with joint 2 centered in the Hooke Joint.


extended positions. The averaged results of the repetitions of the open-loop step test of joint 1

are presented in Table 6.2.

Step tests of joint 2 gave undesirable results. When the sliding joint was actuated with

a step input, the joint responded with a quick jolt and then settled to an increasing velocity as

the valve was held opened. The sluggish response of the joint did not reach a steady or peak

velocity before the full length of the tube was used at which time the step input was

terminated. A typical response of joint 2 to a step input is shown in Figure 6.6. From the

information presented in the figure, the defining parameters for the system were not

determinable. However, important observations were made which aided in developing a

controller for the sliding joint. Due to the static friction between the nylon bushing and the

aluminum tube, the input required to start the tube moving was much larger than that required

to keep it moving. Small control values would not cause a change in the joint's position. On the









Table 6.2. Experimentally determined steady-state gains, damping ratios, and hydraulic
natural frequencies of joint 1 in relation to position of joint 2 and direction of
motion.

steady-state
joint 1 gain hydraulic hydraulic natural
position direction (deg/sec) damping frequency
of joint 2 of motion (D/Aword) ratio rad/sec HZ
retracted negative 0.054 0.29 28 4.5
positive 0.055 0.18 32 5.1
centered negative 0.055 0.32 28 4.5
positive 0.055 022 28 45
extended negative 0.056 0.31 22 3.5
positive 0.058 0.26 22 3.5


other hand, the response of joint 2 to large control values would increase stiffness requirements

for positioning the joint.


Results and Discussion

Design of the control systems for the orange-picking robot required a knowledge of the

each joint's transfer function. Merritt (1967) suggests that the transfer function of most

electrohydraulic servo systems can be estimated as a second-order system. Open-loop step tests

were conducted on each of the robot's joints for verification of Merritt's assumptions and for

establishing the parameters which define the behavior of a second-order system. After

defining the systems' parameters, the second-order systems were simulated for comparison with

the actual systems and verification of the determined parameters.

Analysis of the open-loop step tests responses of joint 0 for various positions of the

sliding tube yielded a range of hydraulic natural frequencies and damping ratios. Repetitions

of the step tests suggested average hydraulic natural frequencies ranging from 17 to 33 rad/sec

(2.8 to 5.2 HZ) and average damping ratio ranging between 0.18 and 0.34 (Table 6.3). The open-

loop gain (Kv) for joint 0 was averaged to be approximately 0.039 (deg/sec)/(D/A word) as the

ratio of the output signal to the computer's D/A converter in deg/sec to the input signal from the

computer's A/D converter in deg/sec.


















S-200-

-300,

-400
0 15 30 45 60 75 90
Time (1/60 sec)


3 800.
M ^ 600-
| 400-
UL 200.
0-
-200 ., 1. .. .
0 15 30 45 60 75 90
Time (1/60 sec)

Figure 6.6. Typical response of joint 2 of the orange-picking robot to a step input of 750 D/A
bits.


Table 6.3. Steady-state gains, hydraulic damping ratios, and hydraulic natural frequencies as
determined by analysis of the step test responses.

averaged averaged
steady-state averaged hydraulic natural
gain hydraulic damping frequency
(deg/sec) ratio (rad/sec (HZ))
joint (D/A word) nin max rin max
0 0.039 0.18 0.34 17 (2.8) 33 (5.2)
1 0.056 0.18 0.32 22 (3.5) 32 (5.1)


Similarly, step test responses of joint 1 produced information for estimating the

parameters of its transfer function. Once again, the tests were conducted in both directions with

different positions of joint 2 for establishing a range of the parameters which were valid for

the manipulator during operation. Also listed in Table 6.3, the system open-loop gain was

estimated as a constant value of 0.056 (deg/sec)/(D/A word), while the average hydraulic










natural frequency spanned a range from 22 to 32 rad/sec (35 to 5.1 HZ). The average damping

ratio ranged from 0.18 to 0.32.

The second-order open-loop dynamic transfer functions were simulated with the

parameters as determined by the step tests for joints 0 and 1. The results of these simulated

systems were plotted for comparison with the experimental results of the step tests.

Representative results from the experimental tests and the simulations are presented in Figures

6.7 through 6.12. These graphs represent cases for joints 0 and 1 spanning the determined

natural frequency and damping ratio ranges. A response pattern was evident across all of the

tests. In each case, the response of the actual joint showed a peak which compared directly to

the first peak of the simulated system. In some, but not all cases, the actual joint oscillated

slightly (usually one cycle) before settling to a steady-state value. The simulated systems, on

the other hand, generally oscillated more.

This discrepancy indicated nonlinearities in the systems which probably resulted from

nonlinear servo valve characteristics. Theoretically, a deadband in the valve would deliver a

much smaller oscillation than would occur for a valve that was purely linear. A region in the

response of a hydraulic valve in which small changes in the control signals have no effect on

the direction or amount of fluid flow through the valve is referred to as the deadband of the

valve. The responses of the servo valve controlled joints of the robot seem to indicate that a

deadband caused by either an overlap of the valve ports or coulomb friction exists in these

systems.

Because design of the robot's control systems was based on linear systems, a linear

approximation of the transfer functions for these joints was necessary. Noting that the step

responses of the systems were best approximated by second-order responses, second-order

systems were chosen to estimate the transfer function of the actual systems. Therefore,

Merritt's assumptions for reducing the electrohydraulic control system to a second-order system

were verified for the cases of joints 0 and 1. These second-order systems were later used to model









each of the joints and aid in the selection and implementation of the controllers of the orange-

picking robot.

The joints' responses to the step input signals gave important information to be used in

the design of the respective controllers. For joints 0 and 1, the ranges in the natural frequencies

and damping ratios were related to the position of joint 2 during the tests. Higher natural

frequencies were calculated for joint 0 when the weight of joint 2 was being lifted. For example,

the highest natural frequencies resulted when the tube was extended with the end-effector

being lifted or when the tube was retracted with the end-effector being lowered. Likewise, the

highest damping ratios for joint 0 were calculated for those responses in which the most weight

was being lifted. When this information was checked against the parameters of equations 6-2

and 6-3, the damping ratio follows the expected trend that increased load inertia would result

in increased damping. However, the natural frequency contradicts the inverse relationship

with the inertia load as indicated in equation 6-2. This contradiction indicated that the

position of the sliding joint influenced the system more as an external torque load than an

inertia load used in equation 6-2.

The step tests for joint 1 involved moving the end-effector in horizontal directions. For

this joint, a steady-state gain of 0.05 (deg/sec)/(D/A word) was calculated for every trial. In

this case, the second-order parameters varied with the position of joint 2 and the direction of

travel. The hydraulic natural frequencies were smallest when the sliding joint was extended

and the highest inertia was expected. This followed the relationship of equation 6-2. On the

other hand, the established damping ratios did not follow the relationship of equation 6-3.

The only evident pattern of the change in damping ratio was that the damping ratio for the

positive direction was smaller than that for the negative direction. This variance could have

been caused by improper alignment of the outer frame causing binding in the bearings or from

different friction values for the different directions of travel.

As previously discussed, the model of joint 2 could not be determined due to the high

static friction values in the bushing and its unpredictable behavior. The behavior of joint 2







68


indicated that the system had a high deadband which required very large signals to initialize

the motion of the joint and much smaller signals to keep it moving. For controller development,

it was considered to have a sluggish second-order response in which special considerations

would have to be made in controller development and implementation.






























0 10 20 30 40 50
Time (1/60 sec)

(a)


o
O ."




.


0 10 20 30 40 50
Time (1/60 sec)

(b)

Figure 6.7. Responses of joint 0 to a step input: (a) actual, (b) simulated.
q = 32.95 rad/sec, Sh = 0.30, Kv = 0.036 (deg/sec)/(D/A word).










0

-10-

-20

S-30

0 -40 -

-50

-60

-70 .
0 10 20 30 40 50 60
Time (1/60 sec)

(a)

0

-10

-20

-30

2] -40

S -50

-60-

-70
0 10 20 30 40 50 60
Time (1/60 sec)

(b)

Figure 6.8. Responses of joint 0 to a step input: (a) actual, (b) simulated.
h = 17.36 rad/sec, h = 0.16, K, = 0.032 (deg/sec)/(D/A word).










0

-10

-20

S -30 -

-40

-50

-60-

-70 ,
0 10 20 30 40 50 60
Time (1/60 sec)

(a)

0

-10-

-20

| -30 -

a. -40-

-50

-60

-70
0 10 20 30 40 50 60
Time (1/60 sec)

(b)

Figure 6.9. Responses of joint 0 to a step input: (a) actual, (b) simulated.
Oh = 16.54 rad/sec, 8 = 0.31, K, = 0.044 (deg/sec)/(D/A word).






























0 10 20 30 40 50
Time (1/60 sec)


u
oh
- U


0 10 20 30 40 50
Time (1/60 sec)

(b)

Figure 6.10. Responses of joint 1 to a step input: (a) actual, (b) simulated.
wh = 31.87 rad/sec, kh = 0.17, Kv = 0.055 (deg/sec)/(D/A word).










0


-10-


0*- -20

>-
c -30


-40


-50
0 10 20 30 40 50 60
Time (1/60 sec)

(a)

0


-10


0^ -20-


S -30


-40


-50
0 10 20 30 40 50 60
Time (1/60 sec)

(b)

Figure 6.11. Responses of joint 1 to a step input: (a) actual, (b) simulated.
h = 22.02 rad/sec, Sh = 0.31, Kv = 0.056 (deg/sec)/(D/A word).










50


40


30


S 20
1

10-



0 10 20 30 40 50 60
Time (1/60 sec)

(a)

50-


40


0- 30-


20


10


0- .
0 10 20 30 40 50 60
Time (1/60 sec)

(b)

Figure 6.12. Responses of joint 1 to a step input: (a) actual, (b) simulated.
h = 21.47 rad/sec, 8h = 0.22, K, = 0.056 (deg/sec)/(D/A word).















CHAPTER 7
PERFORMANCE CRITERIA


Desired performance criteria for the joint control systems of the orange-picking robot

are specified in this chapter. Because joint control was based on position, velocity, and vision

information, performance requirements were defined to give details upon which the control

systems would be designed and evaluated. In order to determine these requirements, the

interaction between the robot and its environment was evaluated. Initially, the motions of a

fruit hanging from the tree were examined. Information acquired from this investigation was

used to establish vision dynamic criteria for the robot's control. To determine the precision

with which the end-effector of the robot was required to be positioned, a picking envelope was

established. This picking envelope defined the volume with respect to the end-effector in

which a fruit must be located to be picked. In other words, the controllers were required to

utilize information from the fruit sensors to position the end-effector within reach of the

targeted fruit. From this definition of fruit motion and the pick envelope, controller

performance criteria for each joint were determined. These requirements make up the static and

dynamic performance criteria which were necessary for choosing and designing controllers to

realize a satisfactory robot response.


Background

All control systems are designed to perform a specific task. Performance specifications

are spelled out as requirements of the control system. These criteria include relative stability,

accuracy, and response rate. In most cases, these specifications are given in precise numerical

values. However, in some cases, the criteria are not as critical and can be specified as

qualitative statements providing leeway for personal judgement. Many times, the requirements

placed upon a system must be modified during the course of implementing and tuning the

75










controller due to the increased expense of the system or conflicting criteria. Sometimes, the

performance specifications simply can not be met. In any case, the performance criteria are

specifications of design goals which are used for choosing and implementing system controllers.

For the orange-picking robot, the main purpose of joint control was to cause the end-

effector to be positioned so that a fruit could be detached from the tree within the shortest

possible pick cycle time. A pick cycle was characterized by the steps required for the robot to

begin from a "home" location, search for and locate a target fruit, position the end-effector so

that the targeted fruit could be detached, actuate the picking lip to girdle the fruit, return to

the specified home position, and release the fruit. The most important requirement of all

control modes was that the system remain stable for any requested action. Second most

important was the accuracy with which the end-effector was positioned with respect to the

fruit. The relation between the end-effector and the fruit was controlled by the vision control

algorithm and the information from the fruit sensors for joints 0 and 1 and by both the position

and velocity control algorithms for joint 2. Therefore, the strictest performance criteria were

specified for the vision control algorithms in addition to the position and velocity control

modes for the sliding joint.


Characteristics of Fruit Motion

Because the environment of the fruit tree was not free from disturbances during the

picking operation, the robot was required to pick moving fruit. The fruit motion usually

resulted from environmental disturbances such as wind or from canopy interference as the

manipulator removed fruit. Regardless of the cause, the resulting fruit motions were

investigated for use in specifying the performance requirements of the robot.

Initially, reactions of the fruit to wind disturbances were examined. Then, the branches

of the tree were disturbed in a manner similar to those disturbances anticipated during robotic

picking. A tape measure was placed below the fruit for determining the magnitude of the fruit










motion. Using a video camera with a timing feature, fruit's reactions to these disturbances were

recorded and analyzed.

Results from these tests indicated that the fruit could swing with a peak-to-peak

magnitudes ranging from 25 cm to 100 cm with cycle times ranging from 0.9 sec to 2.6 sec. The

results of these tests are presented in Figure 7.1 with the shaded region of the plot indicating

the observed fruit motion. Extreme cases of fruit motion which could take place during picking

were noted as the worst case that the robot could encounter. These extreme cases lie along the

sloping line which limits the upper side of the graph's shaded region and is established by

motions of 100 cm peak-to-peak magnitudes at 0.5 HZ and 25 cm peak-to-peak magnitudes at 1.1

HZ. The robot's control algorithms were required to manipulate the robot to be able to track

and pick fruit with any motion. The best case from the picking standpoint would have the

targeted fruit hanging motionless from the branch. Based on the results of this fruit motion test,

the worst cases that the robot would encounter ranged from small magnitudes with small cycle

times (12.5 cm, 1.1 HZ) to large magnitudes with long cycle times (50 cm, 0.5 HZ) (Figure 7.1).



120-

100-
100 3 Fruit Motion

80 -




40 -
40

20
0.2 0.4 0.6 0.8 1.0 1.2

Frequency (HZ)


Figure 7.1. Typical observations of the motion of fruit swinging from the canopy of a tree
indicating the peak-to-peak magnitude of the fruit for various periods of
oscillation.










Picking Envelope Definition

A study was conducted to define the picking envelope of the end-effector by quantifying

the fruit position range, relative to the stationary end-effector, in which fruit capture could be

accomplished. An apparatus was designed and constructed for holding a fruit in front of the

picking mechanism (Figure 7.2). The apparatus consisted of two pieces of aluminum bent at

right angles and mounted on the end-effector of the robot. The pieces were scribed with a

pattern for establishing the location of the fruit which hung from the apparatus and held in

place by two large spring dips. For the testing, an artificial orange (approximately 8 cm in

diameter) was weighted with water and hung from the support by an elastic cord. The elastic

cord allowed the artificial orange to have motion similar to that of a real orange hanging from

a citrus tree.

The picking envelope was defined by measuring the location of the fruit's center with

respect to the picking mechanism. In order for a location to be included in the picking envelope,


Figure 7.2. Apparatus for determining the picking envelope of the robot's end-effector.









the region in which a successful pick could be guaranteed, the end-effector was required to

girdle the fruit successfully in seven of seven attempts. Positions at which the rotating lip

pushed the orange away or the orange was caught between the rotating lip and the body of the

picking mechanism were considered unsuccessful attempts. Initially, the fruit was positioned in

the center of the picking mechanism, touching the protective shield of the camera with its

center located on the Z axis of joint 2 of the robot (home position). Thus, the position of the fruit

was defined in terms of the camera coordinate frame with the home position located at x = 0 cm,

y = 0 cm, and z = 10.2 cm. The fruit was then moved out along the Z axis in 1 cm increments until

the mechanism was unable to successfully girdle the orange in all of seven attempts. From this

location, the orange was moved to a location 1 cm up from the home position along the Y axis

and back to a point which was easily picked by the mechanism. Again, the fruit was moved out

from the picking mechanism until it could no longer be picked. As the orange was moved to the

edge of the picking range of the robot, the increments were reduced to one half centimeter. Each

location was noted along with the number successful attempts. This operation was repeated

until the complete region in which the robot could possibly pick fruit was covered.

The results of the picking envelope tests are graphically presented in Figures 7.3, 7.4,

and 7.5. In each of the figures, the shaded, circular region represents the fruit positioned

against the protective shield of the camera and centered vertically in the tube of the picking

mechanism. The centroid of the fruit in this position was used as the origin of the picking

envelope. The outer ranges of the orange centroid for a successful pick are represented by the

bold lines in the figures. The range in which the picking mechanism could pick a fruit whose

center lay in a vertical plane that intersected the centerline of tube (Z2) is presented in Figure

7.3. The region in which the orange could be picked if its center point was in a vertical plane 1

cm to the right or left of the centerline of the tube is shown in Figure 7.4. Similarly, the

successful picking region in the vertical plane located 2 cm from the centerline is displayed in

Figure 7.5. In these tests, if the center of the orange was more than 2 cm away from the center of











protective cover for camera


y (cm)


Figure 7.3. Picking range of the end-effector in the vertical plane located on the centerline of
axis 2.


protective cover for camera
(1 cm thickness)


y (cm)


Figure 7.4. Picking range of the end-effector in the vertical plane located 1 cm from the
centerline of axis 2.










protective cover for camera
(1 cm thickness)
OC /z (cm)
0 6.2 10.2 14.2 18.2
\ 12.2 16.2 20.2



I I
4 ......... ........ ...... 6





0 Y (cm)







Figure 7.5. Picking range of the end-effector in the vertical plane located 2 cm from the
centerline of axis 2.


the tube, the rotating lip would push the orange out of reach resulting in an unsuccessful pick

attempt.

The required position relationship for successful picking between the robot end-effector

and the fruit center are given in Tables 7.1 and 7.2. In the Z direction, the robot could pick a

fruit whose center was located no farther from the home position than 16.2 cm. Vertically, a

fruit's centroid could be positioned within 5.0 cm above and 1.0 cm below the tube's centerline.

These ranges in the Y and Z directions were valid for all acceptable positions in the X direction.

Therefore, requirements in the horizontal or X direction specified that the fruit be within 2 cm

of the tube's centerline. These figures indicated the position relationship that guaranteed a

successful pick attempt and were used for establishing required performance criteria for the

controlling systems. A summary of these results is presented in Table 7.1. In Table 7.2, values

for the vision system test which correspond to the edges of the picking envelope are shown. The

xcent and ycent pixel values represent the x and y position of the centroid of the fruit's image in

the vision field.
the vision field.









Table 7.1. Range of positions of a fruit's centroid to guarantee a successful pick.

X Z Y
maximum minimum maximum
(cm) (aCMn) (cm) (cm)
0.0 16.2 -4.0 5.0
1.0 17.2 -3.0 5.0
+2.0 16.7 -1.0 5.0


Table 7.2. Values read by vision system corresponding to the established picking envelope.

X Y Z Vision
(cm) (cm) (cm) xoent ycent
0.0 -4.0 16.2 197 303
0.0 5.0 16.7 196 69
1.0 -3.0 17.2 173 239
1.0 5.0 17.2 177 70
-1.0 -3.0 17.2 221 239
-1.0 5.0 17.2 217 70
2.0 -1.0 16.7 150 206
2.0 5.0 16.7 155 75
-2.0 -1.0 16.7 244 206
-2.0 5.0 16.7 239 75


In summary, for the robot to remove a fruit from the tree, its end-effector had to be

positioned so that the vision system possessed values within the following ranges. The vision

system was required to return an xcent value between 150 and 244 (197 47) and a ycent value

between 75 and 206 (140 65). The xcent and ycent values 197 and 140 represent the location of

the center of the fruit's image when the fruit was in the center of the picking envelope. Also,

the fruit was required to be within the minimum Z distance (16.2 cm) from the origin of the

camera frame. These values represent the borders of a cubic volume in which the fruit was

required to be positioned in order to guarantee that it could be girdled by the rotating lip of the

picking mechanism. Robot control algorithms were necessary which could position the end-

effector within these boundaries.


Velocity Control Requirements

Velocity control algorithms for joints 0 and 1 were necessary only for use during times in

which the robot was searching for a fruit (Adsit, 1989). During this operation, constant

velocities were required of joints 0 and 1 to cause the end-effector to scan the tree in search of a










fruit. The desired motions were achieved by setting velocity set points necessary for scanning

and calling the velocity control routines for joints 0 and 1. This scanning technique was

terminated when a fruit was identified by the vision system. Therefore, performance criteria

for velocity control of joints 0 and 1 did not prove to be critical. By adjusting the set points

which determined position of the joint at which the control was switched from one mode to

another, the overshoot specifications for joint 0 and 1 velocity controllers could be relaxed or

tightened. Steady-state error requirements could also be relaxed by increasing the velocity set

points. Experience with the robot operation indicated that actual velocity of joints 0 and 1

could overshoot the set point velocity by as much as 45 percent without greatly affecting the

performance of the search procedure. Also, deviations of 40 percent from the desired velocity

did not adversely affect the picking performance of the manipulator.

Although the velocity requirements of joints 0 and 1 were used only during the fruit

search, the velocity control algorithm for joint 2 was used during the picking operation to

extend the end-effector toward a targeted fruit during the approach states. Therefore, its

performance proved to be more critical than that for joints 0 and 1. Most critical was the ability

of joint 2 to extend in a smooth, rapid manner and respond quickly to velocity set point changes.

Also, the detection of robot/limb collisions during extension and the detection of unremovable

fruit during retraction relied upon the ability to accurately control the joint 2 velocity. The

intelligence base detected these events by monitoring the joint 2 velocity control word which

was generated from the velocity error by the velocity controller. Large velocity control words

over a specified period of time were used to indicate that joint motion was restricted either by

an obstacle in the arm's path or by the inability of the arm to remove a fruit from its stem.

During the picking operation, overshoot values up to 25 percent of the desired joint 2 velocity

were regarded as acceptable and velocity steady-state errors of up to 10 percent were

determined tolerable based on experience with the robot.










Position Control Requirements

Position control algorithms were used primarily for two operations. First, the position

control algorithms were called to return the robot to its home position after a pick cycle was

completed. This motion was accomplished by setting the position set points to the specified

home location and calling the position control routines to move the joints to the required

position. A second use was to stop the joints and hold them stationary while other actions were

performed. For instance, during the detach phase of a pick cycle, joints 0 and 1 position

controllers were used to hold the arm stationary while the lip was actuated for girdling the

fruit.

During the picking phase, a large error in the joint positions would cause the end-

effector to fail in its attempt to girdle the targeted fruit. Therefore, the maximum allowable

error for each joint was the motion of the end-effector which would cause the fruit to be out of

the picking envelope when the picking mechanism was actuated. For joint 0, the maximum

steady-state error was determined to be 3 cm at the end-effector. Likewise, the maximum

steady-state error for joint 1 was 2 cm, and for joint 2, the maximum error was 3 cm. The position

errors for joints 0 and 1 were influenced by the position of joint 2. For a given angular motion of

joint 0 or 1, the maximum error at the end-effector was realized when the sliding tube was in

the extended position. Therefore, the angular position errors allowed for joints 0 and 1 were

calculated based on the maximum allowable extension of joint 2 (158.3 cm). These values

translated to maximum steady-state errors of 1.1 degrees and 0.7 degree for joints 0 and 1,

respectively, and 3 cm for joint 2.

Dynamic response of the position control algorithms was not as critical as steady-state

error criteria. These algorithms caused motion only to return the joints to their home positions.

* The home positions could be set to allow some overshoot of the desired position allowing a

faster response time. Again, experience with the fruit-picking robot suggested that position

overshoots as high as 15 percent could be allowed for each of the axes without causing any










problems with the control of the manipulator. By allowing the dynamic response to overshoot

the desired value, greater speeds were achievable and thus faster pick cycle times.


Vision Control Requirements

Of all the control systems, the most critical operations took place while the robot was

operating under the vision control. After the vision system identified a fruit while in the

search mode, the intelligence base switched control of joints 0 and 1 from velocity control to

vision control. Using vision control, joints 0 and 1 were aligned with the targeted fruit and joint

2 extended to position the end-effector near the fruit. The operations which used vision control

required that the motion of the fruit be tracked by the end-effector and ultimately that the

end-effector be positioned so that the fruit would lie within the picking envelope.

As previously pointed out, the two worst observed cases of fruit motion were: Case I:

swinging motions up to 50 cm in magnitude with 2 sec (0.5 HZ) cycle times and Case II: swinging

motions 12.5 cm in magnitude with cycle times of 0.9 sec (1.1 HZ). Also, the established picking

envelope indicated that the fruit position could be allowed to fluctuate by 2 cm (47 pixels) in

the x direction (joint 1) and 3 cm (65 pixels) in the y direction (joint 0) from the center of the

picking envelope. Controllers for the vision system of the robot were thus needed to cause the

end-effector to be able to track these fruit motions with errors not to exceed 3 cm for joint 0 and 2

cm for joint 1.

Because the units of the vision system were pixels, the amplitudes of the fruit and the

end-effector were converted to pixel units (Figure 7.6). As presented in the figure, the image

plane was assumed to be infinitely large and the fruit was assumed to be its maximum pickable

distance (16.2 cm) from the camera optical center, Oc. The trigonometric relations indicated

that the image of a fruit whose magnitude was 500 mm would have a magnitude of 1077 pixels

on the infinite image plane. Likewise, a fruit magnitude of 125 mm corresponded to an image

magnitude of 269 pixels.











a,
Case I: 500mm
CaseII: 125mm


fruit

01----------------

\






Camera Optical Center, 0O
/
/
/.


fruit

/
/

/
/ 162 mm

/




%\ 8mm

\ Infinite Image Plane


Case I: 1077 pixels
Case II: 269 pixels


Figure 7.6. Relationship between the amplitude of a fruit and the amplitude of its image on
the camera image plane.


To provide more information for determining the performance requirements for the

vision control system, the difference between the location of the targeted fruit and the end-

effector was calculated. First, the previously observed motion of a fruit was expressed as a

vector,

fm = af sin(ot)

where fm = fruit motion (pixels),

at = fruit motion amplitude (pixels),

o = frequency of fruit motion (deg/sec), and

t time (sec).

The predicted motion of the robot's end-effector was also described as a vector,

rm = ar sin(ct+o)

where rm = end-effector motion (pixels),

ar = end-effector motion amplitude (pixels), and

phase lag between fruit and end-effector motion (deg).


I


I




Full Text
xml record header identifier oai:www.uflib.ufl.edu.ufdc:UF0009020000001datestamp 2009-02-27setSpec [UFDC_OAI_SET]metadata oai_dc:dc xmlns:oai_dc http:www.openarchives.orgOAI2.0oai_dc xmlns:dc http:purl.orgdcelements1.1 xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.openarchives.orgOAI2.0oai_dc.xsd dc:title Motion control of a citrus-picking robot dc:creator Pool, Thomas Alan,dc:type Bookdc:identifier http://www.uflib.ufl.edu/ufdc/?b=UF00090200&v=00001001483561 (alephbibnum)21085429 (oclc)dc:source University of Florida


MOTION CONTROL OF A CITRUS-PICKING ROBOT
By
THOMAS ALAN POOL
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1989

ACKNOWLEDGEMENTS
The author wishes to express sincere appreciation to Dr. Roy C. Harrell, his major
advisor and friend, for guidance and assistance provided during the graduate program. For the
enormous amounts of time Dr. Harrell invested reviewing this dissertation, the author is
especially grateful.
Thanks are also due to the professors who graciously gave of their time to serve on the
graduate committee: Dr. Keith Doty, Dr. John Staudhammer, Dr. Robert Peart, and Dr. Carl
Crane. These men provided necessary excitement and instruction for making the author capable
of completing this project.
Mr. Ralph Hoffman provided some very necessary assistance with the tests which are
described within this dissertation. He was always available with an encouraging word, never
even once refusing to assist with even the most mundane chores. For all of this, the author is
grateful.
Mr. Phil Adsit, a fellow graduate student, assisted with many of the programming
tasks which were undertaken in this work. He gave much-needed encouragement and advice as
he worked so closely with the author. Much appreciation is extended to Mr. P.
Financial assistance was awarded to the author in the form of a fellowship under the
USDA Food and Agricultural Sciences National Needs Graduate Fellowships Grants Program.
For this assistance, the author is also grateful.
Funding for the citrus picking robot was provided by Agricultural Industrial
Development, SpA, Catania, Italy.
Most importantly, the author expresses sincere thanks to his parents, Mr. and Mrs.
William H. Pool, for their encouragement and support during this project. Their leadership
and guidance proved invaluable to the completion of this work.

TABLE OF CONTENTS
Bigg
ACKNOWLEDGEMENTS ii
LIST OF TABLES vi
LIST OF FIGURES vii
ABSTRACT xiii
CHAPTERS
1 INTRODUCTION 1
2 OBJECTIVES OF RESEARCH 6
3 REVIEW OF LITERATURE 9
Previous Robotics in Tree Fruit Harvest 9
Robot Kinematics Background 14
Controls Background 16
Performance Specifications 20
4 DESIGN OF THE FLORIDA CITRUS-PICKING ROBOT 21
Mechanical Design 21
Control Computer 25
Hardware 25
Video system 26
Ultrasonics 27
Analog to digital converters 27
Parallel I/O signals 28
Servomechanisms 28
Software 29
Picking Mechanism 31
Construction 31
Fruit Sensor Package 33
CCD camera 33
Ultrasonic range sensor 34
Lights 35
Hydraulic Actuation 36
Position Sensors 37
Velocity Sensors 42
iii

gage
5 ROBOT KINEMATIC MODEL 45
Manipulator Kinematics 45
Imaging Kinematics 49
Vision-Servo Kinematics 50
6 ROBOT OPEN-LOOP DYNAMICS 55
Background 55
Parameter Estimation 58
Results and Discussion 64
7 PERFORMANCE CRITERIA 75
Background 75
Characteristics of Fruit Motion 76
Picking Envelope Definition 78
Velocity Control Requirements 82
Position Control Requirements 84
Vision Control Requirements 85
Summary of Performance Criteria 88
8 CONTROLLER SELECTION AND IMPLEMENTATION 90
Controller Selection 90
Control System Discretization 93
Controller Implementation 97
Velocity Controllers 97
Position Controllers 99
Position Controller With Velocity Control Minor Loop 101
Vision Controllers 103
Controller Tuning 107
Velocity Controller Tuning 110
Position Controller Tuning 113
Position Controller with Velocity Control Minor Loop Tuning 115
Vision Controller Tuning 116
Summary 118
9 RESULTS AND DISCUSSION 120
Velocity Controller Performance 120
Position Controller Performance 127
Vision Controller Performance 131
Dynamic Performance 131
Static Performance 133
Overall Controller Performance 137
Performance in the Search Routine 137
Performance During the Pick Cycle 140
IV

page
10 SUMMARY AND CONCLUSIONS 150
Summary 150
Conclusions 152
REFERENCES 155
BIOGRAPHICAL SKETCH 157
v

LIST OF TABLES
Table page
4.1. Servo amplifier and servo valve characteristics 29
4.2. Conversion factors for changing A/D information to actual positions and
velocities of the robot's joints 44
5.1. Link parameters for the orange-picking robot 48
5.2. Range of motion for the joint parameters of the orange-picking robot 49
6.1. Experimentally determined steady-state gains, damping ratios, and hydraulic
natural frequencies of joint 0 in relation to position of joint 2 and direction of
motion 62
6.2. Experimentally determined steady-state gains, damping ratios, and hydraulic
natural frequencies of joint 1 in relation to position of joint 2 and direction of
motion 64
6.3. Steady-state gains, hydraulic damping ratios, and hydraulic natural
frequencies as determined by analysis of the step test responses 65
7.1. Range of positions of a fruit's centroid to guarantee a successful pick 82
7.2. Values read by vision system corresponding to the established picking
envelope 82
7.3. Summary of performance criteria for the velocity,position, and vision control
algorithms 89
8.1. Velocity control variables as used for the velocity controllers as shown in
Figure 8.6 99
8.2. Position control variables as used in Figures 8.10,8.11 and 8.12 101
8.3. Position control variables as used in Figures 8.14 and 8.15 103
8.4. Vision control variables as used in Figures 8.17 and 8.18 107
8.5. Final velocity controller parameters for joints 0,1, and 2 112
8.6. Final position controller parameters for joints 0 and 1 114
8.7. Final vision controller parameters for joints 0 and 1 118
8.8. Final determined values for all controller parameters 119
vi

LIST OF FIGURES
Figure page
1.1. The Florida Laboratory 2
3.1. Kinematic link frames as attached to the links of a manipulator (Paul, 1981) 15
4.1. The three degree-of-freedom orange-picking robot 22
4.2. Base support stand of the robot 23
4.3. Outer link of the robot 24
4.4. The inner link 25
4.5. The sliding link 26
4.6. I/O hardware architecture of the control computer 27
4.7. Organization of the robot programming environment 30
4.8. Cutaway side view of the picking mechanism showing the position of the
ultrasonic transducer, the color CCD camera, and the lights 32
4.9. Top view of the picking mechanism showing the drive linkage and the lever
arm for actuating the rotating lip mechanism 32
4.10. Picking mechanism actuation assembly 33
4.11. Front view of the picking mechanism showing the color CCD camera, ultrasonic
transducer, and the four lights 34
4.12. Horizontal field of view of the color CCD camera and lens combination in the
vertical plane 35
4.13. Vertical field of view of the color CCD camera and lens combination in the
horizontal plane 35
4.14. Circuit diagram of hydraulic power unit 36
4.15. Circuit diagram of hydraulic actuators for joints 0 and 1 37
4.16 Circuit diagram of hydraulic motor actualtor for joint 2 37
4.17. Circuit diagram of picking mechanism lip actuator 38
4.18. Circuit diagram of the position sensing potentiometers 39
vii

Figure page
4.19. Relationship between position of joint 0 and the A/D value of the position of
joint 0 40
4.20. Relationship between position of joint 1 and the A/D value of the position of
joint 1 41
4.21. Relationship between position of joint 2 and the A/D value of the position of
joint 2 42
4.22. Circuit diagram of the tachometers 43
5.1. Kinematic frames of the three degree-of-freedom robot 46
5.2. Kinematic frames as assigned to the links of the robot 47
5.3. Lens imaging geometry 50
5.4. Coordinate frame representation of the camera frame and the fruit position
with respect to the base frame 52
6.1. Open-loop hydraulic servo system 56
6.2. Reduced block diagram of the open-loop system 56
6.3. Block diagram of the open-loop system with external torque load 58
6.4. Typical response of joint 0 of the orange-picking robot to a step input of 1200
D/A bits with joint 2 centered in the Hooke joint 61
6.5. Typical response joint 1 of the orange-picking robot to a step input of -500 D/A
bits with joint 2 centered in the Hooke Joint 63
6.6. Typical response of joint 2 of the orange-picking robot to a step input of 750 D/A
bits 65
6.7. Responses of joint 0 to a step input: (a) actual, (b) simulated.
(0h = 32.95 rad/sec, 8h = 0.30, Kv = 0.036 (deg/sec)/(D/A word) 69
6.8. Responses of joint 0 to a step input: (a) actual, (b) simulated.
G0h = 17.36 rad/sec, 8h = 0.16, Kv = 0.032 (deg/sec)/(D/A word) 70
6.9. Responses of joint 0 to a step input: (a) actual, (b) simulated.
(Oh = 16.54 rad/sec, 8h = 0.31, Kv = 0.044 (deg / sec)/(D/A word) 71
6.10. Responses of joint 1 to a step input: (a) actual, (b) simulated.
(0h = 31.87 rad/sec, 8h = 0.17,K„ = 0.055 (deg/sec)/(D/A word) 72
6.11. Responses of joint 1 to a step input: (a) actual, (b) simulated.
(0h = 22.02 rad/sec, 8h = 0.31, Kv = 0.056 (deg/sec)/(D/A word) 73
6.12. Responses of joint 1 to a step input: (a) actual, (b) simulated.
(0h = 21.47 rad/sec, Sj, = 0.22, Kv = 0.056 (deg/sec)/(D/A word) 74
viii

mm
Figure
7.1. Typical observations of the motion of fruit swinging from the canopy of a tree
indicating the peak-to-peak magnitude of the fruit for various periods of
oscillation 77
7.2. Apparatus for determining the picking envelope of the robot's end-effector 78
7.3. Picking range of the end-effector in the vertical plane located on the centerline
of axis 2 80
7.4. Picking range of the end-effector in the vertical plane located 1 cm from the
centerline of axis 2 80
7.5. Picking range of the end-effector in the vertical plane located 2 cm from the
centerline of axis 2 81
7.6. Relationship between the amplitude of a fruit and the amplitude of its image
on the camera image plane 86
7.7. Maximum allowable phase lag as a function of amplitude ratio, ar/af, as
described in equation 7-3. Maximum allowable error = 47 pixels (2 cm). Case I:
af = 50 cm (1077 pixels). Case II: af = 12.5 cm (269 pixels) 88
8.1. Bode diagram of the open-loop velocity control system 91
8.2. Bode diagram of the open-loop position control system 92
8.3. Simulated responses of continuous-time and discrete domain controllers and the
percent error differences.
Kj. = -15.00, xd = 3.7, and Tj = 1.0 IQ = 4.00, xd = 0.02, and t¡ = 0.01
(a) continuous-time domain controller (d) continuous-time domain controller
(b) discrete controller (e) discrete controller
(c) percent error (f) percent error 96
8.4. Subroutine to calculate coefficients of the discretized controller from the
continuous domain parameters 97
8.5. Block diagram of the velocity control loop 98
8.6. Implementation of the Lag-Lead velocity controllers as found in the software
environment. Note: change 0's in the variables to l's or 2's for joint 1 or 2 98
8.9. Block diagram of the position control feedback loop for joints 0 and 1 100
8.10. Position error calculation for joints 0 and 1 from ERRORCAL:C subroutine 100
8.11. Position control subroutine for joint 0 100
8.12. Position control subroutine for joint 1 100
8.13. Block diagram of the position control feedback loop with velocity feedback in a
minor loop 102
ix

Figure page
8.14. Position error calculation for joint 2 as accomplished in the ERRORCAL:C
routine 102
8.15. Major loop position control subroutine for joint 2 103
8.16. Block diagram of a vision control loop 104
8.17. Vision gain implementation scheme 105
8.18. Vision error calculations as performed in ERRORCAL-.C routine 106
8.19. Vision control subroutine 106
8.20. Bode diagram of a controlled second-order system indicating the effects changes
in the lag time constant, 108
8.21. Bode diagram of a controlled second-order system indicating the effects changes
in the lead time constant, xd 108
8.22. Bode diagram of a controlled second-order system indicating the effects changes
in the controller gain, Kc 109
8.23. Generalized open-loop Bode diagram of a lag-lead compensated velocity
control system Ill
8.24. Bode diagram of an open-loop compensated position control system 114
8.25. Open-loop Bode diagram for joint 0 vision system indicating the gain
requirements for picking worst case fruit motions 117
9.1. Typical closed-loop response of joint 0 to an alternating step input of
±16.3 deg/sec, joint 2 extended 121
9.2. Typical closed-loop response of joint 0 to an alternating step input of
±39.1 deg/sec, joint 2 positioned at its mid location 122
9.3. Typical closed-loop response of joint 0 to an alternating step input of
±48.8 deg/sec, joint 2 retracted 122
9.4. Typical closed-loop response of joint 1 to an alternating step input of
±32.6 deg/sec, joint 2 retracted 122
9.5. Typical closed-loop response of joint 1 to an alternating step input of
±32.6 deg/sec, joint 2 extended 124
9.6. Typical closed-loop response of joint 1 to an alternating step input of
±32.6 deg/sec, joint 2 centered in the support 125
9.7. Typical closed-loop response of joint 2 to step inputs of ±34.8 cm/sec 126
9.8. Typical closed-loop response of joint 2 to an alternating step input of
±104.4 cm/sec. 126

Figure page
9.9. Typical closed-loop response of joint 0 to a step change in the position setpoint
of+51.8 deg 128
9.10. Worst case closed-loop response of joint 0 to a step change in the position
setpoint of -51.8 deg with joint 2 extended 128
9.11. Typical closed-loop response of joint 1 to a step change in the position setpoint
of+23.8 deg 129
9.12. Worst case closed-loop response of joint 1 to a step change in the position
setpoint of -23.8 deg with joint 2 extended 130
9.13. Typical closed-loop response of joint 2 to a step change in the position setpoint
of 43.8 cm 131
9.14. Worst case closed-loop response of joint 2 to a step change in the position
setpoint of 43.8 cm 131
9.15. Closed-loop magnitude and phase plots for joint 0 vision control system:
K,. = 4.0 (D/A word)/pixel Kp = 2.27 pixels/(D/A word)
Ti = 0.02 sec 8 = 0.18
xd = 0.01 sec (Oh = 17 rad/sec 133
9.16. Closed-loop magnitude and phase plots for joint 1 vision control system:
IQ = 4.0 (D/ A word)/pixel Kp = 3.85 pixels/(D/A word)
ti = 0.02 sec 8 = 0.18
xd = 0.01 sec ©h = 22 rad/sec 134
9.17. Pickable fruit motions as determined from the closed-loop response of the
manipulator along with the fruit motions determined to exist in the grove 135
9.18. Closed-loop vision system response of joint 0 to a setpoint of 200 pixels with the
beginning fruit location of 50 pixels in the vertical direction in the image
plane 136
9.19. Closed-loop vision system response of joint 1 to a setpoint of 192 pixels with a
beginning fruit location of 37 pixels in the horizontal direction in the image
plane 136
9.20. Plot of position and position setpoint of joint 0 during a typical fruit search
routine 138
9.21. Plot of velocity and velocity setpoint of joint 0 during a typical fruit search
routine 138
9.22. Plot of position and position setpoint of joint 1 during a typical fruit search
routine 139
9.23. Plot of velocity and velocity setpoint of joint 0 during a typical fruit search
routine 139
9.24. Control modes and position and velocity of joint 2 during a typical pick cycle 141
xi

Figure page
9.25. Position of joints 0 and 1 and locations of the furit during a typical pick, cycle 142
9.26. Controller responses to large fruit motions using the wait state 144
9.27. Control modes and joint 0 and 1 positions during a pick cycle with large fruit
motion which required use of the wait state 145
9.28. Pick cycle aborted because of a collision during the fruit approach routine 148
xii

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
MOTION CONTROL OF A CITRUS-PICKING ROBOT
By
Thomas Alan Pool
May, 1989
Chairman: Dr. Roy C. Harrell
Major Department: Agricultural Engineering
This work focused on the design and implementation of motion control strategies for a
citrus-picking robot. These control strategies were used by an intelligence base for the robot
which required precise control of the individual joints based on information from velocity,
position, and vision sensors. The type of controller that was used at any instant was determined
by this intelligence base, which called the applicable controller and supplied it with
setpoints.
Initially, the design of the hydraulically actuated, three degree-of-freedom,
spherical coordinate arm was presented. The picking mechanism housed the vision and
ultrasonic sensors, which provided real-time end of the arm fruit position sensing and a rotating
lip for removing the fruit from the tree. From the known dimensions of the robot, a kinematic
model was derived. This model provided a basis upon which the position of the joints could be
related to the information detected by vision sensor. Dynamic models of the robot joints were
experimentally determined for use in designing and tuning the joint controllers. Lag-lead
compensators were chosen for their ability to improve a system's steady state performance
while improving the response rate by increasing the system bandwidth. These controllers were
discretized and programmed into the software environment of the robot.
xiii

The performance of the robot was assessed by its suitability for the specified task.
Thus, typical fruit motions were investigated. Also, a picking envelope was established which
defined the volume with respect to the end-effector in which a fruit must be located to be
picked. These characteristics were used to relate the task of picking citrus fruit to performance
requirements for each of the robot's joint motion controllers.
The controllers achieved acceptable robot performance during a normal pick cycle.
Tests of the velocity and position controllers for all of the joints showed that these controllers
met or exceeded the established requirements. The vision controllers achieved success when
subjected to fruit with slower motions. For large, fast fruit motions, however, the robot was
required to wait for the fruit to slow before a successful pick attempt was achieved.
xiv

CHAPTER 1
INTRODUCTION
Traditionally, the harvest of citrus fruit has been a labor-intensive operation. Much of
this manual labor in America has been provided in the form of seasonal farm workers who were
actually illegal aliens from Mexico and other Latin-American countries (Martin, 1983). Martin
also observed that even with the illegal work force the turnover was very high. In fact,
maintaining a work force of 20 workers has required that some farmers hire as many as 200
workers in a month's time. Another challenge that farmers have been faced with is the rising
cost of harvest. In the United States, Martin noted that the farmer paid 20 percent of the fruit
price for harvesting. In comparison with other countries, the U.S. farm worker wages are 5
times that of Greece and 10 times that of Mexico. Therefore, U.S. farmers start out behind in
the competition for the world market. After identifying these problems, researchers have
turned their attention toward the mechanization of the harvest process. Several mechanical
harvesters such as tree shakers and blowers have been designed and built, only to find that
these attempts caused damage to the fruit trees. These non-selective harvesters also proved
detrimental to future yields from the Valencia orange which is harvested after the immature
fruit for the following season have already formed (Coppock, 1984). Damage and removal of
the small, unripe fruit reduced the following year's production. The conclusions of many of the
researchers was that individual and selective harvest of the fruit would be most desirable.
In 1984, researchers at the University of Florida began an investigation of the physical
and economic feasibility of picking citrus fruit with a robotic mechanism. Initially, a
commercially available robot was acquired for this purpose. A spherical coordinate
manipulator was chosen which allowed for ease of vision-servoing—controlling the motion of
the robot joints based on fruit position as determined by a camera. This spherical coordinate
1

2
(RRP: revolute, revolute, prismatic) configuration consisted of two revolute or rotary joints with
axes of rotation intersecting at a right angle and a prismatic or sliding joint. These first two
joints allowed the distal end of the robot to be "pointed" while the third joint provided the
capability for extension. A computer was interfaced with the robot's controller and the
manipulator was used to demonstrate the vision-servoing concept by picking artificial fruit
from a simulated canopy. Successes with the laboratory robot prompted the construction of a
more portable field robot which could be tested in actual grove settings.
The ideas for the Florida Laboratory (Figure 1.1) sprung forth. The Florida Laboratory
was constructed as a trailer package which could be towed behind a truck to groves around the
state of Florida. Basic construction of the lab consisted of an enclosed front section with an open
flat bed to the rear. The enclosed section sheltered the environment-sensitive hardware, such
as the control computer and electrical connections, and provided a comfortable working area for
the operators. Two software development stations were provided in this control room. The
Figure 1.1. The Florida Laboratory.

3
hydraulically actuated manipulator was mounted on the rear, flatbed portion of the lab. A 15
kW electric generator furnished electricity for the hydraulic power unit, the control computer,
and other hardware used in the development of software for the grove model robot. Visual
access to the robot was furnished by three windows mounted on the rear and picking side of the
control room.
The robot was a three degree-of-freedom, spherical-coordinate geometry arm.
Actuation of the joints was accomplished through the use of servo-hydraulic drives consisting
of servo amplifiers, servo valves, and actuators. For the first two joints, rotary actuators were
used to generate the revolute motion about intersecting horizontal and vertical axes. The third
joint, a sliding joint, was actuated by a hydraulic motor through a rack and pinion drive. The
revolute motion of the first two joints provided the robot with the ability to point toward a
fruit, and the prismatic or sliding joint provided the ability to reach toward the targeted fruit.
A picking mechanism was attached to the end of the arm and enclosed the color CCD camera
and ultrasonic ranging transducer which were used for fruit detection. Also, a rotating lip was
attached to the picking mechanism which was used to grasp the fruit and remove it from the
tree. The motion of the joints was determined by an intelligence base which used the
information from the position and velocity sensors on the joints as well as the fruit sensors to
establish desired actions of the manipulator.
The intelligence for the robot was built around a concept of states or modes of operation
in which decisions were made based on the available information from the sensors. The
intelligence base was developed and programmed for the orange-picking robot by Adsit (1989).
The heart of the intelligence base was a state network which provided robot command
decisions through sensing, action, and reasoning agents. Sensing agents were used to quantify
the robot's work environment and the robot's status. Reasoning agents made decisions in regard
to the information from the sensing agents. Action agents caused motion of the robot to alter the
work environment or the sensor's perception of the work environment. These agents were linked
together by a common database with result fields, parameter fields, and activate fields. The

4
result fields held the results from an agent's operation. Parameter fields specified the criteria
for accomplishing a task. Activate fields contained flags which induced or terminated an
action. The information contained in these fields was compared to models which characterized
significant events which occurred during the picking operation. The results of this comparison
were used to cause the execution to move from one command state to another.
The execution of a pick cycle included stepping through the state network in a logical
manner which resulted in removing a fruit from a tree. Each pick cycle began with the robot in
its home configuration and concluded by dropping the fruit while in this same configuration.
Before any joint motion was specified, the vision sensors were checked for the presence of fruit.
If no fruit were found in the field of view, a search pattern was initialized. When a fruit was
detected, an approach state was activated which actuated the revolute joints to align the arm
with the fruit (vision-servoing). While this vision-servoing operation continued, the sliding
joint was activated to extend to the targeted fruit. When the picking mechanism was
positioned so that the fruit could be captured, robot motion was stopped, and the fruit was
girdled by the rotating lip of the picking mechanism. The sliding joint was then retracted to its
home position. Once the sliding joint reached its home position, both revolute joints were
returned to their home locations, and the fruit was released from the picking mechanism. This
pick cycle was repeated until no more fruit were detected by the fruit sensors.
This picking operation required control of the motion of the joints based on velocity,
position, and vision information. When the robot was requested to search the tree canopy for a
)
fruit, the revolute joints were instructed to move with constant velocity. When a fruit was \
detected, the motion of these two joints was changed to cause the targeted fruit to be positioned
in the center of the image of the camera. Thus, the motion of these two joints was also to be
altered by the commands of the vision system. Since the actual distance between the end-
effector and the targeted fruit was not known, the slider was directed to proceed at a constant
velocity until proximity with the fruit was detected by the ultrasonic system. As the fruit was
being girdled by the rotating lip, all three of the joints were required to remain stationary at

5
their present positions. For the slider to be retracted from the canopy at a constant velocity,
the revolute joints were to hold their positions. The instruction to go to the home location was
provided in the form of positions for each of the joints.
Thus, three modes of control were necessary for the orange-picking robot. First, each of
the joints was to be moved at a constant velocity by a velocity controller. Second, to cause the
joints to go to specified positions, position controllers were needed. Third, vision controllers
were required to change the position of the revolute joints to point the end-effector toward a
targeted fruit. The development of these three motion control strategies was the overall goal
of this work. The accomplishment of this goal would provide controllers which would take
setpoints from the intelligence base and accomplish the desired result in a smooth and accurate
manner.

CHAPTER 2
OBJECTIVES OF RESEARCH
The main objective of this work was to develop motion control strategies for the orange¬
picking robot. This objective was divided into the following specific areas:
1. develop a kinematic model for the orange-picking robot;
2. derive an open-loop dynamic model for each robot joint;
3. define performance criteria necessary for picking citrus fruit;
4. develop and implement control strategies to provide acceptable robot performance; and
5. test and evaluate the performance of the robot.
Algorithms were necessaiy for controlling the robot, based on desired positions and
velocities of the joints of the manipulator and based on fruit position related to the end of the
robot. These motion control algorithms were to be called from the robot intelligence base to
cause the manipulator to move in a specified manner. The control algorithms were to be links
between the software environment, the manipulator, and the manipulator's workspace, with
the ultimate task of removing fruit from the canopy of an orange tree. Because the algorithms
were to be used with a digital computer, they were required to operate in the discrete domain.
Only a minimum of computational complexity was to be permitted because real-time control
was necessary to enable the robot to pick moving fruit.
A kinematic model was necessary to describe the geometric relationship between the
joints and links of the robot. This model was to provide an understanding of the motion of the
manipulator links for specified changes in joint positions. Ultimately, the kinematic model
was to be used for determining the relationship between the position of the robot's end-effector
and the position of a targeted fruit. This relationship provided a basis upon which functions
for the vision control system gains could be derived.
6

An open-loop dynamic model for each robot joint was to be derived for use in selecting
control systems for the manipulator. These dynamic models would provide insight into the
response characteristics of the manipulator's joints, which could be used for tuning the
controllers and thus to achieve desired responses from the joints. The open-loop response of
each joint to different step input signals was to be evaluated for use in determining open-loop
dynamic models. The dynamic models were to be used as plants in closed-loop systems for
selecting and tuning the controllers. Once established, these dynamic models were to be
verified by comparison of the actual response of the joints with the simulated response of the
determined dynamic models.
Final performance of the robot was to be defined by critical performance criteria. These
performance criteria were to be determined from observations of fruit motion in the tree's
canopy and other pick-cycle motion requirements. Along with the robot's ability to track the
motion of fruit in the canopy of the tree, the robot would be required to position the picking
mechanism such that the rotating lip would be able to remove the located fruit from the tree.
The manipulator was also to be required to move through a fruit-locating search pattern with
rapid though smooth actions. These criteria were to be used for designing and evaluating the
strategies and algorithms which were developed for controlling the orange-picking robot.
Based on the information from the kinematic and dynamic models and the performance
criteria, position, velocity, and vision control strategies for the manipulator were to be
developed. These control strategies were to be the basis upon which robot-control algorithms
were to be developed. The algorithms were to be incorporated into a robot-programming
environment which contained intelligence for the orange-picking robot. From the programming
environment, the algorithms could be called when necessary to accomplish a desired motion of
the manipulator.
Once implemented, the performance of each of the motion-control strategies was to be
evaluated. Assessment of the controllers would involve designing tests which would
demonstrate the ability or lack of ability of the controllers to meet the specified performance

8
criteria. First, the controllers would be tested on an individual basis. Finally, the response of
the controllers while operating in the intelligence base would be evaluated for the ability to
control the joint motions of the manipulator during the actual picking operation.

CHAPTER 3
REVIEW OF LITERATURE
Previous Robotics in Tree Fruit Harvest
Researchers have long noticed the necessity for automated harvest of tree fruit. Many
of these researchers have investigated the use of mechanical components. The need for a
proficient citrus harvester that would individually remove the fruit from the tree was
perceived early (Schertz and Brown, 1968). Schertz and Brown pointed out that any method of
mechanical harvest should inflict only minimal damage to the fruit and tree. They observed
that leaf removal of over 25 percent have corresponding yield decreases for the subsequent year.
However, defoliation of up to 25 percent did not provide an indication of reducing the yield.
These men realized that an advantage of individual fruit harvest over mass fruit removal
could be a reduction in damage to the fruit and to the tree. This method would also have less
impact on the succeeding year's production. Although many researchers have indicated the
need for robotic fruit harvesters and presented their ideas, the technology for making it
achievable has developed only within the last decade.
Pejsa and Orrock (1984) studied potential applications of robotics to agricultural
operations. In their work, some of the sensing and control requirements for intelligent robot
systems in agriculture and especially in orange harvesting were presented. These sensing
requirements included the use of vision for detecting the presence of fruit and its location in two-
dimensions. Range and proximity sensing were deemed necessary for determining the third
dimension of the fruit's location and for collision avoidance. These researchers proposed the
use of force and tactile sensors for reporting the status of the end-effector's grasp of the fruit.
Pejsa and Orrock pointed out that a major effort would be necessary to integrate the sensing
functions with the mechanical functions required to pick tree fruit. They stated that most
9

10
industrial robots provided greater accuracy and more degrees of freedom than would be required
of a fruit harvester. Thus, a task-specific robot could be designed for the purpose of fruit
picking. A closed-loop system would be needed that could tie the sensing functions with the
arm motion controllers.
Some of the earliest work in the development of the technology was conducted by
Parrish and Goksel (1977). These men studied the feasibility of analyzing the work space of
the robot by use of machine vision. In their study, a black-and-white video camera was used to
detect the fruit, which were represented by blobs in the two-dimensional picture array. By
analyzing their perimeters, the larger blobs which contained overlapping fruit were
successfully divided into separate fruit. The location of the fruit centroids were determined in
the two-dimensional picture array. Trajectories were calculated from the camera lens center to
the positions of the detected fruit centroids. The mechanical arm was driven to follow these
trajectories toward the fruit. When contact with a fruit was detected by a touch sensor, the
motion of the robot was halted. As fruit removal was not in the scope of this work, a successful
picking attempt was recorded when contact with the fruit was detected. In this work, a scene
was analyzed and one trajectory was calculated for each fruit in the scene. The arm was driven
until all of the trajectories were exhausted. Then, a new scene was analyzed, and the operation
was repeated. Although this system was quite elementary, the concepts and the feasibility of
robotically harvesting tree fruit were inspired. These concepts have been used as a motivation
for many of the later attempts.
Grand d'Esnon (1984 and 1985) developed an apple picker which used similar ideas for
the detection of fruit. This manipulator was a cylindrical coordinate robot (PRP, prismatic in
the first joint, revolute in the second, and prismatic in the third). Using the vision system to
determine the fruit's position in two coordinates, the robot was pointed towards the fruit by
raising the arm along a vertical prismatic joint and then pivoting around a vertical axis. This
motion relied on the concept that the fruit did not move between the time that the image was
acquired and the picking tool reached the fruit. In a later attempt, Grand d'Esnon et al. (1987)

11
developed a fruit picker which consisted of five revolute joints. The first two joints provided
the robot with the pointing ability while the remaining three joints formed an elbow for
extending the end-effector towards a targeted fruit. Operation of the robot again involved
acquiring an image and then adjusting the joints of the robot to align the end-effector with the
camera's line of sight. After the arm was pointed toward the fruit, the joints were moved to
extend the end-effector toward the determined location of the fruit. Again, the robot had no
ability to change its trajectory with the motion of the targeted fruit. In both attempts, the
robot was directed to follow the vector from the camera lens center to the determined position of
the fruit. Forward motion of the robots was continued until contact with a fruit was detected.
Grand d'Esnon et al. reported the removal of 50 percent of the fruit in a hedge at a rate of one
fruit every 4 seconds.
Tutle (1984) developed an idea for an image-controlled robot for harvesting tree fruit.
For his imaginary robot, Tutle proposed the use of a photo-diode-based camera and the
appropriate filters and lighting for detecting the fruit in the canopy of the tree. After the
location of a fruit was determined, the camera was to be displaced so that the arm could be
moved to align with the optical sensor's line of sight towards a detected fruit. Once aligned
with the fruit, the severance module would be extended towards the fruit. The severance
module would contain a second optical sensor that Tutle called a 'seeker' sensor, which
consisted of a four-element photovoltaic detector. The idea behind use of this sensor included
oscillating the severance module until equal light, supposedly reflected from a fruit, was
detected by each of the four elements. This action was intended to align the severance module
with the fruit and adjust for any fruit motion that might have occurred before the robot reached
the fruit. Response from this seeker sensor would also be a signal to slow the forward motion of
the arm. Tactile sensors in the severance module would indicate that a fruit had been scooped
into the module and that forward motion of the arm should be stopped. The fruit would then be
grasped by the severance module, which would twist the fruit while the arm was retracted to
remove the fruit from the tree branch. Since an operational model of this idea was not

12
constructed, its successfulness could not be evaluated. Also, the control problems were only
assumed and never actually encountered.
The application of robotics in fruit harvesting has also been investigated by
researchers at the Laboratory of Agricultural Machinery in Kyoto, Japan (Kawamura et al.,
1985; Kawamura et al., 1986). This work involved the design of a five degree-of-freedom
manipulator for picking tomatoes and oranges. A global color vision system was employed for
the detection of fruit. The camera was mounted on a vertical support and could be moved up or
down the support. An image was acquired with the camera in one location and then the camera
was moved for acquisition of a second image. The two images were analyzed and the centroids
of the fruit in the image were determined. The three-dimensional positions of the fruit were
calculated from the two-dimensional images by triangulation. A trajectory to each of the fruits
and the robot joint angles required to follow the desired path to a fruit were calculated. As the
arm approached the calculated position of the fruit, the speed of the joints was slowed. When
the hand reached the calculated position of the fruit, the fruit was gripped and severed from
its supporting stem. Three-fingered flexible hands were built for use with the manipulator
(Kawamura et al., 1987). These hands provided gripping forces similar to those of a human
hand while picking tomatoes and oranges. Image processing and joint motion calculations were
rather extensive, causing the picking time for one fruit to be approximately 20 sec.
Harrell et al. (1985) examined the concept of real-time vision-servoing for controlling
the manipulator during the picking process. This work involved the use of a commercially
available spherical coordinate (RRP) robot. A small black-and-white camera was mounted in
the end-effector of the robot and aligned with the axis of the prismatic joint. With this
configuration, a fruit whose image was centered in the camera's image plane was directly in
front of the end-effector. Thus, the end-effector could be extended towards the fruit. Since the
vision-servoing was kept active during the picking process, any motions of the fruit could be
followed by making changes in the two revolute joints. In this first generation, signals from the
control computer were sent directly to the electric robot controller for servoing the positions of

13
the joints. In the controlled environment of a laboratory, this vision-servoing method was
proven to have potential for control of a grove model robot.
Tests in the grove, however, indicated that the black-and-white camera could classify
light reflections from the soil as fruit. Therefore, the use of color vision was investigated
(Slaughter et al., 1986; Slaughter, 1987; Slaughter and Harrell, 1987). In his work, a scheme
was developed which segmented the image into fruit and background regions based on the color
of each pixel. From this image, the centroid of each fruit's image could be determined for use in
adjusting the joints of the robot to point towards the fruit. Since the image was processed in
real-time, the robot could be controlled to track the dynamic motion of the targeted fruit.
In a joint project between researchers at the University of Florida and AID of Italy, two
robots were designed and constructed as prototypes for future work aimed at a commercially
produced tree-fruit-picking robot (Harrell and Levi, 1988). The AID robot relied on electrical
servo controllers to position the joints to point the arm towards the fruit. A global vision system
was used to determine the location of the fruit throughout the picking sequence. The Florida
robot further developed the previous concepts while implementing the vision system of
Slaughter. A hydraulically actuated robot was designed and constructed with a spherical
coordinate architecture (RRP).
For this prototype, a controller was not available. Even if a controller were available,
the exclusive use of point-to-point joint positioning would not have provided the desired
flexibility. The robot motion was to be formulated based on velocity and vision requirements as
well. An intelligence base for the robot was designed and programmed (Adsit, 1989). This
intelligence base added a requirement for fast and accurate control of the joints of the robot
based on velocity, position, and vision setpoints. The design and implementation of these
controllers is the scope of this work.

14
Robot Kinematics Background
Craig (1986) describes kinematics as the science of motion, ignoring the forces which
cause the motion. Kinematics deals with the variable joint coordinates as they relate to the
position and orientation of the end-effector. Because the relationships between the joints of a
manipulator can be quite complex, the study of robot kinematics deals with the coordinate
frames that describe the kinematic relationships. Any robot manipulator is made up of links
and joints. Most joints are grouped into one of two categories with one degree-of-freedom:
revolute or hinged joints and prismatic or sliding joints. The links of the manipulator are
usually rigid and define the relationship between the joints. The common normal distance, an,
between the axes of two consecutive joints and the twist angle, a,,, characterize a robot link (see
Figure 3.1). The twist angle is defined as the angle between the consecutive axes in a plane
perpendicular to an. For this work, the Denavit-Hartenberg (1955) notation will be used as
applied by Paul (1981).
The relationships between coordinate frames are expressed as products of rotation and
translation transformations. Homogeneous transformations which represent rotations of one
coordinate frame about the x, y, and z axes of a reference coordinate frame by angles 8 are
represented by the following 4x4 matrices:
Rot(x,0) =
10 0 0
0 cos 8 - sin © 0
0 sin© cos© 0
0 0 0 1
(3-1)
cos© 0 sin© 0
0 0 0 1
and
(3-2)
Rot(z,©) =
cos 0 - sin © 0 0
sin© cos© 0 0
0 0 10
0 0 0 1
(3-3)

15
A translational homogeneous transformation of one coordinate frame with respect to another by
a vector, ai+b j + ck, is described by
Trans(a,b,c) =
The general relationship between two successive frames (the coordinate frame of link n
and the coordinate frame of link n-1, see Figure 3.1) is expressed as the product of two rotation
transformations and two translation transformations. This relationship is referred to as a
general A matrix (Paul, 1981)
n'*An = RotiZn.!,©,,) Trans(0,0,dn) Trans(a„,0,0) Rot (xn,On) (3-5)
where "^Aj, = relationship between frame n-1 and n,
Rot(zn_i,0) s rotation transformation about z^, an angle 0n,
Trans(0,0,dn) s translation along zn_i, a distance dn,
10 0a
0 10b
0 0 1c
0 0 0 1

16
Trans(an,0,0) h translation along rotated xn.-[ = x„ a length an/ and
Rot(xn,a) = rotation about xn, the twist angle a,,.
By multiplying these rotation and translation matrices, the general A matrix for any two
successive links is calculated as
n-l
An =
cos© -sin0cos(x sin0sina aoos0
sin© cos©oosa -cos0sina a sin©
0 sin a cos a d
0 0 0 1
(3-6)
In this work, the term frames refers to the coordinate frames assigned to the links of the
manipulator. Coordinate frames represent a three-dimensional space by three orthonormal
vectors; X, Y, and Z. The origin of each frame is located at the intersection of these vectors.
When referring to these vectors, a trailing subscript will be used to identify the frame in
concern. Links are the physical components which make up the manipulator. The motion of the
links is accomplished by the joints. A joint can be rotational (revolute) or translational
(prismatic). The coordinate frames are fixed to the links, and homogeneous transformations are
used to relate the position and orientation of the frames. A joint axis is the vector about which
joint motion takes place. Link coordinate frames are assigned such that the frame's Z axis
defines the vector about which joint motion occurs. Joint motion will be either around or along
the respective Z axis.
Controls Background
The use of a Bode plot, in which the frequency response of a system can be analyzed,
enables the control system designer to evaluate closed-loop system characteristics based on
knowledge of the open-loop system. A controller can then be designed to achieve the desired
system characteristics. Palm (1983) presented some of the basic considerations used in the
frequency-response methods of control system design. First, the closed-loop system's steady-
state error can be minimized by maintaining a high, open-loop gain in the low-frequency range.
Second, a slope of -1 in the gain curve near the crossover frequency will help to provide an

17
adequate phase margin. The crossover frequency is the frequency at which the open-loop gain
of the system is unity (0 db). Third, a small gain at higher frequencies will help to attenuate
the effects of noise or mechanical vibrations. All of these characteristics proved to be
applicable to the controller design for the orange-picking robot. Thus, controllers were desired
which provided flexibility to shape the phase and gain curves to achieve the necessary phase
and gain margins.
Lag and lead compensators furnish this flexibility by providing the ability to adjust
the phase and gain in a wide variety of frequencies. When tuned properly, a lag-lead
compensator improves the steady-state performance while also improving the transient
response (Palm, 1983; Ogata, 1970). The lag-lead compensator is represented by the transfer
function
where s
Kc
Td
Xi
The design of the controllers involves the placement of the controller gain and the pole and zero
of the controller so that an acceptable response is achieved while meeting the steady-state
requirements. The open-loop system gain can be increased by increasing the controller gain, K,..
The use of the lag-lead compensator increases the order of the system by one in between the lag
and lead factors. In other words, the addition of the lag or lead compensator causes an
attenuation of the system response between the frequencies of the lag and lead factors (1/Xj and
1/td). Thus, the value of Xi determines the frequency at which this attenuation takes place
while the value of Xd determines the frequency at which the attenuation is canceled. The slope
of the gain curve is decreased by 1 between the lag and lead factors.
Hp(s).M
= Laplace operator (sec*1)
s controller gain (appropriate units),
s lead time constant (sec), and
s lag time constant (sec).

The applications of control theory to hydraulic systems were presented by Merritt
(1967) and supported by Gibson and Tuteur (1958), Johnson (1977), and McGoy and Martin
(1980). Merritt presented the background necessary for determining the dynamic characteristics
of many hydraulic systems. He demonstrated the methods for deriving the characteristic
equations for each of the system components. Then, he pointed out that the closed-loop response
of a system is limited by the response of the slowest element. Thus, the selection of the
components should take into consideration the hydraulic natural frequency by choosing
actuators that are capable of the desired system response. By choosing system components with
fast response rates (i.e., large natural frequencies), the response rate of the actuator and load
combination is left as the performance-limiting factor of the system. Merritt noted that after
choosing fast control components a normal position control hydraulic servo can be reduced to a
second-order system with an integration. Thus, the position servo system is represented by
Gp(s) =
2
Kp© h
>(s2+28hcohs + (Oh)
(3-8)
where
A normal velocity control servo
transfer function:
s = Laplace operator (sec*1)
Kp = position system gain (appropriate units),
G>h s system natural frequency (rad/sec), and
8h = system damping ratio (unitless),
can be reduced to a second-order system as in the following
Gv(s) =
2
KytOh
2 2
s +28h0)hS + C0h
(3-9)
where
s - Laplace operator (sec-1)
Kv = velocity system gain (appropriate units),
©h = system natural frequency (rad/sec), and
8h = system damping ratio (unitless).

19
Fast components should have a natural frequency of 10 times or greater than the natural
frequency of the actuator and load. Merritt also indicated that the stability of the servo
system can be determined by the position of the resonant peak which occurs near the hydraulic
natural frequency of the second-order system on the Bode magnitude plot. The loop gain at the
resonant peak must be less than unity for stability. Merritt also noted that the lag-lead
controller usually provides acceptable results for both position and velocity control servos. He
demonstrated that the use of velocity minor feedback loops could be used to reduce errors which
result from drift and load friction.
Merritt summarized hydraulic servo design as follows. A power element which will
meet the basic considerations of the load and response is selected. The other components of the
loop are sized to provide the best accuracy and response under the limitations of the power
element. A controller is selected to give the highest possible gain and crossover frequency
while maintaining stability. The only way to achieve a faster response from the system is to
choose a faster power element. These methods of hydraulic controller design along with the
frequency-response design techniques were used for the selection and design of tuners for this
work.
According to Merritt, all real systems are nonlinear to some extent. However, no general
nonlinear theory exists for design of controllers for these nonlinear systems. But, techniques are
available for this design based on the familiar linear techniques. The most widely used
method is to assume that the nonlinearities are small and that the system is linear. In the case
of the orange-picking robot, the nonlinearities that would cause limit cycles or instabilities
were negligible in the range of operation. The deadband caused by imperfect valve
characteristics and the backlash and hysteresis were minimized by dithering the output signal
from the servo amplifiers. The saturation possibilities which would also cause nonlinear
performance were eliminated by limiting the controller outputs. This nonlinearity was
handled within the intelligence base of the robot. Thus, the effects caused by the

20
nonlinearities of the hydraulic servo systems were considered negligible allowing the design of
controllers based on common linear techniques as previously described.
Performance Specifications
According to Lau et al. (1988), a robot's performance is measured by its ability to
perform a task. Performance measurements are those general operating characteristics that are
important for determining the robot's suitability for a given task. The performance for
industrial robots is usually specified in terms of accuracy, repeatability, positioning resolution,
and speed. These measurements were also defined by Ranky and Wodzinski (1988), who also
presented very precise methods for determining each of them.
These performance measurements prove sufficient for industrial robots which operate in
a structured environment. However, in the unpredictable environment found in agricultural
operations, these methods of performance evaluation have little significance. The ultimate
performance measurement is that of determining the robot's suitability for its intended
operation. Because the location of each fruit in the tree is different, the accuracy and
repeatability of the robot were not pertinent. Performance requirements and evaluation
methods for robots which operate in unstructured environments are much more difficult to
assess. Evaluation of the control strategies for the citrus-picking robot made evident the need
for performance criteria for this specific task.

CHAPTER 4
DESIGN OF THE FLORIDA CITRUS-PICKING ROBOT
An overview of the design of the orange-picking robot, developed by Harrell et al.
(1988), is presented in this chapter. The physical specifications of each part of the robot are
described in the first section along with the position and orientation of the kinematic
coordinate frames as they relate to each physical component. The second section contains a
description of the computer hardware and software designed to control the robot. In the third
section, an illustration of the picking mechanism is introduced showing the configuration of the
components of the fruit sensor package. Hydraulic actuation of the robot is described in the
fourth section of the chapter. Finally, sensing mechanisms for position and velocity of the robot
joints are described in the fifth and sixth sections.
Mechanical Design
A brief description of the physical components that make up the orange-picking robot
are presented in this section. The parts are described along with their relationship to one
another. Also, presented in this section are the axes about which the motion of the robot is
accomplished. These axes of rotation form the Z axes of three-dimensional kinematic frames
which will be presented in a later chapter. The position and orientation of the kinematic
frames as related to the physical components are presented here as an aid in understanding the
kinematics chapter which follows.
The orange-picking robot (Figure 4.1) was built as four major parts: base stand, outer
link, inner link, and sliding tube. The base of the robot was bolted to the flat bed of the
laboratory trailer and acted as a stand to support the other components (Figure 4.2). The first
coordinate frame, frame 0, of the kinematic model was assigned to the base link as shown in the
figure. On the base, the outer link was supported by flange bearings which allowed the outer
21

22
link to rotate about a horizontal axis (Zo). Similarly, the inner link was mounted inside of the
outer frame and provided rotation about a vertical axis (Zj). The inner link included a bearing
assembly which supported the sliding tube and provided linear motion along the Z axis of the
inner link (Z2). The picking mechanism of the robot which held the sensor package was
mounted on the end of the sliding tube.
The outer link (Figure 4.3) was fabricated from rectangular steel stock and reinforced at
the corners for increased rigidity. Two solid-steel cylindrical-shaped shafts were mounted on
either side of the outer link. The outer link was mounted to the support stand by a pair of
bearings which connected between these mounting shafts and the vertical members of the base
stand. Coordinate frame 1 of the kinematic model was assigned to the outer link. The center
line of the two shafts were coincident with the Zo axis of coordinate frame 0 allowing the outer
link and coordinate frame 1 to rotate about Zo by an amount 0j. Connected to these shafts were a
rotary actuator used for rotating the axis through its motion, a tachometer, and a

23
Figure 4.2. Base support stand of the robot.
potentiometer. Motion of the outer link was mechanically limited by two chains to
approximately 39 degrees in either direction from vertical. These chains were connected
between the lower member of the outer link and the cross member of the supporting structure.
The inner link (Figure 4.4) was constructed in two pieces and mounted inside of the outer
link in much the same way as the outer link was mounted to the support. This inner link was
also constructed of rectangular steel with reinforcements at the comers for added rigidity.
Solid steel cylindrical mounting shafts were fastened to the top and bottom of the link allowing
the inner link to rotate about the vertical axis of the outer link, Zv This link was actuated by a
rotary actuator mounted to the bottom of the outer link and connected to the bottom shaft of the
inner link. The motion of this link was measured by the joint variable ©2. Coordinate frame 2

24
Figure 4.3. Outer link of the robot.
was assigned to the inner link and positioned so that its origin was coincident with the origin of
the first two coordinate frames. The vertical axis of this link was always at a right angle to
the horizontal axis of the outer link, resulting in a Hooke joint. Inside of the two part inner link
casing, a split steel pipe was welded as a bushing housing which supported the sliding link.
The two part construction of the inner link allowed shims to be added or removed from between
the two sections to adjust for wear in the nylon slider bushings. The motion of the inner link was
mechanically limited to approximately 30 degrees in either direction from center by
mechanical stops welded to the outer link.
The sliding joint of axis 2 (Figure 4.5) was constructed from a high grade aluminum tube.
Sliding joint motion was accomplished by a rack and pinion drive actuated by a hydraulic
motor. A 1.5 cm square nylon rack was attached to a flat surface machined on the lower side of
the aluminum tube. A10 pitch, 3.81 cm diameter pinion gear was incorporated into the lower
section of the inner link assembly and meshed with the rack for actuation of joint 2. The Z2 axis
was coincident with the centerline of the tube and intersected with Z0 and Zj at their

25
Figure 4.4. The inner link.
intersection point. The motion of the sliding tube was mechanically limited by end caps which
were mounted on either end of the tube. One end cap was welded to the forward or distal end of
the tube and used for mounting the end-effector. The other end cap was bolted to the rear or
proximal end of the tube. These end caps and mechanical stops bolted to the inner link limited
the linear motion of the tube, the joint variable d3, to approximately 1.31 meters.
Control Computer
In this section, the hardware and software used for controlling the robot is introduced.
Components of the computer hardware are presented in systems as they relate to controlling the
robot. A very brief description of the elaborate software environment is also presented here.
Hardware
The control computer for the orange-picking robot was a VME-bussed system with a
Mizar 7120 CPU card. The Mizar card utilized a 12.5 MHZ Motorola MC68020 processor and 1

26
1635 cm
12 cm
11.2 cm
end-cap
actuation
rack
end-cap
Figure 4.5. The sliding link.
MB of RAM. The hardware architecture for the control computer is diagrammed in Figure 4.6.
Mass storage for the computer was provided by a 20 MB hard drive and a 1 MB floppy drive
which were connected to the VME bus. The computer was equipped with three serial ports. The
main system console was connected to the computer through one serial port, while a second port
was wired to a remote connector for connecting a terminal outside of the control room of the
trailer. An Apple Macintosh Plus system, with 2 MB of RAM, a 20 MB hard disk, and a printer,
was used as a printer/plotter station and was connected to the VME bus by way of the third
serial port.
Video system. The video system was composed of the CCD camera, the FOR-A color
decoder, three Datacube VVG-128 video frame grabbers, and a Sony RGB video monitor. The
NTSC output signal from the camera was converted into separate red, green, and blue video
signals by the color decoder. The three Datacube frame grabbers provided the ability to
digitize, store, display, and process full color video images in real-time. The red, green, and
blue signals from the decoder were acquired simultaneously by the frame grabbers at a 60 HZ
rate. The signal for each primary color was quantified with 5 bit resolution based on the
intensity of the signal at each pixel. These acquired video data, ranging in value from 0 to 31,
were stored in memory as three, 384 x 244 pixel arrays, one for each primary color signal. The
red frame grabber also generated a hardware interrupt on the VME bus with each vertical
blanking period. This interrupt was used to synchronize all of the real-time activities. Video

27
Figure 4.6. I/O hardware architecture of the control computer.
output from all three frame grabbers was displayed on the RGB monitor in the control room of
the Florida Lab.
Ultrasonics. The electronic circuitry for the Ocean Motion ultrasonic ranging transducer
provided a TTL pulse with width proportional to the time required for the ultrasonic burst to
echo from an object. A counter-timer module was used to quantify the duration of the TTL pulses
generated by the ultrasonic ranging unit. Output from the counter-timer was a digital value
which represented the distance from the picking mechanism to the targeted fruit. The counter¬
timer was mounted on a card that plugged directly to the VME bus.
Analog to digital converters. Seven analog-to-digital (A/D) converters were used in
the hardware to convert analog voltage signals from the position, velocity, and temperature
sensors to digital values. Six A/D converters were used for the position and velocity sensors as

28
described in the position and velocity sensing sections. The seventh A/D converter was
connected to a type "T" thermocouple panel meter for monitoring the temperature of the
hydraulic fluid during operation. All of the A/D converters represented an input voltage
ranging from -5 volts to +5 volts with a value ranging from 0 to 4095. The A/D converters were
plugged directly to the VME bus of the control computer.
Parallel I/O signals. Control of components which required a signal depicting either on
or off operation was accomplished by the addition of a parallel card and an Opto-22 switching
panel. The parallel port of the card was connected to the Opto-22 panel. The Opto-22 panel
allowed the addition of either input or output modules. The output modules acted as electronic
relays for switching other components based on the signal from the corresponding pin of the
parallel port. Output modules were used to switch 120 VAC for the picking mechanism lights,
the solenoids of the picking mechanism actuator, and the main hydraulic dump valve. Input
modules were added to the card to sense the status of the hydraulic dump valve and the servo
amplifiers. A 5 VDC input module was used to sense the position of push button safety switches
which were located at various strategic locations in the lab and connected in series to one
another. Signals from the input modules were routed to the appropriate pins of the parallel
card.
Servo mechanisms. Joint motion of the manipulator was accomplished by two
hydraulic rotary actuators and a hydraulic motor. Hydraulic fluid flow to these actuators was
controlled by servo valves. The rate of fluid flow through a servo valve was proportional to
the amount of current passing through the coil of the valve. Three Vickers EM-D-20 servo
amplifier modules were used to adapt the output voltage from the control computer to a coil
current usable by the servo valves. The output voltages from the computer were generated by
three 12-bit digital-to-analog (D/A) converters. Gains for the servo amplifiers were adjusted
to produce the maximum coil current to each of the valves at the maximum output voltage of ±
2.5 volts from the D/ A converters as listed in Table 4.1. The bandwidth characteristics for the
servo amplifiers and servo valves are also presented in Table 4.1.

29
Table 4.1. Servo amplifier and servo valve characteristics.
Toint
D/A
Output
(volts)
Serve
Gain
(ma/volt)
) Amplifier
Band)
(rad/sec)
s
vidth
(HZ)
0
+2.5
80
1885
300
1
±2.5
80
1885
300
2
±2.5
16.8
1885
300
Toint
Type
Servo V<
Max. Coil
Current
(ma)
lives
Band)
(rad/sec)
vidth
(HZ)
0
Pegasus
200
3 77
60
1
Pegasus
200
3 77
60
2
Sundstrand
42
189
30
note: Gain = Max. Coil Current / (D/A Output)
Software
The software environment for controlling the robot was written to run in a multi-user
PDOS operating system. The control system was organized into groups of sensing, action, and
control agents as presented in Figure 4.7. These agents exchanged information through a
dynamic database by way of result, parameter, and activate fields. The result fields stored
data which resulted from an agent's operation. Instructions for accomplishing an agent's
desired task were indicated in parameter fields. The ability to activate or deactivate certain
agents was included in activate fields within the database.
Sensing agents were those devices through which the work environment of the robot
and the robot states were quantified. Data from the sensing agents were filtered by fourth order
Integral of Time-multiplied Absolute Error (ITAE) data filters before their storage in the
database. The work environment or the sensors' perception of the work environment were
affected by the action agents. Control agents were used to direct the action agents to cause the
robot to move to a desired state. A desired robot state was characterized by setpoints which
were stored in the database and used by the control agents. For decreased calculation time, the
setpoints were specified in units compatible with the result fields rather than physical
measurements. An error calculator was used to compute the difference between the actual robot

30
WORK ENVIRONMENT
Figure 4.7. Organization of the robot programming environment.
state as perceived by the sensing agents and the desired robot state as prescribed by the control
agents in the setpoint fields. Results from the error calculator were also stored in the database
for used by the control agents.
Models characterized significant features and events within the work environment
through functional relationships which mapped sensing agent results and other system
information to boolean results. These models characterized certain conditions based on
information from the database. The models then returned boolean values to the database to be
used by the state network for directing the intelligence of the robot. The intelligence base for
picking fruit was programmed in the state network. This intelligence gave the robot the
ability to recognize and respond to events that commonly occurred during picking. The state
network mapped elements from the modeled response set to robot reactions through states
linked together by logical exit conditions. Each state in the network defined a different
modeled response or robot reaction. The responsibility of the state network was to cause the

31
robot to take the appropriate action to achieve its goal. The supervisor was responsible for the
orderly execution of the various system agents based on the intelligence programmed into the
state network. The connection between the developer and the database was accomplished
through user shells. These user shells were also the path for retrieving important database
information which was saved by a data-logger at a 60 HZ rate. Explicit details of this robot
programming environment can be found in Adsit (1989).
Picking Mechanism
In this section, the physical design of the picking mechanism is discussed. The
technique for mounting the picking mechanism on the sliding tube is presented along with the
method of mounting its actuation cylinder. The arrangement of fruit sensors and lights
incorporated in the end-effector are presented.
Construction
A picking mechanism (Figures 4.8 and 4.9) was developed with a rotating lip for
removing the fruit from the tree. The rotating lip of the picking mechanism was actuated so
that it encircled the fruit, impinging the stem of the fruit between the upper surface of the end-
effector and the rotating lip. Once the fruit was collected, the stem was broken as the end-
effector was retracted from the canopy of the tree. The detached fruit was secured with an
elastic collection sock as the end-effector was retracted and then dropped onto the ground or
into a collection bin.
The picking mechanism was constructed from a hollow aluminum cylinder (13 cm OD, 12
cm ID, 45 cm long). To aid in the ability of the end-effector to penetrate the canopy of a citrus
tree, its front end was machined on the top and bottom at an angle of approximately 34 degrees
from the centerline. A plastic collection scoop was added to the top of the picking mechanism
to aid in collection of the fruit as the rotating lip girdled it. The rotating lip was mounted to
the end-effector by shafts on either end which rotated in brass bushings. The lip was
constructed from spring steel formed into a slight oval profile. On the outer end of the shafts

32
Rear
Shaft
Rotating
Lip
Collection
Sock
Plexiglas Collection
Shield Scoop
Rear Drive
Sprocket
Front
Drive
Sprocket
Tube
Centerline
25 mm
Lens
Center
Picking
Mechanism
Housing
Lights
Collection
Sock Shield
Color CCD
Camera
Image
Plane
Lens
Optical
Center
Figure 4.8. Cutaway side view of the picking mechanism showing the position of the
ultrasonic transducer, the color CCD camera, and the lights.
Rotating Lip
(Extended Position)
Bushing
Front Drive
Sprocket
Collection Scoop.
Drive Chain
Lever Arm
Bushing
Rear Drive
Sprocket
Collection Sock
Bushing
Front Drive
Sprocket
Picking Mechanism
Housing
Drive Chain
Rear Shaft
Bushing
Rear Drive
Sprocket
Cotter Key
Adjustable
Linkage
Figure 4.9. Top view of the picking mechanism showing the drive linkage and the lever arm
for actuating the rotating lip mechanism.

33
were mounted sprockets which were driven by a 25 pitch chain and a larger set of sprockets
providing a 3:1 drive ratio. The rear drive shaft, holding the larger set of sprockets, was
turned by a 5 cm long lever arm which converted the linear motion of the actuating cylinder to
rotary motion of the drive sprockets (Figure 4.10). A square aluminum linkage was connected
between the actuating cylinder and the lever arm. On the rear end of the sliding tube, the end
cap was bolted to the tube and used for mounting the actuator for the rotating lip picking
mechanism. On the forward end of the tube, an end cap was welded for mounting the end-
effector. Kinematic coordinate frame 3 was assigned to the end-effector (see Figure 4.1).
Fruit Sensor Package
The sensor package for locating the fruit in the canopy of the tree was mounted inside of
the tube of the picking mechanism (Figure 4.11). The sensor package included a color CCD
camera, an ultrasonic ranging transducer, and four small light sources and provided the real¬
time three-dimensional position sensing between the end of the arm and a fruit in the
manipulator's workspace.
CCD camera. A Sony DXC-101 color CCD video camera with an 8 mm fixed focal length
and automatic aperture control lens was employed for detecting the fruit in the canopy of the
tree. The camera was mounted in the picking mechanism so that the optical axis of its lens was
approximately 25 mm below and parallel to the Z axis of the tube. The sensing element of the
camera was an 8.8 mm x 6.6 mm Charge Coupled Device (CCD) array. The CCD array was
Picking
Mechanism
Figure 4.10. Picking mechanism actuation assembly.

34
Bulb
Lip Drive
Sprocket
Lights
Ultrasonic
Transducer
Lip Drive
Sprocket
Light
Plexiglas
Protector
Collection Sock
Shield
Light
Color Camera
Rotating Lip
Figure 4.11. Front view of the picking mechanism showing the color CCD camera, ultrasonic
transducer, and the four lights.
composed of a usable array of 384 pixels horizontally and 488 lines vertically. Since each
image corresponded to an acquired field, virtual resolution was reduced to 244 rows, with each
image using alternating even and odd rows. The image in the even rows (0,2,4,...) was processed
while a new image was being acquired in the odd rows (1,3,5,...). Integrated with the 8 mm
fixed focal length of the lens, the CCD gave the camera a field of view of ± 22.4° vertically and
± 28.8° horizontally as shown in Figures 4.12 and 4.13. The opening in the iris of the lens was
controlled by the control computer and based on the brightness of the targeted fruit (see
Slaughter, 1987). The NTSC color video information from the camera was decoded into red-
green-blue (RGB) format by a FOR.A, DEC-100 RGB color decoder. The video information was
processed by the control computer to obtain two-dimensional fruit-position data in real time (60
HZ).
Ultrasonic range sensor. The third dimension of the fruit, the distance from the picking
mechanism to the targeted fruit, was obtained by an Ocean Motion ultrasonic ranging
transducer. This transducer was equipped with a focusing horn to minimize reflection of the
ultrasonic burst from objects other than the targeted fruit. The transducer was positioned in the
picking mechanism above the camera and angled 10 degrees below the optical axis of the
camera so that the axis of the camera and the axis of the transducer intersected approximately
30 cm in front of the picking mechanism. The electronics provided with the ultrasonic ranging
transducer produced a TTL pulse with width proportional to the distance of the fruit from the

35
Figure 4.12. Horizontal field of view of the color CCD camera and lens combination in the
vertical plane.
Figure 4.13. Vertical field of view of the color CCD camera and lens combination in the
horizontal plane.
picking mechanism. This signal was quantified by a counter-timer module in the control
computer.
Lights. Four small flashlights were used as supplemental light sources. These lights
were needed to illuminate a targeted fruit as the arm was extended to the fruit and the picking
mechanism shaded the ambient light from the fruit. A pair of AA size flashlights were
secured on either side of the camera and powered by a separate 5 volt power supply.

Hydraulic Actuation
Joint motion was accomplished by hydraulic actuators controlled by servo valves. A
36
pressure compensated hydraulic power unit (Figure 4.14) provided hydraulic power to the
actuators. A1 liter accumulator, charged to 7000 kPa, was added to help maintain constant
hydraulic pressure. Bird-Johnson SS-2-100 rotary actuators were utilized for actuating joints 0
and 1 (Figure 4.15). These actuators had splined shafts which interlaced with the splines that
were machined into the steel spindles that served as mounts for the outer and inner links.
Control of the fluid flow to these two actuators was achieved by Pegasus 3.8 liter-per-minute
(1.0 GPM), 120 series servo valves. The servo valves were connected to the actuators with
hydraulic manifolds which provided cross port pressure relief. Motion of the prismatic joint 2
was performed by a Hartmann HT-5 hydraulic motor (Figure 4.16) which was mounted to the
inner link of the robot. This motor was connected to the drive shaft of the pinion gear by a
Lovejoy coupling. It was controlled by a 18.9 liter-per-minute (5.0 GPM) Sundstrand MCV103A
Charged to 6900 kPa
Figure 4.14. Circuit diagram of hydraulic power unit.

37
Figure 4.15. Circuit diagram of hydraulic
actuators for joints 0 and 1.
Figure 4.16. Circuit diagram of hydraulic
motor actuator for joint 2.
series servo valve. The Sundstrand valve was mounted to the motor by a manifold block that
also provided for a case drain to the motor. Actuation of the rotating-lip picking mechanism
(Figure 4.17) was accomplished with a double-acting hydraulic cylinder (Allenair, 3500 kPa,
2.22 cm bore x 5.08 cm stroke) which was controlled by a 3-way solenoid valve energized by 120
volt AC current. Two solid-state relays were utilized to control the AC current. A pressure
reducing valve was used to reduce the hydraulic pressure to 3500 kPa for the actuating cylinder.
Position Sensors
The kinematics of the robot manipulator was developed with the understanding that
the position of each of the joints would be known. Control of the manipulator was based on the
ability to calculate the difference in the actual position from the desired position of each joint.
Rotary potentiometers were used to sense the actual position of each joint at any given time
(Figure 4.18).
The position of each of the joints of the robot was sensed by 2k ohm potentiometers
directly connected to the actuators. For joints 0 and 1, Spectral single turn potentiometers were

38
AHenair double acting
hydraulic cylinder
222 cm bore
5.08 cm stroke
Manifold
Figure 4.17. Grcuit diagram of picking mechanism lip actuator.
chosen for their high precision and linearity. In both cases, the potentiometer body was
mounted to a plate which was attached to the actuator. The shaft of the potentiometer was
connected directly to the back side of the moving shaft of the actuator. A voltage was applied
across each of the potentiometers. The voltage across the wiper of the potentiometer was
proportional to the angular position of the rotary actuator and thus the position of the axis.
This voltage drop was quantified by a 12-bit, ± 5 volts analog-to-digital (A/D) converter.
On joint 0, the potentiometer was required to relate a total motion of approximately 78
degrees to a voltage ranging between -5 volts and +5 volts. The potentiometer was supplied
with +5 volts to the positive side and -12 volts to the negative side creating a voltage
difference of 17 volts across the 360 degrees of the single turn potentiometer. The result was a
resolution of approximately 19 bits per degree of rotation of the potentiometer wiper shaft
(0.052°/bit). A summary of the range of motion for joint 0 and the A/D bits read for some critical
positions is presented in Figure 4.19.

39
———— Pot + Supply
l
r—i
*—1
Joint 0
variable:
P0
potentiometer:
Spectral, 2K, Single turn, 132-0-0-202
+ supply:
+5 V
- supply:
-12 V
Toint 1
variable:
PI
potentiometer:
Spectral, 2K, Single turn, 132-0-0-202
+ supply:
+12 V
- supply:
-12 V
Toint 2
variable:
P2
potentiometer:
Bourns, 2K, Ten turn, 536
+ supply:
+5 V
- supply:
GND
Figure 4.18. Circuit diagram of the position sensing potentiometers.
The potentiometer on joint 1 converted a total motion of approximately 46 degrees to a
voltage that could be used by the A/D converter. Because of the smaller motion of joint 1, a
larger voltage drop across the potentiometer was needed to increase the resolution. The
positive side of the potentiometer was connected to a +12 volts supply while the negative side
was connected to a -12 volts supply. This 24 volt difference across the 360 degrees of the
potentiometer resulted in a change of approximately 3.15 volts through the joint's 46 degree
range of motion. For this joint, the resolution was approximately 27 bits per degree or 0.037
degree per bit. The summary of the range of motion and the critical positions for joint 1 is
presented in Figure 4.20.
For determining the position of the sliding joint of the robot, a Bourns 10 turn, 2k ohm
potentiometer was used. In order to move the full length of the tube, the sliding joint actuator

40
Position of
Joint 0
Position of
TointO
Computer
A/D Value
Description
+38.7*
2324
upper mechanical limit
+34.6’
2400
low
+29.3*
2500
min
-1.6*
3100
home
-32.7*
3700
max
-37.8*
3800
high
-38.7*
3819
lower mechanical limit
Figure 4.19. Relationship between position of joint 0 and the A/D value of the position of
joint 0.
was required to make almost 11 complete revolutions. For measuring the position of the tube
with the Bourns potentiometer, a gear reduction was necessary to keep the motion within the
allowable 10 turns. This potentiometer was connected to the shaft of the Hartmann motor by
way of a small set of miter gears with a drive ratio of 2/3 turn of the potentiometer per
revolution of the motor. The 2:3 gear reduction caused the potentiometer to turn 7.3 revolutions
over the entire length of the tube. The positive supply voltage of this potentiometer was
connected to a +5 volts source while the negative supply was tied to ground. Again, a 12-bit
A/D converter was used to convert the analog voltage to a digital value that could be used by
the control computer. This set-up yielded a resolution of approximately 11 bits per centimeter

41
Position of
Tointl
Computer
A/D Value
Description
67.0*
2518
left mechanical limit
69.9*
2600
low
73.5*
2700
min
88.7*
3125
home
103.8*
3550
max
107.4*
3650
high
113.0*
3807
right mechanical limit
Figure 4.20. Relationship between position of joint 1 and the A/D value of the position of
joint 1.
of linear travel (0.088 cm per A/D bit). A range of motion summary for joint 2 is presented in
Figure 4.21.
Even though the calculations for the resolution of the position sensors show high
sensitivity, other components also effect the precision of the measured positions. Variations in
the power supply for the entire Florida Laboratoiy influence the output voltage from the
voltage supply to the potentiometers. These fluctuations along with noise in the connections to
and from the potentiometers add error to the signals from the position sensors. Due to these and
other factors effecting the accuracy of the measurements, the accuracy of the revolute joint
position sensors was assumed to be limited to ±0.5 degree. Likewise, the assumed accuracy of
the prismatic joint was limited to ±0.5 cm. These limitations seemed necessary but did not

42
joint 2.
significantly reduce the ability to control the position of the orange-picking manipulator. A
summary of the conversion factors for converting A/D values to actual positions of the joints is
presented in Table 4.2.
Velocity Sensors
Effective control of the robot required a direct reading of the velocity of each joint. The
velocity of the joints was monitored by the use of DC tachometers (Figure 4.22) mounted to the
actuator or linkage of each of the joints. The voltage output from each of the tachometers was
quantified by 12-bit A/D converters with an input range of ±5 volts. This range gave a digital
resolution of 409.6 bits per input volt from each of the tachometers.

43
V r
Toint 0
variable:
VO
tachometer:
Servo-Tek SU-780D-1
output:
45 volts per 1000 RPM
drive ratio:
1:1
filter gain:
10
Toint 1
variable:
VI
tachometer:
Servo-Tek SU-780D-1
output:
45 volts per 1000 RPM
drive ratio:
1:1
filter gain:
10
Joint 2
variable:
V2
tachometer:
Servo-Tek SA-740A-2
output:
7.0 volts per 1000 RPM
drive ratio:
1:1
filter gain:
5
Figure 4.22. Circuit diagram of the tachometers.
For joints 0 and 1, Servo-Tek D series tachometers were chosen (Figure 4.22). The shaft
of each tachometer was directly connected to the mounting shaft of the link so that any motion
of the link created a voltage across the tachometer. Using 12-bit A/D converters and a software
filter with a gain of 10, the resulting resolution of the tachometers was 30.7 bits per degree per
second (0.033 degrees per second per bit). The velocity of the sliding tube was determined by a
Servo-Tek model SA-740A-2 tachometer. The 740A tachometer was mounted on the back side of
the Hartmann motor but connected to the motor's shaft through the 1:1 miter gear. This
mounting arrangement allowed the linear velocity of the sliding joint to be measured by the
angular velocity of the tachometer. A 12-bit A/D converter and a software filter with a gain of
5 were used to quantify the tachometer voltage. The resolution of the velocity sensor for the

44
sliding tube was 71.9 bits per cm per second (0.014 cm per second per bit). A full summary of the
velocity conversion factors is presented in Table 4.2.
Table 4.2. Conversion factors for changing A/D information to actual positions and velocities
of the robot's joints.
Conversion Factors
Toint
Position
Velodtv
0
0.052 deg/bit
0.033 (deg/sec) / bit
1
0.037 deg/bit
0.033 (deg/sec) / bit
2
0.088 cm/bit
0.014 (cm/sec)/bit

CHAPTER 5
ROBOT KINEMATIC MODEL
The kinematic relationships between the joints and links of the robot are presented in
this section. In the field of robotics, homogeneous transformations are used to describe the
position and orientation of one link coordinate system with respect to another one. By
describing the position and orientation of a coordinate frame which is assigned to a link of the
manipulator, the homogeneous transformation describes the position and orientation of the link
itself. According to Paul's method (1981), the product of these homogeneous transformations
(called a T matrix) will be used to calculate the position values of each joint necessary to place
the final coordinate frame (corresponding to the robot camera) at a given position and
orientation in the robot's workspace. The inverse of this T matrix will be useful in calculating
the position and orientation of the camera coordinate frame when given the joint variable
positions. A vector will be defined to relate the position of the centroid of a fruit in the camera
coordinate frame. The T matrix will then be used to relate the position of the fruit to the origin
of the base frame of the manipulator. A similar kinematic relationship will be used to relate
the position of a fruit in the robot's workspace to the position of the fruit's image in the
imaging array of the CCD camera. After establishing this relationship, the information will
be used to present the change in position of the fruit in the imaging array for small changes in
the joint angles of the robot. The vision-servoing gains will be established for adjusting the
gains of the vision control system based on the position of the fruit and position of the robot joint
angles.
Manipulator Kinematics
The citrus-picking robot consisted of three joints which were numbered 0,1, and 2. Joints
0 and 1 were revolute with intersecting and perpendicular axes of rotation (Z0 and Zv
45

46
respectively). Joint 2 was prismatic which slid about its Z2 axis that passed through the
intersection of axes 0 and 1. A robot with this order and configuration of the joints and links is
referred to as a spherical-coordinate manipulator.
The order of assignment of the coordinate frames on the orange-picking robot is
presented in Figures 5.1 and 5.2. The first coordinate frame (frame 0, labeled Xq , Y0, and Z0)
was assigned to the stationary base of the robot. Frame 1 was attached to the outer link and
positioned to rotate about Zq an angle ©j. The third frame (frame 2) was designated to the inner
moving link (link 2) of the robot and allowed to rotate 02 about Zv The final coordinate frame
(frame 3) was assigned to the sliding tube of the robot and fixed to have linear motion along
axis Z2 which was coincident with Z3. This final frame was positioned in the end-effector of
the robot so that its origin corresponded with the optical lens center of the robot camera. This
arrangement caused the final coordinate frame of the manipulator and the camera's coordinate
frame to be coincident.
For the orange-picking robot, the joint parameters were specified as variables for
rotation and translation about the axes of motion and as constants to establish the fixed
frame 0
frame 2
frame 3,
camera frame
Figure 5.1. Kinematic frames of the three degree-of-freedom robot.

47
Figure 5.2. Kinematic frames as assigned to the links of the robot.
relationships between the successive coordinate frames. The joint variables and geometry
constants for the orange-picking robot are listed in Table 5.1. Based on these parameters, the
following A matrices were determined
C: 0 -S-i 0
Si 0 C, 0
0-100
0 0 0 1
1
A2 =
C2
S2
0
0
0 S2 0
0 -C2 0
1 0 0
0 0 1
(5-1)
(5-2)

48
Table 5.1. Link parameters for the orange-picking robot.
Link
Axis of
Motion
Joint
Variable
0
d
a
a
1
Zo
0j
©1
0
0
-90°
2
Zi
©2
©2
0
0
90°
3
Z2
0
<^3
0
0
2
A3 =
10 0 0
0 10 0
0 0 1 d3
0 0 0 1
(5-3)
where Sj = sin 0j, Q = cos 0*, and d3 is the distance along Z2 from the axis of rotation Zi to the
origin of frame 3. Multiplying these A matrices, the position and orientation of the image
plane of the manipulator's vision system with respect to the base was established as T3:
CtC2
-Si
C1S2
CiS2d3
SiC2
Cl
Si S2
SiS2d3
-s2
0
C2
C2d3
0
0
0
1
(5-4)
The orientation of Z3 with respect to the robot base frame (frame 0) was determined by the 3 x 3
matrix in the upper left-hand comer of T3. The three column vectors of the 3x3 matrix, from
left to right, defined the direction of the X3, Y3, and Z3 axes, respectively. The fourth column
vector of the T3 matrix defined the position of the origin of the camera frame (frame 3). Due to
the configuration of the manipulator, this position vector, [ QS^ SiS^ C2d3 1 ]T, was
always colinear with the Z3 = [ QSj» S1S2 C2 1F vector of the camera frame.
Due to the importance of these position vectors in establishing the imaging and vision-
servoing kinematics, it was also important to understand the configuration of the robot for the
possible values of the joint variables. First, let all of the joint variables be equal to 0. In this
case, all of the coordinate frames of the robot had a common point as their origins. Frames 0,2,
and 3 were completely coincident with common X, Y, and Z vectors. Frame 1, on the other hand,
was positioned so that X! and Xq, Yj and -Z0, and Zj and Yq were coincident. As a result, if all of

49
the variables could be set to 0, the robot would be configured so that the outer link would be
parallel with the supports of the base. The inner link would be positioned at a right angle to
the outer link so that the sliding tube would point through the actuated mounting shaft of the
outer link. The sliding tube would be retracted so that the axis of the inner link would pass
through the lens of the camera in the end-effector.
However, the action of the orange-picking robot was limited by the mechanical stops
on each of the joints. In addition, these mechanical stops restricted the boundaries of the
individual parameters which governed the motion of the coordinate frames. The range of
motion for each of the joint variables is shown in Table 5.2. These ranges of motion for each joint
defined the working envelope of the orange-picking robot.
Table 5.2. Range of motion for the joint parameters of the orange-picking robot.
Range
Parameter Minimum Maximum
©! -39° +39°
©z +67° +113°
d3 +51.0 cm +182.5 cm
Imaging Kinematics
Vision-servoing of the robot required that the relationship between actual position of a
fruit and the position of the fruit's image in the imaging array of the camera be established
(see Figure 5.3). For this derivation, the position of the fruit was defined by a vector, pc = [ x y
z 1 ]T, from the origin of the camera coordinate frame to the centroid of the fruit. The position
of the fruit's image was defined by another vector, pj = t xj y¡ Zj 1 ]T, from the camera coordinate
frame to the centroid of the fruit's image in the imaging array.
The CCD imaging array of the camera was parallel to the X-Y plane of the camera
frame and positioned in the negative Z direction from the origin of the frame the distance of
the focal length of the lens, z¡ = -f. The position of a fruit's projection in the image plane, pj,
was related to p„ its actual position, by
R = TpPc
(5-5)

50
Ve
Figure 5.3. Lens imaging geometry.
where
T =
p
-f/ 0 0 0
'z
0 -f/ 0 0
'z
0 0 -f/ 0
'z
0 0 0 1
(5-6)
pc = [ x y z 1 F,and
p¡ = t *i yi zi 1 F-
Calculating x¡ and y¡, the relationship between the actual position of the fruit and the position
of the fruit's projection on the image plane was established,
xj = x (-f/z), and
yi = y(-f/z)
A change in the fruit's position in the camera frame resulted in a position change of the image
in the image array scaled by the -f/z factor.
Vision-Servo Kinematics
In the end-effector of the robot, the camera was mounted in such a way that its optical
axis was coincident with Z3. The later addition of the ultrasonic ranging horn required that the

51
position of the camera be lowered by a small amount. This amount was very small and
considered negligible in the further derivation of the vision geometry. The camera was
assumed to be positioned so that the center of its lens was at the origin of frame 3. Therefore,
the coordinate frame of the camera was the same as frame 3.
The relationship between the position of the fruit in the camera frame, pc, and the
position of its image on the imaging array, p¡, was important in formulating the effects of
changes in the position of the manipulator's joints on the position of the image. To vision-servo
the robot, it was necessary to develop closed-form solutions that related changes in and 02 to
changes in x¡ and yt. These relationships were referred to as vision gains and expressed as
_ dyi
d0i , and
(5-7)
cbq
‘ d©2
(5-8)
Because the position of the fruit was assumed to remain the same regardless of the
configuration of the robot, it became necessaiy to define the position of the fruit with respect to
the stationary base frame (see Figure 5.4). Using the T3 matrix to specify the position of the
fruit in the coordinates of the base frame, p0, was established as
Po= T3Pc. (5-9)
Utilizing this relationship, the position of the fruit in the camera coordinate frame was
determined to be
-1
Pc= T3 Po. (5-10)
Substituting pc into equation 5-5, the position of the fruit's projection in the image array, p¡, was
found
Pj=TpT3 p0
(5-11)

52
Figure 5.4. Coordinate frame representation of the camera frame and the fruit position with
respect to the base frame.
where
-i
T3 =
Po s the position of the fruit in the base frame coordinates.
The derivation of the vision gains began by assuming the manipulator was initially
aligned with a fruit which was located at some position p0 in the base frame coordinates and
some distance z from the camera. The joints of the manipulator were located at some position
CiC2
SiC2
-s2
0
-Si
Cl
0
0
CiS2
SiS2
C2
-d3
0
0
0
1
and
(5-12)
©i, ©2, and d3 when the fruit was aligned. This arrangement caused the fruit to lie along Zc at a
radial distance (d3 + z) from the origin of the base frame. Therefore, p0 was expressed as
Po =
(ds+zjC! S2
(d3+z)Sj S2
(d3+z)C2
1
(5-13)
Substituting equation 5-13 into equation 5-11 and solving for p¡,

53
Pi-TpTg P0-
(5-14)
x¡ and yi were found to be 0 as expected for the aligned position of the fruit. Also as expected, z¿
was found to be the negative value of the focal length of the camera and lens (Zj = -0.
Assuming that the manipulator position was changed to some position (0j + d©lf ©2 + d©2, d3) by
rotating joints 1 and 2 by some very small increments d©i and d©2, the position of the fruit in the
image array was offset from the center by incremental amounts dxi and dyi. Because of the
increments were veiy small, the second order terms of d@i and d©2 were assumed to be 0. Also,
for small d©,, sin(d©i) = d©¡ and cos(d©¡)«1. Solving equation 5-11 with the new T3_1 (equation
5-12) for pi yielded
dx¡=
f d©2(d3+z)
z , and
dyj=
f d©i S2(d3+z)
z
(5-15)
(5-16)
Solving for the vision gains resulted in
Kvx=f I—+1
Kv=f S2I—2+1
z 1 , and
^3
(5-17)
(5-18)
The vision gains were approximately proportional to d3 and inversely proportional to z.
Therefore, during a pick cycle, as the picking mechanism was extended toward the targeted
fruit, smaller motions of the two revolute joints were required to compensate for misalignment of
the robot with the targeted fruit. Additionally, Kyy was proportional to the sine of 02. This
term indicated that smaller adjustments in ©i were required to compensate for the misalignment
of the robot and the fruit as the position of ©2 moved to greater distances from 90°.
Another important indication from this kinematic analysis of the relationships among
the position of the joints of the robot, the position of the camera frame, and the position of the

54
fruit was that the vision-servo problem was geometrically decoupled. In other words, changes
in 0! did not affect Xi, and changes in 02 did not affect yj. This decoupling was indicated by the
absence of a d©j term in equation 5-15 and the absence of a d02 term in equation 5-16. The
geometry contributed to the decoupling effect allowing the two-dimensional vision control
problem to be treated as separate problems, greatly simplifying the development of the control
algorithms.

CHAPTER 6
ROBOT OPEN-LOOP DYNAMICS
In this chapter, the open-loop dynamic models of the robot are presented. The joint
components of a generic electrohydraulic servo system and their interaction are discussed first.
The mathematical form of each of the components is presented. The open-loop model is then
reduced to a representative model which approximates the dynamic response of a servo system
and can be used for selecting and tuning control algorithms. Open-loop step tests of the robot
joints are then presented and used to estimate model parameters. Simulated responses to step
inputs are compared to the responses of the actual joints to step inputs for model and parameter
verification.
Background
Merritt (1967) discusses the design of control systems for electrohydraulic servo
mechanisms. He derives a mathematical model for each of the components of the generic
electrohydraulic servo system. An open-loop servo system (Figure 6.1) includes servo amplifier
dynamics, servo valve dynamics, external torque load dynamics, and actuator and load
dynamics. In his presentation, Merritt points out that the servo amplifier, servo valve, and no-
load system all respond as second-order systems. Merritt discusses the selection of components
of the servo system stressing the fact that the bandwidth of the servo amplifiers and servo
valves should be higher than that of the selected actuators. By choosing fast servo amplifiers
and valves, their dynamics can be reduced to a single gain as in Figure 6.2. In this case, the
open-loop transfer function for the velocity control servo system of each joint of the orange¬
picking robot is approximated as a second-order system:
55

56
D/A
Figure 6.1. Open-loop hydraulic servo system.
D/A
Output
Signal
Figure 6.2. Reduced block diagram of the open-loop system.
Au(s)
Kvfi>h
s +26hC0hS + tOh
(6-1)
where Au(s) = open-loop transfer function ((deg/sec)/(D/A word)),
s s Laplacian operator (sec1),
Kv = open-loop gain of the system ((deg/sec)/(D/A word)),
Oh a open-loop hydraulic natural frequency (rad/sec), and
5h = open-loop damping ratio (dimensionless).
In this system, the open-loop gain includes the gains of the D/A converter, the servo amp/servo
valve comination, and the actuator and load dynamics.
The hydraulic natural frequency and the damping ratio are functions of parameters of
the fluid and the mechanical components of the controlled system and can generally be
approximated as
(Dh=
8h
Kce,. /~Pe Jt
Dm Y vt
(6-2)
(6-3)

where:
Pe s bulk modulus of hydraulic fluid (N/m2),
Dm = volumetric displacement of rotary actuator or motor (ml/rad),
Vt = total compressed volume of fluid (ml),
Jt s total inertia of load and actuator (N • m • sec2), and
Kce s servo valve flow-pressure coefficient (ml/sec/N/m2).
Each of these parameters can vary during operation. However, by keeping the temperature of
the hydraulic fluid constant during operation of a servo hydraulic system, the bulk modulus (pe)
of the fluid can be considered constant. As rotary actuators and motors rotate, the volume of
fluid in one chamber decreases while the volume in another chamber increases. Since the total
volume of fluid in the actuators and motors changes only very small amounts due to pressure
differential during operation, the volumetric displacement (Dm) can also considered to be
constant. Likewise, if the total compressed volume of fluid (Vt) in the system changes only very
small amounts if any during operation, it can be considered constant. Because the quantities, pe,
Dm, and Vt, are fairly constant, they cause only minor changes in the values of CDj, and 5*, during
operation of the servo hydraulic system.
Another important effect on the performance of an electrohydraulic servo system is the
external torque load on the output shaft of the actuator as shown in the block diagram of Figure
6.3. External loads on the system must be accounted for in the derivation of the open-loop
transfer function. In the case of the orange-picking robot, this external load was altered by the
position of the joints 0 and 2. When the sliding joint was moved from a balanced position, an
external torque was added to joint 0 actuator. This torque was proportional to the position of
joint 2 with positive and negative maximum values occurring when the tube was extended or
retracted, respectively. When joint 0 was moved from a horizontal position, an external load
was induced on the motor which actuated joint 2 by the pull of gravity on the sliding tube. This
load was greatest when joint 0 was positioned to its maximum or minimum rotation. Each of
these loads affected the operation of the robot.

58
External
Output
Signal
Figure 6.3. Block diagram of the open-loop system with external torque load.
During critical performance times for the citrus-picking robot, the tube was already
extended toward the fruit. During these periods, motion of the sliding tube was so small that
changes in the torque load caused by its changing motion were considered negligible. Therefore,
the dynamics of the external torque on joint 0 were also considered constant. Similarly, changes
in position of the sliding tube were required only during occasions in which motion of joint 0 was
very small or nonexistent. As the end-effector was extended toward a targeted fruit, the
position of joint 0 was controlled by the vision system to follow the small vertical motion of the
fruit. This vertical fruit motion was very small and resulted in very small and negligible
position changes in joint 0. While joint 2 was being retracted from the tree, joints 0 and 1 were
held practically motionless to prevent manipulator damage caused by collisions with large
limbs or other obstacles. Therefore, the external touque load on joint 2 due to changes in the joint
0 position was also constant during the motion of joint 2. In other words, the external torque
loads that affected joint 2 could be considered constant during any operation of the sliding joint.
Parameter Estimation
In the general case, the actuator and load dynamics is the limiting factor for the
response of a servo system. As Merritt points out, servo amplifiers and valves should have
faster response rates than the actuator and load combinations. In this case, the dynamic
response characteristics of the servo amplifiers and servo valves can be neglected. In the case of
the orange-picking robot, servo amplifiers and servo valves were chosen with this criteria in
mind. All three of the servo amplifiers had bandwidths of 1885 rad/sec (300 HZ) (Table 4.1).

59
Also, servo valves with bandwidths of 377 rad/sec (60 HZ) for joints 0 and 1 and 189 rad/sec (30
HZ) for joint 2 were used. Equation 6-2 was used to approximate the hydraulic natural
frequencies for the joints of the robot. For the revolute joints, the maximum natural frequency
was extimated to be approximately 28 rad/sec which was classified as slow when compared to
the response rate of the actuators. Assuming that the sliding tube was a simple mass for the
motor actuator, a natural frequency of 67 rad/sec was estimated. Not included in this
estimation was the decrease in the response of the slider which developed as a result of the
friction in the bearing. Therefore, the response of the chosen actuator for joint 2 was adequate to
be considered fast enough to be neglected in the further analysis.
Theoretically, the steady-state gains, hydraulic natural frequencies, and damping
ratios could have been calculated from the known characteristics of the manipulator.
However, for the orange-picking robot, such parameters as link mass and mass moment of
inertia as well as some hydraulic fluid characteristics which affected the actuator and load
dynamics were unknown. Also, flow characteristics of the servo valves were undeterminable.
Therefore, the steady-state gain, hydraulic natural frequency, and hydraulic damping ratio
for each joint were determined experimentally. The experimental tests consisted of actuating
each joint by stepping the reference voltage to the servo amplifier and measuring the joint
response. These open-loop tests were conducted on each joint individually. For each joint, the
computer was programmed to signal the servo amplifier to send a current to the servo valve
holding it opened for a given amount of time while the computer recorded the velocity and
position of the joint as it moved. A routine was added to the user interface of the robot control
program to obtain a description of the step from the user and send the appropriate control signal
to the D/A board. The step was maintained until the joint reached a constant velocity or the
position of the joint reached a specified maximum or minimum. The valve was then closed to
stop the action and bring the joint to rest.
Typical graphs for step test results are shown in Figures 6.4,6.5, and 6.6 for joints 0,1,
and 2, respectively. Information from the graphs was used to estimate the gain, the hydraulic

60
natural frequency and the hydraulic damping ratio for each joint. The steady-state gain of a
joint was the ratio of the achieved steady-state velocity to the input value. The gain for each
joint was determined as
V,
Kv=-
out
sp
where: Kv s steady-state gain ((deg/sec)/(D/A word)),
Vout s steady-state output velocity (deg/sec), and
Vsp 3 velocity control signal (D/A word).
The damping ratio was approximated with (Palm, 1983):
where:
8h = hydraulic damping ratio (dimensionless), and
V -V
os 3 overshoot (decimal value) ~ max 88
The hydraulic natural frequency was approximated with (Palm, 1983)
71
coh =
tDVu
Sh
where
(6-4)
(6-5)
(6-6)
ft)h 3 hydraulic natural frequency (rad/sec),
Sj, 3 damping ratio (dimensionless), and
tp 3 time to peak (sec).
A typical response of joint 0 of the orange-picking robot to a step input is shown in
Figure 6.4. The response signals from the A/D converters were converted from the bit values as
used by the control computer to deg/sec by the conversion factor 0.033 (deg/sec)/bit from Table
4.2. For a step input to the actuator of 1200 D/A bits, the joint started from a velocity of 0
deg/sec (0 A/D bits) and peaked at a velocity of 65 deg/sec (1980 A/D bits) before returning to
an average steady-state velocity of 46 deg/sec (1400 A/D bits). Thus, the steady-state gain for

61
1500]
*<3 “ ■ ' . .
I „ 1000.:
en *g |
| I SOth
<3 £ :
o Q o
I _J
^ -50Q-f—T~nr~i | | ■ i ! | i i | i i ■'i—i—i—| i i |—i i
O 15 30 45 60 75 90 105 120
Time (1/60 see)
Figure 6.4. Typical response of joint 0 of the orange-picking robot to a step input of 1200 D/A
bits with joint 2 centered in the Hooke joint.
this system was calculated using equation 6-4 as approximately 0.038 (deg/sec)/(D/A word).
These values represent an overshoot of 19 deg/sec (580 A/D bits) which corresponds to 41
percent. Using this measured overshoot in equation 6-5, a damping ratio of 0.27 was calculated.
The time to peak was determined by finding the number of counter ticks required for the
velocity of the joint to reach its maximum and dividing by the scale factor, 60 ticks per sec. In
this case, the joint reached its maximum velocity in 10 counter ticks or 0.17 sec. This value along
with the already determined damping ratio was used in equation 6-6 to find the hydraulic
natural frequency of the joint of 20 rad/sec or 3.1 HZ.
Open-loop step tests were conducted on joint 0 for different directions of motion and
different positions of joint 2. The tests were conducted with the tube extended, in the center of
its working range, and retracted. Repetitions of the tests included step inputs that caused the
end-effector to be moved down from a raised position and up from a lowered position, or in

62
response to positive and negative steps. The results of the repetitions were averaged. The
average steady-state gains, hydraulic natural frequencies, and damping ratios are presented in
Table 6.1.
A typical response of joint 1 of the robot to a step input of -500 D/A bits is shown in
Figure 6.5. This step caused the joint to move the end-effector of the robot from left to right.
The step input was initialized at 1/2 sec (30 counter timer ticks). The joint which began from a
velocity of approximately 0 deg/sec (0 A/D bits) responded to the input by reaching a peak
velocity of -38 deg/sec (-1150 A/D bits) before returning to an average steady-state velocity of
-28 deg/sec (-850 A/D bits). The values for this step test represent an overshoot of -10 deg/sec
(-300 A/D bits) or 35 percent of the steady-state velocity. Joint 1 reached its maximum or peak
velocity in 7 counter timer ticks or 0.12 sec. Using these values in equations 6-4,6-5, and 6-6, the
hydraulic natural frequency and damping ratio of joint 1 were found to be 28 rad/sec (4.5 HZ)
and 0.32, respectively. The steady-stale gain, Kv, for joint 1 was found to be
0.056 (deg/sec)/(D/A word).
For step test response of joint 1, the position of joint 0 was held constant while joint 1
was free to respond to the step input from the control computer. These tests included both
positive and negative step inputs from the computer resulting in horizontal motions of the end-
effector. The test was also conducted in repetition for joint 2 in the retracted, centered, and
Table 6.1. Experimentally determined steady-state gains, damping ratios, and hydraulic
natural frequencies of joint 0 in relation to position of joint 2 and direction of
motion.
position
joint 0
direction
steady-state
gain
(deg/sec)
hydraulic
damping
hydraulic natural
frequency
of joint 2
of motion
(D/Aword)
ratio
rad/sec
HZ
retracted
down
0.035
0.30
33
5.2
up
0.M2
021
22
3.4
centered
down
0.033
0.18
17
2.8
up
0.038
0.26
20
3.1
extended
down
0.044
0.31
17
2.8
up
0.040
0.34
27
4.3

63
| | -200-
ál •
- p -400-
| W . I
-600- | | .| |, | | | ■ "i" i | i i | r""'r i i ■ i i t—
0 15 30 45 60 75 90 105 120
Tune (1/60 see)
Figure 6.5. Typical response joint 1 of the orange-picking robot to a step input of -500 D/A bits
with joint 2 centered in the Hooke Joint.
extended positions. The averaged results of the repetitions of the open-loop step test of joint 1
are presented in Table 6.2.
Step tests of joint 2 gave undesirable results. When the sliding joint was actuated with
a step input, the joint responded with a quick jolt and then settled to an increasing velocity as
the valve was held opened. The sluggish response of the joint did not reach a steady or peak
velocity before the full length of the tube was used at which time the step input was
terminated. A typical response of joint 2 to a step input is shown in Figure 6.6. From the
information presented in the figure, the defining parameters for the system were not
determinable. However, important observations were made which aided in developing a
controller for the sliding joint. Due to the static friction between the nylon bushing and the
aluminum tube, the input required to start the tube moving was much larger than that required
to keep it moving. Small control values would not cause a change in the joint's position. On the

64
Table 6.2. Experimentally determined steady-state gains, damping ratios, and hydraulic
natural frequencies of joint 1 in relation to position of joint 2 and direction of
motion.
position
offoint2
joint 1
direction
of motion
steady-state
gain
(deg/sec)
(D/Aword)
hydraulic
damping
ratio
hydraulii
frequ
rad/sec
; natural
ency
HZ
retracted
negative
0.054
0.29
28
4.5
positive
0.055
0.18
32
5.1
centered
negative
0.055
0.32
28
4.5
positive
0.055
022
28
4 5
extended
negative
0.056
0.31
22
3.5
positive
0.058
0.26
22
3.5
other hand, the response of joint 2 to large control values would increase stiffness requirements
for positioning the joint.
Results and Discussion
Design of the control systems for the orange-picking robot required a knowledge of the
each joint's transfer function. Merritt (1967) suggests that the transfer function of most
electrohydraulic servo systems can be estimated as a second-order system. Open-loop step tests
were conducted on each of the robot's joints for verification of Merritt's assumptions and for
establishing the parameters which define the behavior of a second-order system. After
defining the systems' parameters, the second-order systems were simulated for comparison with
the actual systems and verification of the determined parameters.
Analysis of the open-loop step tests responses of joint 0 for various positions of the
sliding tube yielded a range of hydraulic natural frequencies and damping ratios. Repetitions
of the step tests suggested average hydraulic natural frequencies ranging from 17 to 33 rad/sec
(2.8 to 5.2 HZ) and average damping ratio ranging between 0.18 and 0.34 (Table 6.3). The open-
loop gain (Kv) for joint 0 was averaged to be approximately 0.039 (deg/sec)/(D/A word) as the
ratio of the output signal to the computer's D/A converter in deg/sec to the input signal from the
computer's A/D converter in deg/sec.

65
Time (1/60 sec)
Figure 6.6. Typical response of joint 2 of the orange-picking robot to a step input of 750 D/A
bits.
Table 6.3. Steady-state gains, hydraulic damping ratios, and hydraulic natural frequencies as
determined by analysis of the step test responses.
averaged
steady-state
averaged
averaged
hydraulic natural
gain
hydraulic damping
frequency
(deg/sec)
ratio
(rad/sec (HZ))
joint
(D/A word)
min
max
min
max
0
0.039
0.18
0.34
17 (2.8)
33 (5.2)
1
0.056
0.18
0.32
22 (3.5)
32 (5.1)
Similarly, step test responses of joint 1 produced information for estimating the
parameters of its transfer function. Once again, the tests were conducted in both directions with
different positions of joint 2 for establishing a range of the parameters which were valid for
the manipulator during operation. Also listed in Table 6.3, the system open-loop gain was
estimated as a constant value of 0.056 (deg/sec)/(D/A word), while the average hydraulic

66
natural frequency spanned a range from 22 to 32 rad/sec (3.5 to 5.1 HZ). The average damping
ratio ranged from 0.18 to 0.32.
The second-order open-loop dynamic transfer functions were simulated with the
parameters as determined by the step tests for joints 0 and 1. The results of these simulated
systems were plotted for comparison with the experimental results of the step tests.
Representative results from the experimental tests and the simulations are presented in Figures
6.7 through 6.12. These graphs represent cases for joints 0 and 1 spanning the determined
natural frequency and damping ratio ranges. A response pattern was evident across all of the
tests. In each case, the response of the actual joint showed a peak which compared directly to
the first peak of the simulated system. In some, but not all cases, the actual joint oscillated
slightly (usually one cycle) before settling to a steady-state value. The simulated systems, on
the other hand, generally oscillated more.
This discrepancy indicated nonlinearities in the systems which probably resulted from
nonlinear servo valve characteristics. Theoretically, a deadband in the valve would deliver a
much smaller oscillation than would occur for a valve that was purely linear. A region in the
response of a hydraulic valve in which small changes in the control signals have no effect on
the direction or amount of fluid flow through the valve is referred to as the deadband of the
valve. The responses of the servo valve controlled joints of the robot seem to indicate that a
deadband caused by either an overlap of the valve ports or coulomb friction exists in these
systems.
Because design of the robot's control systems was based on linear systems, a linear
approximation of the transfer functions for these joints was necessaiy. Noting that the step
responses of the systems were best approximated by second-order responses, second-order
systems were chosen to estimate the transfer function of the actual systems. Therefore,
Merritt's assumptions for reducing the electrohydraulic control system to a second-order system
were verified for the cases of joints 0 and 1. These second-order systems were later used to model

67
each of the joints and aid in the selection and implementation of the controllers of the orange¬
picking robot.
The joints' responses to the step input signals gave important information to be used in
the design of the respective controllers. For joints 0 and 1, the ranges in the natural frequencies
and damping ratios were related to the position of joint 2 during the tests. Higher natural
frequencies were calculated for joint 0 when the weight of joint 2 was being lifted. For example,
the highest natural frequencies resulted when the tube was extended with the end-effector
being lifted or when the tube was retracted with the end-effector being lowered. Likewise, the
highest damping ratios for joint 0 were calculated for those responses in which the most weight
was being lifted. When this information was checked against the parameters of equations 6-2
and 6-3, the damping ratio follows the expected trend that increased load inertia would result
in increased damping. However, the natural frequency contradicts the inverse relationship
with the inertia load as indicated in equation 6-2. This contradiction indicated that the
position of the sliding joint influenced the system more as an external torque load than an
inertia load used in equation 6-2.
The step tests for joint 1 involved moving the end-effector in horizontal directions. For
this joint, a steady-state gain of 0.05 (deg/sec)/(D/A word) was calculated for every trial. In
this case, the second-order parameters varied with the position of joint 2 and the direction of
travel. The hydraulic natural frequencies were smallest when the sliding joint was extended
and the highest inertia was expected. This followed the relationship of equation 6-2. On the
other hand, the established damping ratios did not follow the relationship of equation 6-3.
The only evident pattern of the change in damping ratio was that the damping ratio for the
positive direction was smaller than that for the negative direction. This variance could have
been caused by improper alignment of the outer frame causing binding in the bearings or from
different friction values for the different directions of travel.
As previously discussed, the model of joint 2 could not be determined due to the high
static friction values in the bushing and its unpredictable behavior. The behavior of joint 2

68
indicated that the system had a high deadband which required very large signals to initialize
the motion of the joint and much smaller signals to keep it moving. For controller development,
it was considered to have a sluggish second-order response in which special considerations
would have to be made in controller development and implementation.

Simulated Velocity Joint 0 Velocity
(deg/sec) (deg/sec)
69
(a)
(b)
Figure 6.7. Responses of joint 0 to a step input: (a) actual, (b) simulated.
CDh = 32.95 rad/sec, Sj, = 0.30, Kv = 0.036 (deg/ sec)/(D/A word).

Simulated Velocity Joint 0 Velocity
(deg/ sec) (deg/sec)
70
(a)
(b)
Figure 6.8. Responses of joint 0 to a step input: (a) actual, (b) simulated.
Oh = 17.36 rad/sec, §h = 0.16, Kv = 0.032 (deg/sec)/(D/A word).

Simulated Velocity Joint 0 Velocity
(deg/ sec) (deg/sec)
71
(a)
(b)
Figure 6.9. Responses of joint 0 to a step input: (a) actual, (b) simulated.
©h = 16.54 rad/sec, 8h = 0.31, Kv = 0.044 (deg/sec)/(D/A word).

Simulated Velocity Joint 1 Velocity
(deg/sec) (deg/sec)
(a)
(b)
Figure 6.10. Responses of joint 1 to a step input: (a) actual, (b) simulated.
C0h = 31.87 rad/sec, 5h = 0.17, Kv = 0.055 (deg/sec)/(D/A word).

Simulated Velocity Joint 1 Velocity
(deg/sec) (deg/sec)
(a)
(b)
Figure 6.11. Responses of joint 1 to a step input: (a) actual, (b) simulated.
©h = 22.02 rad/sec, Sh = 0.31, Kv = 0.056 (deg/sec)/(D/A word).

Simulated Velocity Joint 1 Velocity
(deg/ sec) (deg/sec)
74
(a)
(b)
Figure 6.12. Responses of joint 1 to a step input: (a) actual, (b) simulated.
ton = 21.47 rad/sec, 6h = 0.22, Kv = 0.056 (deg/sec)/(D/A word).

CHAPTER 7
PERFORMANCE CRITERIA
Desired performance criteria for the joint control systems of the orange-picking robot
are specified in this chapter. Because joint control was based on position, velocity, and vision
information, performance requirements were defined to give details upon which the control
systems would be designed and evaluated. In order to determine these requirements, the
interaction between the robot and its environment was evaluated. Initially, the motions of a
fruit hanging from the tree were examined. Information acquired from this investigation was
used to establish vision dynamic criteria for the robot's control. To determine the precision
with which the end-effector of the robot was required to be positioned, a picking envelope was
established. This picking envelope defined the volume with respect to the end-effector in
which a fruit must be located to be picked. In other words, the controllers were required to
utilize information from the fruit sensors to position the end-effector within reach of the
targeted fruit. From this definition of fruit motion and the pick envelope, controller
performance criteria for each joint were determined. These requirements make up the static and
dynamic performance criteria which were necessary for choosing and designing controllers to
realize a satisfactory robot response.
Background
All control systems are designed to perform a specific task. Performance specifications
are spelled out as requirements of the control system. These criteria include relative stability,
accuracy, and response rate. In most cases, these specifications are given in precise numerical
values. However, in some cases, the criteria are not as critical and can be specified as
qualitative statements providing leeway for personal judgement. Many times, the requirements
placed upon a system must be modified during the course of implementing and timing the
75

76
controller due to the increased expense of the system or conflicting criteria. Sometimes, the
performance specifications simply can not be met. In any case, the performance criteria are
specifications of design goals which are used for chosing and implementing system controllers.
For the orange-picking robot, the main purpose of joint control was to cause the end-
effector to be positioned so that a fruit could be detached from the tree within the shortest
possible pick cycle time. A pick cycle was characterized by the steps required for the robot to
begin from a "home" location, search for and locate a target fruit, position the end-effector so
that the targeted fruit could be detached, actuate the picking lip to girdle the fruit, return to
the specified home position, and release the fruit. The most important requirement of all
control modes was that the system remain stable for any requested action. Second most
important was the accuracy with which the end-effector was positioned with respect to the
fruit. The relation between the end-effector and the fruit was controlled by the vision control
algorithm and the information from the fruit sensors for joints 0 and 1 and by both the position
and velocity control algorithms for joint 2. Therefore, the strictest performance criteria were
specified for the vision control algorithms in addition to the position and velocity control
modes for the sliding joint.
Characteristics of Fruit Motion
Because the environment of the fruit tree was not free from disturbances during the
picking operation, the robot was required to pick moving fruit. The fruit motion usually
resulted from environmental disturbances such as wind or from canopy interference as the
manipulator removed fruit. Regardless of the cause, the resulting fruit motions were
investigated for use in specifying the performance requirements of the robot.
Initially, reactions of the fruit to wind disturbances were examined. Then, the branches
of the tree were disturbed in a manner similar to those disturbances anticipated during robotic
picking. A tape measure was placed below the fruit for determining the magnitude of the fruit

77
motion. Using a video camera with a timing feature, fruit's reactions to these disturbances were
recorded and analyzed.
Results from these tests indicated that the fruit could swing with a peak-to-peak
magnitudes ranging from 25 cm to 100 cm with cycle times ranging from 0.9 sec to 2.6 sec. The
results of these tests are presented in Figure 7.1 with the shaded region of the plot indicating
the observed fruit motion. Extreme cases of fruit motion which could take place during picking
were noted as the worst case that the robot could encounter. These extreme cases lie along the
sloping line which limits the upper side of the graph's shaded region and is established by
motions of 100 cm peak-to-peak magnitudes at 05 HZ and 25 cm peak-to-peak magnitudes at 1.1
HZ. The robot's control algorithms were required to manipulate the robot to be able to track
and pick fruit with any motion. The best case from the picking standpoint would have the
targeted fruit hanging motionless from the branch. Based on the results of this fruit motion test,
the worst cases that the robot would encounter ranged from small magnitudes with small cycle
times (±12.5 cm, 1.1 HZ) to large magnitudes with long cycle times (±50 cm, 05 HZ) (Figure 7.1).
Figure 7.1. Typical observations of the motion of fruit swinging from the canopy of a tree
indicating the peak-to-peak magnitude of the fruit for various periods of
oscillation.

78
Picking Envelope Definition
A study was conducted to define the picking envelope of the end-effector by quantifying
the fruit position range, relative to the stationary end-effector, in which fruit capture could be
accomplished. An apparatus was designed and constructed for holding a fruit in front of the
picking mechanism (Figure 7.2). The apparatus consisted of two pieces of aluminum bent at
right angles and mounted on the end-effector of the robot. The pieces were scribed with a
pattern for establishing the location of the fruit which hung from the apparatus and held in
place by two large spring clips. For the testing, an artificial orange (approximately 8 cm in
diameter) was weighted with water and hung from the support by an elastic cord. The elastic
cord allowed the artificial orange to have motion similar to that of a real orange hanging from
a citrus tree.
The picking envelope was defined by measuring the location of the fruit's center with
respect to the picking mechanism. In order for a location to be included in the picking envelope,
Figure 7.2. Apparatus for determining the picking envelope of the robot's end-effector.

79
the region in which a successful pick could be guaranteed, the end-effector was required to
girdle the fruit successfully in seven of seven attempts. Positions at which the rotating lip
pushed the orange away or the orange was caught between the rotating lip and the body of the
picking mechanism were considered unsuccessful attempts. Initially, the fruit was positioned in
the center of the picking mechanism, touching the protective shield of the camera with its
center located on the Z axis of joint 2 of the robot (home position). Thus, the position of the fruit
was defined in terms of the camera coordinate frame with the home position located at x = 0 cm,
y = 0 cm, and z = 10.2 cm. The fruit was then moved out along the Z axis in 1 cm increments until
the mechanism was unable to successfully girdle the orange in all of seven attempts. From this
location, the orange was moved to a location 1 cm up from the home position along the Y axis
and back to a point which was easily picked by the mechanism. Again, the fruit was moved out
from the picking mechanism until it could no longer be picked. As the orange was moved to the
edge of the picking range of the robot, the increments were reduced to one half centimeter. Each
location was noted along with the number successful attempts. This operation was repeated
until the complete region in which the robot could possibly pick fruit was covered.
The results of the picking envelope tests are graphically presented in Figures 7.3,7.4,
and 7.5. In each of the figures, the shaded, circular region represents the fruit positioned
against the protective shield of the camera and centered vertically in the tube of the picking
mechanism. The centroid of the fruit in this position was used as the origin of the picking
envelope. The outer ranges of the orange centroid for a successful pick are represented by the
bold lines in the figures. The range in which the picking mechanism could pick a fruit whose
center lay in a vertical plane that intersected the centerline of tube (Z2) is presented in Figure
7.3. The region in which the orange could be picked if its center point was in a vertical plane 1
cm to the right or left of the centerline of the tube is shown in Figure 7.4. Similarly, the
successful picking region in the vertical plane located 2 cm from the centerline is displayed in
Figure 7.5. In these tests, if the center of the orange was more than 2 cm away from the center of

80
6
4
2
0
y (cm)
-2
-4
-6
Figure 7.3. Picking range of the end-effector in the vertical plane located on the centerline of
axis 2.
protective cover for camera
(1 cm thichness)
z (cm)
6.2 10.2 14.2 18.2
1 12.2 16.2 20.2
Figure 7.4. Picking range of the end-effector in the vertical plane located 1 cm from the
centerline of axis 2.

81
protective cover for camera
(1 cm thichness)
Oc/z (cm)
Figure 7.5. Picking range of the end-effector in the vertical plane located 2 cm from the
centerline of axis 2.
the tube, the rotating lip would push the orange out of reach resulting in an unsuccessful pick
attempt.
The required position relationship for successful picking between the robot end-effector
and the fruit center are given in Tables 7.1 and 7.2. In the Z direction, the robot could pick a
fruit whose center was located no farther from the home position than 16.2 cm. Vertically, a
fruit's centroid could be positioned within 5.0 cm above and 1.0 cm below the tube's centerline.
These ranges in the Y and Z directions were valid for all acceptable positions in the X direction.
Therefore, requirements in the horizontal or X direction specified that the fruit be within ±2 cm
of the tube's centerline. These figures indicated the position relationship that guaranteed a
successful pick attempt and were used for establishing required performance criteria for the
controlling systems. A summary of these results is presented in Table 7.1. In Table 7.2, values
for the vision system test which correspond to the edges of the picking envelope are shown. The
xcent and ycent pixel values represent the x and y position of the centroid of the fruit's image in
the vision field.

82
Table 7.1. Range of positions of a fruit's centroid to guarantee a successful pick.
X
(cm)
Z
maximum
(cm)
minimum
(cm)
maximum
(cm)
0.0
16.2
-4.0
5.0
±1.0
17.2
-3.0
5.0
±2.0
16.7
-1.0
5.0
Table 7.2. Values read by vision system corresponding to the established picking envelope.
X Y Z Vision
(cm)
(cm)
(cm)
xcent
vcent
0.0
-4.0
16.2
197
303
0.0
5.0
16.7
196
69
1.0
-3.0
17.2
173
239
1.0
5.0
17.2
177
70
-1.0
-3.0
17.2
221
239
-1.0
5.0
17.2
217
70
2.0
-1.0
16.7
150
206
2.0
5.0
16.7
155
75
-2.0
-1.0
16.7
244
206
-2.0
5.0
16.7
239
75
In summary, for the robot to remove a fruit from the tree, its end-effector had to be
positioned so that the vision system possessed values within the following ranges. The vision
system was required to return an xcent value between 150 and 244 (197 ±47) and a ycent value
between 75 and 206 (140 ±65). The xcent and ycent values 197 and 140 represent the location of
the center of the fruit's image when the fruit was in the center of the picking envelope. Also,
the fruit was required to be within the minimum Z distance (16.2 cm) from the origin of the
camera frame. These values represent the borders of a cubic volume in which the fruit was
required to be positioned in order to guarantee that it could be girdled by the rotating lip of the
picking mechanism. Robot control algorithms were necessary which could position the end-
effector within these boundaries.
Velocity Control Requirements
Velocity control algorithms for joints 0 and 1 were necessary only for use during times in
which the robot was searching for a fruit (Adsit, 1989). During this operation, constant
velocities were required of joints 0 and 1 to cause the end-effector to scan the tree in search of a

83
fruit. The desired motions were achieved by setting velocity set points necessary for scanning
and calling the velocity control routines for joints 0 and 1. This scanning technique was
terminated when a fruit was identified by the vision system. Therefore, performance criteria
for velocity control of joints 0 and 1 did not prove to be critical. By adjusting the set points
which determined position of the joint at which the control was switched from one mode to
another, the overshoot specifications for joint 0 and 1 velocity controllers could be relaxed or
tightened. Steady-state error requirements could also be relaxed by increasing the velocity set
points. Experience with the robot operation indicated that actual velocity of joints 0 and 1
could overshoot the set point velocity by as much as 45 percent without greatly affecting the
performance of the search procedure. Also, deviations of 40 percent from the desired velocity
did not adversely affect the picking performance of the manipulator.
Although the velocity requirements of joints 0 and 1 were used only during the fruit
search, the velocity control algorithm for joint 2 was used during the picking operation to
extend the end-effector toward a targeted fruit during the approach states. Therefore, its
performance proved to be more critical than that for joints 0 and 1. Most critical was the ability
of joint 2 to extend in a smooth, rapid manner and respond quickly to velocity set point changes.
Also, the detection of robot/limb collisions during extension and the detection of unremovable
fruit during retraction relied upon the ability to accurately control the joint 2 velocity. The
intelligence base detected these events by monitoring the joint 2 velocity control word which
was generated from the velocity error by the velocity controller. Large velocity control words
over a specified period of time were used to indicate that joint motion was restricted either by
an obstacle in the arm's path or by the inability of the arm to remove a fruit from its stem.
During the picking operation, overshoot values up to 25 percent of the desired joint 2 velocity
were regarded as acceptable and velocity steady-state errors of up to 10 percent were
determined tolerable based on experience with the robot.

84
Position Control Requirements
Position control algorithms were used primarily for two operations. First, the position
control algorithms were called to return the robot to its home position after a pick cycle was
completed. This motion was accomplished by setting the position set points to the specified
home location and calling the position control routines to move the joints to the required
position. A second use was to stop the joints and hold them stationary while other actions were
performed. For instance, during the detach phase of a pick cycle, joints 0 and 1 position
controllers were used to hold the arm stationary while the lip was actuated for girdling the
fruit.
During the picking phase, a large error in the joint positions would cause the end-
effector to fail in its attempt to girdle the targeted fruit. Therefore, the maximum allowable
error for each joint was the motion of the end-effector which would cause the fruit to be out of
the picking envelope when the picking mechanism was actuated. For joint 0, the maximum
steady-state error was determined to be 3 cm at the end-effector. Likewise, the maximum
steady-state error for joint 1 was 2 cm, and for joint 2, the maximum error was 3 cm. The position
errors for joints 0 and 1 were influenced by the position of joint 2. For a given angular motion of
joint 0 or 1, the maximum error at the end-effector was realized when the sliding tube was in
the extended position. Therefore, the angular position errors allowed for joints 0 and 1 were
calculated based on the maximum allowable extension of joint 2 (158.3 cm). These values
translated to maximum steady-state errors of 1.1 degrees and 0.7 degree for joints 0 and 1,
respectively, and 3 cm for joint 2.
Dynamic response of the position control algorithms was not as critical as steady-state
error criteria. These algorithms caused motion only to return the joints to their home positions.
The home positions could be set to allow some overshoot of the desired position allowing a
faster response time. Again, experience with the fruit-picking robot suggested that position
overshoots as high as 15 percent could be allowed for each of the axes without causing any

85
problems with the control of the manipulator. By allowing the dynamic response to overshoot
the desired value, greater speeds were achievable and thus faster pick cycle times.
Vision Control Requirements
Of all the control systems, the most critical operations took place while the robot was
operating under the vision control. After the vision system identified a fruit while in the
search mode, the intelligence base switched control of joints 0 and 1 from velocity control to
vision control. Using vision control, joints 0 and 1 were aligned with the targeted fruit and joint
2 extended to position the end-effector near the fruit. The operations which used vision control
required that the motion of the fruit be tracked by the end-effector and ultimately that the
end-effector be positioned so that the fruit would lie within the picking envelope.
As previously pointed out, the two worst observed cases of fruit motion were: Case I:
swinging motions up to 50 cm in magnitude with 2 sec (0.5 HZ) cycle times and Case II: swinging
motions 12.5 cm in magnitude with cycle times of 0.9 sec (1.1 HZ). Also, the established picking
envelope indicated that the fruit position could be allowed to fluctuate by ±2 cm (47 pixels) in
the x direction (joint 1) and ±3 cm (65 pixels) in the y direction (joint 0) from the center of the
picking envelope. Controllers for the vision system of the robot were thus needed to cause the
end-effector to be able to track these fruit motions with errors not to exceed 3 cm for joint 0 and 2
cm for joint 1.
Because the units of the vision system were pixels, the amplitudes of the fruit and the
end-effector were converted to pixel units (Figure 7.6). As presented in the figure, the image
plane was assumed to be infinitely large and the fruit was assumed to be its maximum pickable
distance (16.2 cm) from the camera optical center, Oc. The trigonometric relations indicated
that the image of a fruit whose magnitude was 500 mm would have a magnitude of 1077 pixels
on the infinite image plane. Likewise, a fruit magnitude of 125 mm corresponded to an image
magnitude of 269 pixels.

86
Case I: 1077 pixels
Case II: 269 pixels
Figure 7.6. Relationship between the amplitude of a fruit and the amplitude of its image on
the camera image plane.
To provide more information for determining the performance requirements for the
vision control system, the difference between the location of the targeted fruit and the end-
effector was calculated. First, the previously observed motion of a fruit was expressed as a
vector,
fm = af sin(wt)
where
fm
= fruit motion (pixels),
af
= fruit motion amplitude (pixels),
0)
e frequency of fruit motion (deg/sec), and
t
= time (sec).
The predicted motion of the robot's end-effector was also described as a vector,
rm = ar sin((Dt+)
where rm = end-effector motion (pixels),
ar = end-effector motion amplitude (pixels), and
4> h= phase lag between fruit and end-effector motion (deg).

87
Thus, the error was calculated as the difference between these two vectors:
error = af sin(cot) - ar sin(iot-) (7-1)
Through the use of vector algebra, the magnitude of this error was calculated as:
error
(a f (1 - AR
where I error I = magnitude of the error (pixels) and
AR = amplitude ratio (ar/af).
To express the error in terms of the maximum allowable phase lag for a given
amplitude ratio, equation 7-2 was solved for <() as
-l
<)> = cos
1 AR
2AR + 2
2
error
2 AR a?
(7-2)
(7-3)
Given the maximum allowable error from the established picking envelope (47 pixels) and the
amplitudes of the fruits' motions from the fruit motion tests, equation 7-2 was solved to
represent the maximum allowable phase lag for the end-effector (equation 7-3). This
calculation was made for both cases of fruit motion. The results are presented in Figure 7.7.
Because the motion of the fruit was much greater in the horizontal direction and the
allowable error for joint 1 was smaller, it was assumed that calculation of the maximum
allowable phase lag for joint 1 provided sufficient margin for both components of the vision
system. A plot of this maximum allowable phase lag versus amplitude ratio is presented in
Figure 7.7. For the smaller, high-frequency fruit motions as in Case II, a larger phase lag of
approximately 10 degrees was allowable. For the large-amplitude/low-frequency fruit motion,
Case I, a smaller allowable phase lag of approximately 2.5 degrees was calculated. Also from
Figure 7.7, necessary amplitude ratios were determined. For Case I, an amplitude ratio of 0.96
or better was required of the vision control system to be able to pick a fruit moving at 0.5 HZ (3.1
rad/sec) with a magnitude of 50 cm. Likewise, the control system was required to have an
amplitude ratio of 0.83 or better for fruit motions of 12.5 cm magnitude and 1.1 HZ (6.9 rad/sec),

88
-e-
bb
2
Ph
Figure 7.7. Maximum allowable phase lag as a function of amplitude ratio, ar/af, as described
in equation 7-3. Maximum allowable error = 47 pixels (2 cm). Case I: af = 50 cm
(1077 pixels). Case II: af = 12.5 cm (269 pixels).
Case II. Each of these cases provided certain requirements of the control system. The case
which should ultimately be met could not be determined from this information. Therefore, both
cases were established as requirements of the vision control system.
Summary of Performance Criteria
The overall goal for the orange-picking robot's control systems was to control the robot
through smooth and fast motions to precise configurations. A fast pick cycle time was necessary
to make the manipulator feasible as a replacement for manual picking techniques while smooth
operation was imperative to prevent damage to the fruit sensors which were housed in the end-
effector. The overall performance of the orange-picking robot was limited by the performance
of each of the joints. Stiff performance criteria were imposed only on those cases in which the
control was considered critical.
The velocity controllers for joints 0 and 1 were not used for critical operations, so, only
loose performance requirements were necessary. On the other hand, the position control
algorithms carried out important positioning tasks during critical phases of operation and thus,
tighter requirements were necessary. A summary of the desired performance criteria for the

89
velocity and position control systems as presented in this chapter is tabulated in Table 7.3.
Because of the desire to have very fast pick cycle times, dynamic response times for the
algorithms were required to be kept as short as possible. Another very important criterion of
all of the control systems was that they remain stable during all phases of operation.
The performance of the vision control system was more critical than that of either
other control mode. The vision control system was required to maintain a steady-state error of
65 pixels or less on joint 0 and 47 pixels or less for joint 1. Maximum phase angles are also
presented in this chapter. These phase angles were used later in defining and tuning the vision
controller. Also, requirements were specified for the amplitude ratio for the vision control
system. Because the worst of the two cases was not distinguishable, both cases were passed on
to the controller design and tuning phase.
Table 7.3. Summary of performance criteria for the velocity, position, and vision control
algorithms.
Static
Dynamic
Max. Allowable
Steadv-State Error
Max. Allowable
Overshoot
Joint 0
Velocity Control
40%
45%
Position Control
±0.7 degree (±25 bits)
15%
Vision Control
65 pixels
see Figure 7.7
Joint 1
Velocity Control
40%
45%
Position Control
±1.1 degrees (±12 bits)
15%
Vision Control
47 pixels
see Figure 7.7
Joint 2
Velocity Control
10%
25%
Position Control
±3 cm (±33 bits)
15%

CHAPTER 8
CONTROLLER SELECTION AND IMPLEMENTATION
Controller Selection
Motion of the robot was generated by the actuators based on velocity, position, and
vision information. For each of the systems, the most important aspect was that the controller
keep the system stable for all operations. The accuracy of each of the controllers was governed
by the steady-state errors as specified by the performance criteria. Although not specified as
values, the desire was that the response time of each joint be as fast as possible. Thus, a
maximum bandwidth was requested for each control procedure. Also, these controller systems
were to be designed with minimum reaction to disturbances such as noise, drift, and external
loads.
In the case of the citrus-picking robot, the manipulator was constructed before the
controllers were considered. The control problem involved designing controllers for a system
which could not easily be altered to gain optimum performance. Thus, the performance was
limited by the manipulator rather than the controller.
Approximations of the joint open-loop transfer functions were established in Chapter 6.
The open-loop velocity transfer functions for all joints were approximated as second-order
systems as demonstrated by
Gv(s) =
2
Kvcoh
2 2
s +28hcohs + (Oh
(8-1)
Open-loop position and vision dynamics were approximated as second-order systems with
integrators with the following form:
90

91
2
Gp(s) =
s
>h(ÚhS + coh
2
(8-2)
Note that the vision control modes were actually position control with feedback of the position
of the fruit rather than the position of the robot joint. Representative open-loop Bode
diagrams for these uncompensated systems are shown in Figures 8.1 and 8.2.
The selection of a controllers for each of these systems involves choosing a controller
which will meet the previously specified performance criteria while maintaining an adequate
stability margin. If the resonant peak in the plot of the quadratic rises above unity gain, then
the system becomes unstable. This occurrence is comparable to the critical point encirclement on
the Nyquist plot. Therefore, a controller was desired that would guarantee that the resonant
peak of the Bode diagram would never rise above the unity gain. The selection of a controller
that would place the peak far below unity would cause an increase in the stability margin.
However, this guideline would also cause a decrease in the system response rate. For the
fastest system response rate, the compensator was also required to keep the resonant peak from
log scale
lGv(ja>)
Kv
1
1
-2 slope
log scale
(0
rad/sec
Figure 8.1. Bode diagram of the open-loop velocity control system.

92
Figure 8.2. Bode diagram of the open-loop position control system.
dropping far below unity. An increase in low-frequency gain of the system would decrease
steady-state error, improve control accuracy in the low frequency range, and increase steady-
state and low-frequency closed-loop stiffness. Therefore, the controllers were required to give
an increase in the low-frequency system gain while providing the ability to adjust the gain of
the resonant peak for guaranteed stability and maximum system response rate.
Two methods were considered best for increasing the low-frequency gain: introduction of
lag compensation in the loop and addition of velocity feedback in a minor loop (Merritt, 1967).
The properties of a lag compensator alone would allow a definite increase in the low-frequency
response of the joint, but it would also result in an undesirable decrease in the higher frequency
response time. Therefore, a lead compensator was needed to counteract the effects of the lag
compensator at higher frequencies. The lead compensator would also increase the system
bandwidth and response speed and reduce the overshoot. All of these results were desired of
the controllers for the manipulator. Therefore, lag-lead compensators were selected for each

control mode (velocity, position, and vision) for accomplishing the desired response of each
joint. These lag-lead compensators had the form
93
where
Hp (s) =
KcfcdS+l)
XiS +1
(8-3)
s = Laplace operator (sec-1)
Kc
= controller gain,
units:
joints 0 and 1:
velocity control:
position control:
vision control:
joint 2:
velocity control:
position control:
(D/A Word)/(deg/sec)
(D/A Word)/(deg)
(D/A Word)/(pixel)
(D/A Word)/(cm/sec)
(cm/sec)/(cm)
td = time constant of the lead controller (sec), and
Xi = time constant of the lag controller (sec).
In response to the high static friction (stiction) of the slider bearing, a minor velocity
loop was added to the position control loop of joint 2 to increase the major loop stiffness
(Merritt, 1967). The advantage of the velocity minor loop was the ability to increase the gain
in the minor loop to reduce the errors due to drift and load friction. Also noted by Merritt was
the fact that the inclusion of a minor loop would cause a decrease of bandwidth in the major
loop. The minor velocity control loop involved the inclusion of the velocity control feedback
loop between the position controller and the robot joint. Thus, the output from the position
controller for joint 2 would be the input to the velocity controller which calculated the valve
control signal for joint 2.
Control System Discretization
Implementation of the lag-lead controller in the software environment required that
the controller be converted to the discrete form. The discretized version of the controllers was
accomplished by approximating the Laplace variable of the continuous domain function by
Tustin's bilinear transformation. According to Tustin's rule (Franklin and Powell, 1980),

94
where
2 z-1
s=
T z + 1
s = Laplace operator (sec1),
z = z-transform operator, and
T s sample period (sec).
Thus, the discretized compensator was converted to
(8-4)
H(z) =
^+kcUK<-2K^
*Ii+l z-lIUl
T / T
(8-5)
And, the difference equation for implementation of the digitized compensator was
u„ =
2tj
-1
2x<
+ 1
un-i +
2Kcxd
+ K.
2xj
+ 1
6n "*â–  ; r 6n.|
2xj
+ 1
T / \ T / \T
where un ancj un_: s output control signal at time t and t-1, respectively, and
en and en_i = error signal calculated for time t and t-1, respectively.
For implementation, equation 8-6 was simplified as
(8-6)
Un = B1 un-! + Al en + A2 en.!
(8-7)
where
B1 =
2Xj
-1
2xi
+ 1
(8-8)
A1 =
2Xj
+ 1
, and
(8-9)

95
2Kcxd
A2 =
(8-10)
were the coefficients of the difference equation.
A simulation of both the continuous and discrete versions of the lag-lead compensator
was conducted for verification of the discretization and for selection of a sampling time that
would best duplicate the performance of the continuous compensator. Initially, the continuous
controller response to a step input was determined via inverse Laplace transformation. In the
continuous time domain, the lag-lead controllers were functions of the system gain, IQ, the lag
and lead time constants, x¡ and xd, and time, t, as in
(8-11)
The discrete difference equation (equation 8-7) was programmed for a simulated response to a
unit step input. A comparison was conducted for various values of IQ, and xd. Since vision
data was updated at 60 HZ, a discrete sampling time of 0.01667 sec (1/60 sec) was initially
chosen. Typical responses of the controllers along with the differences between the signals are
presented in Figure 8.3. For this presentation, the controller parameter values for the joint 0
position and vision controllers were used. Thus, these simulations were repeated for the final,
tuned controller parameters after the tuning process was complete. These plots indicated that
the discrete version of the lag-lead controller had a maximum error of 22 percent which
decreased to less than 0.6 percent in less than 0.08 sec or 5 sampling periods. These response
curves were used to verify that the discrete version of the lag-lead controller did adequately
imitate the performance of the continuous-time controller and that the theory of the continuous
domain controller could be used in tuning the discrete controller.
After the discretized version of the lag-lead compensator was verified, a section was
added to the software environment to aid in tuning the discrete lag-lead compensator. This
section calculated the coefficients of the difference equations from the analog parameters Xi, xd,

% Error DiscreteSystem Output Continuous System Output
96
Figure 8.3. Simulated responses of continuous-time and discrete domain controllers and the
percent error differences.
IQ = -15.00, xd = 3.7, and Xj = 1.0 IQ = 4.00, xd = 0.02, and Xi = 0.01
(a) continuous-time domain controller (d) continuous-time domain controller
(b) discrete controller (e) discrete controller
(c) percent error (f) percent error

97
and Kc as in equations 8-8,8-9, and 8-10. This addition allowed an operator to tune the discrete
compensators as if they were in the continuous domain that they emulated. The calculations
were a part of a subroutine (Figure 8.4) which was called only during startup or when the
parameters were changed.
Controller Implementation
Velocity Controllers
The velocity controlled system for each joint of the manipulator was represented by the
block diagram of Figure 8.5. Input to each system was a desired velocity in the form of a
velocity set point. These velocity setpoints were set in the intelligence base for the robot for
the various applications of the velocity controllers. When the intelligence base requested
velocity control, it also specified the desired velocity. The velocity set point was compared
with a maximum allowable velocity for each direction of travel (v#max and v#min) and
limited if necessary. The desired velocity was compared with the actual velocity of the joint
by calculation of the difference or error signal. This error signal was then used by the controller
for calculation of the valve control word. From the current and previous error signals and the
previous control word, a new valve control word was calculated by use of equation 8-7. The
valve control words were converted to an analog voltage by D/A convertors. This voltage was
coeff(kp,ti,td)
double kp,ti,td
r
{ if ((ti =
0.0) || (td == 0.0))
/* Allow direct setting
*/
{
al = kp;
/* of al coefficients
*/
a2 = 0.0;
/* from kp,ti,td
*/
bl = 0.0;
/* Mainly for axis 2
*/
}
/* and safety in SET:C
*/
else
{
al = (2.0*kp*td/TIME
+ kp)/(2.0*ti/TIME + 1.0);
a2 = (kp - 2.0*kp*td/TIME)/(2.0*ti/TIME + 1.0);
}
bl = (2.0*ti/TIME - 1
.0)/(2.0*ti/TIME + 1.0);
}
Figure 8.4. Subroutine to calculate coefficients of the discretized controller from the continuous
domain parameters.

98
sent to the servo amplifiers for conversion to a current which drove the servo valves. The
velocity of each joint was determined by a tachometer connected to the joint. The output
voltage from the tachometer was quantified by an A/D convertor to a digital velocity value.
This velocity value was the feedback value for comparison with the desired velocity.
The program code for the velocity controllers as implemented in the software
environment is presented in Figure 8.6, for all three joints. These controllers were designed as
subroutines and called by the supervisor program at a 60 HZ rate. Variables used in these
subroutines are described in Table 8.1.
Valve
Velocity Control
Error Signal
Velocity a
Setpoint
Velocity Controller
Robot Axis
Kc ( Td s + 1)
/
IW
Tach
Velocity
Ti S + 1
S2 + 2 Sh ©b S + (0j2
Velocity
\
Figure 8.5. Block diagram of the velocity control loop.
/********************* AXIS 0 VELOCITY CONTROL CODE ***********/
vOctl()
{ static double vOcwd = 0.0;
if(vOsp > vOmax) vOsp = vOmax;
else if(vOsp < vOmin) vOsp = vOmin;
vOerl = vOer; /* Save previous error */
vOer = vOsp - vO; /* Calculate error */
/* LAG-LEAD COMPENSATOR */
vOcwd = vObl * vOcwd + vOal * (double)vOer + v0a2 * (double)vOerl;
vOcw = (int)vOcwd;
}
/★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★★■sir** i
Figure 8.6. Implementation of the Lag-Lead velocity controllers as found in the software
environment. Note: change 0's in the variables to l's or 2's for joint 1 or 2.

99
Table 8.1. Velocity control variables as used for the velocity controllers as shown in Figure
8.6.
Joint Variab
es
TointO
Tointl
Toint2
vOcwd
vlcwd
v2cwd
vOsp
vlsp
v2sp
vOmax
vlmax
v2max
vOmin
vlmin
v2min
vOerl
vlerl
v2erl
vOer
vler
v2er
vO
vl
v2
vObl
vlbl
v2bl
vOal
vial
v2al
v0a2
vla2
v2a2
vOcw
view
v2cw
Description
valve control signal
velocity set point
maximum velocity allowed
minimum velocity allowed
previous velocity error value
current velocity error value
current velocity value
coefficient from equation 8-8
coefficient from equation 8-9
coefficient from equation 8-10
integer value of valve control signal
Position Controllers
Position control of joints 0 and 1 of the orange-picking robot was accomplished in much
the same manner as velocity control. A block diagram of a typical position control loop for
joints 0 and 1 is shown in Figure 8.9. In this loop, a desired position was specified as the
position setpoint. Again, the position setpoints were determined by the intelligence base when
the intelligence base requested the position control for the joint. The position setpoint was
compared with the maximum and the minimum positions for the joint and limited to this range
if necessary. The position error was then calculated as the difference between the setpoint and
the actual position of the joint. This position error calculation was accomplished in a
subroutine called ERRORCAL:C as shown in Figure 8.10. The position of the joint was sensed by
a potentiometer and quantified by an A/D convertor. The position value was fedback as the
present position value to close the loop. This position error was then available for use by the
position controller.
In the C source position control subroutines (Figures 8.11 and 8.12), the previous control
signal value and the present and previous position errors were used to calculate a new valve
control signal according to equation 8-7. Definitions of the variables used in Figures 8.10,8.11,
and 8.12 are presented in Table 8.2. Output from the controller was a valve control signal which

100
Position
Error
Valve
Control
Signal
Figure 8.9. Block diagram of the position control feedback loop for joints 0 and 1.
©EX027S ***■*’'*’* * * ★★★★★★★★★ ★ ★ ★ j
if(pOsp > pOmax)
pOsp = pOmax;
else if(pOsp < pOmin)
pOerl = pOer;
pOer = pOsp - pO;
pOsp = pOmin;
if(plsp > plmax)
plsp = plmax;
else if (plsp < plmin)
plerl = pier;
pier = plsp - pi;
plsp = plmin;
Figure 8.10. Position error calculation for joints 0 and 1 from ERRORCAL:C subroutine.
pOctl() /************* axIS 0 POSITION CONTROL CODE *******/
{ static double vOcwd = 0.0;
/** LEAD - LAG CONTROLLER **/
vOcwd = pObl * vOcwd + pOal * (double)pOer + p0a2 * (double)p0erl;
vOcw = (int)vOcwd;
Figure 8.11. Position control subroutine for joint 0.
plctl() /************* AXIS 1 POSITION CONTROL CODE *******/
{ static double vlcwd = 0.0;
/** LEAD - LAG CONTROLLER **/
vlcwd = plbl * vlcwd + pial * (double)pier + pla2 * (double)plerl;
view = (int)vlcwd;
Figure 8.12. Position control subroutine for joint 1.

101
Table 8.2. Position control variables as used in Figures 8.10,8.11 and 8.12.
Joint Variables
Joint 0
Tointl
Description
vOcwd
vlcwd
valve control signal
pOsp
plsp
position set point
pOmax
plmax
maximum position allowed
pOmin
plmin
minimum position allowed
pOerl
plerl
previous position error value
pOer
pier
current position error value
pO
Pi
current position value
pObl
plbl
coefficient from equation 8-8
pOal
pial
coefficient from equation 8-9
p0a2
pla2
coefficient from equation 8-10
vOcw
view
integer value of valve control signal
was sent to the D/A converter which output a voltage to the servo amplifier based on the
integer value of the valve control signal.
Position Controller with Velocity Control Minor Loop
Static friction was previously determined to be the cause of the sparatic behavior of
the robot's sliding joint. Implementation of a single lag-lead position controller did not provide
adequate stiffness or gain to overcome the stiction problem. To overcome this obstacle, the
position controller for joint 2 included velocity feedback in a minor loop (Merritt, 1967). Merritt
warns that these minor loops sometimes limit the response capabilities of the major loop and
should be used only when some clear-cut objective is being accomplished. One of the
disadvantages of using minor velocity loops is a decrease in the bandwidth of the major loop.
Sluggish system responses usually result from decreases in the system bandwidth. On the other
hand, this type of compensation allows a large gain which in turn reduces errors due to drift and
load friction. A block diagram of this controller is shown in Figure 8.13. In this case, rather
than having the position controller output a valve control signal, its output was a velocity
setpoint. This velocity set point was passed into the velocity controller for calculation of the
valve control signal.
The position control algorithm for joint 2 was accomplished as three steps in the
software environment. First, in the ERRORCALrC routine (Figure 8.14), the desired position

102
setpoint was tested for its indusion within the allowable range for joint 2. Following this
check, the position error was calculated as the difference between the position setpoint and the
actual position of the joint. The position controller for joint 2 was then called as a subroutine as
indicated in Figure 8.15. In this subroutine, a lag-lead controller (equation 8-7) was used to
calculate a velocity setpoint which was used by the minor velodty control loop. This velocity
setpoint was used as the input setpoint to the velodty control subroutine as depicted in Figure
8.8. The valve control signal was output from the velocity controller to the servo amplifier by
way of the D/A converter. The position of the sliding joint was sensed by a potentiometer
while the velocity was sensed by a tachometer. Both of these values were fedback to the
control computer through separate channels of the A/D converter, Variables for the major loop
controller are presented in Table 8.3.
Figure 8.13. Block diagram of the position control feedback loop with velocity feedback in a
minor loop.
Position OE'iro^s *****★★★★★★★ ★ ★ ★★ ★★ j
if(p2sp > p2max)
p2sp = p2max;
else if(p2sp < p2min)
p2sp = p2min;
p2erl = p2er;
p2er = p2sp - p2;
Figure 8.14. Position error calculation for joint 2 as accomplished in the ERRORCAL:C routine.

103
p2ctl() /************* AXIS 2 POSITION CONTROL CODE *******/
{ static double v2spd = 0.0;
/** LEAD - LAG CONTROLLER **/
v2spd = p2bl * v2spd + p2al * (double)p2er + p2a2 * (double)p2erl;
v2sp = (int)v2spd;
Figure 8.15. Major loop position control subroutine for joint 2.
Table 8.3. Position control variables as used in Figures 8.14 and 8.15.
Joint 0
Variables
Description
v2spd
velocity set point
p2sp
position set point
p2max
maximum position allowed
p2min
minimum position allowed
p2erl
previous position error value
p2er
current position error value
P2
current position value
p2bl
coefficient from equation 8-8
p2al
coefficient from equation 8-9
p2a2
coefficient from equation 8-10
v2sp
integer value of velocity set point
Vision Controllers
Control of the manipulator based on the information from the robot vision system was
similar to the position control method. However, for the vision controller, the input to the
controller was the position of the centroid of a targeted fruit in the image plane of the CCD
camera rather than the position of the joint. The output from the controller was a servo valve
control signal (D/A word). Therefore, a feedback loop was created as shown in the block
diagram (Figure 8.16). In this feedback loop, the vision block was essentially a position
measurement device with a variable gain. The vision system determined the position of the
targeted fruit in the image and the gain was a function of the position of the sliding joint. The
vision system did not contain any dynamic attributes which affected the system.

104
Valve
Actual Fruit
Vision
Error
Control
Signal
Position in
Canopy
Fruit
Centroid
Setpoint
Vision Controller
Robot Axis
Kc(xds +1)
/
j—
TjS + 1
s (s2 + 2 8h (O,, s + (Oh2)
+
o-
Robot
Vision
System
\
Fruit Position
relative to robot
Figure 8.16. Block diagram of a vision control loop.
As previously derived in the kinematics chapter, the vision gains were a function of the
position of the sliding joint and the location of the targeted fruit. These gains were expressed
as
Kvx=f
and
(8-12)
K^=f S2|^+l
(8-13)
These equations gave important information for controlling the velocity of the end-effector
with information from the vision system. These relationships indicated that as the end-
effector was extended toward a fruit W3 increased and z decreased) equal changes of the fruit's
position resulted in larger and larger position changes of the fruit's image in the image plane.
As the end-effector approached the fruit, these changes increased exponentially to infinity.
Therefore, as the fruit was approached by the end-effector, the valve control signals needed to
be scaled down based on the distance from the end-effector to the fruit. Because the motion of
joint 1 was limited to be between 71 and 109 degrees, sin(©2), was confined to a range between
0.95 and 1.0. Because its effect on the scale factor was so small, this component was ignored.
Thus, one scale factor was calculated and used for reducing both valve control signals
proportionate to the distance from the end-effector to the fruit.
A relationship for the scale factor was calculated so that the value would be
maximized when the tube was retracted, decreasing linearly to the minimum value of 0.351

105
(vilk) (Figure 8.17). The minimum scale value was also used when the ultrasonic sensor
detected that the fruit was "close" to the picking mechanism. Thus, at the instant the
ultrasonic sensor detected that the fruit was with in picking range, the scale value was reduced
to its minimum value.
Equation 8-7 was used to actuate the lag-lead controllers for joints 0 and 1 based on the
vision error information. Both valve control signals were scaled by the previously determined
value and sent to the respective D/A convertors. Motion in joints 0 and 1 resulted in a change in
the position of the fruit's image in the camera image plane. The vision control feedback loop
was repeated beginning with the calculation of the error or the difference between the location
of the fruit image's centroid and the setpoints to complete the loop.
The vision control routine was called by the supervising program only after a fruit had
been located in the image during the search routine. The position of the center of a targeted
fruit's image (centroid) was determined in the robot vision system. Preset fruit centroid
setpoints indicated the position of this centroid when the fruit was located at its optimum
p2max = 3400
d3 = 889 mm
Retracted
p2 = 2648 p2min = 2600
d3 = 1541 mm d3 = 1583 mm
Extended
Position of Joint 2
Figure 8.17. Vision gain implementation scheme.

106
position for removal from the tree. These setpoints were determined as previously described in
the picking envelope section. In the ERRORCAL:C routine (Figure 8.18), the differences
between setpoint values and the actual position of the fruit's centroid in the camera image
plane (ycent for joint 0 and xcent for joint 1) were calculated. These error values were then used
by the vision control algorithm for determining the servo valve control signals. The routine
from the control computer is shown in Figure 8.19 with descriptions for all of the variables in
Table 8.4.
vision oiTuroirs *'*'*,'*,‘*,,*,*‘*,'*,,*,'*,*"*,,*,*'?ink,*,*,,*,TAr* f
viOerl = viOer;
viOer = viOsp - (int) ycent;
vilerl = viler;
viler = vilsp - (int) xcent;
l'k'kmk'k'k’kmkmkmkmkmkwkis-kmkmk'k-k’k'k-kmkmkmk'kmk-kmk-k-k-kmk’k'kmk-k-k-k'k-kiz‘k-k-k-kmk'k'k'k'k’k’k'kmkmk'k j
Figure 8.18. Vision error calculations as performed in ERRORCAL:C routine.
victl()
{ enum STATE dummyst;
double scale,view;
static double vOcwd = 0.0;
static double vlcwd = 0.0;
dummyst = ostate; /* for safety reasons */
scale = (double)p2 * viOk - 1.934;
if(scale < vilk) scale = vilk;
if((dummyst = vi_touch) || (dummyst = occluded)) scale = vilk;
vOcwd = vi0bl*v0cwd + viOal*(double)viOer + vi0a2*(double)viOerl;
view = vOcwd * scale;
vOcw = (int)view;
vlcwd = vilbl*vlcwd + vilal*(double)viler + vila2*(double)vilerl;
view = vlcwd * scale;
view = (int)view;
Figure 8.19. Vision control subroutine.

107
Table 8.4. Vision control variables as used in Figures 8.17 and 8.18.
Joint Variables
Toint 0
Toint 1
Both
Description
viOerl
vilerl
previous vision error value
viOer
viler
current vision error value
viOsp
vilsp
vision set point
ycent
xcent
location of fruit centroid in the image
dummyst
temporary state storage variable
ostate
state which called vision control
scale
valve control scale factor
P2
current joint 2 position value
viOk
scale calculation factor
vilk
minimum scale value
vi_touch
vision touch state
occluded
occluded state
vOcwd
vlcwd
view
valve control signal
viObl
vilbl
coefficient from equation 8-8
viOal
vilal
coefficient from equation 8-9
vi0a2
vila2
coefficient from equation 8-10
vOcw
view
integer value of valve control signal
Controller Tuning
After implementation of each of the control schemes, values of the lag-lead controller
parameters for each joint were needed. These values were determined from the knowledge of
the systems being controlled. As previously mentioned, one distinguishing characteristic of a
stable system was that the resonant peak which was located at the hydraulic natural
frequency would remain less than unity. Also noted was the point that the steady-state error
could be decreased by an increased gain value for the lower frequencies. Likewise, faster system
response and reduced overshoot were desired and achievable by higher values of the
bandwidth or crossover frequency. A knowledge of these principles was used during the tuning
phase of the control system implementation. In the design of the compensators according to the
frequency-response method, Bode diagrams were useful for placing the lag and lead values (t¡
and Td, respectively). The time constants of the controller, and xd, were adjusted to change the
frequencies at which the controller effected the system frequency response (see Figures 8.20 and
8.21). Note that the break points of the frequency-response curve occurred at the reciprocal
value of the respective time constant. For instance, a value of 2.0 sec would decrease the

108
Figure 8.20. Bode diagram of a controlled second-order system indicating the effects changes in
the lag time constant, Tí .
Figure 8.21. Bode diagram of a controlled second-order system indicating the effects changes in
the lead time constant,
system frequency response at a rate of 20 db per decade (10 fold increase in the input frequency)
for frequencies greater than 1/xi or 0.5 rad/sec. Similarly, the lead time constant, would
cause a increase in the system frequency response of 20 db per decade, effecting frequencies

109
greater than l/xd rad/sec. The value of xd effected the frequency response of the system as
indicated in Figure 8.21. The gain, IQ, was used to raise or lower the entire diagram as in Figure
8.22.
Merritt (1967) pointed out some general criteria that are applicable to any "good" servo
system design. He stated that a range of frequencies with a loop gain greater than unity is a
mandatory requirement for any closed-loop system and gain values greater than 5 are usually
required. This requirement is amplified by the accuracy requirements placed on the system.
Also, the open-loop Bode diagram should have an asymptotic slope of -1 or -20 db per decade at
the crossover frequency to insure satisfactory stability. The system bandwidth is always
limited by the requirement that the system not react to high frequency noise and by the
stability requirements.
Figure 8.22. Bode diagram of a controlled second-order system indicating the effects changes in
the controller gain, Kc.

110
Tuning of the implemented motion controllers for the citrus-picking robot utilized these
concepts of altering the frequency-response curves and these criteria of a good servo design. For
each category of controller, the following steps were taken to tune the controllers:
1) A frequency-response plot for the open-loop system as specified by the open-loop
dynamic model was plotted for the appropriate system.
2) The lag and lead time constants were chosen to ensure the desired slope at the crossover
frequency.
3) The controller gain was chosen to give the system the highest response possible in the
low frequency range without causing the system to be unstable. For stability, the
resonant peak which occurred at the system natural frequency was kept less than unity.
4) The calculated values of the controller parameters were implemented.
5) The implemented controllers were tested in the closed-loop system.
6) The controller parameters were adjusted to provide the best achievable performance of
the system.
Velocity Controller Tuning
According to the stability criteria, the uncompensated velocity control loop as shown in
Figure 8.1 was unstable due to the fact that the peak was above unity. Therefore, the first
objective of the velocity compensator for each joint was that of lowering the resonant peak to a
value less than unity. Initial choices of the lag or integrating factor, 1/t¡, placed the break
frequency much less than the experimentally determined hydraulic natural frequency (Figure
8.23). The lead factor, l/xd, was then placed between the crossover frequency and the peak to
cancel the effects of the lag factor and cause the peak to be stabilized. Then, the controller
gain, Kc, was set to raise the entire curve so that the resonant peak would be just below the unity
line.
By using the worst determined cases of the open-loop transfer function for each joint as a
basis, initial choices of the factors resulted in stable systems that could be tuned on line as
suggested by Palm (1983). The joint was actuated and its reaction was observed. This tuning

Ill
Figure 8.23. Generalized open-loop Bode diagram of a lag-lead compensated velocity control
system.
process was completed by increasing the lag factor allowing the gain, Kc, and the bandwidth of
the compensator to be increased. Thus, the low-frequency gain of the system was increased for
minimized steady-state error and the bandwidth was increased for maximum response speed
and lowered overshoot values.
The worst case for controlling the velocity system for joint 0 occurred when the actuator
was fully retracted and moving in the upward direction (Kv = 0.039 (deg/sec)/(D/ A word), coh =
21.4 rad/sec, and 8 = 0.21). This case was considered worst because the resonant peak elevated
higher above the unity magnitude than any of the other trials. Therefore, this case would
limit the maximum value for the controller's gain and establish a conservative lag factor.
Initial choices of the controller's parameters placed the lag factor at 1 rad/sec (Xj = 1.0 sec) to
lower the resonant peak. The lead factor was set at 100 rad/sec (x eliminating its effect on the system. A very conservative controller gain, Kc, of 3.0 (D/A
word)/(deg/sec) was chosen to decrease the steady-state error without causing instability.

112
From these points, the lag and lead factors and the controller gain were adjusted to give the
maximum possible low-frequency gain with the highest possible bandwidth while retaining
stability. Final values for the parameters of the controller are presented in Table 8.5.
For joint 1, the worst case occurred when the following system parameters were
determined: Kv = 0.056 (deg/sec)/(D/A word), C0h = 31.8 rad/sec, and 8 = 0.18. Again, this
system possessed the highest peak at the hydraulic natural frequency. The controller for this
system was also initialized with the lag factor at x¡ = 1.0 sec and the lead factor as zd = 0.01 sec.
The gain, IQ, for the controller was set to 2.0 (D/A word)/(deg/sec). Similar to the controller
for joint 0, the parameters of this controller were tuned on line to achieve the best possible
controller for joint motion in both directions and any position of joints 0 and 2. Again, the final
parameters are presented in Table 8.5.
The process for determining values for the parameters of the velocity controller for joint
2 proved to be much more difficult due to the lack of a well defined open-loop transfer function.
However, Merritt's (1967) discussion of hydraulic control systems gave information that the
system could be modeled as an ill-behaved second-order system. Initial values of the controller
were established: IQ = 1.0 (D/A word)/(cm/sec), = 1.0 sec, and xd = 0.01 sec. During
implementation, however, these values did not produce a stable system. The gain and lead
factor were held constant while the value of x¡ was increased, dropping the resonant peak well
below unity. A stable system was finally achieved, and the tuning process was continued until a
suitable controller for joint 2 was in operation. The final parameters for the lag-lead velocity
controllers are presented in Table 8.5.
Table 8.5. Final velocity controller parameters for joints 0,1, and 2.
Joint
Kr
*1
(sec)
td
(sec)
0
2.50 (D/A word)/(deg/sec)
0.50
0.05
1
6.00 (D/A word)/(deg/sec)
2.00
0.01
2
10.00 (D/A word)/(cm/sec)
20.00
0.10

113
Position Controller Tuning
Unlike the velocity control loop, the position control loop was normally stable in its
uncompensated form, unless, however, the plant gain was very large. As shown in Figure 8.2,
the resonant peak of the position loop Bode diagram was below unity before any compensation
was added. Therefore, the addition of the lag-lead compensator provided the ability to
increase the low-frequency gain of the system without changing the position of the peak. In
Figure 8.24, the dashed line represented an uncompensated system while the solid plot
depicted a compensated system with increased low-frequency gain and unaffected resonant
peak. Based on the relationships of this plot, the lag and lead factors, 1/Xj and l/xd, of the
position controllers were tuned.
First, both factors were placed one decade apart with a small controller gain. As the
position controller was used to actuate the joint, the reaction was observed. The controller gain,
Kc, was increased until the system reached instability indicating that the peak was at or above
unity. Then, Xj and xd were increased lowering the frequency at which they effected the system
and causing the peak to drop below unity while keeping the high controller gain. The interval
between 1/Xj and l/xd was varied to decrease the overshoot and steady-state error while
increasing the stiffness of the controlled system. This process was completed for both joints 0
and 1 to create an overall system with the best possible characteristics.
Since the highest resonant peak in the open-loop uncompensated plot for joint 0 existed
when the system parameters were Kp = 0.032 deg/(D/A word), o>h = 17.4 rad/sec, and 8 = 0.18,
this experimentally determined transfer function was used for initial placement of the
controller parameters. Initial controller parameters were located at IQ = 15 (D/A word)/deg, x¡
= 1.0 sec, and xd = 0.1 sec. These values produced an overall system with good response speed but
only marginal stability. The position of the lag factor was decreased to cause the resonant
peak to be lowered, and the response of the system was again observed. This process was
continued with small adjustments to each of the parameters until a completely stable system
with small steady-state error, high stiffness, and fast response was established. During this

114
Figure 8.24. Bode diagram of an open-loop compensated position control system.
tuning process, the position of joint 2 was varied so that the resulting controller would retain
the system's stability through any motion of the sliding joint. The final values for the position
controller parameters are shown in Table 8.6.
Table 8.6. Final position controller parameters for joints 0 and 1.
Kc
*1
Joint
(D/A word)/deg
(sec)
(sec)
0
15.0
3.7
1.5
1
15.0
3.7
1.0

115
The position controller for joint 1 was tuned in a similar manner. For joint 1, the highest
resonant peak was found in the experimentally determined system with parameters Kp = 0.056
deg/(D/A word), toj, = 21.7 rad/sec, and 8 = 0.26. After tuning the position controller for joint 0
and noticing that the diagram for joint 1 was similar, the values for the joint 1 controller were
initialized to Kc = 10 (D/A word)/deg, ti = 3.0 sec, and td = 0.3 sec. For these values, the system
was stable, but the response was less than desired. The tuning process was completed as
previously described resulting in a controller that minimized the steady-state error and
possessed adequate response. The joint 1 position controller parameters are also presented in
Table 8.6.
Position Controller with a Velocity Control Minor Loop Tuning
A position controller with a minor velocity loop was implemented for controlling the
position of the sliding joint. Merritt (1967) points out that the system with the velocity minor
loop can be approximated as a system with a lag at the corrected crossover frequency and a
quadratic at the hydraulic natural frequency. The response of this system would thus be
limited by the crossover frequency rather than the hydraulic natural frequency. This new
system was similar to the uncompensated position systems previously discussed and could be
tuned accordingly.
After tuning a stable velocity loop, the main objective in tuning the outer loop was to
increase the gain to overcome the friction of the sliding joint. Initial choices for the parameters
of the major position loop controller were a high gain and lag and lead factors that would
cancel at a frequency lower than the new crossover frequency. The initial estimates were K,. =
30.0 (cm/sec)/cm, tt = 15.0 sec, and xd = 1.0 sec. As the tuning process progressed, the
improvements in the system response resulted when the values for and xd of the position loop
were moved closer together. Continued observance of the reaction of joint 2 to this controller
indicated that the lag-lead controller of the major loop could be replaced with a proportional
controller. Therefore, the lag and lead function was omitted, leaving a simple proportional
controller. Using the proportional controller, the gain of the major loop was increased to

116
provide acceptable response of the joint while minimizing the effects of stiction between the
sliding tube and its support bushing. The final value of the controller gain, of 20.0
(cm/sec)/cm was used.
Vision Controller Tuning
The open-loop transfer functions for the vision control loops were similar to the position
control loops as shown in Figure 8.2. However, the control objectives for the vision controllers
were much different. In the case of the vision controllers, the response of the system to a
frequency disturbance was much more important because the vision system would be required to
follow the sinusoidal motion of a fruit swinging from the tree. Thus, the desired performance of
the vision control scheme was based on the motion of the fruit as covered in the previous
chapter.
As presented in equations 7-1 and 7-2, rather than being calculated as the difference
between the actual and desired positions of the joint, the error for the vision controllers would
be the error as the robot tracked a fruit in motion. These equations were used to determine
desired amplitude ratios of the system for two critical cases: AR = 0.96 for cofruit = 3.1 rad/sec
(0.5 HZ) and AR = 0.83 for cofruit = 6.9 rad/sec (1.1 HZ). These amplitude ratios were a function
of the loop gain of the entire system, KL, as
1 +Kl (8-12)
where the loop gain was the produce of the open-loop system gain, Kp, and the controller gain,
Kc, (Kl = Kp * Kc). Equation 8-12 was solved for the open-loop system gain:
Kl=
AR
1 - AR
(8-13)
Thus, a normalized open-loop system gain of 24 was desired for Case I at 3.1 rad/sec to give an
amplitude ratio of 0.96. And, a normalized loop gain of 4.9 was calculated as the desired value
for Case II at 6.9 rad/sec. While striving to meet these requirements of the system gain, the
requirements placed on the phase angles were also a consideration in tuning the vision

117
compensators. These constraints were a maximum phase lag of 2.5 degrees at 3.1 rad/sec or 10
degrees at 6.9 rad/sec. Because the experimentally determined natural frequency for joint 0 was
slower than joint 1, design of a stable compensator for joint 0 would almost certainly provide a
stable compensator for joint 1. Also, the lack of ability to meet the requirements by joint 0 would
also indicate that the same shortcoming would carry over to joint 1.
Observations of the Bode plots for the vision plant of joint 0 (Figure 8.25) indicated
that these requirements could not be met. An increase in the gain of the overall system would
have caused the position of the peak to rise above unity, causing the system to be unstable.
Since a slope of -1 was also desired at the crossover frequency, the addition of the lag factor at
a frequency less than the crossover frequency would have to be countered by placing the lead
breakpoint less than the crossover frequency. Even with an increased gain of the system to move
the peak to a value near unity, the required open-loop system gains as specified could not be
met. Therefore, the fact was recognized that some motions of the fruit would create an
impossible picking situation for the robot.
Figure 8.25. Open-loop Bode diagram for joint 0 vision system indicating the gain requirements
for picking worst case fruit motions.

118
With the understanding that the desired performance of the robot could not be met, the
vision controllers were tuned on line to achieve the best possible results. The concentration was
initially placed on tuning the controllers to be able to approach non-moving fruit positioning
the end-effector within reach of the targeted fruit. The controllers were adjusted for tracking
fruit with small motions. This process of tuning the vision controllers continued until acceptable
performance was achieved while picking fruit as a continuous operation in an orange grove.
Adjustments to the controller parameters led to controller gains of 4.0 (D/A word)/pixel and lag
and lead factors of 0.02 sec and 0.01 sec, respectively, as indicated in Table 8.7.
Table 8.7. Final vision controller parameters for joints 0 and 1.
Kc
*1
td
Joint
(D/A word)/pixel
(sec)
(sec)
0
4.0
0.02
0.01
1
4.0
0.02
0.01
Summary
For each of the control methods, the lag-lead parameters were determined adjusting
the parameters until the best response of the system was achieved. In all cases, the parameters
were chosen to produce stable systems under all operations of the manipulator. Some sacrifices
were made in the less important areas to address more important requirements of the robot. In
the process of tuning the vision controllers, it was found that the ability to track large, fast
fruit motions was impossible for this manipulator. In this case, the criteria for large motions
could not be met, but the ability to position the end-effector within reach of a targeted fruit
with small or no motion was achieved. A summary of the values which were determined to
provide respectable control of the citrus-picking robot are presented in Table 8.8.
These parameters for the compensators were used for the robot during actual grove tests
of the robot. With the knowledge that some large fruit motions would not be pickable for this
manipulator, the intelligence base (Adsit, 1989) was altered to cause the robot to either wait
for the motion to settle or to search for another fruit. In conjunction with the intelligence base

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for the robot, these compensators provided acceptable performance for this second generation
orange-picking robot.
Table 8.8. Final determined values for all controller parameters.
Joint
Control
Scheme
Kc
(sec)
xd
(sec)
0
Position
15.00 (D/A word)/deg
3.70
1.50
1
Position
15.00 (D/A word)/deg
3.70
1.00
2
Position
20.00 (cm/sec)/cm
N/A
N/A
0
Velocity
2.50 (D/A word)/(deg/sec)
0.50
0.05
1
Velocity
6.00 (D/A word)/(deg/sec)
2.00
0.01
2
Velocity
10.00 (D/A word)/(cm/sec)
20.00
0.10
0
Vision
4.00 (D/A word)/pixel
0.02
0.01
1
Vision
4.00 (D/A word)/pixel
0.02
0.01
Note: N/A = Not Applicable

CHAPTER 9
RESULTS AND DISCUSSION
Performance requirements for the orange-picking robot were presented in chapter 7.
These requirements were specified as desired criteria upon which controllers for each joint could
be designed and tuned. The controller selection and tuning process was completed in chapter 8.
In this chapter, the final performance of each joint is presented. Initially, the performance of
each of the controllers was assessed individually, describing the ability of the controllers to
meet the performance specifications of chapter 7. Then, the combined performance of the
controllers during the picking operation was evaluated.
Velocity Controller Performance
Operation of the velocity controllers for joints 0 and 1 occurred only during the search
procedure. In this procedure, constant velocity setpoints were used to control the motion of the
end-effector. The robot's intelligence base made the decisions which were used to change the
direction of the end-effector by changing the sign of a velocity setpoint. Therefore, the most
common inputs to the velocity controllers of joints 0 and 1 during the operation of the robot were
steps in equal magnitude but opposite signs. Thus, the performance of the velocity controllers
for joints 0 and 1 was observed and quantified using inputs similar to those used during robot
operation. The velocity controller for joint 2 was used to extend the end-effector into the canopy
of the tree. Its operation was more critical in the picking operation and thus, smaller errors
were allowed.
For joint 0, velocity setpoints of ±16.3 deg/sec were used by the intelligence base during
the fruit search action. For this analysis, velocity setpoints of ±16.3 deg/sec, ±39.1 deg/sec, and
±48.8 deg/sec were used, imitating the action of the search pattern. Closed-loop step responses
of joint 0 are presented in Figures 9.1,9.2, and 9.3. In Figure 9.1, alternating input steps of ±16.3
120

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Figure 9.1. Typical closed-loop response of joint 0 to an alternating step input of ±16.3 deg/sec,
joint 2 extended.
deg/sec were used to direct the joint. In this case, the end-effector was extended, resulting in
the maximum load on joint 0. For the negative velocity value, the joint reached a steady-state
velocity of -13.0 deg/sec after achieving an overshoot of -20.0 deg/sec. For the positive
velocity value, a steady-state velocity of 11.2 deg/sec was achieved while recovering from an
overshoot of 4.0 deg/sec. Thus, for alternating step inputs of ±16.3 deg/sec, the joint
demonstrated an average steady-state error of 11.5 deg/sec (28 percent) with overshoot values
averaging 3.8 deg/sec (24 percent). The response of the system to inputs of ±39.1 deg/sec with
joint 2 centered in its support are shown in Figure 9.2. For all positions of joint 2, joint 0 settled to
average velocities of 28.5 deg/sec and -29.4 deg/sec for the positive and negative input values,
respectively. These values translated to an average steady-state error of 26 percent. The
maximum overshoot of 12.9 deg/sec (33 percent) occurred when joint 0 was excited by a -39.1
deg/sec input while the end-effector was in its extended position. Step inputs of ±48.8 deg/sec
were indicated by the plots of Figure 9.3. For these plots, joint 2 was retracted. In this case, the
joint settled to a positive velocity of 35.1 deg/sec and a negative velocity of -35.5 deg/sec
indicating errors of 28 percent. A maximum overshoot of 12.9 deg/sec occurred while joint 2 was
extended and joint 0 was excited by an input of -48.8 deg/sec. Thus, the maximum overshoot for

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Figure 9.2. Typical closed-loop response of joint 0 to an alternating step input of ±39.1 deg/sec,
joint 2 positioned at its mid location.
Figure 9.3. Typical closed-loop response of joint 0 to an alternating step input of ±48.8 deg/sec,
joint 2 retracted.
this input value was 26 percent. For joint 0 velocity control, a maximum steady-state velocity
error of 40 percent and a maximum overshoot of 45 percent were specified as the performance
requirements (see chapter 7). The closed-loop response of the system to various magnitude steps

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were well below these specified máximums. Therefore, the velocity controller for joint 0
fulfilled the specified requirements.
Velocity setpoints used for joint 1 during the search operation varied from -50 to +50
deg/sec. The action of the search routine for joint 1 was almost identical to that of joint 0 with
velocities switching between the positive and negative values of the velocity setpoint. Thus,
the performance tests simulated this action by switching the velocity setpoints between the
positive and negative values of the desired velocities. Plots which represent the closed-loop
responses of joint 1 to step inputs of different magnitudes are shown in Figures 9.4,9.5, and 9.6. In
Figure 9.4, velocity setpoints of ±32.6 deg/sec were used for achieving the joint's response to
alternating steps while joint 2 was retracted. Average positive and negative steady-state
velocities of 29.3 deg/sec and -29.4 deg/sec were observed indicating steady-state errors of 11
percent with no overshoot. Also using alternating input steps of ±32.6 deg/sec, the response of
the system was examined while joint 2 was extended from the center of its support (Figure 9.5).
In this case, overshoot values as large as 5.9 deg/sec (18 percent) were observed. Steady-state
velocities of 29.0 deg/sec (12 percent) and -29.8 deg/sec (10 percent) were attained. For
Figure 9.4.
Typical closed-loop response of joint 1 to an alternating step input of ±32.6 deg/sec,
joint 2 retracted.

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Figure 9.5. Typical closed-loop response of joint 1 to an alternating step input of ±32.6 deg/sec,
joint 2 extended.
input steps of ±48.8 deg/sec (Figure 9.6), the system responded with average steady-state
velocities of 43.6 deg/sec (11 percent) and -44.3 deg/sec (9 percent). For this case, joint 2 was
centered in its support, and no overshoot was observed. In summary, the lag-lead velocity
controller as implemented for joint 1 achieved very good results. With large input step values,
steady-state errors of no more than 12 percent and overshoot values of no more than 18 percent
were observed. These values fell well below the maximum allowable errors as specified as
performance requirements (40 percent allowable steady-state error and 45 percent allowable
overshoot).
Unlike the uses of the velocity controllers for joints 0 and 1, the velocity controller for
joint 2 was used during fruit removal. Velocity control of joint 2 was used for extending the end-
effector toward a targeted fruit. Also, the velocity error of joint 2 was used for detection of
collisions and unremovable fruit. Therefore the performance of the joint 2 velocity controller
was much more critical than that of the other two joints. Typical step response plots for joint 2
velocity controller are shown in Figures 9.7 and 9.8. The response of the system to two
individual step inputs is presented in Figure 9.7. In the first step, a velocity setpoint of

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Figure 9.6. Typical closed-loop response of joint 1 to an alternating step input of ±32.6 deg/sec,
joint 2 centered in the support.
-34.8 cm/sec was issued to the controller. The joint's response was to achieve a steady-state
velocity of -35.1 cm/sec (3 percent steady-state error) with a maximum value of -38.5 cm/sec (11
percent overshoot). The second step input of Figure 9.7 was a positive step of 34.8 cm/sec. For
the positive step, the joint settled to 33.1 cm/sec (5 percent error) after achieving a maximum
velocity of 35.7 cm/sec, corresponding to an overshoot of 3 percent. Plots shown in Figure 9.8 are
a representation of the response of joint 2 to velocity setpoints alternating between ±104.4
cm/sec. Because these step inputs were generated from an imperfect joystick, some jitter in the
input signal occurred as the joystick passed through its centered position as evidenced in the
setpoint signal of Figure 9.8. For the negative setpoint values, the joint achieved an average
steady-state velocity of -105.9 cm/sec (1 percent error). A maximum velocity of -119.2 cm/sec
(14 percent overshoot) occurred. With a positive velocity setpoint, the joint achieved steady-
state values averaging 97.1 cm/sec or an error of 7 percent. The maximum velocity of 120.0
cm/sec which occurred at about 1.6 sec (95/60 sec) indicated an overshoot of 8 percent. For all of
the closed-loop velocity control tests of joint 2, an worst case velocity error of 7 percent and an
average overshoot of 10 percent resulted. The steady-state error value was averaged from error

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Figure 9.7. Typical closed-loop response of joint 2 to step inputs of ±34.8 cm/sec.
Figure 9.8. Typical closed-loop response of joint 2 to an alternating step input of ±104.4 cm/sec.
values ranging from a minimum of 0 percent to a maximum of 10 percent both of which took place
at small velocities. Overshoot values between 3 percent and 25 percent yielded the average
overshoot value. In chapter 7, maximum allowable error and overshoot values were presented
(10 percent steady-state error, and 25 percent overshoot). On the average, these criteria were

127
achieved with a relatively large margin. However, the specified maximum values were
pressed to their limits during occasional trials.
Position Controller Performance
Position control for each of the joints was critical because changes in the position of a
joint during the picking operation could have been the difference between successful and
unsuccessful attempts. As described chapter 7, this factor was the foundation for tight position
requirements. The performance of the position controllers was quantified by examining the
response of each joint to a step change in the position setpoint. Since the largest joint control
signals were generated by large position errors, maximum position changes were used for
generating the position step changes.
Operation of joint 0 was confined to positions between 29.3 and -32.7 deg by the
intelligence base. To quantify the performance of the position controller for joint 0, a step
change of 51.8 deg was chosen. In this case, the setpoint was changed from -25.9 deg to 25.9 deg
while recording the reaction of the joint. The response of the system to a step change in the
position setpoint while joint 2 was centered in its support is shown in Figure 9.9. The joint
moved up to a maximum position of 31.5 deg before returning to a steady-state position of 26.0
deg. Thus, an overshoot of 11 percent (5.7 deg) was recorded along with a steady-state error of
0.1 deg. The worst case encountered in the trials occurred when the joint was excited by a
negative step with the end-effector in its extended position (Figure 9.10). The joint responded
by dropping to a position of -32.4 deg (13 percent overshoot). A steady-state error of 0.5 deg was
evident when the joint was returned to a steady-state position of -26.3 deg. Even these worst
case measurements were within the allowable range of operation for the position controller of
joint 0. From all of the trials, average values of 0.1 deg steady-state error and 11 percent
overshoot were found.
The position of joint 1 was limited in the software to ±15.6 degrees from its centered
location. Thus, the step tests for quantifying the performance of the position controller were

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Figure 9.9. Typical closed-loop response of joint 0 to a step change in the position setpoint of
+51.8 deg.
Figure 9.10. Worst case closed-loop response of joint 0 to a step change in the position setpoint
of -51.8 deg with joint 2 extended.
also limited to have position setpoints within this range. For these tests, position setpoints of
±11.9 deg were implemented, resulting in position steps with 23.8 deg magnitude. A
representative response of the closed-loop position controlled system is presented in Figure 9.11.
For this trial, joint 2 was held steady at its centered position. Joint 1 responded to the step
change in its setpoint by overshooting the desired position by 3.3 deg or 14 percent. It settled to

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Figure 9.11. Typical closed-loop response of joint 1 to a step change in the position setpoint of
+23.8 deg.
12.0 deg which represented a steady-state error of 0.1 deg. In the worst observed trial (Figure
9.12), the system responded to a negative step with a maximum position of -15.7 deg or 16
percent overshoot. In this case, the joint settled back to an average value equal to the desired
position. These results were obtained when the sliding tube was held steady in an extended
position. For all the trials with different directions and positions of joint 2, a maximum steady-
state error of 0.14 deg resulted. The steady-state errors from all of the trials averaged to a
value of 0.1 deg. The maximum overshoot from all trials (16 percent) occurred in the example
which produced the plots of Figure 9.12. Based on the specified criteria for this controller, the
actual steady-state errors were all well below the maximum allowable providing adequate
error margin. On the other hand, the overshoot was desired to be less than 15 percent.
Adjustments in the controller to compensate for the larger overshoot value caused an
undesirable sluggish system response. Even though this controller allowed an average
overshoot of 14 percent, only 1 percent less than the maximum, it provided very good
performance when used in the picking operation. Therefore, the specified performance
requirements were relaxed to allow its use.

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Figure 9.12. Worst case closed-loop response of joint 1 to a step change in the position setpoint
of -23.8 deg with joint 2 extended.
In conjunction with the velocity controlled minor loop, the lag-lead controller for joint 2
provided very respectable results. For quantifying the performance of this position controller,
steps of 43.8 cm in each direction were used as the input to the system. These steps were input to
cause to the link to slide in both directions while being pointed up, down, and straight ahead.
Thus, the gravity load on the joint worked both with and against the controller assisting and
hindering the controller's action on the joint. In the typical trial (Figure 9.13), the position
setpoint was changed from 45.7 cm to 89.5 cm (a step of 43.8 cm). In this case, joint 0 was causing
the end-effector to be pointing down, and the action of joint 2 was extending the end-effector
toward the ground. As with all of the cases in which joint 2 was begin extended, the controller
prevented any overshoot. In this case, the controller kept the steady-state error to less than 0.5
cm. For all of the twelve trials, the controller proved to be capable of keeping the steady-state
error less than 0.7 cm and to an average of 0.3 cm. In both trials in which the end-effector was
pointed up and joint 2 being retracted (Figure 9.14), the position controller allowed an overshoot
of 1.5 cm or 3 percent. Even in its worst case, the position controller for joint 2 proved to perform
well within the allowable errors of 3 cm steady-state and 15 percent overshoot.

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Figure 9.13. Typical closed-loop response of joint 2 to a step change in the position setpoint of
43.8 cm.
Figure 9.14. Worst case closed-loop response of joint 2 to a step change in the position setpoint
of -43.8 cm.
Vision Controller Performance
Dynamic Performance
In chapter 8, the vision system controllers for joints 0 and 1 were designed and tuned. As
noted, the amplitude ratios which were defined for the worst case fruit motions could not be met

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with a stable system. Thus, the fact that the vision systems could not meet the specified
amplitude ratios was realized. Along with the stipulation placed on the amplitude ratios, two
worst case phase lags were presented in chapter 7. These phase angles were calculated from
the motion of the fruit and the known position relationship between the end-effector and the
fruit for successful picking. For larger magnitude fruit motions, a maximum phase lag of 2.5
degrees was specified. A phase lag of 10 degrees was determined as the maximum allowable
for smaller, faster fruit motions. Therefore, meeting these provisions would have indicated an
adequate performance of the vision controllers. When the closed-loop analyses of the
completed systems were conducted, it was found that the vision controllers could not achieve
these high expectations.
A Bode plot for the joint 0 vision controlled closed-loop system is presented in Figure
9.15. The transfer function of the closed-loop vision compensated system had the form
KcKp(0h(xdS +1)
4/e. » 3 / 2 \ 2 f 2 2 \ 2
XiS +(25h(0hx1+l)s +|(0hXi+25hC0h|s +[ coh+KcKptohxd js + KcKp(oh
At the frequency of the large fruit motions, 3.1 rad/sec, an amplitude ratio of 0.988 and a phase
lag of 19 degrees were calculated. At 6.9 rad/sec, the frequency of the smaller, faster motions,
the amplitude was calculated to be 0.95 while the phase lag was found to be 37 degrees.
Adjustments in the system controller could not be made to achieve the desired system response.
For joint 1, the results were similar to those for joint 0 (Figure 9.16). At the frequency of the
slower motions, the amplitude ratio was found to be 0.997 with a phase lag of 11.4 degrees. The
higher frequency requirements were an amplitude ratio of 0.995 and a phase lag of 23.9 degrees.
Again, these values showed much need for improvement if the specified requirements were to be
met. Based on the closed-loop responses of Figures 9.15 and 9.16, the fruit motions which would
be pickable by the robot were calculated. These motions are presented in Figure 9.17 along with
the fruit motions that were found to exist in actual grove conditions.

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Figure 9.15. Closed-loop magnitude and phase plots for joint 0 vision control system:
Kc = 4.0 (D/A word)/pixel Kp = 2.27 pixels/(D/A word)
Ti = 0.02 sec 8 = 0.18
Td = 0.01 sec Wh = 17 rad/sec
Static Performance
Even though the requirements for the amplitude ratio and the phase lag were not met
for the vision systems, the responses of the controlled systems were still respectable. The
actual performance of each of the vision systems to position the end-effector within reach of a
targeted fruit proved sufficient for most cases. In fact, their steady-state performance proved
that still fruit could be approached with errors of 6 pixels or less (Figures 9.18 and 9.19). The
first test (Figure 9.18), an artificial fruit was positioned so that it was above the center of the

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Figure 9.16. Closed-loop magnitude and phase plots for joint 1 vision control system:
IQ = 4.0 (D/ A word)/pixel Kp = 3.85 pixels/(D/A word)
Ti = 0.02 sec 8 = 0.18
id = 0.01 sec C0h = 22 rad/sec
end-effector, but within the camera's field of view. The fruit was positioned so that its
centroid was determined to be at 51 pixels in the vertical direction of the image plane. The
vision setpoint was fixed at 200 pixels. At 34 ticks (34/60 sec), the vision system was actuated
to provide a vision step of 149 pixels. The joint 0 vision controller responded by overshooting
the setpoint by 25 pixels before settling to a steady-state value of 206 pixels or a steady-state
error of 6 pixels. In all trials with different response directions, the steady-state error was

135
Frequency (HZ)
Pickable Fruit
Motions
Determined Actual
Fruit Motions
Figure 9.17. Pickable fruit motions as determined from the closed-loop response of the
manipulator along with the fruit motions determined to exist in the grove.
found to be 6 pixels or less which was much less than the 65 pixel maximum allowed error. For
joint 0, a maximum overshoot of 40 pixels was evident in similar tests of the compensated vision
system. Similar tests were conducted for the joint 1 vision controller as shown in Figure 9.19. In
this case, the fruit was placed away from the setpoint in the horizontal direction. The initial
centroid was determined to be at 37 pixels in the horizontal direction of the image plane. The
setpoint was set to 192 pixels, and the vision controller was actuated at 36 ticks on the plot. The
vision controller positioned the end-effector so that the steady-state position of the fruit's
centroid was at 191 pixels in the image plane with no overshoot. The performance of the joint 1
controller was better than that of the joint 0 controller providing steady-state errors of only 1
pixel while an error of 47 pixels would still have been acceptable.
The ability of the robot to track and pick moving fruit could not be totally solved by the
vision controllers. The over design of this first prototype citrus picker resulted in large link
inertias and the use of oversized actuators which contributed to its slow frequency response.
Because physical changes in the robot (e.g. different actuators and reduced link masses) which
would improve its frequency response were not practical, the solution for this obstacle was to

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Figure 9.18. Closed-loop vision system response of joint 0 to a setpoint of 200 pixels with the
beginning fruit location of 50 pixels in the vertical direction in the image plane.
Figure 9.19. Closed-loop vision system response of joint 1 to a setpoint of 192 pixels with a
beginning fruit location of 37 pixels in the horizontal direction in the image plane.
come from a source which could work with the controllers to achieve acceptable results. For
this task, the intelligence base was altered to cause the robot to wait for the velocity of the
fruit to slow to a velocity which could be tracked and ultimately picked by the robot. If the

137
fruit motion was large enough that the fruit would be lost by the vision system, the supervising
program would cause the robot to return to the search mode in search of another fruit.
Overall Controller Performance
Although acceptable performance was not demonstrated for all of the controllers when
operated separately, their performance within the intelligence base was most important for
this application. As previously mentioned, the ability of the controllers to move the end-
effector to a previously determined position and orientation in its workspace was not of
importance in this case. The capability of the controllers to repeat a motion was not important
either. Rather, the usefulness of these controllers in the fruit-picking operation as governed by
the intelligence base was of great significance. This capacity could be demonstrated only by
examination of the pick cycle and the response of the motion controllers to the commands from
the intelligence base. The velocity controllers for joints 0 and 1 were used only during the fruit
search routine. Thus, data from a typical search routine are presented and discussed. Data
plots from a typical pick cycle are presented for explaining the effectiveness of the position and
vision controllers for joints 0 and 1 and the position and velocity controllers for joint 2. Also, the
ability of the intelligence base to enhance the operation of the vision controllers for tracking
the large and fast fruit motions is presented. The output from the velocity controller for joint 2
was used for detection of collisions during the extension of the joint. The results of this
technique are exhibited here.
Performance in the Search Routine
In the initial stages of the pick cycle, if a fruit was not detected in the image of the
vision system, the robot was instructed to begin a search routine. In this search routine, the
intelligence base called for velocity control on joints 0 and 1 for scanning the robot's workspace
and position control on joint 2 to hold the slider stationary. The direction of motion for both
revolute joints was changed when the joint reached a specified position. Data from a typical
search routine is presented in Figures 9.20 - 9.23. For this presentation, the robot began with

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Figure 9.20. Plot of position and position setpoint of joint 0 during a typical fruit search routine.
Figure 9.21. Plot of velocity and velocity setpoint of joint 0 during a typical fruit search
routine.
each joint in its home position. The supervisor called for position control on all joints to hold
the robot motionless for a period of 1.75 sec (105 ticks). The search routine began by setting the
velocity setpoints to the values which were contained in the data base. At 1.75 sec, velocity
control was initiated by the intelligence base activating the search routine. During the search
routine, the joint 0 velocity setpoint was alternated between ±16.3 deg/sec (Figure 9.21) while
the joint 1 velocity setpoint was alternated between ±8.1 deg/sec (Figure 9.23).

139
Figure 9.22. Plot of position and position setpoint of joint 1 during a typical fruit search routine.
Figure 9.23. Plot of velocity and velocity setpoint of joint 0 during a typical fruit search
routine.
For joint 0, the direction of motion was changed when the joint was within 2.6 deg of the
upper position setpoint of 23.3 deg and the lower position setpoint of -28.4 deg. The smooth
operation of joint 0 during the search routine is shown by the smooth straight lines of Figure
9.20. The alternating motion of joint 1 during the search routine was much smaller than that of
joint 0. The motion of joint 1 was limited by position setpoints of -0.9 deg and -8.2 deg. With
this range, the robot was allowed only limited horizontal motion while the robot was slowly
being pulled forward in the grove. The horizontal motion of the robot during the search routine
was demonstrated by the plot of Figure 9.22 with velocity setpoint switching between 8.1

140
deg/sec and -8.1 deg/sec. The velocity of joint 1 during the search routine was much less uniform
than that of joint 0.
At approximately 6 sec (360 ticks) into the routine, as the position of joint 0 increased,
the sliding joint slid about 1 cm in its bearing. This motion was caused by the changing gravity
forces on the slider as the position of joint 0 was increased. This change in the load of joint 1
caused a deviation from the smooth operation of the velocity controller for joint 1. Even though
the velocity errors were quite large when compared to the velocity setpoints, they did not
hinder the successful completion of the fruit search routine. Maximum velocity errors for both
joints 0 and 1 were specified as 40 percent of the desired velocity. This specification was
obviously over extended, but the motion robot was still acceptable for the search routine.
Performance During the Pick Cycle
The ultimate test for the motion control strategies was performance evaluation during a
pick cycle. A typical pick cycle began with the robot in the home position. The vision system
was checked for a fruit in the image. When no fruit was found in the image, the search routine
was invoked. But, when a fruit was found in the image, the intelligence base proceeded to
remove the fruit from the tree.
For this evaluation, the actions of the robot were examined during a simple pick cycle
in which the fruit was found without the search routine. The control modes and the motions of
the joints during the pick cycle are presented in Figures 9.24 and 9.25. In Figure 9.24, the control
modes which were used during the entire action and took 3 sec (180 ticks) are shown. When the
intelligence base determined that a fruit was centered in the image, the robot was instructed to
approach the fruit. This approach was conducted using vision control on joints 0 and 1 to
maintain alignment with the fruit while the end-effector was extended towards the fruit under
velocity control of joint 2 (ViViV). When the intelligence base determined that the fruit was
within the pick envelope (63 ticks), all joint motions were stopped under position control (PPP),
and the rotating lip was actuated, grasping the fruit. Once the fruit was grasped (80 ticks), the
slider was actuated under velocity control of joint 2 to retract the end-effector from the canopy

141
Time (1/60 sec)
Figure 9.24. Control modes and position and velocity of joint 2 during a typical pick cycle.
of the tree while joints 0 and 1 were held stationary under position control (PPV). When the
slider reached its home location (150 ticks), the control of all joints were switched to position
control, all joints were instructed to go to their home locations, and the fruit was released from
the picking mechanism. Thus, a pick cycle was completed and the intelligence base was ready
to check for another fruit.
During this pick cycle, joints 0 and 1 acted under the control of the vision and position
controllers while joint 2 acted under velocity control and position control. The motion
controllers provided adequate control over the joints of the robot for removing a fruit from the
tree. As the end-effector was extended towards the fruit, changes in the velocity setpoint for

Vertical Location of Fruit Horizontal Location of Joint 1 Position Joint 0 Position Control Mode
Centroid (pixels) Fruit Centroid (pixels) (deg) (deg)
Figure 9.25. Position of joints 0 and 1 and locations of the fruit during a typical pick cycle.

143
joint 2 resulted when the fruit was determined to be close to the end-effector. During the
extension, a steady-state velocity error of approximately 6 cm/sec was determined as shown in
Figure 9.24. Also during the extension, joints 0 and 1 were adjusted for changes in the location of
the fruit as determined by the vision system. The determined location of the fruit's centroid is
presented in Figure 9.24 as horizontal and vertical components in the image plane with errors
up to 100 pixels in the vertical direction (joint 0) and less than 50 pixels in the horizontal
direction (joint 1). These errors apparently resulted from motion of the fruit which was faster
than could be followed by the arm. The errors were larger than determined as allowable in the
tests for determining the picking envelope for the end-effector, but the pick attempt was still
successful. Note that the picking envelope described the location of fruit which could be
grasped in all of the trials. During the girdle, retract, and drop phases of the pick cycle, joints
0 and 1 were governed by the respective position controllers. These responses are shown in
Figure 9.25. Maximum errors of 0.5 deg for joint 0 and 1.0 deg for joint 1 were within the
tolerances as determined for these position controllers. The other actions of joint 2 which
completed this pick cycle were governed by the position controller during the girdle and drop
phases and by the velocity controller during the retract phase. As shown in Figure 9.24, the
errors for these controllers were also within the tolerances indicating that these controllers
performed acceptably during the typical pick cycle. Therefore, all of the vision and position
controllers performed satisfactorily for the completion of a successful pick cycle
As discussed in chapter 8, the vision controllers could not be designed so that large and
fast fruit motions could be successfully followed. Therefore, a wait state was added to the
intelligence base for overseeing this problem. In Figures 9.26 and 9.27, the results of this
addition can be observed. In this pick cycle, a fruit was found during the search routine. The
vision controllers for joints 0 and 1 were used to point towards the fruit while the sliding joint
was held fixed by the joint 2 position controller. Once the arm was aligned with the fruit, the
control of joint 2 was switched to the velocity controller for approach of the fruit. As can be seen
from the fruit centroid position plots (Figure 9.26), the fruit motion was greater than that of the

Figure 9.26. Controller responses to large fruit motions using the wait state.
Joint 2 Velocity
(cm/sec)
Joint 2 Position
(cm)
Vertical Location of
Fruit Centroid
Horizontal Location
of Fruit Centroid
Control Mode

145
Figure 9.27. Control modes and joint 0 and 1 positions during a pick cycle with large fruit motion
which required use of the wait state.
arm and the fruit was lost at 416 ticks on the plot. When the fruit was lost, the motion of joints
0 and 1 was halted by switching the control to the position controllers and setting the position
setpoints to the present locations. This action is shown in Figure 9.27. During the wait state,
the motion of the sliding joint was continued under the velocity controller. When the fruit was
located in the image again (426 ticks), the approach of the fruit was continued with the vision
controllers guiding the position of joints 0 and 1 and the velocity controller extending the end-

146
effector towards the targeted fruit. When proximity of the fruit was detected, the actions of
the typical pick cycle were continued by detaching the fruit, retracting the end-effector from
the tree, and releasing the fruit. The implementation of the wait state in the intelligence base
was necessary to give the robot the ability to pick those fruit with large and fast motions that
the vision controllers could not cause the arm to follow. With this addition, the robot motion
controllers proved successful in handling most motions of the fruit in a manner similar to that
demonstrated here. However, some fruit motions were still out of the scope of these controllers.
After a set amount of time in the wait state without an fruit in the image, the pick cycle was
aborted and a new pick cycle was begun.
Another important function of the intelligence base which relied heavily on the action
of the velocity controller for joint 2 was that of collision detection. During the operation of the
robot, the path from the end-effector to the targeted fruit could be obstructed by a limb or other
object. Thus, the detection of collision with such an object was pertinent. A collision during the
extension of the sliding joint would cause a decrease in the velocity for a given command from
the joint 2 velocity controller. As the velocity decreased, the velocity error would increase and
the magnitude of the control word (output from the controller) would continue to increase.
Therefore, the detection of a collision was based on the magnitude of the control word. During
the operation of the joint 2 velocity controller, this control word was monitored. If the control
word sustained an absolute value greater than 600 for a period of time longer than 25 ticks (0.4
sec), the intelligence base determined that a collision had taken place. When a collision was
detected, the pick cycle was aborted, and the end-effector was retracted from the tree canopy.
This same principle was used for aborting a pick cycle when a fruit was grasped that required a
large amount of force for removal from its stem. In some cases, the bond between the fruit and its
supporting stem was so great that the arm could not apply enough force to break the bond. By
aborting the pick cycle, another grip could be applied to the fruit later which could possibly
remove the fruit.

147
A representative example of such a collision and its detection is presented in
Figure 9.28. In this example, a fruit was located during the search routine. The intelligence
base passed the control of the robot through a point state (alignment on the fruit without
extension of joint 2) and into the fruit approach state. After loosing the fruit two times and
returning to the approach state, the extension towards the fruit continued. Beginning at 172
ticks on the plot, the control word exceeded the 600 D/A word limit for a period of 25 ticks, the
time limit. Therefore, at 197 ticks, the pick cycle was aborted and control of the joints was
switched to position control for joints 0 and 1 and velocity control for joint 2, holding joints 0 and
1 stationary while joint 2 was retracted from the canopy and away from the obstacle.
In the normal case of vision servoing, collision detection was not needed because the
path to the fruit would normally be clear of obstructions if the vision system could 'see' the
targeted fruit. However, this method of collision detection proved sufficient for preventing
damage to the picking mechanism.
In response to the requests of the intelligence base, the controllers' performance during
the search routine and the pick cycle were adequate for the robot's intended purpose. During
the time that the joints were under position control, the joints' responses were immediate to
minimize the error between the actual and desired positions. However, the errors were not
brought to values less than were specified as allowable for acceptable performance of the robot
in all cases. These errors are evidenced in Figures 9.24 - 9.27. The response of the velocity
controllers was impressive. During the search routine (Figures 9.20,9.21,9.22, and 9.23), the
velocity controllers for joints 0 and 1 produced a smooth motion for scanning the workspace.
Even though the velocity error was rather large at times, a steady-state error less than the
allowable 40 percent was achieved for both joints 0 and 1. The velocity controller for joint 2 also
performed well with the robot's intelligence base as demonstrated in Figure 9.24. During the
extension and retraction of the end-effector, the controller responded to changing values in the
velocity setpoint smoothly and rapidly meeting the previously specified requirements of not
more than 10 percent steady-state error and not more than 25 percent overshoot. The

148
Figure 9.28. Pick cycle aborted because of a collision during the fruit approach routine.
performance of the vision control systems was not as easily envisioned as the performance of the
other controllers. The performance of the vision controller for joint 0 was illustrated in the plot
of the Vertical Location of the Fruit Centroid in Figure 9.25 while the performance of the vision

149
controller for joint 1 was illustrated by the Horizontal Location of the Fruit Centroid. As
indicated in these diagrams, the vision controllers were not able to maintain perfect alignment
between the robot arm and the fruit. And, the resulting errors were greater than specified as
allowable for a successful pick. However, the controllers' actions still enabled the robot to be
able to track the fruit and remove it from the tree.
The addition of the wait state in the intelligence base aided the controllers in the
tracking of moving fruit. This state provided a period of time for a swinging fruit to return to
the field of view of the vision system. This addition added a period of time to the pick cycle
time, but it made the difference in a successful pick attempt and an unsuccessful attempt. Thus,
in the overall picture, the time for removal of all of the fruit from a tree would be shortened.
The use of the joint 2 velocity controller output for detection of a collision proved very
successful. The sensitivity of the controller to changes in the error provided an effective
method for detecting collisions before damage was done to the robot. This method of sensing the
force required to move the sliding joint also achieved good results when used for determining
when a fruit required more force for removal than was achievable by the arm.

CHAPTER 10
SUMMARY AND CONCLUSIONS
Summary
The objective of this work was to design and implement motion control strategies for the
orange-picking robot. At the onset of the work, a plan for undertaking this task was developed.
First, the configuration and critical dimensions of the robot were investigated along with the
software environment from which the motion control strategies would be summoned. Then the
kinematic relationships between each of the joints was examined. Open-loop dynamic models
for the joints of the robot were estimated from the joints' responses to input signals. The
required performance of each of the controllers was defined based on typical fruit motions and
the necessary relationship between the fruit and the picking mechanism for successful fruit
removal from the tree. Finally, motion control strategies were developed, implemented, and
tested for control of the robot based on velocity, position, and vision information.
Kinematic relationships between the robot's joints provided a means for determining
changes in the position and orientation of the end-effector based on changes in the position of
the joints. More importantly, the kinematic relationships furnished a means for determining
the relationship between the actual position of a fruit and the position of the fruit's image in
the camera's image plane. This knowledge of the fruit's position supplied vital information for
developing the vision system gains. These vision gains were later used for scheduling the
changes in the position of the revolute joints as the picking mechanism was extended toward
the targeted fruit.
The dynamic models of the joints provided needed information for designing and tuning
the motion control strategies. From step tests, the dynamic characteristics of each joint were
determined. These tests confirmed that the joints responded as second order systems allowing
150

151
the use of second order characteristics in the controller design phase of the work. Simulations
of second order systems were conducted using the experimentally determined parameters for the
robot joints. These simulations again enforced the assumptions that were made to reduce the
hydraulically actuated joints to a second order system. Comparisons between the responses of
the actual systems and the simulated systems were made to further enforce this principle.
The performance of the controlled robot would have been useless without its ability to
pick fruit in an actual grove situation. Thus, the motions of fruit in an actual orange grove were
investigated. A picking envelope was determined as the volume around the picking mechanism
in which a targeted fruit must lie in order to be pickable. Requirements were specified that
would ensure that the robot could position the end-effector within reach of a targeted fruit.
Using the results from the fruit motion test and the picking envelope, the performance
requirements for the vision controllers were derived. Performance specifications for the
velocity and position controllers were determined from the worst case requirements of each of
the controllers.
Upon the recommendations of Merritt (1967) and Palm (1983), lag-lead controllers were
chosen for their ability to meet the various control problems which were posed by the orange¬
picking robot. These controllers were discretized according to Tustin's bilinear transformation
method for use with the digital control computer. The controllers were programmed into the
software environment of the robot for operation by the supervising program. For on-line
controller tuning, a routine was added which converted the continuous domain controller
parameters to the variables of the controller in the discrete domain. Thus, the controllers could
be tuned from the continuous domain while used in the discrete domain. The use of this concept
was verified by the joint simulations of the continuous and discrete controllers.
Velocity and position controllers were added to the software environment. Deficiencies
in the joint 2 position controller's capabilities led to the addition of a velocity minor loop
which increased the controller's ability to overcome the inherent static friction of the sliding
joint. Initial parameters for each of the controllers were estimated from the desired

152
performance and the known responses of the joints. The parameters were adjusted to achieve
acceptable responses from the joints and respectable performance in the robot's picking process.
With the tuned velocity and position controllers, all of the performance requirements were met.
After tuning the velocity and position controllers, vision controllers were added to the
software package. These controllers used information from the vision system to align the robot
with a targeted fruit. These controllers were first tuned to achieve acceptable performance
with nonmoving fruit. After showing exceptional steady-state errors of 6 pixels or less, their
response to moving fruit was investigated. From the worst case motions of fruit as determined in
the fruit motion test, amplitude ratio and phase lag requirements were specified. These
requirements could not be met by the vision controllers. By utilizing frequency response curves
for the design of the controllers, it was found that meeting these amplitude ratio requirements
would cause the system to be unstable. Also, the vision controllers could not be tuned to achieve
the small phase lags which were required. These obstacles were overcome by altering the
intelligence base of the robot to either wait for the velocity of moving fruit to slow to a more
achievable rate or to search for another fruit.
Conclusions
While incorporated into the robot software environment, these controllers for the
orange-picking robot provided acceptable performance, enabling the robot to successfully locate
and pick fruit. Ultimately, the controllers would have provided a very fast response to input
signals with a minimum steady-state error and overshoot. Since the robot had been designed
and constructed before the controllers were designed, major changes to the construction of the
manipulator were not possible that would make the control process easier and better. However,
these controllers furnished sufficient responses of the joints to changing input signals. When
incorporated with the intelligence software of the robot, picking rates of 1 fruit every 4 seconds
were achieved. Also, in 75 percent of the attempts to pick a fruit, a fruit was removed from the
tree. These controllers also aided in proving the concept of mechanically picking oranges

153
causing only minimum damage to the trees. The knowledge gained from this project is a
beginning for further enhancements of the robot and encouragement toward the final goal of a
production model citrus harvesting machine.
During the development of this manipulator, some recommendations have become
evident. Because this manipulator was the first prototype, its links were massive and rigid.
Larger and more rigid links were initially designed so that collisions with obstacles during the
tuning and controller design process would not render the robot inoperable. Activation of these
large links required much larger actuators than would be desired in later models. The reduced
inertia of smaller and lighter links would increase the hydraulic natural frequency of the
joints, thereby enabling the robot to achieve the motions necessary for picking fruit with large
and fast motions. The lighter links would also require smaller actuators which would also
result in increased response rates of the manipulator. After increasing the natural frequency
and the response rate of the manipulator, the controllers could be tuned to aid in increasing the
robot's overall efficiency.
The behavior of the sliding joint could be improved by choosing a different bearing
surface or a different type of mounting arrangement. During the process of this work, the
bushing was changed from nylon to oil impregnated nylon and then to teflon. Each change made
a significant difference in the action of the joint. It is assumed that an even better choice could
be made.
The technique which was developed for defining the pick envelope could be adapted to
assist in the design process of a more effective picking mechanism. This technique provided a
means for determining the relationship between the end-effector and the fruit for successful
picking. The need of a better picking mechanism has been established. However, all of the
requirements of this picking mechanism have not. A similar concept to that discussed for
determining the picking envelope could expedite the research and testing of a better picking
mechanism.

154
In its present form, this manipulator provided a great insight to the control and
programming problems that are associated with the task of citrus harvesting. The concepts
that were developed provide a new stepping stones in the journey toward a fully autonomous
tree-fruit harvester.

REFERENCES
Adsit, P.D. 1989. Real-time intelligent control of vision-servoed fruit picking robot.
Unpublished Ph.D. dissertation. Agricultural Engineering Department, University of
Florida, Gainesville, FL 32611.
Coppock, G.E. 1984. Robotic principles in the selective harvest of Valencia oranges, in
Proceedings of the First International Conference on Robotics and Intelligent Machines
in Agriculture, ASAE, St. Joseph, MI. pp. 138-145.
Craig, J.J. 1986. Introduction to Robotics Mechanics & Control. Addison-Wesley Publishing
Company, Inc. Reading, MA.
Denavit, J. and R.S. Hartenberg. 1955. A kinematic notration for lower-pair machanisms based
on matrices. Trans, of the ASME, Journal of Applied Mehanics 22:215-221.
Franklin, G.F. and J.D. Powell. 1980. Digital Control of Dynamic Systems. Addison-Wesley
Publishing Company, Inc. Reading, MA.
Gibson, J.E. and F.B. Tuteur. 1958. Control System Components. McGraw-Hill Book Company,
Inc. New York, NY.
Grand d'Esnon, A. 1984. Robotic harvesting of apples. Proc. of the First International
Conference on Robotics and Intelligent Machines in Agriculture. Oct. 2-4,1983. ASAE.
St. Joseph, MI. pp. 112-113.
Grand d'Esnon, A. 1985. Robotic harvesting of apples. Proc. of the Agri-Mation 1 Conf. and
Expo. Feb. 25-28,1985, Chicago, IL pp. 210-214.
Grand d'Esnon, A., G. Rabatel, R. Pellenc, A. Joumeau, and M.J. Aldon 1987. Magali: a self-
propelled robot to pick apples. ASAE Paper No. 87-1037, St. Joseph, MI.
Harrell, R.C., P.D. Adsit, and D.C. Slaughter. 1985. Real-time vision-servoing of a robotic tree
fruit harvester. ASAE Paper No. 85-3550, St. Joseph, MI.
Harrell, R.C., P.D. Adsit, R. Hoffman, R. Munnilla, D.C. Slaughter, and T. Pool. 1988. Robotic
citrus harvester. U.S. Patent Application Serial No. 279198. December 2,1988.
Harwell, R.C., and P. Levi. 1988. Vision controlled robots for automatic harvesting of citrus.
Paper No. 88.426. presented at AG ENG 88, Agricultural Engineering International
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Johnson, J.E. 1977. Electrohydraulic Servo Systems. Penton/IPC, Cleveland, OH.
Kawamura, N., K. Namikawa, R. Fujiura, and M. Ura. 1986. Study on agrucultural robot.
Memoirs of the College of Agriculture, Kyoto University, Koyoto, Japan. No. 129:29-46.
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agricultural robot (IV): improvement of manipulator of fruit harvesting robot.
Published in Kansai Branch Report of the Japanese Society of Agricultural Machinery,
Japan. 58:109-110
Kawamura, N., K. Namikawa, T. Fujiura, M. Ura, and Y. Ogawa. 1987. Study on agricultural
robot (VII): hand of fruit harvesting robot. Research Report on Agricultural
Machinery, Kyoto University, Kyoto, Japan. No. 17:1-7.
Lau, K., N. Dagalakis, and D. Myers. 1988. Testing. International Encyclopedia of Robotics:
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Martin, P.L. 1983. Labor-intensive agriculture. Scientific American. 249(4):54-60.
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Merritt, H.E. 1967. Hydraulic Control Systems. John Wiley and Sons, Inc. New York.
Ogata, K. 1970. Modem Control Engineering. Prentice-Hall, Inc. Englewood Cliffs, NJ.
Palm III, W.J. 1983. Modeling, Analysis, and Control of Dynamic Systems. John Wiley and
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Ranky, P.G. and M. Wodzinski. 1988. Accuracy. International Encyclopedia of Robotics:
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ASAE30(4):1144-1148.
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1983. ASAE. St. Joseph, MI. pp. 84-95.

BIOGRAPHICAL SKETCH
Thomas Alan Pool was bom May 19,1960, in Tifton, Georgia, to Mr. and Mrs. William
H. Pool as the youngest of three sons. He graduated from the Tift County High School in June of
1978. At the age of ten, Thomas joined the 4-H Club, selecting petroleum power, beef, and swine
as chief areas of interest. During his tenure in 4-H Club, he showed many award-winning beef
and swine animals. He became a national winner in the petroleum power project in 1976,
receiving a scholarship from the Standard Oil Company of Illinois. Also in 1976, Thomas
placed fourth in the Eastern United States Tractor Operators Contest, judged on tractor
operation and safety skills.
After graduation from high school, Thomas continued his education by attending
Abraham Baldwin Agricultural College (ABAC) in Tifton while continuing to help his father
on the family farm. He graduated from ABAC in December of 1980 with an Associate of Science
degree in agricultural engineering. He received the Bachelor of Science degree in agricultural
engineering from the University of Georgia in December of 1982. During the summers of his
junior and senior years, Thomas was employed by the University of Georgia and the Coastal
Plain Experiment Station. He assisted with research projects which involved testing new
concepts in crop spraying, analyzing the use of vegetable oils as alternate fuel sources for drying
tobacco, and evaluating the use of silica gels and clay products for reducing the moisture content
of pecans.
Upon completion of his undergraduate degree, Thomas began work towards a Master of
Science degree in agricultural engineering at Texas A&M University. Project work for the MS
degree involved designing, constructing, and evaluating an automatic guidance system for
tractors with open-center hydraulic systems. The degree was completed in August of 1984.
During the fall of 1984, Thomas was again employed by the Coastal Plain Experiment Station
157

158
as a research engineer. While at the experiment station, he assisted with testing sensors for use
with an automatic seedling sorting machine.
In January of 1985, Thomas was awarded the USDA National Needs Fellowship to
pursue the Doctor of Philosophy degree at the University of Florida . While studying at the
University of Florida, he concentrated his course work and research in the areas of robotics and
automatic controls. His project work included developing and implementing control algorithms
for a citrus-picking robot.

I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
J?¿Roy C. Harrell, Chair
Associate Professor of Agricultural
Engineering
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
JdúLJr
Dr. Robert M. Peart
Graduate Research Professor of
Agricultural Engineering
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Dr. Keith L! Doty
Professor of Electrical Engineering
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
ClAA.
¡)r. John Staudhammer
Professor of Electrical Engineering
I certify that I have read this study and that in my opinion it conforms to acceptable
standards of scholarly presentation and is fully adequate, in scope and quality, as a
dissertation for the degree of Doctor of Philosophy.
Dr. Carl Crane
Assistant Professor of Mechanical
Engineering

This dissertation was submitted to the Graduate Faculty of the college of Engineering
and to the Graduate School and was accepted as partial fulfillment of the requirements for the
degree of Doctor of Philosophy.
lljLJt a L
May 1989
Dean, College of Engineering
Dean, Graduate School

Page 2 of 2
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AUTHOR: Pool, Thomas
TITLE: Motion control of a citrus-picking robot / (record number: 1483561)
PUBLICATION DATE: 1989
I, l i oo\ , as copyright holder for the aforementioned dissertation, hereby
grant specific and limited archive and distribution rights to the Board of Trustees of the University of Florida and its
agents. I authorize the University of Florida to digitize and distribute the dissertation described above for nonprofit,
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This is a non-exclusive grant of permissions for specific off-line and on-line uses for an indefinite term. Off-line uses
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This grant of permissions prohibits use of the digitized versions for commercial use or profit.
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11/18/2008




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