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A Lateral Vision-Based Autopilot for Micro Air Vehicles Using a Horizon Detection Approach


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A LA TERAL VISION-B ASED CONTR OL A UT OPILO T FOR MICR O AIR VEHICLES USING A HORIZON DETECTION APPR O A CH By R Y AN SCO TT CA USEY A THESIS PRESENTED T O THE GRADU A TE SCHOOL OF THE UNIVERSITY OF FLORID A IN P AR TIAL FULFILLMENT OF THE REQ UIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORID A 2003

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I dedicate this w ork to my lo v ely wife, Liza P Cause y that has supported me e v ery step of the w ay Her lo v e and understanding through the years ha v e brought my passion for life be yond boundaries.

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A CKNO WLEDGMENTS I w ant to ackno wledge and thank AFRL-MN and Eglin Air F orce for the funding of this project. I w ant to thank all the research members in v olv ed with this project for their dedication and long hours in the lab and in the eld which includes Dr Peter Ifju and his team K yuho Lee, and Se w oong Jung that de v eloped and f abricated the MA Vs, Dr Michael Nechyba and his team Jason Grzywna, Jason Ple w and Ashish Jain that did an e xtraordinary job designing and de v eloping all the on-board and ground station hardw are along with the horizon detection algorithm, my colleagues in the Dynamics and Controls Lab: Helen Garica, Kristin Fitzpatrick for her S ight, the ne w graduate students Joe K ehoe and Jason Jack o wski. A special thanks to the pilots K yuho Lee and especially Mujahid Abdulrahim for his advice and e xtremely long ight hours, and most importantly Dr Andre w K urdila and Dr Rick Lind for their remarkable guidance and inspiration that will truly last a life time and nally to my parents James and Sandra Cause y who pro vided me the guidance and discipline needed for success. iii

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T ABLE OF CONTENTS page A CKNO WLEDGMENTS . . . . . . . . . . . . . . . . iii LIST OF T ABLES . . . . . . . . . . . . . . . . . vi LIST OF FIGURES . . . . . . . . . . . . . . . . . vii ABSTRA CT . . . . . . . . . . . . . . . . . . . ix CHAPTER1 INTR ODUCTION . . . . . . . . . . . . . . . . 1 1.1 Moti v ation . . . . . . . . . . . . . . . . 1 1.2 Background . . . . . . . . . . . . . . . . 2 1.2.1 Micro Air V ehicles . . . . . . . . . . . . 2 1.2.2 Image Processing . . . . . . . . . . . . 7 1.2.3 V ision Control . . . . . . . . . . . . . 9 1.3 Ov ervie w . . . . . . . . . . . . . . . . 11 2 DERIV A TION OF COUPLED CAMERA AND AIRCRAFT EQ U A TIONS OF MO TION . . . . . . . . . . . . . . . . . 13 2.1 Problem F ormulation . . . . . . . . . . . . . 13 2.2 Aircraft P arameters . . . . . . . . . . . . . . 13 2.3 Dening Camera P arameters . . . . . . . . . . . 14 2.4 Camera Equations of Motion . . . . . . . . . . . 17 2.4.1 Feature Point Position . . . . . . . . . . . 18 2.4.2 Feature Point V elocity . . . . . . . . . . . 19 3 CAMERA NONLINEARITIES . . . . . . . . . . . . 23 3.1 F ocal Length P arameter . . . . . . . . . . . . . 23 3.1.1 F ocal Plane Position . . . . . . . . . . . . 23 3.1.2 F ocal Plane V elocity . . . . . . . . . . . 28 3.2 Lens Distortion . . . . . . . . . . . . . . . 28 4 LA TERAL A UT OPILO T CONTR OL DESIGN . . . . . . . . 31 4.1 Roll Control Design . . . . . . . . . . . . . . 32 4.2 Heading Control Design . . . . . . . . . . . . 33 4.3 Closed-Loop Control . . . . . . . . . . . . . 34 i v

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4.3.1 Bank Hold . . . . . . . . . . . . . . 34 4.3.2 Heading Hold . . . . . . . . . . . . . 35 5 EXPERIMENT AL SETUP . . . . . . . . . . . . . . 37 5.1 Micro Air V ehicle Description . . . . . . . . . . . 37 5.2 Hardw are Architecture . . . . . . . . . . . . . 41 5.3 Camera Model for Horizon . . . . . . . . . . . . 43 6 CLOSED-LOOP LA TERAL CONTR OL . . . . . . . . . . 46 6.1 Controller Implementation . . . . . . . . . . . . 46 6.2 Flight T esting and Results . . . . . . . . . . . . 48 6.2.1 Gain T uning . . . . . . . . . . . . . . 48 6.2.2 Lateral Response . . . . . . . . . . . . 50 6.3 Future W ork . . . . . . . . . . . . . . . . 51 7 CONCLUSION . . . . . . . . . . . . . . . . . 53 REFERENCES . . . . . . . . . . . . . . . . . . 55 BIOGRAPHICAL SKETCH . . . . . . . . . . . . . . . 59 v

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LIST OF T ABLES T able page 4–1 Discrete Roll Command Output V alues . . . . . . . . . . 34 5–1 MA V Properties . . . . . . . . . . . . . . . . 38 vi

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LIST OF FIGURES Figure page 1–1 Fle xible W ing Concept on a 6 in MA V . . . . . . . . . 4 1–2 UF MA V Fleet . . . . . . . . . . . . . . . . 6 2–1 MA V Kinematics . . . . . . . . . . . . . . . 14 2–2 Coordinate Systems . . . . . . . . . . . . . . . 15 2–3 Dening Feature Points . . . . . . . . . . . . . . 16 2–4 V ector Diagram . . . . . . . . . . . . . . . . 17 3–1 Feature Point Grid . . . . . . . . . . . . . . . 24 3–2 Grid Rotation . . . . . . . . . . . . . . . . 25 3–3 Planar Feature Points . . . . . . . . . . . . . . 26 3–4 Sk e wed Feature Points Sloping 2.5 Units . . . . . . . . . 26 3–5 Sk e wed Feature Points Sloping 5 Units . . . . . . . . . 27 3–6 Sk e wed Feature Points Sloping 10 Units . . . . . . . . . 27 3–7 Lens Curv ature . . . . . . . . . . . . . . . . 29 4–1 Roll Control Autopilot . . . . . . . . . . . . . . 32 4–2 Heading Control Autopilot . . . . . . . . . . . . . 33 4–3 Closed-Loop Roll Control Design . . . . . . . . . . . 35 4–4 Closed-Loop Heading Control Design . . . . . . . . . . 36 5–1 MA V Prototype for V ision-Based Control . . . . . . . . . 38 5–2 T orque Rod Design . . . . . . . . . . . . . . . 39 5–3 Morphing Control Ef fectors . . . . . . . . . . . . 39 5–4 Push T ail Propeller Design . . . . . . . . . . . . . 40 5–5 Hardw are Architecture . . . . . . . . . . . . . . 41 5–6 Image Plane Depth Comparison . . . . . . . . . . . 44 vii

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5–7 Lens Curv ature for a Horizon . . . . . . . . . . . . 44 5–8 Lens Curv ature with Horizon Approximation . . . . . . . . 45 6–1 Roll Control Block Diagram . . . . . . . . . . . . 47 6–2 Heading Control Block Diagram . . . . . . . . . . . 47 6–3 Roll Response . . . . . . . . . . . . . . . . 51 viii

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Abstract of Thesis Presented to the Graduate School of the Uni v ersity of Florida in P artial Fulllment of the Requirements for the De gree of Master of Science A LA TERAL VISION-B ASED CONTR OL A UT OPILO T FOR MICR O AIR VEHICLES USING A HORIZON DETECTION APPR O A CH By Ryan Scott Cause y December 2003 Chair: Andre w J. K urdila Cochair: Richard C. Lind, Jr Major Department: Mechanical and Aerospace Engineering The concept of autonomous ight has been realized as a feasible concept with the current technology where small electronics ha v e adv anced to standard equipment that is ine xpensi v e. The aircraft platform to head these ef forts has shifted to small agile v ehicles that can maneuv er within conned en vironments such as urban terrains. Some capabilities needed for autonmon y include sensors that detect the physical surroundings, data processing, path planning, and the control algorithms. Micro air v ehicles (MA Vs), structurally ha v e e v olv ed to house the required payload for autonomous research. The capabilities of MA Vs ha v e demonstrated maneuv erability for conned spaces, on-board processing, and camera inte gration with vision feedback. This thesis will establish the required analytical relationships for a camera on-board an MA V along with image processing for feature e xtraction, and nally control design and implementation using this physical feature. The relationship rst deri v ed, couples the nonlinear equations of motion of an aircraft to the trajectory of feature points in the image plane for cameras attached to the v ehicle. Algorithms using statistical models for pattern recognition are used to dene the horizon in the image plane. Based on ix

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geometry this horizon line is used to calculate a roll estimate and pitch percentage which are used as feedback to design controllers. A testbed w as f abricated along with a particular MA V and a single camera of kno wn parameters to implement vision-based lateral control. The camera nonlinearities were studied for this particular feature (i.e. the horizon) through some observ ations. By using the horizon, these nonlinearities were able to be ne glected from the controls system. Numerous ight tests were then conducted to impro v e the lateral control design by adjusting gains to acquire a desired response. x

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CHAPTER 1 INTR ODUCTION 1.1 Moti v ation Micro air v ehicles, or better kno wn as MA Vs, are currently the platform for research in autonomous ight at the Uni v ersity of Florida. A typical MA V scale consists of a wingspan and fuselage that range from 30 inches do wn to 6 inches and operate in ight speeds of 25 m ph or less [ 31 ]. The moti v ation behind Micro Air V ehicles are their mission capabilities in dangerous en vironments. F or instance, MA Vs are being considered for missions that in v olv e surv eillance, damage assessment, search and rescue, and re gion mapping. The interest behind using MA Vs are their fundamental features. These v ehicles are highly agile and can bank and climb within the conned space of an urban en vironment. Because of this feature, MA Vs ha v e the ability to change the en vironment in which standard aircrafts ha v e been kno wn to operate. F or instance, MA Vs can be used y within and around the connes of b uildings and subw ays. Additional benets of MA Vs, re garding implementation, are readiness to y and a compact size for storage. Most importantly MA Vs are lo w cost, which w ould allo w multiple MA Vs to be standard equipment for a v ariety of users, ranging from soldiers on the battle eld to police and re agencies in our local districts. An autonomous MA V is particularly suited to accomplish missions with minimal risk to personnel. Consider a scenario of particular concern where a biological agent has been released in an urban en vironment. Current operations require humans gather equipment and v enture into hazardous re gions. Instead, future operations could be conducted by autonomous MA Vs deplo yed from a nearby emer genc y station. MA Vs w ould assist in a di v erse range of missions including detection, mapping, and search 1

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2 and rescue during this type of situation. In the case of detection, the v ehicle could transport a sensor that detects infectious agents. A map of the re gion and the infected areas could then be generated to inform ci vilians from real time updates. The images could also be used as a surv eillance tool to search and locate possible survi v ors. The v ehicle' s small size and agility w ould allo w access inside b uildings and subw ays therefore increasing the search area. Analyzing image information, rescue teams can assess damage to the surroundings to plan a safe rescue route. This scenario, along with man y others, v alidates the gro wing interest for such sophisticated systems using vision. 1.2 Background 1.2.1 Micro Air V ehicles Ov er the past v e years, MA V designs ha v e been de v eloped to impro v e ight characteristics, payload capacity and structural inte grity W ith these signicant impro v ements, v ery small v ehicles are being considered an achie v able technology for autonomous ight with man y applications. Here, autonomy is re garded as the controls system making decision on the trajectory without human interv ention. The size constraints in v olv ed in using such small v ehicles has lead to man y adv ances in miniaturized digital electronics, communications, and computer technologies to mak e autonomous MA Vs a reality [ 46 ]. These de v elopments ha v e allo wed MA Vs to be equipped with the latest computer and sensor technology such as video cameras, data processors, and communications de vices. Ov er the last fe w years, the inte gration of these electronics onto an MA V has made considerable adv ances to w ard the o v erall goal of on-board processing and mission capability in real time. The rst successful MA V that demonstrated mission capabilities w as Aero vironment' s Blac k W idow [ 13 ]. This 6 in MA V w as electrically po wered and consisted of a rigid-wing design with three v ertical stabilizers. The on-board systems included a data logger sampling 16 channels at 20 Hz and a custom video camera system that

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3 optimized weight, po wer and size with image quality A ya w damper w as implemented to damp out a lo w frequenc y Dutch roll oscillation to impro v e not only ight stability b ut also stabilizing the video to obtain a steady image. An autopilot system w as also incorporated using three modes: dynamic pressure hold, altitude hold, and heading hold. The nal o v erall system, with a mass of 80 g w as able to sustain 30 min ights for a maximum range of 1.8 k m while transmitting video images to the ground. These images were used by the pilot to control the aircraft when the range of the v ehicle became too lar ge from an RC pilot' s standpoint. Most importantly the images demonstrated the functional capability of MA Vs by streaming real time video to the ground to establish their role in implementing vision-based autonomous ight. The rigid-wing concept w as common in man y other successful designs including the T r oc hoid de v eloped by MLB Compan y and Micr ostar also funded by D ARP A [ 17 ]. The disadv antage to using rigid-winged MA Vs is the y require additional gyro stabilizers to assist in controlling the aircraft. This is due to the unsteady aerodynamic loading that dominates a v ehicle at such lo w Re ynolds numbers. F or e xample, wind gust will ha v e a much greater af fect on MA Vs than lar ger aircrafts because of their size and speeds at which the y operate. Research e v entually lead to the concept of e xible wings that are able to adapt to unsteady ight conditions. Dr Peter Ifju and his team, at the Uni v ersity of Florida, has de v eloped a wing concept that consists of an e xtensible late x rubber membrane that is o v erladed onto a carbon ber sk eleton for structural support [ 17 ]. This concept w as tak en from sail v essels which use the sail twist to e xtend the wind range producing a more constant thrust e v en in gusty conditions [ 45 ]. An illustration of this wing structure is depicted in Figure 1–1 for a 6 in MA V The important feature that one should realize is the e xibility of these wings. The e xibility can be so dramatic that the wings can be folded around the fuselage creating a more compact storage en v elope. Implementing

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4 this feature, MA Vs could then be deplo yed from missiles moments before impact to loiter around the tar get space for damage assessment. Figure 1–1: Fle xible W ing Concept on a 6 in MA V The aerodynamic benets of e xible wings appear to be signicant b ut are currently being studied in detail. By adjusting to the air o w e xible wings produce a more f a v orable aerodynamic o w in such lo w Re ynolds number en vironments, as documented in the research [ 17 44 46 ]. This is mainly caused by maintaining an attached o w and pre v enting o w separation. As Re ynolds number decreases, the o w around the wing surf ace separates f aster and therefore increases the drag on the aircraft. So by implementing e xible wings, MA Vs appear to ha v e better ight qualities compared to the gyro stabilized rigid winged design. Later a more structural analysis and o w interaction approach using nonlinear mo ving boundary techniques coupled with Na vier -Stok es solv ers to quantify the resulting o w eld [ 22 ]. Results obtained in this paper consist of v orticity structure, pressure distrib ution, and lift and drag characteristics associated with both membrane and rigid wings concepts for comparison. Modal analysis of this interaction has been done using Proper Orthogonal Decomposition to e xtract most ener getic modes from the resulting o w eld and the wings natural response [ 48 ]. W ith this e xible wing concept, researchers be gan an approach to analyze ight techniques seen in nature. This ight concept opened the e yes of man y researchers to

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5 mimic the ight of small birds and insects into the design of an MA V This approach seems ob vious because of their common size and the bird' s ability to maneuv er in conned spaces, b ut is e xtremely dif cult to reproduce mechanically The common motion between small birds is high frequenc y apping to produce lift as well as directional control, which is reminiscent of Hummingbirds. Man y w orks are pursuing apping ight techniques with e xible wings to add agility The mechanisms and actuators required for such a task are being e xplored in the lab en vironment [ 32 ]. The dif culty for this type of MA V consist of producing an ef cient ying machine with on board actuators that operate with lo w po wer consumption. As one can imagine, the comple x motions at such high frequencies will require ef cient, durable, and compact actuators along with sophisticated control systems. Studies ha v e sho wn comparable wingtip trajectories between their vibratory apping testbed and those e xhibited by Hummingbirds in v arious ight modes [ 32 ]. Currently these actuators are signicantly lar ger than a MA V' s fuselage so other techniques are being e xplored. Other studies in Shyy et al. [ 44 ], be gan to in v estigate dif ferent aspects of apping e xible wings such as wing loading, models for lift, drag and po wer issues with lo w Re ynolds number o ws, and recent w ork with e xible structures adjusting to free-stream conditions. Some preliminary results indicate impro v ements in lift-to-drag ratio and aerodynamic performance o v er the standard rigid-winged counter -partner Ho we v er the complete understanding of e xible wings requires the full Na vier -Stok es o w model to accurately represent the coupling between apping dynamics and ight at lo w Re ynolds numbers. The comple xities in v olv ed in this approach has lead man y researchers to adopt a potential o w or thin-layer o w model e v en though these solutions contain inadequate details of the o w at these sizes and ight re gimes. Ov er the last se v eral years, Dr Ifju has established a systematic f abrication f acility for MA Vs at the Uni v ersity of Florida. This f acility enables the rapid production of MA Vs in a range of sizes and the ability to customize a design for a particular mission.

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6 The standard MA V eet at UF range in wingspan from 6 in to 24 in and are depicted in Figure 1–2 Notice all the MA Vs in this gure consists of a common design: a carbon ber airframe with a wing that consists of a e xible membrane and a reinforced leading edge made of carbon ber The airframe houses specic components needed for ight testing and typically consist of accelerometers, rate gyros, a GPS sensor data processors and loggers, serv os, and camera components. Figure 1–2: UF MA V Fleet The control surf aces of a standard aircraft are typically incorporated on an MA V Although, implementing an aileron on a e xible wing design has caused some dif culty during f abrication. F or simplicity UF has o v ercome this problem be implementing symmetric and antisymmetric ele v ator This in v olv es splitting the ele v ator do wn the center into tw o control surf aces. The symmetric ele v ator occurs when the tw o surf aces act together to produce pitching moments while the antisymmetric occurs when these surf aces act opposite to produce rolling moments. Recently a ne w technique called morphing has e v olv ed into the MA V design to act as ailerons. This concept will be e xplained in more detail in Chapter 5.1 Depending on the directional stability of each MA V design, a rudder can be implemented to reduce side slip during maneuv ers and is commonly incorporated on the smaller MA Vs. T o test MA Vs ef ciently with sophisticated control algorithms, models need to be generated from ight test or wind tunnel data. Only recently MA Vs ha v e been considered a feasible technology from a controls aspect. Researchers are no w emphasizing the need for MA V models, especially nonlinear models, for control synthesis. The rst MA V similar to the one sho wn in Figure 1–1 w as tested in a wind

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7 tunnel, the Basic Aerodynamics Research T unnel (B AR T), at N ASA Langle y Research Center [ 34 ]. These test pro vided researchers with aerodynamic coef cients and control properties to further analyze the stability The w orks of W aszak et al. in [ 46 ], documented the aerodynamic performance and control properties from this wind tunnel data by in v estigating trim conditions and the aircraft' s response to a control deection at v arious angles of attack and dynamic pressures. These w orks proceeded by a second publication [ 45 ], in which linearized models were generated from the same data using linear re gression techniques o v er a range of dynamic pressures. Control simulations were then constructed for these models to in v estigate v ehicle trim and basic stability and control properties. The control structure consisted of a nonlinear dynamic in v erter which con v erted measured angular rates to control surf ace deections. The success of the e xible wing MA V has been demonstrated, by the UF team, at the International Society of Structural and Multidisciplinary Optimization Micro Aerial V ehicle Competition by recei ving the o v erall rst place a w ard for the last four years. This competition continues to gro w e v ery year as more uni v ersities become in v olv ed. Some other uni v ersities that are intensely pursuing MA Vs include BYU, Arizona, and Notre Dame. 1.2.2 Image Processing The task of ying autonomous MA Vs in en vironments that are conned by b uildings, trees and additional features, as well as poor weather conditions, requires a host of inno v ations in vision-based ight control. T w o areas, in particular that need to be addressed before vision controllers can be designed include vision processing and pattern recognition. The images acquired by a standard camera contain an enormous amount of data for processing, such as pix el color Ev en MA Vs tra v eling at speeds around 25 mph still require a signicant number of frames per second to incorporate vision in the feedback loop. In real time, an algorithm using the complete image data for control design w ould be computationally e xpensi v e. Therefore, strate gies in the last

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8 se v eral years ha v e e v olv ed in attempt to process and compress this data without the loss of important image features for controller design. Image processing attempts to handle lar ge data by e xtracting features from the image that are signicant in the en vironment to reduce computation time. F or e xample, in a city the outline of b uildings w ould be a signicant feature for an aircraft while the details of windo ws and doors may not be as important. The dif culty in v olv es training smart algorithms to recognize and distinguish between important features and details that may be omitted, as well as free space and occupied space. Some techniques using fuzzy logic or statistical color matching ha v e been studied to reduce such lar ge data sets while determining occupied space through surf ace triangulation [ 25 29 30 ]. Once an image has been reduced within the bandwidth limits, pattern recognition is required to classify re gions based on particular features using this reduced image. Some important features that may be used from an image include color and te xture. Although, the common feature used for a still shot are the color components for each pix el, which are di vided into red, blue and green components (i.e., the RGB color cube). Statistical modeling of the distrib ution of pix el color using Expectation Maximization algorithms (EM), is a classical technique for classication. This concept w as demonstrated to detect a horizon line based on the classication of each pix el to a set of kno wn distrib ution models [ 8 ]. These kno wn distrib ution models are computed based on a kno wn data set, which in this case w ould be a picture of the sk y and ground on a particular day and is considered the training data. The models are then applied to unkno wn data sets (i.e., images) and decides on the classication of each pix el belonging to the sk y or ground distrib ution. Therefore, the boundary between these tw o distrib ution is called the decision boundary or in this case the horizon line. Kalman lters or pattern tree structures can be added to this particular case to account for small v ariations in color which happens throughout the day or in dif ferent weather

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9 conditions, and noise to add rob ustness. This can account for small v ariations b ut will not apply to conditions where the sk y has changed color signicantly such as dusk or da wn. Other studies in recognition ha v e led to adv ances in areas such as object motion estimation and obstacle detection. Soatto, et al. ha v e documented se v eral methods in [ 37 38 39 40 41 42 ] which estimates the three dimensional motion of an object from a sequence of image projections commonly referred to as “Structure from Motion. ” These techniques pertain to nonlinear estimation and identication theory and can be solv ed by decoupling the states of the dynamic observ er that estimates motion and the structure parameters. Obstacle detection is based on similar concepts that identies objects tra v eling in and out of the image. The detection of these object and tracking requires some additional methods to estimate the motion of an y pix el o v er time. Se v eral recent studies [ 19 27 ] use Sarnof f s stereo processing for obstacle detection along with Mark o v Random Field Models to analyze and interpret the pix el motion. Once object detection algorithms become ef cient for real-time applications, controllers can be designed using this information as feedback for obstacle a v oidance in urban en vironments. A particular study for urban traf c situations has be gan to implement a f ast detection algorithm to a v oid hitting unseen pedestrians by using stereo vision and classication stages to control the brak e system [ 10 ]. 1.2.3 V ision Control The research done to address vision-based control on v ehicles has mainly been done in robotics for the 2-D case [ 1 2 15 28 ]. W ith motion constraints in certain directions, a robot has the ability to stop it' s motion before making a decision on the path based obstructions detected by the camera. This critical feature does not require the controls system to act in real-time and the v ehicle is able to tra v el along the circumference of an obstacle. On the other hand, an airplane is required to mak e decisions of the en vironment ahead in real-time to a v oid obstacles while maintaining

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10 forw ard v elocity required for ight. Other control e xamples in 2-D in v olv e highw ay dri ving, where studies ha v e used vision sensors to track lane di viders and obstacles within a x ed range in both forw ard and lateral directions [ 4 6 20 23 24 26 ]. Some open control problems and issues with hardw are de v elopment using vision feedback are assessed in Sznaier and Camps [ 43 ]. Some research has applied vision control in free oating objects such as underw ater v ehicles, lighter than air blimps, and space docking [ 7 9 16 36 35 ]. These studies ha v e demonstrated object detection and tracking ability in man y dif ferent objecti v es. A common feature in these particular v ehicles is the ability to ho v er in a x ed position. This adv antage w as described abo v e in the 2-D case where the v ehicle stops it' s motion to process visual data before making a decision. Helicopters are a prime e xample, although the controls required to ho v er are comple x, computation time can be gained when a path is unkno wn. Mission capabilities for tar get search and tracking ha v e been demonstrated using helicopters and are documented in the literature [ 3 33 ]. As this vision control concept slo wly progress to w ard aircrafts, the computations for image processing and obstacle detection for path planning in real-time become e xtremely dif cult. By considering vision control for aircrafts, one has to be a w are of the additional de grees of freedom and performance constraints of the v ehicle. The ability to turn or climb at lar ge rates will strongly depend on the agility of the aircraft. The speed of an aircraft, e v en around 25 mph requires f ast image processing to detect and track obstacles that continuously enter the eld of vie w Obstacle detection for aircraft has been e xamined in [ 11 ] where a morphological lter w as used for image processing and object detection by retaining small sized features, which were assumed tar gets, while remo ving lar ge features, which w as assumed to be the background. An estimation problem of the aircraft' s motion can then be calculated using an e xtended Kalman lter approach to subspace constraints, which arises when points stationary

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11 on the en vironment are track ed on the image plane [ 14 ]. Recent studies ha v e gone further by inte grating object detection with control designs for autonomous aerial refueling [ 47 21 ] and state determination for night landings [ 5 ]. The simulations for these studies both documented precise tar get tracking for aerial refueling and the feasibility of night landings, both with good disturbance rejection. The design of autopilots for unmanned MA Vs using vision as the primary control sensor has only be gun in the research community Signicant strides were made at the Uni v ersity of Florida when a horizon detection algorithm, described in Section 1.2.2 w as used to feedback roll angle for lateral control [ 8 ]. The control design used in this paper consisted of a proportional/deri v ati v e (PD) feedback loop along with conditions to maintain the horizon in the image plane. 1.3 Ov ervie w This thesis documents the initial progress made in vision-based autonomous ight for micro air v ehicles at the Uni v ersity of Florida. First, a relationship is deri v ed between feature points vie wed in the image plane and the aircraft equations of motion. Analytical simulations were then studied for this system to nd the relation between the horizon' s roll angle and the aircraft' s body roll angle through camera nonlinearities. A v ehicle w as w as then f abricated at the Uni v ersity of Florida equipped with a single camera for e xtensi v e autopilot testing. The algorithms for image processing and horizon detection were used from pre vious w ork done at the Uni v ersity of Florida' s Machine Intelligence Lab and is documented in Ettinger et al. [ 8 ]. This thesis attempts to b uild on the w orks done in this particular paper by incorporating an autopilot methodology to both roll and heading using vision feedback. The control systems were designed for lateral directional using standard proportional and inte gral control structures. Flight test were then used to adjust the controller gains for the desired performance.

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12 The vision feedback in this thesis uses the horizon detection algorithm to deter mine the roll angle of the aircraft. The main disadv antage to this algorithm restricts the aircraft to operate in an open en vironment where the horizon is al w ays in vie w Therefore, the w ork presented in this thesis is a small step in the o v erall vision control problem for urban en vironments, where the horizon is no longer in vie w The detection methodology can be e xpanded to to features such as b uildings instead of the horizon approach presented in this thesis.

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CHAPTER 2 DERIV A TION OF COUPLED CAMERA AND AIRCRAFT EQ U A TIONS OF MO TION 2.1 Problem F ormulation The goal of this chapter is to formulate and deri v e the coupling between the equations of motion for MA V' s and the motion of feature points, vie wed by cameras attached to the aircraft, in the focal plane. These equations will be deri v ed in a general form that will include indicies for the number of cameras, k and the number of feature points, a e xtracted by from the image. An important assumption made re garding feature points is an image processing algorithm has been created to e xtracted critical features of the en vironment, such as corners of b uildings, trees and so forth. The equations will in v olv e kno wledge of each camera' s mounting position and orientation relati v e to the aircraft' s center of mass. An illustration of this formulation is depicted in Figure 2–1 which describes the kinematics of a MA V in ight with details of the k t h camera. The coordinate frames, or basis frames, in this deri v ation consist of an inertial frame, E a body x ed frame, B and the k t h camera x ed frame, C k which also can be seen in Figure 2–1 Each frame is represented as a right-handed, orthonormal basis e xpressed as unit v ectors. The Figure also contains an image, where feature points are e xtracted, to emphasize the application of vision for autonomous v ehicles in cluttered en vironments for closed-loop control. 2.2 Aircraft P arameters The aircraft equations of motion for a MA V are the standard equations which ha v e been deri v ed in a typical aircraft mechanics book. The important aircraft states needed for the camera motion consist of the v elocity of the center of mass of the aircraft, E v c with respect to the inertial frame, the angular v elocity E w B of the body frame with 13

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14 Figure 2–1: MA V Kinematics respect to the inertial frame, the position of the center of mass of the aircraft, R c with respect to the inertial frame, and the orientation angles of the aircraft with respect to the inertial frame. These v ectors will appear e xplicitly in the deri v ation of the camera equations and are written belo w in terms of their components. Here the notation for a v ector quantity is denoted using an under -bar ( e .g v is a v ector quantity). E v cu ˆ b 1v ˆ b 2w ˆ b 3 E w Bp ˆ b 1q ˆ b 2r ˆ b 3 R cX c ˆ e 1Y c ˆ e 2Z c ˆ e 3 The angular v elocity E w B is a function of the time rate of change of the orientation angles. These angles correspond to a sequence of 2-D rotations which denes the orientation of the body axis relati v e to the inertial frame and are usually dened for an aircraft as roll, pitch, and ya wfqyor also referred to as a (3-2-1) Euler rotation. 2.3 Dening Camera P arameters The parameters that will be in v olv ed in deri ving the equations for a camera mounted to an aircraft include the position of the camera relati v e to the body basis, position of a feature point relati v e to an inertial basis, the position of a feature point relati v e to the camera basis, and the aircraft states described in the pre vious section.

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15 The position v ector of the k t h camera relati v e to the body basis is denoted as D k and is e xpressed belo w in component form. D kD k1 ˆ e 1D k2 ˆ e 2D k3 ˆ e 3 The orientation angles dened by a 3-2-1 Euler rotation matrix also relate the camera basis to the body basis in a similar f ashion. This is also represented in a general form based on the number of cameras, k to allo w multiple cameras with dif ferent orientations. These angles are dened to bef kq ky kcorresponding to roll, pitch, and ya w for the k t h Camera basis. Both the position and orientation of the k t h camera are illustrated in Figure 2–2 Figure 2–2: Coordinate Systems Thus, the parameters dening the k t h camera described abo v e can be assembled into a v ector to simplify and compact the notation and will be referred to as a k a T kt D k1D k2D k3f kq ky kf kThe parameter f k is the focal length of the k t h camera and can v ary for multiple cameras. K eep in mind this v ector can be e xtended to include radial lens distortion,

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16 CCD array misalignment and so forth b ut this deri v ation will retain only the position, orientation, and the focal length for each camera without loss of generality The image captured by an on-board camera requires processing to e xtract feature points that are critical to the aircraft' s path planning. This w ork has been done for man y applications using pattern recognition techniques and vision processing [ 27 ]. The assumption made for this deri v ation is the vision processing has been addressed, e xtracting a minimum amount of feature points, lines, and/or planes to learn the current surroundings. A typical scenario is depicted in Figure 2–3 which sho ws an image of a b uilding being reduced to feature points and lines for guidance, na vigation, and control through this urban terrain. Man y problems with free and occupied space still arise when a f amily of feature points are predetermined. Some statistical methods, based on color in pattern recognition ha v e attempted to address this problem with a reasonable de gree of accurac y b ut problems arise when using this statistical model in a cluttered en vironment [ 30 ]. Figure 2–3: Dening Feature Points The remaining parameters characterize the geometry between the aircraft' s center of mass, the k t h camera' s lens position and the a t h feature point located on points, lines and planes e xtracted from an image. A v ector diagram of this geometry is illustrated in Figure 2–4

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17 Figure 2–4: V ector Diagram Here the position of the center of mass of the aircraft is sho wn and is again denoted by R c The remaining parameters sho wn in this gure consist of the position of the a t h feature point relati v e to the both the inertial frame and the camera frame, denoted as x a and h a The components of these tw o v ectors are e xpressed in the basis written belo w x ax a1 ˆ e 1x a2 ˆ e 2x a3 ˆ e 3 h ah a1 ˆ c 1h a2 ˆ c 2h a3 ˆ c 3 2.4 Camera Equations of Motion Recall that the basis frames dened earlier are right-handed, orthonormal meaning the ax es permutate according to the cross product and the dot product between normal unit v ectors are zero. A 2D axis rotation can then be dened through the direction cosine, relating one set of coordinates to a ne w set which is only a rotation from the rst. The 2D transformations dened belo w are rotations about a particular axis. The subscript denes the axis of rotation, for e xample l 3fis a rotation about the three axis by an angle f .l 3y k c y k s y k 0s y k c y k 0 0 0 1 n l 2q k c q k 0s q k 0 1 0 s q k 0 c q k n l 1f k 1 0 0 0 c f k s f k 0s f k c f k n

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18 Using a series of three 2-D rotations, a set of coordinates can be transformed uniquely into an y desired orientation. Therefore, the basis transformation between body basis and the k t h camera basis can be dened as follo ws: ˆ c 1 ˆ c 2 ˆ c 3 k c l 1f k l 2q k l 3y k ˆ b 1 ˆ b 2 ˆ b 3 k b (2.1) Lik e wise, the same sequence can be used to relate the inertial basis with the body basis through the aircraft' s orientation angles. ˆ b 1 ˆ b 2 ˆ b 3 b l 1f l 2q l 3y ˆ e 1 ˆ e 2 ˆ e 3 e (2.2) 2.4.1 Feature Point Position The deri v ation of the camera equations of motion starts by summing the position v ectors, illustrated in Figure 2–4 for the a t h feature point relati v e to the inertial frame. x aR cD kh a (2.3) Solving Equation 2.3 for the position of the a t h feature point relati v e to the camera basis, results with the follo wing v ector equation. h ax aR cD k (2.4) Each term in Equation 2.4 can be e xpressed in the camera basis by applying the Euler transformations, sho wn in Equations 2.1 and 2.2 resulting in the nal v ector equation for the feature position relati v e to the camera basis.

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19 h a c l 1f k l 2q k l 3y k l 1f l 2q l 3y x aR c e l 1f k l 2q k l 3y kD a b (2.5) Writing this in a more compact form using indicial notation results with the the nal e xpression of the position of the a t h feature point relati v e to the camera basis. h ailf kq ky ki j lfqyj sx aR cslfqyi j D k j (2.6) 2.4.2 Feature Point V elocity W e can characterize a feature point in the focal plane further by deri ving it' s v elocity v ector The v elocity of the a t h feature point in the focal can be found by taking the time deri v ati v e of Equation 2.4 with respect to the inertial frame. E d d th a E d d tx a E d d tR c E d d tD k(2.7) Looking at each term indi vidually the deri v ati v e is with respect to the inertial frame while most of these v ectors are e xpressed in other basis. Therefore, the Deri v ati v e Theorem is emplo yed on terms not e xpressed in the inertial basis. F or a general v ector A e xpressed in the J frame, the Deri v ati v e Theorem states the time rate of change of A in the I frame is equal to the time rate of change of A in J plus the angular v elocity of frame J with respect to frame I crossed with A Mathematically this is sho wn as follo ws: I d d tA J d d tA I w JA The position v ector x a is constant in magnitude and direction with respect to time in the inertial frame and therefore the rst term on the right hand side of Equation 2.7 is zero. The position v ector of the aircraft' s center of mass, R c is e xpressed in the inertial basis and therefore the time deri v ati v e becomes the follo wing:

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20 E d d tR c R c Using the Deri v ati v e Theorem described abo v e for the remaining v ectors h a and D k and combining results discussed for each term, Equation 2.7 becomes the follo wing: C d d th a E w Ch a R cB d d tD k E w BD k (2.8) This equation can be reduced further by analyzing the term B d d tD k. This is the time rate of change of D k with respect to the body basis. F or a x ed camera position, this deri v ati v e is zero because it' s constant in magnitude and direction relati v e to the body basis and therefore reduces Equation 2.8 to the follo wing C d d th a E w Ch a R cE w BD k Solving this equation for the v elocity of the a t h feature point with respect to the camera basis is found by manipulating the abo v e equation. C d d th a R cE w BD kE w Ch a (2.9) Using the Addition Theorem, each angular v elocity term can be e xpressed as a sum of intermediate coordinate transformations until the desired basis is reached. F or e xample, the angular v elocity of A w C is the sum of the angular v elocity going from frames A to B and the angular v elocity going from frames B to C where frame B is dened as an intermediate frame. In this deri v ation transforming from frame E to B requires tw o intermediate frames to accomplish this task, where F and G are the intermediate frames for the angular v elocity belo w E w BE w FF w GG w B y ˆ f 3 q ˆ g 2 f ˆ b 1

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21 Each component of this equation can be written in the B basis by the rotational transformations dened in Equation 2.2 E w B l 1f l 2q 00 y f l 1f 0 q 0 g f 00 b Recall, this angular v elocity e xpressed in the B basis as the follo wing E w B p q rT b The angular v elocity of the C frame with respect to the E frame requires tw o additional intermediate frames, O and P from the angular v elocity sho wn abo v e. E w CE w FF w GG w BB w OO w PP w C y ˆ f 3 q ˆ g 2 f ˆ b 1 y k ˆ o 3 q k ˆ p 2 f k ˆ c 1 Lik e wise, each component of this equation can be written in the C basis by the rotational transformations dened in Equations 2.1 and 2.2 E w C l 1f k l 2q k l 3y k l 1f l 2q 00 y f l 1f k l 2q k l 3y k l 1f 0 q 0 g l 1f k l 2q k l 3y k f 00 b l 1f k l 2q k 00 y k o l 1f k 0 q k 0 p f k 00 c

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22 Dening the components of the equation abo v e as W k for each camera e xpressed in the corresponding camera basis. E w CW k W x W y W zk c Therefore, Equation 2.9 becomes the follo wing: C d d th a R cE w BD kW kh a (2.10) h x h y h z X c Y c Z c e q D kzr D ky r D kxp D kz p D kyq D kx b W ky h azW kz h ay W kz h axW kx h az W kx h ayW ky h ax c (2.11) T ransforming all coordinate components into the C basis and using indicial notation results with a nal e xpression for the v elocity of the a t h relati v e to the k t h camera frame. h ai lf kq ky ki j lfqyj s R cslf kq ky ki je io p E w Bo D k p e il k E W C l h ak (2.12)

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CHAPTER 3 CAMERA NONLINEARITIES 3.1 F ocal Length P arameter 3.1.1 F ocal Plane Position The coordinates dened in the focal plane arenwhich represents a tw odimensional projection vie wed by the camera. Therefore, the a t h feature point will appear in the focal plane with the coordinates an afrom the component equation listed belo w af h x ac x h z ac z n af h y ac y h z ac z (3.1) Again, the parameter f k is the focal length of the k t h camera. The v ector componentsc xc yc z, dened as c are the of fset distances of the lens relati v e to the camera basis. F or e xample, c x is the distance the lens is of fset in the x -direction from the camera basis. If the origin of the camera basis is place at the lens, Equation 3.1 reduces to Equation 3.2 (i.e. c 0). af h x a h z a n af h y a h z a (3.2) F or simplicity it is assumed for the remainder of the deri v ation the lens location and camera basis coincide and therefore Equation 3.2 will be used. This equation is only a function of the position relati v e to the camera basis to a feature point, deri v ed in Chapter 2.4.1 and the camera' s focal length. In summary the position of each feature point in space can no w be character ized by it' s position in the focal plane by substituting the required components of Equation 2.6 into Equation 3.2 23

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24 A simple e xperiment w as done using Equation 3.2 to characterize the mapping associated with feature points in the inertial frame transforming to the focal plane. A pattern of feature points w as dened in the inertial frame as a plane perpendicular to the Y axis and is sho wn in Figure 3–1 The feature points on this plane were then rotated se v eral times to create a series of planes. Each plane w as x ed on the left side while rotating the right side closer to the camera' s position. An illustration of this setup is depicted in Figure 3–2 where point C is dened as the camera' s position and is gi v en as C 0 0 100T 20 15 10 5 0 5 10 15 20 80 85 90 95 100 105 110 115 120 X (ft)Z (ft) Figure 3–1: Feature Point Grid Each plane contains this set of grid points which are then substituted into Equation 2.6 assuming a x ed aircraft with a single camera placed at the center of mass along with x ed basis frames. The feature point positions were then determined relati v e to the camera basis. Therefore, the follo wing aircraft and camera parameters reduce to the follo wing:

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25 20 10 0 10 20 0 50 100 80 90 100 110 120 Y (ft) X (ft) C Z (ft) (a) 3D 15 10 5 0 5 10 15 0 10 20 30 40 50 60 70 80 C X (ft) Y (ft) (b) XY Plane Figure 3–2: Grid Rotation E v c 0 0 0T E w B 0 0 0T R c 0 0 100T D 0 0 0T Also, the rotation matrices reduce to the follo wing for a le v el camera and MA V :l 1f k l 2q k l 3y k 0 0 1 01 0 1 0 0 n l 1f l 2q l 3y 0 1 0 1 0 0 0 01 n

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26 After the position of each feature point, h a w as determined relati v e to the camera basis, the focal plane position w as then calculated using Equation 3.2 through direct substitution. Figures 3–3 3–6 sho w the feature point position for each grid plane as it' s rotated to w ard the camera' s position for a set focal length, where the plane in the rst set of plots is parallel to the inertial XZ plane. Here the focal length, f w as set to a constant v alue of f01 mm for all the plots belo w 20 15 10 5 0 5 10 15 20 80 85 90 95 100 105 110 115 120 X (ft)Z (ft) (a) Inertial Frame 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 m (mm)n (mm) (b) F ocal Plane Figure 3–3: Planar Feature Points 20 15 10 5 0 5 10 15 20 80 85 90 95 100 105 110 115 120 X (ft)Z (ft) (a) Inertial Frame 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 m (mm)n (mm) (b) F ocal Plane Figure 3–4: Sk e wed Feature Points Sloping 2.5 Units

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27 20 15 10 5 0 5 10 15 20 80 85 90 95 100 105 110 115 120 X (ft)Z (ft) (a) Inertial Frame 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 m (mm)n (mm) (b) F ocal Plane Figure 3–5: Sk e wed Feature Points Sloping 5 Units 20 15 10 5 0 5 10 15 20 80 85 90 95 100 105 110 115 120 X (ft)Z (ft) (a) Inertial Frame 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 m (mm)n (mm) (b) F ocal Plane Figure 3–6: Sk e wed Feature Points Sloping 10 Units Notice as each plane is rotated to w ard the camera, the focal plane image becomes increasingly distorted. The rst set of plots re v eals when the depth, inertial Y direction, is held constant the focal plane mapping retains the the initial shape with some scaling f actor proportional to the focal length. As the plane is rotated by changing the depth, the feature points which are closer appear to be spreading further apart while points that are at a greater distance appear to con v er ge closer together As seen in Figure 3–6 the feature points contained in the right half plane ha v e increased their

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28 separation distance signicantly compared to the pre vious cases. Each grid plane rotation w as doubled so a comparison can be made with the distortion distance. As the plots illustrate, as the rotation plane is doubled the resulting distortion distance has increased more than twice. Therefore, the focal length relation between feature point location and depth is nonlinear A formal mathematical statement is presented belo w in Equation 3.3 .n Gf kx ay(3.3) The function G describes some nonlinear function which maps feature point position in inertial space to the focal plane. This function only relates the nonlinearities describing depth perception onto the image plane through focal length and is strongly a function of the x y component. 3.1.2 F ocal Plane V elocity The nal step is to formulate an e xpression for the v elocity of feature points in the focal plane. Therefore, the focal plane v elocity is found by taking the time deri v ati v e of the position dened in Equation 3.2 af h ax h azf h ax h az2 h az n af h ay h azf h ay h az2 h az (3.4) The focal plane v elocity of the a t h feature point relati v e to the k t h is nalized by substituting both equations for position and v elocity deri v ed in Equation 2.6 and 2.12 into Equation 3.4 3.2 Lens Distortion Another important nonlinearity associated with a camera is image distortion due to the curv ature of the lens. This ef fect can be described as a tunnel vision image, where feature points on the e xtreme sides are dra wn to w ard the horizon centerline. This is a

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29 planar distortion unlik e the the focal length mapping described in the pre vious section in which the shape w as unchanged for the planar case. An e xperiment w as conducted using a standard Marshell CMOS color camera with 310 TV lines of resolution to characterize image distortion due to lens curv ature. Figure 3–7 illustrates the dramatic w arping done to a set of e v enly spaced grid points. Figure 3–7: Lens Curv ature The horizontal and v ertical centerlines retain a linear curv e while lines abo v e and belo w follo w this parabolic conca v e and con v e x mapping that is axisymmetric. Lik e wise, this mapping can be e xpressed mathematically as a nonlinear function depending on inertial space and the focal length, as gi v en in Equation 3.5 .n Lf kx axx az(3.5)

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30 The camera nonlinearities described abo v e will ha v e a signicant ef fect on a controller design for obstacle detection and a v oidance. Buildings appearing in the image plane, depending on their location, will appear closer or further a w ay than the y actually are due these distortions. Therefore, the functions G and L are required to accurately describe the motion of feature points in real space for control designs and will v ary for each particular camera.

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CHAPTER 4 LA TERAL A UT OPILO T CONTR OL DESIGN The long term goal of this autopilot is to structure the controls system that w ould allocate GPS w aypoint tracking for MA Vs using vision feedback. The controls layout for an aircraft is typically separated into lateral directional and longitudinal controllers. This section will document the design of a lateral autopilot control system for a MA V by continuing the in v estigation of vision-based antonomy presented in the literature [ 8 18 ]. This design can be easily e xtended to lateral w aypoint tracking by incorporating an outer -loop that in v olv es guidance algorithms. The lateral control system deals with maintaining a desired roll and/or heading angle through aileron and rudder deections. By designing the lateral controls system independently some coupling in longitudinal states will result from these surf ace deections. F or e xample, the sideslip induced by a roll angle can ha v e a signicant on the longitudinal states with the loss of altitude. This may be modied in future w orks by considering an aileron-rudder interconnect to pre v ent the nose from drifting do wnw ard during a bank hold. This thesis will only consider the ef fects directly related to the lateral states and will disre gard these coupling terms. The only lateral directional terms that are of interest for this control design include roll and heading angle. F or this section, these measurements are assumed to be kno wn perfectly The sensors which pro vide these quantities will introduce a nite sampling rate along with some uncertainty which will be discussed later in the chapter and again in Chapter 6.1 The control architecture for this autopilot will be gin with an inner -loop controller and continue to an outer -loop design. The inner -loop controller will attempt to maintain a desired roll angle, while the outer -loop will control the heading direction. 31

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32 The general designs of these controls system will be discussed in further detail during the remaining sections. 4.1 Roll Control Design A standard approach using proportional and inte grator blocks w as chosen for this particular loop. This classical controls technique computes an error based on the dif ference between the desired and measured state and mak es that proportional to a serv o deection. The inte grator block helps to manipulate both the steady state error and the rate of the response. The lateral steady state error correction w as used to account for asymmetries in the airplane due to construction and an y net torques caused by the motor F or the case of a roll controller the architecture can be accurately described in block diagram form in Figure 4–1 K f 1 z K I f c e f d a D d a t r im d a f + + Figure 4–1: Roll Control Autopilot The trim control block consist of a discrete time inte gral, and a proportional gain, K I The inte gral block is used primarily for impro ving steady state by continuously dri ving the roll error to zero. Therefore, for a zero de gree roll command the control will maintain straight and le v el ight. The proportional gain is then applied to the inte gral state to con v ert this v alue to a trim deection, d a t r im which is then sent to the serv os. The remaining control element is a proportional gain where the dif ference between the measured roll, f and the roll command, f c is dened as the error This roll error is then con v erted to an aileron deection, d a D by the proportional gain, K f The total

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33 aileron deection is then computed by summing the indi vidual deections determined from both loops, as sho wn in Equation 4.1 d ad a t r imd a D (4.1) This controls system is only considering maintaining roll angle to a desired v alue and does not incorporate coupling terms during this maneuv er such as maintaining altitude during a bank hold. 4.2 Heading Control Design F or the heading control design, a nonzero roll angle will be used to change the measured heading direction. Therefore, the roll controller designed in the pre vious section will be implemented in the heading controller as the inner loop. The controls structure is k ept consistent by using a proportional feedback controller for heading as well. The block diagram for this open-loop controls system is depicted in Figure 4–2 K y K f 1 z K I f c e f d a D d a t r im d a f y y c + + Figure 4–2: Heading Control Autopilot The heading error is computed and set proportional to a roll command through K y As the aircraft tracks a roll angle, the heading will be gin to change which in turn will reduce the heading error So ef fecti v ely as the measured heading approaches the commanded heading the error will go to zero and the MA V will be gin to roll back and e v entually reach 0 de g roll angle. The aileron deections are again computed using Equation 4.1

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34 4.3 Closed-Loop Control 4.3.1 Bank Hold Careful consideration of the vision-based sensor should be tak en before designing the closed-loop roll control system. The resolution of the measured roll angle w as found to be a constant445 de g Potential problems will e xist if the roll error is computed and used in the control loop. F or e xample, if the roll command w as 2 de g the error in roll angle w ould al w ays be a nonzero v alue, due to the f act that the vision system is unable to resolv e belo w 4.45 de g al w ays resulting with a nonzero aileron command. Physically the airplane will continuously try to dri v e the error to zero by deecting in the correct direction causing an o v ershooting to the measured resolution follo wed by an opposite deection to correct for the o v ershoot. This type of response can be described as a limit c ycle oscillation centered around the desired command. The roll command is replaced with discrete v alues between the range40f c40 de g where the maximum roll command w as set to40 de g to a v oid this resolution issue. A bench test w as then done to v erify all possible v alues the roll sensor w ould measure between 0 and40 de g and is documented in T able 4–1 T able 4–1: Discrete Roll Command Output V alues Roll Command Discrete Roll Roll Command Discrete Roll Range ( de g ) Command ( de g ) Range ( de g ) Command ( de g ) 0f c22 0 22f c0 0 22f c66 4.45 66f c 22 -4.45 66f c111 8.90 111f c 66 -8.90 111f c155 13.35 155f c 111 -13.35 155f c200 17.80 200f c 151 -17.80 200f c244 22.25 244f c 200 -22.25 244f c289 26.70 289f c 244 -26.70 289f c333 31.15 333f c 289 -31.15 333f c370 35.60 370f c 333 -35.60 Another potential resolution problem occurs when computing the roll error for the inte gration block. F or the e xample gi v en abo v e, the v alue of the error will alternate

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35 between 2 when the measured roll angle is zero and 2.45 when the measured roll is angle is 4.45; again creating a possible limit c ycle oscillation due a nonzero roll error Therefore, when the roll error is less than the resolution for a gi v en command, the error is then set to zero. The closed-loop design of the roll controller can be described in block diagram form through Figure 4–3 Some additional blocks were added to account for these uncertainties in the system and camera nonlinearities. D K f M A V L G R 1 z K I f c fc e f T r im d a D d a t r im f d a + + Figure 4–3: Closed-Loop Roll Control Design The discretizer blocks, D and R were used to eliminate limit c ycle oscillations associated with a lo w resolution in roll angle. Block D con v erts the gi v en roll command into discrete v alues associated with the horizon sensor where these v alues are gi v en in T able 4–1 The error associated with the horizon resolution, as described abo v e, is represented as block R The remaining blocks G and L describe the nonlinear mapping of feature points in inertial space to the focal plane due to depth and lens distortion, which is discussed in Chapter 3 4.3.2 Heading Hold As stated before, the heading controller consists of an outer -loop feedback using ya w angle to command the inner -loop bank hold. The closed-loop block diagram for a proportional heading controller is depicted in Figure 4–4

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36 K y D K f M A V L G R 1 z K I y c e y f c fc e f T r im d a D d a t r im f y d a + + Figure 4–4: Closed-Loop Heading Control Design The lateral control system using the roll control will be applied to a particular MA V testbed, described in the Chapter 5.1 using the horizon detection algorithm as a sensor to estimate roll. The gains will be determined through numerous ight tests and documented in the remaining sections. These results along with the nal response plots will be presented in Chapter 6.2

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CHAPTER 5 EXPERIMENT AL SETUP 5.1 Micro Air V ehicle Description As stated in Chapter 1.2.1 the Uni v ersity of Florida has an on campus f acility to f abricate MA Vs in v arious sizes customized for a particular mission. In each case, the v olume of the fuselage is designed to house ight components and payload necessary for a particular mission. In the case of an vision-based autopilot MA V data and video packages along with the required batteries must be incorporated in the design of the fuselage. Once the total weight of the v ehicle is determined the required wing area and propulsion system can be selected. The MA V b uild for this particular mission w as a modied design of the standard MA V at UF The structural material of the airframe w as still constructed using layers of composite carbon ber attached to a e xible wing design, as described in Chapter 1.2.1 A series of pictures of this MA V are sho wn in Figure 5–1 Notice the location of the camera has replaced the traditional position of a propeller design. Some adv antages of this camera position are (1) a direct correlation between horizon roll angle and body axis roll and (2) a camera pointing out the nose will acquire better images due to the steady o w conditions. The propeller is then placed behind the wing on a shaft that connects the fuselage to the horizontal and v ertical stabilizers. This type of propulsion system allo ws for a more steady laminar o w around the wing due to the absence of shed v ortices from the propeller The nal design of the MA V testbed used for vision-based autopilot control has typical properties listed in T able 5–1 A wing morphing technique w as applied to the e xible wings to ef fecti v ely control the roll state. The term morphing, w as coined because of the bending or twisting of 37

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38 Figure 5–1: MA V Prototype for V ision-Based Control T able 5–1: MA V Properties W ingspan 24 in W eight 500 gr ams P ayload Capacity 200 gr ams Actuators 4 the wings to change camber cord, span, area, etc which ef fecti v ely changes the ight characteristics of the v ehicle through angle of attack. This w as rst implemented mainly because MA V' s with these types of e xible wings are dif cult to incorporate a standard aileron, due to additional structural reinforcements needed to di vide the wing. After e xtensi v e ight test, the morphing of the wing demonstrated a substantial control authority in roll with little induced ya w (i.e. a more pure roll response). The Uni v ersity of Florida has been looking at se v eral simple w ays to morph the wing for roll control [ 12 ], one in particular w as used in the design of this MA V This design used a torque rod mounted near the wing tip and connected to a serv o inside the fuselage which morphed the wing by pushing or pulling on the rod. The implementation of this concept on the current MA V is illustrated in Figure 5–2

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39 Figure 5–2: T orque Rod Design An illustration in Figure 5–3 sho ws the slight change in ef fecti v e wing area by comparing the undeected wing to the morphing deection. F or this particular e xample, the left wing is deected do wnw ard which in turn produces a positi v e roll (i.e. right wing do wn) by the additional lift on the left wing. Flight test ha v e sho wn that morphing only requires a small amount of serv o deection to produce reasonable bank angles. (a) W ings Undeected (b) W ings Deected using Morphing Figure 5–3: Morphing Control Ef fectors The remaining control surf aces, ele v ator and rudder were implemented in more traditional w ay using the basic ele v ator on the horizontal stabilizer and rudder on the v ertical stabilizer These surf aces along with the morphing deection constitutes full

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40 rotational de grees of freedom for the MA V The serv o connectors to both the ele v ator and rudder were placed through a concentric metal pipe which passes in the middle of the propeller bearings. This design pro vides a compact method which helps to conceal these connectors mainly from being damaged. The serv os used in this MA V were model DS 281 made by JR Serv o. The control surf aces required four serv os; tw o for the morphing and one for each ele v ator and rudder which all weighs approximately 80 gr ams The propulsion system is po wered through a Hack er brushless electric motor that spins roughly at 60,000 RPM and can produce a maximum of 16 oz of thrust. The motor is attached to a 6 in propeller through a tw o stage gearing system, which is sho wn in Figure 5–4 Considering the weight of the v ehicle and the on board po wer ight durations usually last approximately 15 min at full throttle using a single 3 cell Lithium battery This 3 cell battery also po wers the serv os through a transcei v er board. Figure 5–4: Push T ail Propeller Design The on board sensors include GPS for location, speed, and course, an altimeter for altitude, and the vision system for horizon detection. The GPS sensor manuf actured by Furuno, uses the current and last position to calculate both speed and course with an accurac y of 5 de g where the position itself is accurate to 20 ft The output units consist of longitude and latitude in de grees, course in de grees, and the speed in ft/s The altimeter is a pressure based sensor which measures the relati v e gage pressure and

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41 has a resolution of 20 feet when con v erted to altitude. The camera of the vision system is a Marshall color CMOS camera with a resolution of 310 TV lines. The camera introduces a nonlinear mapping of feature onto the image plane due to the focal length and the curv ature of the lens, which w as described in Chapter 3 5.2 Hardw are Architecture The components used to demonstrate vision control w as restricted to a 200 gr am on-board payload with a size constraint of 3 inc hes Therefore, it w as decided for the initial platform to transfer all data processing to a ground station laptop. This also allo wed for human monitoring of the data on the ground during ight test. The main hardw are components consist of an on-board computer netw ork ed through a wireless data-link, transcei v ers, a ground station laptop, a Son y V ideo W alkman, and USB con v erters. An illustration of the system architecture is depicted in Figure 5–5 The red and the black transmission lines indicate the video and sensor data steams correspondingly Trainer Switch Autopilot Control when Trainer = 1 Futaba Control when Trainer = 0 Firewire Figure 5–5: Hardw are Architecture Here the MA V contains an on-board custom microcontroller -based computer which communicates all sensor and video data to the ground station. This microcontroller is a modied v ersion of an Ateml A VR Me ga128. An additional board w as de v eloped to increase the amount of Flash memory of the A VR Me ga128 from 128kB to 256MB through an optional attachment and w as used for data logging. The

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42 complete computer system is 2-inches by 1.5 inches by 0.5 inches and weighs approximately 36 gr ams The video and sensor data is collected through the this on-board computer and streamed do wned to the ground station for data processing. The ground station, after processing this data, closes the control loop by sending serv o commands back to the MA V Additional data, such as serv o command and deection, w as also sent to the ground station through the microcontroller to v erify the control design. The sensor data and video streams are broadcast ed through separate transmission frequencies. The sensor data transcei v er operates at 900MHz, pro viding rates up to 57.6kbps and is connected to the ground station through a U AR T based serial port. This transcei v er w as a model A C4490 made by Aerocomm. Meanwhile, the video stream operates at 2.4GHz and is interf aced to the ground station through a Son y V ideo W alkman, via re wire. F or the initial ight test stages, a pilot w as k ept in the control loop to pro vide an o v erride capability during tak eof f, landing, and autopilot reco v ery This system w as incorporated by rerouting the control commands sent to the MA V through a standard Futaba controller using a custom interf ace. This interf ace emplo yed a trainer function which allo wed switching between autopilot and human control instantaneously and is also depicted in Figure 5–5 A custom board w as made for this communication link to pulse-width modulate the control signal sent from the autopilot. The serial connectors for both data communication and Futaba control were con v erted to USB through a K e yspan adapter which allo wed easy plug and play options for the ground station. The ground station laptop consisted of a Apple 12-inch Po werbook running at 1GHz with 512MB of RAM. The video processing on the laptop w as implemented in real-time using the described horizon detection algorithm. The video re wire communication w as then coded in softw are to couple the on-line ight image with the resulting horizon line. This w as mainly done so the ground station can pro vide

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43 a visual image to analyze during autopilot testing, which became a critical tool for de v elopment. 5.3 Camera Model for Horizon The camera nonlinearities described in Chapter 3 will ha v e a strong ef fect on the controller design using obstacle detection for a v oidance. Buildings vie wed by the camera will be w arped in the image plane resulting in f alse representation of distance. F or e xample, a b uilding could appear further a w ay in the image plane causing the controller to delay commands for a v oiding this object until it' s too late. Therefore, for a clutter en vironment, the functions G and L need to be incorporated in the control design. In the case of horizon detection, simple analysis can v alidate some assumptions for these functions. The plots in Figures 3–3 and 3–4 re v ealed that (1) if the depth of an object is constant the original shape is maintained in the image plane and (2) a small rotation to change the depth results with a small distortion. Therefore, if the distance between the object and the camera is increased to where it' s much lar ger than the distance in depth, the object' s shape is retained in the image plane. Figure 5–6 demonstrates this by increasing the relati v e distance from the camera to the grid points with the same rotation. The relati v e distance from the camera to the horizon line is much lar ger than the depth of the horizon and therefore can be approximated as a planar line in 3D space. This approximates the G function to a linear mapping from inertial space to the image plane. The lens distortion due to curv ature still remains a nonlinearity in the system and is depicted in Figure 5–7 for a horizon e xample. The image on the left is of a MA V in ight at straight and le v el and contains the horizon roughly in the center which correlates to little distortion. The image on the right no w sho ws a MA V in bank ed ight which lo wers and rises the horizon line in the image. The resulting horizon has

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44 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 m (mm)n (mm) (a) 70 ft 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 m (mm)n (mm) (b) 120 ft Figure 5–6: Image Plane Depth Comparison w arping ef fects associated with both sides. Depending if the horizon is abo v e or belo w the centerline, the w arping will be either conca v e or con v e x. W ith the horizon at such a f ar distance the w arping has little ef fect until the sides are approached. Figure 5–7: Lens Curv ature for a Horizon A better study of the horizon detection algorithm may re v eal a similar simplication for the function L The horizon line is determined by characterizing each pix el to a kno wn sk y or ground color distrib ution. F or e xample, shades of blue w ould be a common feature for the sk y while shades of green and bro wn w ould model the ground. Some structure is added to the algorithm that checks the neighboring pix els to add rob ustness. This accounts for an y misclassied shades of blue in the ground or greens and bro wns in the sk y A decision boundary is the found when the pix el distrib ution is shifted from sk y to ground in the image and is approximated by the linear line through statistical re gression. This linear line represents the determine horizon from which

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45 roll and pitch percentage are calculated. Figure 5–8 sho ws an o v erlay of the horizon algorithm onto the images gi v en Figure 5–7 Figure 5–8: Lens Curv ature with Horizon Approximation When applying a linear re gression curv e t, the w arped ends of the horizon are statistical outliers compared to the o v erall distrib ution and are not represented. The resulting linear t therefore, loses this nonlinearity and approximations can be made to ne glect this distortion for this particular case.

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CHAPTER 6 CLOSED-LOOP LA TERAL CONTR OL 6.1 Controller Implementation This section will interf ace the controls system with the hardw are described in Chapter 5 The architecture describes a close interaction between RC and autopilot modes. The ground station code allo wed easy implementation of the controller by summing the determined control deections around a trim condition. The commands are then o v er -written when the signal is transfered to RC mode, gi ving the pilot complete control of the MA V This transition from RC mode to the autopilot requires some consistent deection during this period. An of fset deection w as then coded for the initial serv o positions which matched the RC trim. This of fset helped remo v e an y transition bias sent to the serv os when the autopilot is acti v ated. Therefore, Equation 4.1 no w becomes Equation 6.1 with the additional of fset deection. d ad a t r imd a Dd a o f f se t (6.1) The on-board sensors that pro vide the roll and heading angles include the horizon detection algorithm and GPS. The horizon detection calculates the roll angle made by the horizon in the image plane and is updated at 35 Hz Meanwhile, the GPS sensor determines the course heading angle, relati v e to North, from past and present GPS location and is a v ailable at 1 Hz At this sample rate, the aircraft will potentially e xhibit oscillations around a gi v en heading command. In Chapter 5.3 the nonlinearities associated with the camera were assumed to ha v e little ef fect on the horizon because of the relati v e distance in depth. W ith 46

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47 this information, the roll angle determined from the horizon detection sensor can be approximated as the MA V' s body axis roll angle and is used directly in feedback. The control systems for both roll and heading commands no w reduce to the block diagrams sho wn in Figures 6–1 and 6–2 D K f M A V R 1 z K I f c fc e f T r im d a D d a t r im d a o f f se t f d a + + + Figure 6–1: Roll Control Block Diagram K y D K f M A V R 1 z K I y c e y f c fc e f T r im d a D d a t r im d a o f f se t f y d a + + + Figure 6–2: Heading Control Block Diagram The sample rate of this outer loop is 1 Hz in Figure 6–2 causing the performance of the heading track er to diminish. F or f ast mo ving v ehicle, the lo w sampling rate will cause o v ershoot oscillations in the heading response due to a lo w time constant. The response of the MA V during a heading command should be e xpected to f all within a threshold v alue abo v e and belo w the required heading, e v en when the controller is

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48 designed properly Commercial GPS sensor are also kno wn to ha v e a lar ge de gree of uncertainty with some reliability issues. Some issues include interference or e v en loss of satellite co v erage. W ith the loss of data due to dropouts, the performance of the controller can decrease tremendously Drifting of f course and lar ge sudden maneuv ers will result due to these types of dropouts. 6.2 Flight T esting and Results 6.2.1 Gain T uning As mentioned earlier a limited amount of MA V models ha v e been generated for control synthesis so little is kno wn for implementation. T ypically when a dynamic model is kno wn of the aircraft, a rough estimation of the gains can be made using a theoretical approach such as root locus. W ithout a model, as in this case, ight test iterations are required to adjust the gains for the desired response. F or the roll controller tw o gains need to be determined, the proportional gain and the inte gral gain, K f and K I F or the rst fe w ights, these gains were set v ery small to ef fecti v ely eliminate the controller Once the trim of the aircraft w as found for straight and le v el ight, using RC mode, adjustments were made to the of fset deections for autopilot transition. When a rough estimate of trim is then found for the autopilot, the gains in the controls systems are increased The rst controller gain that w as increased w as the proportional gain. This gain determines the transient portion of the controller by rolling the MA V to within a steady state of fset of the command. Some interesting responses occurred while increasing this gain. When the gain w as too high a noticeable oscillation about the command w as observ ed. This oscillation could ha v e been cause by se v eral dif ferent f actors. The gain could be too lar ge resulting in a lo w damping ratio in Dutch roll for the closed-loop system. The other f actor under consideration is the wind gust. A MA V tra v eling at 25 mph can e xperience wind gust on the same order which w ould drastically change the ight characteristics and most importantly the trim conditions. By decreasing this

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49 gain, the response of the MA V w ould maintain a bank angle. When this gain w as slightly lar ge the bank angle response w ould settle do wn abo v e the desired command. Lik e wise, when the gain w as slightly lo wer than the nal v alue, the response w ould center around a v alue less than the desired command. Final ight iterations were done to acquire a response that is centered about the desired roll angle with some steady state of fset. The gain is then determined through more ight iterations, where the response of the aircraft w as used to determine the direction in which the gain should be changed. When the response oscillates or o v ershoots to a lar ger roll angle the gain should be decreased and increased when the response has some undershoot and settles to a smaller roll angle. Finally the proportional gain that achie v ed a response centered around the desired command w as determined to be K f075. The inte gral gain w as then increased to mak e small corrections around the desired command for steady state conditions. Some aggressi v e maneuv ers were observ ed when the inte gral gain w as set to a lar ge v alue. This inte gral gain is proportional to the inte gral of roll error so, when the MA V w as straight and le v el and a 0 de g roll command is gi v en, a high inte gral gain has a smaller ef fect on the response because of the small error Although, the aggressi v e maneuv ers occurred when the MA V w as placed at an initial bank angle, making the roll error lar ge and the inte gral to roll error increase, when the autopilot is acti v ated the resulting aileron deection is lar ge. W ind gust also had an ef fect on the inte gral loop by creating oscillations to correct for the of fset. When this gain w as lar ge the wind gust w ould be corrected by a lar ge deection causing an o v ershoot in the opposite direction resulting in a correction for the o v ershoot. This beha vior describes a limit c ycle oscillation caused by the controller interacting with the physical o w Some additional blocks or other control methods can be used for disturbance rejection from wind gust.

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50 The inte gral gain also helps limit the rate at which the maneuv er is performed. A slo w response with some delay occurred when the gain w as set too small. Therefore, by slo wly increasing this gain the desired rate and steady state condition can be acquired. The inte gral gain that generated a reasonable response to commands w as determined to be K I019. W ith these gains coded in the control loop, ight test were then documented to record the data for a range of commands at v arious initial conditions. 6.2.2 Lateral Response Using the gains found in the pre vious section, the data recorded from the ight test will be analyzed. The sampling rate of the data-logging w as being sampled at 25 Hz while the controller w as operating at 5 Hz This means for roughly e v ery fth data sample a control is send up to command the airplane. A control systems for an aircraft commanding on 5 Hz is unreasonable to e xpect a high le v el of performance. These sampling frequencies are an estimate and therefore e v ery fth data point cannot be plotted against the command. So to try and gi v e an estimate of the response of the MA V during the command an a v erage of the measured roll angle between control changes w as used to plot the response, and is sho wn in Figure 6–3 This gure sho ws the response of the MA V during a human commanded roll doublet. From this response plot, one can see reasonable transient response during the command from le v el to roughly18 d e g A steady state of fset is sho wn for the rst bank command and for the le v el command, which can be adjusted by slightly increasing the inte gral. F or both bank commands of18 d e g there e xists some oscillations which could be caused from se v eral dif ferent f actors. This oscillation could be a dutch roll mode being e xcited, a resolution issue, or a response to wind gust corrections. If these oscillations are caused by the dutch roll mode, a ya w damper can be used to control this mode.

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51 0 5 10 15 20 30 20 10 0 10 20 30 time (s)roll angle (deg) measurementcommand Figure 6–3: Roll Response 6.3 Future W ork There w as some dif culty testing the heading controller and determining K y The GPS had frequent dropouts at the test site and e v en had dif cultly locking on to satellites to acquire data. Some simple alterations can be made, such as placing copper tape around the sensor to increase the antenna area to acquire a stronger signal. The GPS will then be used for w aypoint tracking, where longitude and latitude are used as feedback for the outer loop to control both heading and roll inner loops. The current roll controller described in this thesis, will require some alterations to reduce the oscillation observ ed during steady state, such as implementing a ya w damper The ya w damper can also aid in stabilizing the aircraft during small wind gust as well. The longitudinal control system needs to be designed and implemented for an altitude hold where the inner loop commands a climb rate. Combining these tw o controller system, GPS w aypoint tracking w ould be ready for implementation. The ne xt steps for vision-based autonomy w ould include the fusion of vision sensors with the standard inertia sensors. This could be used for increasing the

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52 sampling rate, sensor bias corrections, and state estimation. The modeling of MA Vs will be conducted through ight data acquired from testing and wind tunnel data in the lab In the future, the models will aid in the control design process through simulation.

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CHAPTER 7 CONCLUSION In conclusion, this thesis has demonstrated that Micro Air V ehicles (MA Vs) are a reasonable platform for vision-based autonomous research. The military describes man y scenarios where this technology can be applied to sa v e li v es and help protect our country from possible terrorist attacks. A nal relation w as deri v ed between the dynamics of a MA V and the motion of feature points vie wed by a camera attached to this v ehicle. These equations, being nonlinear then ga v e some insight into ho w objects are vie wed as the MA V passes around them. This re v ealed ho w depth could change the shape of an object when its mapped into the focal plane. Another nonlinearity related to the camera w as described as lens curv ature. This mapping ef fected the outside portion of the image by w arping feature points into a con v e x and conca v e pattern. A physical feature w as then e xtracted from the images to control the MA V where the horizon line w as determined. The image processing used a linear t to track the horizon line. Using the horizon also allo wed the camera nonlinearities to be ne glected in the control design therefore, making the horizon' s roll angle an estimate of the aircraft' s roll angle. Controller designs for the lateral states using roll and heading angle feedback were described using a classical proportional/inte gral control approach. W ith the design and f abrication of a 24 in MA V a test-bed w as constructed along with the required hardw are and softw are to test the autopilot controls system. Due to some GPS dropouts, data w as only tak en for the roll controller A response to a roll doublet w as plotted and v eried se v eral issues. First, some steady state of fset occurs during a bank hold with some oscillations possibly due to a dutch roll mode. Second, the 53

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54 synchronization between data-logging and the controller w as inconsistent with the data sampling a 25 Hz and the control w orking at 5 Hz T o get an approximate response of the MA V during the doublet, an a v erage measured roll angle w as tak en o v er the course of a control pulse. The roll response acquired from the data, w as tracking with a reasonable per formance for a 5 Hz controller F or future w orks, the data-logger and the control should be operating at the same frequenc y to a v oid an y uncertainty in ho w the MA V is responding. Once this issue is resolv ed, ight test for the heading controller will preclude to determine the proportional gain. Finally implementing a longitudinal controller to track altitude to complete the aircraft states. Further research will then lead onto implementing these controls systems into a fully autonomous w aypoint track er

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REFERENCES [1] Ak ec, J.A., Steiner S.J., and Stenger F ., “ An Experimental V isual Feedback Control System for T racking Applications Using a Robotic Manipulator ” IEEE 0-7803-4503-7/98, pp. 1125-1130. [2] Bonnin, P ., Stasse, O., Hugel, V ., Blaze vic, P ., M'Sirdi, N., Coif fet, P ., “Ho w to Extract and to Exploit V ision Data for Autonomous and Mobile Robots to Operate in Kno wn En vironments, ” IEEE International W orkshop on Robot and Human Inter active Communication 2001, pp. 231-236. [3] Bosse, M., Karl, W .C., Castanon, D., and DeBitetto, P ., “ A V ision Augmented Na vigation System, ” IEEE 0-7803-4269-0/97, 1998, pp. 1028-1033. [4] Castro, A.P .A., Silv a J. D., Simoni, P .O., “Image Based Autonomoue Na vigation with Fuzzy Logic Control, ” IEEE 0-7803-7044-9/01, 2001, pp. 2200-2205. [5] Chatterji, G.B., “V ision-Based Position and Attitude Determination for Aircraft Night Landing, ” AIAA Guidance Navigation and Contr ol Confer ence AIAA-963821, July 29-31, 1996. [6] Choi, J.Y ., Kim, C.S., Hong, S., Lee, M.H., Bae, J. II, and Harashima, F ., “V ision Based Lateral Control by Y a w Rate Feedback, ” The 27th Annual Confer ence of the IEEE Industrial Electr onics Society 2001, pp. 2135-2138. [7] Cohen, R., Hunt, T ., and Seeliger O., “V ision Based Control and Na vigation of an Underw ater T elerbot, ” AIAA, Guidance Navigation and Contr ol Confer ence AIAA-96-3899, July 29-31, 1996. [8] Ettinger S.M., Nechyba, M.C., Ifju, P .G., and W aszak, M.R., “V ision-Guided Flight Stability and Control for Micro Air V ehicles, ” IEEE International Confer ence on Intellig ent Robots and Systems October 2002. [9] Fleischer S.D., Rock, S.M., and Burton, R., ”Global Position Determination and V ehicle P ath Estimation from a V ision Sensor for Real-T ime V ideo Mosaicking and Na vigation, ” IEEE 0-7803-4108-2/97, 1997, pp.641-647. [10] Frank e, U., and Heinrich, S., “F ast Obsticle Detection for Urban T raf c Situation, ” IEEE T r ansactions on Intellig ent T r anspor ation Systems V ol. 3, No. 3, September 2002, pp. 173-181. [11] Gandhi, T ., Y ang, M.T ., Kasturi, R., Camps, O., Coraor L., and McCandless, J., “Detection of Obstacles in the Flight P ath of an Aircraft, ” IEEE T r ansaction 1063-6919/00, 2000. 55

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56 [12] Garcia, H., Abdulrahim, M., and Lind, R., “Roll Control for a Micro Air V ehicle Using Acti v e W ing Morphing, ” AIAA Guidance Navigation and Contr ol Confer ence Austin, TX, AIAA-2003-5347, August 2003. [13] Grasme yer J.M., and K eennon, M.T ., “De v elopment of the Black W ido w MicroAir V ehicle, ” AIAA 2001-0127, 2001. [14] Gurl, P ., and Rotstein, H., “P artial Aircarft State Estimation from V isual Motion Using the Subspace Contraints Approach, ” J ournal of Guidance Contr ol, and Dynamics V ol. 24, No. 5, September -October 2001, pp. 1016-1028. [15] Herv e, J.Y ., “ V isual Feedback for Autonomous Na vigation, ” IEEE 0-7803-02338/91, 1991, pp. 219-224. [16] Huster A., Fleischer S.D., and Rock, S.M., “Demonstration of a zvision-Based Dead-Reck oning System for Na vigation of an Underw ater V ehicle, ” IEEE 0-7803-5045-6/98, 1998, pp. 326-330. [17] Ifju, P .G., Jenkins, D.A, Ettinger S., Lian, Y ., Shyy W ., and W aszak, M.R., “Fle xible-W ing-Based Micro Air V ehicles, ” AIAA 2002-0705, 2002. [18] Jung, J.S., and T omlin, C.J., “ Autopilot Design for the Stanford DragonFly U A V : V alidation through Hardw are-in-the-Loop Simulation, ” AIAA Guidance Navigation and Contr ol Confer ence and Exhibt AIAA 2001-4179, 2001. [19] Kasetkasem, T ., and V arshne y P .K., “ An Image Detection Algorithm Based on Mark o v Random Fields Models, ” IEEE T r ansactions on Geoscience and Remote Sensing V ol. 40, No. 8, August 2002, pp. 1815-1823. [20] Kato, T ., Ninomiya, Y ., and Masaki, I., “ An Obsticle Detection Method by Fusion of Radar and Motion Stereo, ” IEEE T r ansactions on Intellig ent T r ansportation Systems V ol. 3, No. 3, September 2002, pp. 182-188. [21] Kimmett, J., V alasek, J., and Junkins J.K., “ Autonomous Aerial Refueling Utilizing a V ision Based Na vigation System, ” AIAA Guidance Navigation and Contr ol Confer ence AIAA-2002-4468, August 5-8, 2002. [22] Lian, Y ., and Shyy W ., “Three-Dimensional Fluid-Structure Interactions of a Membrane W ing for Micro Air V ehicle Applications, ” 44th AIAA/ASME/ASCE/AHS Structur es, Structur al Dynamics, and Materials Confer ence AIAA 2003 1726, April 2003. [23] K osecka, J., Blasi, R., T aylor C.J., and Malik, J., “V ision-Based Lateral Control of V ehicles, ” IEEE 0-7803-4269-0/97, 1998, pp. 900-905. [24] K osecka, J., Blasi, R., T aylor C.J., and Malik, J., “ A Comparati v e Study of V ision-Based Control Strate gies for Autonomous Highw ay Dri ving, ” Pr oceedings of the 1998 IEEE International Confer ence on Robotics & A utomation May 1998, pp. 1903-1908.

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BIOGRAPHICAL SKETCH Ryan Scott Cause y w as born in Miami, Florida, on May 10, 1978. He gre w up in a stable f amily with one brother in a typical sub urban home. During his teenage years and into early adolescence, Ryan b uilt and maintained a small b usiness pro viding la wn care to the local neighborhood. The tools acquired from this w ork carried o v er into his colle ge career After graduating from Miami Killian Senior High School, Ryan attended Miami Dade Community Colle ge for tw o years that commenced with an Associate in Arts de gree in engineering. A transfer student to the Uni v ersity of Florida, Ryan w as prepared to tackle the stresses of a uni v ersity aside from the poor statistics. A fe w years later he recei v ed a Bachelor of Science in Aerospace Engineering de gree with honors and w as considered in the top three of his class. During his summers before and after graduation, he w ork ed for Hone ywell Space Systems in Clearw ater Florida, as an intern applying his education to guided defense missiles. Ryan soon after chose to attend graduate school back at the Uni v ersity of Florida under Dr Andre w K urdila and Dr Richard Lind in the Dynamics and Controls Laboratory V ision-based control of air -v ehicles became his interest and he is no w pursuing a doctorate de gree on this topic. 59


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Permanent Link: http://ufdc.ufl.edu/UFE0002841/00001

Material Information

Title: A Lateral Vision-Based Autopilot for Micro Air Vehicles Using a Horizon Detection Approach
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0002841:00001

Permanent Link: http://ufdc.ufl.edu/UFE0002841/00001

Material Information

Title: A Lateral Vision-Based Autopilot for Micro Air Vehicles Using a Horizon Detection Approach
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0002841:00001


This item has the following downloads:


Full Text











A LATERAL VISION-BASED CONTROL AUTOPILOT FOR MICRO AIR
VEHICLES USING A HORIZON DETECTION APPROACH
















By
RYAN SCOTT CAUSEY


A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2003
















I dedicate this work to my lovely wife, Liza P. Causey, that has supported me

every step of the way. Her love and understanding through the years have brought my

passion for life beyond boundaries.















ACKNOWLEDGMENT S

I want to acknowledge and thank AFRL-MN and Eglin Air Force for the funding

of this project. I want to thank all the research members involved with this project for

their dedication and long hours in the lab and in the field which includes Dr. Peter Ifju

and his team Kyuho Lee, and Sewoong Jung that developed and fabricated the MAVs,

Dr. Michael Nechyba and his team Jason Grzywna, Jason Plew, and Ashish Jain that

did an extraordinary job designing and developing all the on-board and ground station

hardware along with the horizon detection algorithm, my colleagues in the Dynamics

and Controls Lab: Helen Garica, Kristin Fitzpatrick for her S flight, the new graduate

students Joe Kehoe and Jason Jackowski. A special thanks to the pilots Kyuho Lee

and especially Mujahid Abdulrahim for his advice and extremely long flight hours,

and most importantly Dr. Andrew Kurdila and Dr. Rick Lind for their remarkable

guidance and inspiration that will truly last a life time and finally to my parents James

and Sandra Causey who provided me the guidance and discipline needed for success.


















TABLE OF CONTENTS



ACKNOWLEDGMENTS . . iii

LIST OF TABLES . . vi

LIST OF FIGURES . . vii

ABSTRACT. ............................ . ix

CHAPTER

1 INTRODUCTION . 1

1.1 Motivation . 1
1.2 Background . . 2
1.2.1 Micro Air Vehicles . . 2
1.2.2 Image Processing . . 7
1.2.3 Vision Control . . 9
1.3 Overview . . 11

2 DERIVATION OF COUPLED CAMERA AND AIRCRAFT EQUATIONS
OF MOTION . ................... 13

2. 1 Problem Formulation . .. 13
2.2 Aircraft Parameters .. . 13
2.3 Defining Camera Parameters . ......... 14
2.4 Camera Equations of Motion . ......... 17
2.4.1 Feature Point Position . ......... 18
2.4.2 Feature Point Velocity . ......... 19

3 CAMERA NONLINEARITIES . . 23

3.1 Focal Length Parameter . . 23
3.1.1 Focal Plane Position . . 23
3.1.2 Focal Plane Velocity . ......... 28
3.2 Lens Distortion . . 28

4 LATERAL AUTOPILOT CONTROL DESIGN .. . . 31

4. 1 Roll Control Design ........ . . 32
4.2 Heading Control Design . . 33
4.3 Closed-Loop Control . .. 34











4.3.1 Bank Hold . . 34
4.3.2 Heading Hold . .. 35

5 EXPERIMENTAL SETUP .. . . 37

5.1 Micro Air Vehicle Description . . 37
5.2 Hardware Architecture . . 41
5.3 Camera Model for Horizon . . 43

6 CLOSED-LOOP LATERAL CONTROL . ...... 46

6. 1 Controller Implementation . . ..46
6.2 Flight Testing and Results . . 48
6.2.1 Gain Tuning .. . . 48
6.2.2 Lateral Response . . 50
6.3 Future Work . . 51

7 CONCLUSION . ........ . 53

REFERENCES . . 55

BIOGRAPHICAL SKETCH . . 59
















LIST OF TABLES
Table pg

4-1 Discrete Roll Command Output Values . ...... 34

5-1 MAV Properties . . 38



















LIST OF FIGURES


Figure

1-1


n MAV . . 4




. 14

. 15

16

. 17

... 24

. 25

. 26

2.5 Units . . 26

5 Units . . 27

10 Units . . 27

. 29

. 32

. 33


gn . ...... .. 35

)esign . . 3..... 6

:d Control . . 38

. 39

. 39

. 40

. 41

. 44


Flexible Wing Concept on a 6 ii

UF MAV Fleet ....

MAV Kinematics ....


Coordinate Systems . .

Defining Feature Points .

Vector Diagram . .

Feature Point Grid . .

Grid Rotation ....

Planar Feature Points ....


Skewed Feature Points Sloping

Skewed Feature Points Sloping

Skewed Feature Points Sloping

Lens Curvature ....


Roll Control Autopilot .. .

Heading Control Autopilot .

Closed-Loop Roll Control Desie

Closed-Loop Heading Control D

MAV Prototype for Vision-Base


Torque Rod Design . .

Morphing Control Effectors .

Push Tail Propeller Design .

Hardware Architecture ....


Image Plane Depth Comparison


1-2











5-7 Lens Curvature for a Horizon ...._.. .. 44

5-8 Lens Curvature with Horizon Approximation ... .. .. 45

6-1 Roll Control Block Diagram . . 47

6-2 Heading Control Block Diagram . .... .. 47

6-3 Roll Response . ......... .. .. 51















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

A LATERAL VISION-BASED CONTROL AUTOPILOT FOR MICRO AIR
VEHICLES USING A HORIZON DETECTION APPROACH

By

Ryan Scott Causey

December 2003

Chair: Andrew J. Kurdila
Cochair: Richard C. Lind, Jr.
Major Department: Mechanical and Aerospace Engineering

The concept of autonomous flight has been realized as a feasible concept with

the current technology, where small electronics have advanced to standard equipment

that is inexpensive. The aircraft platform to head these efforts has shifted to small

agile vehicles that can maneuver within confined environments such as urban terrains.

Some capabilities needed for autonmony include sensors that detect the physical

surroundings, data processing, path planning, and the control algorithms. Micro

air vehicles (MAVs), structurally have evolved to house the required payload for

autonomous research. The capabilities of MAVs have demonstrated maneuverability

for confined spaces, on-board processing, and camera integration with vision feedback.

This thesis will establish the required analytical relationships for a camera on-board

an MAV, along with image processing for feature extraction, and finally control design

and implementation using this physical feature. The relationship first derived, couples

the nonlinear equations of motion of an aircraft to the trajectory of feature points in the

image plane for cameras attached to the vehicle. Algorithms using statistical models

for pattern recognition are used to define the horizon in the image plane. Based on










geometry, this horizon line is used to calculate a roll estimate and pitch percentage

which are used as feedback to design controllers. A testbed was fabricated along with

a particular MAV and a single camera of known parameters to implement vision-based

lateral control. The camera nonlinearities were studied for this particular feature (i.e.

the horizon) through some observations. By using the horizon, these nonlinearities

were able to be neglected from the controls system. Numerous flight tests were then

conducted to improve the lateral control design by adjusting gains to acquire a desired

response.















CHAPTER 1
INTRODUCTION

1.1 Motivation

Micro air vehicles, or better known as MAVs, are currently the platform for

research in autonomous flight at the University of Florida. A typical MAV scale

consists of a wingspan and fuselage that range from 30 inches down to 6 inches

and operate in flight speeds of 25 mph or less [31]. The motivation behind Micro

Air Vehicles are their mission capabilities in dangerous environments. For instance,

MAVs are being considered for missions that involve surveillance, damage assessment,

search and rescue, and region mapping. The interest behind using MAVs are their

fundamental features. These vehicles are highly agile and can bank and climb within

the confined space of an urban environment. Because of this feature, MAVs have

the ability to change the environment in which standard aircraft have been known

to operate. For instance, MAVs can be used fly within and around the confines of

buildings and subways. Additional benefits of MAVs, regarding implementation, are

readiness to fly and a compact size for storage. Most importantly, MAVs are low

cost, which would allow multiple MAVs to be standard equipment for a variety of

users, ranging from soldiers on the battle field to police and fire agencies in our local

di stri cts.

An autonomous MAV is particularly suited to accomplish missions with minimal

risk to personnel. Consider a scenario of particular concern where a biological agent

has been released in an urban environment. Current operations require humans gather

equipment and venture into hazardous regions. Instead, future operations could be

conducted by autonomous MAVs deployed from a nearby emergency station. MAVs

would assist in a diverse range of missions including detection, mapping, and search










and rescue during this type of situation. In the case of detection, the vehicle could

transport a sensor that detects infectious agents. A map of the region and the infected

areas could then be generated to inform civilians from real time updates. The images

could also be used as a surveillance tool to search and locate possible survivors. The

vehicle's small size and agility would allow access inside buildings and subways

therefore increasing the search area. Analyzing image information, rescue teams can

assess damage to the surroundings to plan a safe rescue route. This scenario, along

with many others, validates the growing interest for such sophisticated systems using

V1S10H.

1.2 Background

1.2.1 Micro Air Vehicles

Over the past five years, MAV designs have been developed to improve flight

characteristics, payload capacity, and structural integrity. With these significant

improvements, very small vehicles are being considered an achievable technology for

autonomous flight with many applications. Here, autonomy is regarded as the controls

system making decision on the trajectory without human intervention.

The size constraints involved in using such small vehicles has lead to many ad-

vances in miniaturized digital electronics, communications, and computer technologies

to make autonomous MAVs a reality [46]. These developments have allowed MAVs

to be equipped with the latest computer and sensor technology such as video cameras,

data processors, and communications devices. Over the last few years, the integration

of these electronics onto an MAV has made considerable advances toward the overall

goal of on-board processing and mission capability in real time.

The first successful MAV that demonstrated mission capabilities was Aeroviron-

ment's Black Widow [13]. This 6 in MAV was electrically powered and consisted of

a rigid-wing design with three vertical stabilizers. The on-board systems included a

data logger sampling 16 channels at 20 Hz and a custom video camera system that










optimized weight, power and size with image quality. A yaw damper was implemented

to damp out a low frequency Dutch roll oscillation to improve not only flight stability

but also stabilizing the video to obtain a steady image. An autopilot system was also

incorporated using three modes: dynamic pressure hold, altitude hold, and heading

hold. The final overall system, with a mass of 80 g, was able to sustain 30 min flights

for a maximum range of 1.8 km while transmitting video images to the ground. These

images were used by the pilot to control the aircraft when the range of the vehicle

became too large from an RC pilot's standpoint. Most importantly, the images demon-

strated the functional capability of MAVs by streaming real time video to the ground to

establish their role in implementing vision-based autonomous flight.

The rigid-wing concept was common in many other successful designs including

the Trochoid developed by MLB Company and M~icrostar, also funded by DARPA [17].

The disadvantage to using rigid-winged MAVs is they require additional gyro stabiliz-

ers to assist in controlling the aircraft. This is due to the unsteady aerodynamic loading

that dominates a vehicle at such low Reynolds numbers. For example, wind gust will

have a much greater affect on MAVs than larger aircraft because of their size and

speeds at which they operate. Research eventually lead to the concept of flexible wings

that are able to adapt to unsteady flight conditions.

Dr. Peter Ifju and his team, at the University of Florida, has developed a wing

concept that consists of an extensible latex rubber membrane that is overladed onto

a carbon fiber skeleton for structural support [17]. This concept was taken from sail

vessels which use the sail twist to extend the wind range producing a more constant

thrust even in gusty conditions [45]. An illustration of this wing structure is depicted

in Figure 1-1 for a 6 in MAV. The important feature that one should realize is the

flexibility of these wings. The flexibility can be so dramatic that the wings can be

folded around the fuselage creating a more compact storage envelope. Implementing









this feature, MAVs could then be deployed from missiles moments before impact to

loiter around the target space for damage assessment.














Figure 1-1: Flexible Wing Concept on a 6 in MAV


The aerodynamic benefits of flexible wings appear to be significant but are

currently being studied in detail. By adjusting to the air flow, flexible wings produce

a more favorable aerodynamic flow in such low Reynolds number environments, as

documented in the research [17, 44, 46]. This is mainly caused by maintaining an

attached flow and preventing flow separation. As Reynolds number decreases, the

flow around the wing surface separates faster and therefore increases the drag on

the aircraft. So by implementing flexible wings, MAVs appear to have better flight

qualities compared to the gyro stabilized rigid winged design.

Later, a more structural analysis and flow interaction approach using nonlinear

moving boundary techniques coupled with Navier-Stokes solvers to quantify the

resulting flow field [22]. Results obtained in this paper consist of vorticity structure,

pressure distribution, and lift and drag characteristics associated with both membrane

and rigid wings concepts for comparison. Modal analysis of this interaction has been

done using Proper Orthogonal Decomposition to extract most energetic modes from the

resulting flow field and the wings natural response [48].

With this flexible wing concept, researchers began an approach to analyze flight

techniques seen in nature. This flight concept opened the eyes of many researchers to









mimic the flight of small birds and insects into the design of an MAV. This approach

seems obvious because of their common size and the bird's ability to maneuver in

confined spaces, but is extremely difficult to reproduce mechanically. The common

motion between small birds is high frequency flapping to produce lift as well as

directional control, which is reminiscent of Hummingbirds. Many works are pursuing

flapping flight techniques with flexible wings to add agility. The mechanisms and

actuators required for such a task are being explored in the lab environment [32]. The

difficulty for this type of MAV consist of producing an efficient flying machine with

on board actuators that operate with low power consumption. As one can imagine, the

complex motions at such high frequencies will require efficient, durable, and compact

actuators along with sophisticated control systems. Studies have shown comparable

wingtip trajectories between their vibratory flapping testbed and those exhibited by

Hummingbirds in various flight modes [32]. Currently these actuators are significantly

larger than a MAV's fuselage so other techniques are being explored.

Other studies in Shyy et al. [44], began to investigate different aspects of flapping

flexible wings such as wing loading, models for lift, drag and power, issues with

low Reynolds number flows, and recent work with flexible structures adjusting to

free-stream conditions. Some preliminary results indicate improvements in lift-to-drag

ratio and aerodynamic performance over the standard rigid-winged counter-partner.

However, the complete understanding of flexible wings requires the full Navier-Stokes

flow model to accurately represent the coupling between flapping dynamics and flight

at low Reynolds numbers. The complexities involved in this approach has lead many

researchers to adopt a potential flow or thin-layer flow model even though these

solutions contain inadequate details of the flow at these sizes and flight regimes.

Over the last several years, Dr. Ifju has established a systematic fabrication facility

for MAVs at the University of Florida. This facility enables the rapid production of

MAVs in a range of sizes and the ability to customize a design for a particular mission.










The standard MAV fleet at UF range in wingspan from 6 in to 24 in and are depicted

in Figure 1-2. Notice all the MAVs in this figure consists of a common design: a

carbon fiber airframe with a wing that consists of a flexible membrane and a reinforced

leading edge made of carbon fiber. The airframe houses specific components needed

for flight testing and typically consist of accelerometers, rate gyros, a GPS sensor, data

processors and loggers, servos, and camera components.









Figure 1-2: UF MAV Fleet

The control surfaces of a standard aircraft are typically incorporated on an MAV.

Although, implementing an aileron on a flexible wing design has caused some difficulty

during fabrication. For simplicity, UF has overcome this problem be implementing

symmetric and antisymmetric elevator. This involves splitting the elevator down the

center into two control surfaces. The symmetric elevator occurs when the two surfaces

act together to produce pitching moments while the antisymmetric occurs when these

surfaces act opposite to produce rolling moments. Recently, a new technique called

morphing has evolved into the MAV design to act as ailerons. This concept will be

explained in more detail in Chapter 5.1. Depending on the directional stability of each

MAV design, a rudder can be implemented to reduce side slip during maneuvers and is

commonly incorporated on the smaller MAVs.

To test MAVs efficiently with sophisticated control algorithms, models need

to be generated from flight test or wind tunnel data. Only recently MAVs have

been considered a feasible technology from a controls aspect. Researchers are now

emphasizing the need for MAV models, especially nonlinear models, for control

synthesis. The first MAV, similar to the one shown in Figure 1-1, was tested in a wind










tunnel, the Basic Aerodynamics Research Tunnel (BART), at NASA Langley Research

Center [34]. These test provided researchers with aerodynamic coefficients and

control properties to further analyze the stability. The works of Waszak et al. in [46],

documented the aerodynamic performance and control properties from this wind tunnel

data by investigating trim conditions and the aircraft's response to a control deflection

at various angles of attack and dynamic pressures. These works proceeded by a second

publication [45], in which linearized models were generated from the same data using

linear regression techniques over a range of dynamic pressures. Control simulations

were then constructed for these models to investigate vehicle trim and basic stability

and control properties. The control structure consisted of a nonlinear dynamic inverter

which converted measured angular rates to control surface deflections.

The success of the flexible wing MAV has been demonstrated, by the UF team, at

the International Society of Structural and Multidisciplinary Optimization Micro Aerial

Vehicle Competition by receiving the overall first place award for the last four years.

This competition continues to grow every year as more universities become involved.

Some other universities that are intensely pursuing MAVs include BYU, Arizona, and

Notre Dame.

1.2.2 Image Processing

The task of flying autonomous MAVs in environments that are confined by

buildings, trees and additional features, as well as poor weather conditions, requires a

host of innovations in vision-based flight control. Two areas, in particular, that need to

be addressed before vision controllers can be designed include vision processing and

pattern recognition. The images acquired by a standard camera contain an enormous

amount of data for processing, such as pixel color. Even MAVs traveling at speeds

around 25 mph still require a significant number of frames per second to incorporate

vision in the feedback loop. In real time, an algorithm using the complete image data

for control design would be computationally expensive. Therefore, strategies in the last










several years have evolved in attempt to process and compress this data without the

loss of important image features for controller design.

Image processing attempts to handle large data by extracting features from the

image that are significant in the environment to reduce computation time. For example,

in a city the outline of buildings would be a significant feature for an aircraft while the

details of windows and doors may not be as important. The difficulty involves training

smart algorithms to recognize and distinguish between important features and details

that may be omitted, as well as free space and occupied space. Some techniques using

fuzzy logic or statistical color matching have been studied to reduce such large data

sets while determining occupied space through surface triangulation [25, 29, 30].

Once an image has been reduced within the bandwidth limits, pattern recognition

is required to classify regions based on particular features using this reduced image.

Some important features that may be used from an image include color and texture.

Although, the common feature used for a still shot are the color components for each

pixel, which are divided into red, blue and green components (i.e., the RGB color

cube).

Statistical modeling of the distribution of pixel color, using Expectation Maxi-

mization algorithms (EM), is a classical technique for classification. This concept was

demonstrated to detect a horizon line based on the classification of each pixel to a

set of known distribution models [8]. These known distribution models are computed

based on a known data set, which in this case would be a picture of the sky and ground

on a particular day and is considered the training data. The models are then applied

to unknown data sets (i.e., images) and decides on the classification of each pixel

belonging to the sky or ground distribution. Therefore, the boundary between these two

distribution is called the decision boundary, or in this case the horizon line. Kalman

filters or pattern tree structures can be added to this particular case to account for

small variations in color, which happens throughout the day or in different weather










conditions, and noise to add robustness. This can account for small variations but will

not apply to conditions where the sky has changed color significantly, such as dusk or

dawn.

Other studies in recognition have led to advances in areas such as object motion

estimation and obstacle detection. Soatto, et al. have documented several methods

in [37, 38, 39, 40, 41,42] which estimates the three dimensional motion of an obj ect from

a sequence of image projections commonly referred to as "Structure from Motion."

These techniques pertain to nonlinear estimation and identification theory and can be

solved by decoupling the states of the dynamic observer that estimates motion and the

structure parameters. Obstacle detection is based on similar concepts that identifies

objects traveling in and out of the image. The detection of these object and tracking

requires some additional methods to estimate the motion of any pixel over time.

Several recent studies [19, 27] use Sarnoff's stereo processing for obstacle detection

along with Markov Random Field Models to analyze and interpret the pixel motion.

Once object detection algorithms become efficient for real-time applications,

controllers can be designed using this information as feedback for obstacle avoidance

in urban environments. A particular study for urban traffic situations has began to

implement a fast detection algorithm to avoid hitting unseen pedestrians by using stereo

vision and classification stages to control the brake system [10].

1.2.3 Vision Control

The research done to address vision-based control on vehicles has mainly been

done in robotics for the 2-D case [1, 2, 15, 28]. With motion constraints in certain

directions, a robot has the ability to stop it's motion before making a decision on

the path based obstructions detected by the camera. This critical feature does not

require the controls system to act in real-time and the vehicle is able to travel along

the circumference of an obstacle. On the other hand, an airplane is required to make

decisions of the environment ahead in real-time to avoid obstacles while maintaining










forward velocity required for flight. Other control examples in 2-D involve highway

driving, where studies have used vision sensors to track lane dividers and obstacles

within a fixed range in both forward and lateral directions [4, 6, 20, 23, 24, 26]. Some

open control problems and issues with hardware development using vision feedback are

assessed in Sznaier and Camps [43].

Some research has applied vision control in free floating objects such as underwa-

ter vehicles, lighter than air blimps, and space docking [7, 9, 16, 36, 35]. These studies

have demonstrated object detection and tracking ability in many different objectives. A

common feature in these particular vehicles is the ability to hover in a fixed position.

This advantage was described above in the 2-D case where the vehicle stops it's motion

to process visual data before making a decision. Helicopters are a prime example,

although the controls required to hover are complex, computation time can be gained

when a path is unknown. Mission capabilities for target search and tracking have been

demonstrated using helicopters and are documented in the literature [3, 33]. As this

vision control concept slowly progress toward aircraft, the computations for image

processing and obstacle detection for path planning in real-time become extremely

difficult.

By considering vision control for aircraft, one has to be aware of the additional

degrees of freedom and performance constraints of the vehicle. The ability to turn

or climb at large rates will strongly depend on the agility of the aircraft. The speed

of an aircraft, even around 25 mph, requires fast image processing to detect and

track obstacles that continuously enter the field of view. Obstacle detection for

aircraft has been examined in [11] where a morphological filter was used for image

processing and object detection by retaining small sized features, which were assumed

targets, while removing large features, which was assumed to be the background. An

estimation problem of the aircraft's motion can then be calculated using an extended

Kalman filter approach to subspace constraints, which arises when points stationary










on the environment are tracked on the image plane [14]. Recent studies have gone

further by integrating object detection with control designs for autonomous aerial

refueling [47, 21] and state determination for night landings [5]. The simulations

for these studies both documented precise target tracking for aerial refueling and the

feasibility of night landings, both with good disturbance rejection.

The design of autopilots for unmanned MAVs using vision as the primary control

sensor has only begun in the research community. Significant strides were made at the

University of Florida when a horizon detection algorithm, described in Section 1.2.2,

was used to feedback roll angle for lateral control [8]. The control design used in this

paper consisted of a proportional/derivative (PD) feedback loop along with conditions

to maintain the horizon in the image plane.

1.3 Overview

This thesis documents the initial progress made in vision-based autonomous flight

for micro air vehicles at the University of Florida. First, a relationship is derived

between feature points viewed in the image plane and the aircraft equations of motion.

Analytical simulations were then studied for this system to find the relation between

the horizon's roll angle and the aircraft's body roll angle through camera nonlinearities.

A vehicle was was then fabricated at the University of Florida equipped with a single

camera for extensive autopilot testing. The algorithms for image processing and

horizon detection were used from previous work done at the University of Florida's

Machine Intelligence Lab and is documented in Ettinger et al. [8]. This thesis attempts

to build on the works done in this particular paper by incorporating an autopilot

methodology to both roll and heading using vision feedback. The control systems

were designed for lateral directional using standard proportional and integral control

structures. Flight test were then used to adjust the controller gains for the desired

performance.










The vision feedback in this thesis uses the horizon detection algorithm to deter-

mine the roll angle of the aircraft. The main disadvantage to this algorithm restricts

the aircraft to operate in an open environment where the horizon is always in view.

Therefore, the work presented in this thesis is a small step in the overall vision control

problem for urban environments, where the horizon is no longer in view. The detection

methodology can be expanded to to features such as buildings instead of the horizon

approach presented in this thesis.















CHAPTER 2
DERIVATION OF COUPLED CAMERA AND AIRCRAFT EQUATIONS OF
MOTION

2.1 Problem Formulation

The goal of this chapter is to formulate and derive the coupling between the

equations of motion for MAV's and the motion of feature points, viewed by cameras

attached to the aircraft, in the focal plane. These equations will be derived in a general

form that will include indicies for the number of cameras, k, and the number of feature

points, a, extracted by from the image. An important assumption made regarding

feature points is an image processing algorithm has been created to extracted critical

features of the environment, such as corners of buildings, trees and so forth.

The equations will involve knowledge of each camera's mounting position and

orientation relative to the aircraft's center of mass. An illustration of this formulation is

depicted in Figure 2-1 which describes the kinematics of a MAV in flight with details

of the kth camera. The coordinate frames, or basis frames, in this derivation consist

of an inertial frame, E, a body fixed frame, B, and the kth camera fixed frame, Ck,

which also can be seen in Figure 2-1. Each frame is represented as a right-handed,

orthonormal basis expressed as unit vectors. The Figure also contains an image, where

feature points are extracted, to emphasize the application of vision for autonomous

vehicles in cluttered environments for closed-loop control.

2.2 Aircraft Parameters

The aircraft equations of motion for a MAV are the standard equations which have

been derived in a typical aircraft mechanics book. The important aircraft states needed

for the camera motion consist of the velocity of the center of mass of the aircraft, E,

with respect to the inertial frame, the angular velocity, Eo3, of the body frame with











k" C~lrwra Fixed
FMme
Lrfl*
OpticHI
Axis
\ 4L~~


Figure 2-1: MAV Kinematics


respect to the inertial frame, the position of the center of mass of the aircraft, Rc, with

respect to the inertial frame, and the orientation angles of the aircraft with respect to

the inertial frame. These vectors will appear explicitly in the derivation of the camera

equations and are written below in terms of their components. Here the notation for a

vector quantity is denoted using an under-bar, (e.g. v_ is a vector quantity).


Eci =18 ut- +v,R +-wb

Em3 = ~ pt- qb,+-rbi3

Rc =- Xc~ 1- +Yc2 +-Zc ^3

The angular velocity, Eo3, is a function of the time rate of change of the orienta-

tion angles. These angles correspond to a sequence of 2-D rotations which defines the

orientation of the body axis relative to the inertial frame and are usually defined for an

aircraft as roll, pitch, and yaw (#,6,W) or also referred to as a (3-2-1) Euler rotation.

2.3 Defining Camera Parameters

The parameters that will be involved in deriving the equations for a camera

mounted to an aircraft include the position of the camera relative to the body basis,

position of a feature point relative to an inertial basis, the position of a feature point

relative to the camera basis, and the aircraft states described in the previous section.









The position vector of the kth camera relative to the body basis is denoted as Ak and is

expressed below in component form.





The orientation angles defined by a 3-2-1 Euler rotation matrix also relate the camera

basis to the body basis in a similar fashion. This is also represented in a general

form based on the number of cameras, k, to allow multiple cameras with different

orientations. These angles are defined to be ( k Bk k) corresponding to roll, pitch,

and yaw for the kth Camera basis. Both the position and orientation of the kth camera
are illustrated in Figure 2-2.

k'' famrurr Fixed

C,i



Body Fi~iced'BI r
ha, Fame c n.






Figure 2-2: Coordinate Systems


Thus, the parameters defining the kth camera described above can be assembled

into a vector to simplify and compact the notation and will be referred to aS Oak.




The parameter fk, is the focal length of the kth camera and can vary for multiple
cameras. Keep in mind this vector can be extended to include radial lens distortion,










CCD array misalignment and so forth but this derivation will retain only the position,

orientation, and the focal length for each camera without loss of generality.

The image captured by an on-board camera requires processing to extract feature

points that are critical to the aircraft's path planning. This work has been done for

many applications using pattern recognition techniques and vision processing [27].

The assumption made for this derivation is the vision processing has been addressed,

extracting a minimum amount of feature points, lines, and/or planes to learn the current

surroundings. A typical scenario is depicted in Figure 2-3 which shows an image of a

building being reduced to feature points and lines for guidance, navigation, and control

through this urban terrain. Many problems with free and occupied space still arise

when a family of feature points are predetermined. Some statistical methods, based on

color, in pattern recognition have attempted to address this problem with a reasonable

degree of accuracy but problems arise when using this statistical model in a cluttered

environment [30].














Figure 2-3: Defining Feature Points


The remaining parameters characterize the geometry between the aircraft's center

of mass, the kth camera's lens position and the ath feature point located on points, lines

and planes extracted from an image. A vector diagram of this geometry is illustrated in

Figure 2-4.









k'b Camera Fixed


i:::


Figure 2-4: Vector Diagram

Here the position of the center of mass of the aircraft is shown and is again

denoted by Rc. The remaining parameters shown in this figure consist of the position

of the ath feature point relative to the both the inertial frame and the camera frame,

denoted as 5a and rla. The components of these two vectors are expressed in the basis
written below.





2.4 Camera Equations of Motion

Recall that the basis frames defined earlier are right-handed, orthonormal meaning

the axes permutate according to the cross product and the dot product between normal

unit vectors are zero. A 2D axis rotation can then be defined through the direction

cosine, relating one set of coordinates to a new set which is only a rotation from the

first. The 2D transformations defined below are rotations about a particular axis. The

subscript defines the axis of rotation, for example 13( ) is a rotation about the three

axis by an angle ~.

cfk sfj 0 cek 0 --sek 1 0 0

13~( K)]= -sul cur 0 [12(6)]= 0 1 0 li k)= c" kSk"

0 0 1 sek 0 cek 0 -s~k Ck










Using a series of three 2-D rotations, a set of coordinates can be transformed uniquely

into any desired orientation. Therefore, the basis transformation between body basis

and the kth camera basis can be defined as follows:

k k
c1 by


c b

Likewise, the same sequence can be used to relate the inertial basis with the body basis

through the aircraft's orientation angles.


by dil

K2 = i ] 26]13y] g (2.2)

b3 e^3e

2.4.1 Feature Point Position

The derivation of the camera equations of motion starts by summing the position

vectors, illustrated in Figure 2-4, for the ath feature point relative to the inertial frame.



5" = Rc +- k t-Ta (2.3)

Solving Equation 2.3 for the position of the ath feature point relative to the camera

basis, results with the following vector equation.



Tlaga Rc Ak (2.4)

Each term in Equation 2.4 can be expressed in the camera basis by applying the Euler

transformations, shown in Equations 2.1 and 2.2 resulting in the final vector equation

for the feature position relative to the camera basis.













(2.5)


Writing this in a more compact form using indicial notation results with the the final

expression of the position of the ath feature point relative to the camera basis.



pa=1 k k )ij ,GVjs -Rc~-l(,6,yijA(2.6)

2.4.2 Feature Point Velocity

We can characterize a feature point in the focal plane further by deriving it's

velocity vector. The velocity of the ath feature point in the focal can be found by

taking the time derivative of Equation 2.4 with respect to the inertial frame.


Ed Ed Ed Ed
(n)= (5") (c (Ak) (2.7)
dt dt -dt dt

Looking at each term individually, the derivative is with respect to the inertial

frame while most of these vectors are expressed in other basis. Therefore, the Deriva-

tive Theorem is employed on terms not expressed in the inertial basis. For a general

vector, A expressed in the J frame, the Derivative Theorem states the time rate of

change of A in the I frame is equal to the time rate of change of A in J plus the angu-

lar velocity of frame J with respect to frame I crossed with A. Mathematically, this is

shown as follows:


Id Jd
()=(A_) +- lo3J xA
dt dt

The position vector, 5a, is constant in magnitude and direction with respect to time in

the inertial frame and therefore the first term on the right hand side of Equation 2.7

is zero. The position vector of the aircraft's center of mass, Rc, is expressed in the

inertial basis and therefore the time derivative becomes the following:











Ed


Using the Derivative Theorem described above for the remaining vectors rla and Ak and

combining results discussed for each term, Equation 2.7 becomes the following:


Cd Bd
(r" a E 0C Ta -R~ (Ak) E 03B k (2.8)
dt --dt

This equation can be reduced further by analyzing the term (AkL\). This~ is the

time rate of change of ~k with respect to the body basis. For a fixed camera position,

this derivative is zero because it's constant in magnitude and direction relative to the

body basis and therefore reduces Equation 2.8 to the following


ed
(Tla) E 0C Ta _-R c E 0B k

Solving this equation for the velocity of the ath feature point with respect to the camera

basis is found by manipulating the above equation.


Cd
(paU _- E- k~ _~ E "C ar (2.9)

Using the Addition Theorem, each angular velocity term can be expressed as a

sum of intermediate coordinate transformations until the desired basis is reached. For

example, the angular velocity of A oC is the sum of the angular velocity going from

frames A to B and the angular velocity going from frames B to C, where frame B

is defined as an intermediate frame. In this derivation transforming from frame E to

B requires two intermediate frames to accomplish this task, where F and G are the

intermediate frames for the angular velocity below.



Eo3 _E 0 tF CiG tG 3

=-\~t vb 6g+ b-~s








Each component of this equation can be written in the B basis by the rotational
transformations defined in Equation 2.2.






Recall, this angular velocity expressed in the B basis as the following


iWD.~b}{ T
The angular velocity of the C frame with respect to the E frame requires two
additional intermediate frames, O and P, from the angular velocity shown above.


EoC_~E 0 tF 0GtG 0B tB iO O tP 0C

=- 97 t-2 t-~1 t- d3 t k 2 t kC81
Likewise, each component of this equation can be written in the C basis by the
rotational transformations defined in Equations 2.1 and 2.2.



IO 0O

EC 1r("]l2~~ kI 2 W~o rk 1 2 1(0K1128)] o 0 I(k 2k 3 1


tV 0r("l ekoI P









Defining the components of the equation above as Zk for each camera expressed

in the corresponding camera basis.





Therefore, Equation 2.9 becomes the following:


Cd
(71a _-,-E 03 k k Ta (2.10)
dt





4, =- Ic A -pA 0 p kqa(2.11)



Transforming all coordinate components into the C basis and using indicial

notation results with a final expression for the velocity of the ath relative to the kth

camera frame.



lia= l( kk,~k Wkij, BW)js{(Rc )s-l k I(k, s )ijI~o EopE ~k
(2.12)















CHAPTER 3
CAMERA NONLINEARITIES

3.1 Focal Length Parameter

3.1.1 Focal Plane Position

The coordinates defined in the focal plane are (pu,v) which represents a two-

dimensional projection viewed by the camera. Therefore, the ath feature point will

appear in the focal plane with the coordinates (pa av) from the component equation

listed below.
rlxa -- Cx rya -- C
pa- Va y (3.1)
lza -- cz rlza cz

Again, the parameter fk is the focal length of the kth camera. The vector components

(cx, c,, cz), defined as c, are the offset distances of the lens relative to the camera basis.

For example, cx is the distance the lens is offset in the x-direction from the camera

basis. If the origin of the camera basis is place at the lens, Equation 3.1 reduces to

Equation 3.2 (i.e. c =- 0).



pa- Exaa Ev (3.2)

For simplicity, it is assumed for the remainder of the derivation the lens location and

camera basis coincide and therefore Equation 3.2 will be used. This equation is only

a function of the position relative to the camera basis to a feature point, derived in

Chapter 2.4.1, and the camera's focal length.

In summary, the position of each feature point in space can now be character-

ized by it's position in the focal plane by substituting the required components of

Equation 2.6 into Equation 3.2.










A simple experiment was done using Equation 3.2 to characterize the mapping

associated with feature points in the inertial frame transforming to the focal plane. A

pattern of feature points was defined in the inertial frame as a plane perpendicular to

the Y axis and is shown in Figure 3-1. The feature points on this plane were then

rotated several times to create a series of planes. Each plane was fixed on the left side

while rotating the right side closer to the camera's position. An illustration of this

setup is depicted in Figure 3-2, where point C is defined as the camera's position and

10 IT

120
115 ***
110-
105 *
S100 ***




9Y0- *o gt I ?



Figure 3-1: Feature Point Grid

Each plane contains this set of grid points which are then substituted into Equa-

tion 2.6, assuming a fixed aircraft with a single camera placed at the center of mass

along with fixed basis frames. The feature point positions were then determined rel-

ative to the camera basis. Therefore, the following aircraft and camera parameters

reduce to the following:









C-
iX- ~h
*-
h-
*-


120-
110-
h
v 100-
N


S40


15 to sX (ft)


5 10 15


20 0


Y (ft)


X (ft)


(a) 3D


(b) XY' Plane


Figure 3-2: Grid Rotation


"P(




(


T

}
0 0


IT
0 0


IT
0 100


IT


Also, the rotation matrices reduce to the following for a level camera and MAV:


0 1
--1 0
00O

10O
0 0
0 --1


1
0


li1( )] 12(6) 13 (W)]













After the position of each feature point, If", was determined relative to the camera


basis, the focal plane position was then calculated using Equation 3.2 through direct


substitution. Figures 3-3 3-6 show the feature point position for each grid plane as


it's rotated toward the camera's position for a set focal length, where the plane in the


first set of plots is parallel to the inertial X-- Z plane. Here the focal length, f, was set


to a constant value of f =- 0. 1 mm for all the plots below.


120

115

110

105



95

90

85

-20


0 08





0 0







-0



p (mm)


(b) Focal Plane


ii to iX (ft) i


(a) Inertial Frame


10 15 20


Figure 3-3: Planar Feature Points


120

115

110




90


85

-20


0 08



002 0








-0



g (mm)


(b) Focal Plane





10 15 20


-10 -5



(a) Inertial Frame


Figure 3-4: Skewed Feature Points Sloping 2.5 Units













120

115

110

105

S100

95

90

85

sc-
-20


*


*
,
* *
*


* *


***~~~ ~ ** ** ** 8
4 (mm)


(b) Focal Plane


l 5X (ft) j


(a) Inertial Frame


10 15 20


Figure 3-5: Skewed Feature Points Sloping 5 Units


120

115

110

105

v 100

95

90

85


0 08





0 02~ r




-004~





4 (mm)


(b) Focal Plane


15 -10 -5 0~ 5


(a) Inertial Frame


10 15 20


Figure 3-6: Skewed Feature Points Sloping 10 Units



Notice as each plane is rotated toward the camera, the focal plane image becomes


increasingly distorted. The first set of plots reveals when the depth, inertial Y direction,


is held constant the focal plane mapping retains the the initial shape with some


scaling factor proportional to the focal length. As the plane is rotated by changing the


depth, the feature points which are closer appear to be spreading further apart while


points that are at a greater distance appear to converge closer together. As seen in


Figure 3-6, the feature points contained in the right half plane have increased their










separation distance significantly compared to the previous cases. Each grid plane

rotation was doubled so a comparison can be made with the distortion distance. As

the plots illustrate, as the rotation plane is doubled the resulting distortion distance has

increased more than twice. Therefore, the focal length relation between feature point

location and depth is nonlinear. A formal mathematical statement is presented below in

Equation 3.3.



(pwv) = Grcfk a)l (3.3)

The function G describes some nonlinear function which maps feature point

position in inertial space to the focal plane. This function only relates the nonlinearities

describing depth perception onto the image plane through focal length and is strongly a

function of the (z, component.

3.1.2 Focal Plane Velocity

The final step is to formulate an expression for the velocity of feature points in the

focal plane. Therefore, the focal plane velocity is found by taking the time derivative

of the position defined in Equation 3.2.





The focal plane velocity of the ath feature point relative to the kth is finalized by

substituting both equations for position and velocity derived in Equation 2.6 and 2.12

into Equation 3.4

3.2 Lens Distortion

Another important nonlinearity associated with a camera is image distortion due to

the curvature of the lens. This effect can be described as a tunnel vision image, where

feature points on the extreme sides are drawn toward the horizon centerline. This is a










planar distortion unlike the the focal length mapping described in the previous section

in which the shape was unchanged for the planar case.

An experiment was conducted using a standard Marshell CMOS color camera

with 310 TV lines of resolution to characterize image distortion due to lens curvature.

Figure 3-7 illustrates the dramatic warping done to a set of evenly spaced grid points.



























Figure 3-7: Lens Curvature


The horizontal and vertical centerlines retain a linear curve while lines above

and below follow this parabolic concave and convex mapping that is axisymmetric.

Likewise, this mapping can be expressed mathematically as a nonlinear function

depending on inertial space and the focal length, as given in Equation 3.5.



(pwv) = L(fk,( ,t() (3.5)










The camera nonlinearities described above will have a significant effect on a

controller design for obstacle detection and avoidance. Buildings appearing in the

image plane, depending on their location, will appear closer or further away than they

actually are due these distortions. Therefore, the functions G and L are required to

accurately describe the motion of feature points in real space for control designs and

will vary for each particular camera.















CHAPTER 4
LATERAL AUTOPILOT CONTROL DESIGN

The long term goal of this autopilot is to structure the controls system that

would allocate GPS waypoint tracking for MAVs using vision feedback. The controls

layout for an aircraft is typically separated into lateral directional and longitudinal

controllers. This section will document the design of a lateral autopilot control system

for a MAV by continuing the investigation of vision-based antonomy presented in the

literature [8, 18]. This design can be easily extended to lateral waypoint tracking by

incorporating an outer-loop that involves guidance algorithms.

The lateral control system deals with maintaining a desired roll and/or heading

angle through aileron and rudder deflections. By designing the lateral controls system

independently, some coupling in longitudinal states will result from these surface

deflections. For example, the sideslip induced by a roll angle can have a significant

on the longitudinal states with the loss of altitude. This may be modified in future

works by considering an aileron-rudder interconnect to prevent the nose from drifting

downward during a bank hold. This thesis will only consider the effects directly related

to the lateral states and will disregard these coupling terms.

The only lateral directional terms that are of interest for this control design include

roll and heading angle. For this section, these measurements are assumed to be known

perfectly. The sensors which provide these quantities will introduce a finite sampling

rate along with some uncertainty, which will be discussed later in the chapter and again

in Chapter 6.1.

The control architecture for this autopilot will begin with an inner-loop controller

and continue to an outer-loop design. The inner-loop controller will attempt to

maintain a desired roll angle, while the outer-loop will control the heading direction.










The general designs of these controls system will be discussed in further detail during

the remaining sections.

4. 1 Roll Control Design

A standard approach using proportional and integrator blocks was chosen for

this particular loop. This classical controls technique computes an error based on the

difference between the desired and measured state and makes that proportional to a

servo deflection. The integrator block helps to manipulate both the steady state error

and the rate of the response. The lateral steady state error correction was used to

account for asymmetries in the airplane due to construction and any net torques caused

by the motor.

For the case of a roll controller, the architecture can be accurately described in

block diagram form in Figure 4-1.











Figure 4-1: Roll Control Autopilot

The trim control block consist of a discrete time integral, and a proportional gain,

K,. The integral block is used primarily for improving steady state by continuously

driving the roll error to zero. Therefore, for a zero degree roll command the control

will maintain straight and level flight. The proportional gain is then applied to the

integral state to convert this value to a trim deflection, 6,arns, which is then sent to the

servos.

The remaining control element is a proportional gain where the difference between

the measured roll, 4, and the roll command, #c is defined as the error. This roll error

is then converted to an aileron deflection, 6a by the proportional gain, K4. The total









aileron deflection is then computed by summing the individual deflections determined

from both loops, as shown in Equation 4.1.



6a =- 6,ayns + 6, (4.1)

This controls system is only considering maintaining roll angle to a desired value

and does not incorporate coupling terms during this maneuver, such as maintaining

altitude during a bank hold.

4.2 Heading Control Design

For the heading control design, a nonzero roll angle will be used to change the

measured heading direction. Therefore, the roll controller designed in the previous

section will be implemented in the heading controller as the inner loop. The controls

structure is kept consistent by using a proportional feedback controller for heading as

well. The block diagram for this open-loop controls system is depicted in Figure 4-2.



Vc _e Ky 6, e4 Sa







Figure 4-2: Heading Control Autopilot


The heading error is computed and set proportional to a roll command through

Ky. As the aircraft tracks a roll angle, the heading will begin to change which in turn

will reduce the heading error. So effectively, as the measured heading approaches the

commanded heading the error will go to zero and the MAV will begin to roll back and

eventually reach 0 deg roll angle. The aileron deflections are again computed using

Equation 4.1i.










4.3 Closed-Loop Control

4.3.1 Bank Hold

Careful consideration of the vision-based sensor should be taken before designing

the closed-loop roll control system. The resolution of the measured roll angle was

found to be a constant +r4.45 deg. Potential problems will exist if the roll error is

computed and used in the control loop. For example, if the roll command was 2 deg

the error in roll angle would always be a nonzero value, due to the fact that the vision

system is unable to resolve below 4.45 deg, always resulting with a nonzero aileron

command. Physically the airplane will continuously try to drive the error to zero by

deflecting in the correct direction causing an overshooting to the measured resolution

followed by an opposite deflection to correct for the overshoot. This type of response

can be described as a limit cycle oscillation centered around the desired command.

The roll command is replaced with discrete values between the range --40 < #c <

40 deg, where the maximum roll command was set to +r40 deg, to avoid this resolution

issue. A bench test was then done to verify all possible values the roll sensor would

measure between 0 and +r40 deg and is documented in Table 4-1.

Table 4-1: Discrete Roll Command Output Values

Roll Command Discrete Roll Roll Command Discrete Roll
Range (deg) Command (deg) Range (deg) Command (deg)
0 4 Oc < 2.2 0 --2.2 4 Oc < 0 0
2.2 4 Oc < 6.6 4.45 --6.6 4 Oc < --2.2 -4.45
6.64 O < 1.18.90 --11.1 4 Oc < --6.6 -8.90
11.14 O < 5.5 13.35 --15.5 4 Oc < --11.1 -13.35
15.5 4 Oc < 20.0 17.80 --20.0 4 Oc < --15.1 -17.80
20.0 4 Oc < 24.4 22.25 --24.4 4 Oc < --20.0 -22.25
24.4 4 Oc < 28.9 26.70 --28.9 4 Oc < --24.4 -26.70
28.9 4 Oc < 33.3 31.15 --33.3 4 Oc < --28.9 -31.15
33.3 4 Oc < 37.0 35.60 --37.0 4 Oc < --33.3 -35.60


Another potential resolution problem occurs when computing the roll error for the

integration block. For the example given above, the value of the error will alternate










between 2 when the measured roll angle is zero and 2.45 when the measured roll is

angle is 4.45; again creating a possible limit cycle oscillation due a nonzero roll error.

Therefore, when the roll error is less than the resolution for a given command, the error

is then set to zero.

The closed-loop design of the roll controller can be described in block diagram

form through Figure 4-3. Some additional blocks were added to account for these

uncertainties in the system and camera nonlinearities.





Trim








Figure 4-3: Closed-Loop Roll Control Design


The discretizer blocks, D and R, were used to eliminate limit cycle oscillations as-

sociated with a low resolution in roll angle. Block D converts the given roll command

into discrete values associated with the horizon sensor, where these values are given

in Table 4-1. The error associated with the horizon resolution, as described above, is

represented as block R. The remaining blocks G and L describe the nonlinear mapping

of feature points in inertial space to the focal plane due to depth and lens distortion,

which is discussed in Chapter 3.

4.3.2 Heading Hold

As stated before, the heading controller consists of an outer-loop feedback using

yaw angle to command the inner-loop bank hold. The closed-loop block diagram for a

proportional heading controller is depicted in Figure 4-4.















Trim










Figure 4-4: Closed-Loop Heading Control Design


The lateral control system using the roll control will be applied to a particular

MAV testbed, described in the Chapter 5.1, using the horizon detection algorithm as a

sensor to estimate roll. The gains will be determined through numerous flight tests and

documented in the remaining sections. These results along with the final response plots

will be presented in Chapter 6.2.















CHAPTER 5
EXPERIMENTAL SETUP

5.1 Micro Air Vehicle Description

As stated in Chapter 1.2. 1, the University of Florida has an on campus facility to

fabricate MAVs in various sizes customized for a particular mission. In each case, the

volume of the fuselage is designed to house flight components and payload necessary

for a particular mission. In the case of an vision-based autopilot MAV, data and video

packages along with the required batteries must be incorporated in the design of the

fuselage. Once the total weight of the vehicle is determined the required wing area and

propulsion system can be selected.

The MAV build for this particular mission was a modified design of the standard

MAV at UF. The structural material of the airframe was still constructed using

layers of composite carbon fiber attached to a flexible wing design, as described in

Chapter 1.2.1. A series of pictures of this MAV are shown in Figure 5-1. Notice the

location of the camera has replaced the traditional position of a propeller design. Some

advantages of this camera position are (1) a direct correlation between horizon roll

angle and body axis roll and (2) a camera pointing out the nose will acquire better

images due to the steady flow conditions. The propeller is then placed behind the wing

on a shaft that connects the fuselage to the horizontal and vertical stabilizers. This type

of propulsion system allows for a more steady laminar flow around the wing due to the

absence of shed vortices from the propeller.

The final design of the MAV testbed used for vision-based autopilot control has

typical properties listed in Table 5-1.

A wing morphing technique was applied to the flexible wings to effectively control

the roll state. The term morphing, was coined because of the bending or twisting of




























Figure 5-1: MAV Prototype for Vision-Based Control
Table 5-1: MAV Properties

Wingspan 24 in
Weight 500 grams
Payload Capacity 200 grams
Actuators 4


the wings to change camber, cord, span, area, etc, which effectively changes the flight

characteristics of the vehicle through angle of attack. This was first implemented

mainly because MAV's with these types of flexible wings are difficult to incorporate

a standard aileron, due to additional structural reinforcements needed to divide the

wing. After extensive flight test, the morphing of the wing demonstrated a substantial

control authority in roll with little induced yaw (i.e. a more pure roll response).

The University of Florida has been looking at several simple ways to morph the

wing for roll control [12], one in particular was used in the design of this MAY

This design used a torque rod mounted near the wing tip and connected to a servo

inside the fuselage which morphed the wing by pushing or pulling on the rod. The

implementation of this concept on the current MAV is illustrated in Figure 5-2.























Figure 5-2: Torque Rod Design

An illustration in Figure 5-3 shows the slight change in effective wing area

by comparing the undeflected wing to the morphing deflection. For this particular

example, the left wing is deflected downward which in turn produces a positive roll

(i.e. right wing down) by the additional lift on the left wing. Flight test have shown

that morphing only requires a small amount of servo deflection to produce reasonable

bank angles.


(a) Wings Undefbcted (b) Wings Defbcted using Morphing

Figure 5-3: Morphing Control Effectors


The remaining control surfaces, elevator and rudder, were implemented in more

traditional way using the basic elevator on the horizontal stabilizer and rudder on the

vertical stabilizer. These surfaces along with the morphing deflection constitutes full










rotational degrees of freedom for the MAV. The servo connectors to both the elevator

and rudder were placed through a concentric metal pipe which passes in the middle of

the propeller bearings. This design provides a compact method which helps to conceal

these connectors mainly from being damaged. The servos used in this MAV were

model DS 281 made by JR Servo. The control surfaces required four servos; two for

the morphing and one for each elevator and rudder, which all weighs approximately

80 grams.

The propulsion system is powered through a Hacker brushless electric motor that

spins roughly at 60,000 RPM~ and can produce a maximum of 16 oz of thrust. The

motor is attached to a 6 in propeller through a two stage gearing system, which is

shown in Figure 5-4. Considering the weight of the vehicle and the on board power,

flight durations usually last approximately 15 min at full throttle using a single 3 cell

Lithium battery. This 3 cell battery also powers the servos through a transceiver board.














Figure 5-4: Push Tail Propeller Design


The on board sensors include GPS for location, speed, and course, an altimeter for

altitude, and the vision system for horizon detection. The GPS sensor, manufactured

by Furuno, uses the current and last position to calculate both speed and course with

an accuracy of 5 deg, where the position itself is accurate to 20 ft. The output units

consist of longitude and latitude in degrees, course in degrees, and the speed in ft/s.

The altimeter is a pressure based sensor which measures the relative gage pressure and









has a resolution of 20 feet when converted to altitude. The camera of the vision system

is a Marshall color CMOS camera with a resolution of 310 TV lines. The camera

introduces a nonlinear mapping of feature onto the image plane due to the focal length

and the curvature of the lens, which was described in Chapter 3.

5.2 Hardware Architecture

The components used to demonstrate vision control was restricted to a 200 gramn

on-board payload with a size constraint of 3 inches. Therefore, it was decided for

the initial platform to transfer all data processing to a ground station laptop. This

also allowed for human monitoring of the data on the ground during flight test. The

main hardware components consist of an on-board computer networked through a

wireless data-link, transceivers, a ground station laptop, a Sony Video Walkman, and

USB converters. An illustration of the system architecture is depicted in Figure 5-5.

The red and the black transmission lines indicate the video and sensor data steams

correspondingly.



~ 4 Autopilot Control when Trainer = 1









Figure 5-5: Hardware Architecture


Here the MAV contains an on-board custom microcontroller-based computer,

which communicates all sensor and video data to the ground station. This micro-

controller is a modified version of an Ateml AVR Megal28. An additional board

was developed to increase the amount of Flash memory of the AVR Megal28 from

128kB to 256MB through an optional attachment and was used for data logging. The










complete computer system is 2-inches by 1.5 inches by 0.5 inches and weighs approx-

imately 36 grams. The video and sensor data is collected through the this on-board

computer and streamed downed to the ground station for data processing. The ground

station, after processing this data, closes the control loop by sending servo commands

back to the MAV. Additional data, such as servo command and deflection, was also

sent to the ground station through the microcontroller to verify the control design.

The sensor data and video streams are broadcast ed through separate transmission

frequencies. The sensor data transceiver operates at 900MHz, providing rates up to

57.6kbps and is connected to the ground station through a UART based serial port.

This transceiver was a model AC4490 made by Aerocomm. Meanwhile, the video

stream operates at 2.4GHz and is interfaced to the ground station through a Sony Video

Walkman, via firewire.

For the initial flight test stages, a pilot was kept in the control loop to provide an

override capability during takeoff, landing, and autopilot recovery. This system was

incorporated by rerouting the control commands sent to the MAV through a standard

Futaba controller using a custom interface. This interface employed a trainer function

which allowed switching between autopilot and human control instantaneously, and is

also depicted in Figure 5-5. A custom board was made for this communication link to

pulse-width modulate the control signal sent from the autopilot. The serial connectors

for both data communication and Futaba control were converted to USB through a

Keyspan adapter, which allowed easy plug and play options for the ground station.

The ground station laptop consisted of a Apple 12-inch Powerbook running at

1GHz with 512MB of RAM. The video processing on the laptop was implemented

in real-time using the described horizon detection algorithm. The video firewire

communication was then coded in software to couple the on-line flight image with

the resulting horizon line. This was mainly done so the ground station can provide










a visual image to analyze during autopilot testing, which became a critical tool for

development.

5.3 Camera Model for Horizon

The camera nonlinearities described in Chapter 3, will have a strong effect on

the controller design using obstacle detection for avoidance. Buildings viewed by the

camera will be warped in the image plane resulting in false representation of distance.

For example, a building could appear further away in the image plane causing the

controller to delay commands for avoiding this object until it's too late. Therefore,

for a clutter environment, the functions G and L need to be incorporated in the control

design.

In the case of horizon detection, simple analysis can validate some assumptions

for these functions. The plots in Figures 3-3 and 3-4 revealed that (1) if the depth

of an object is constant the original shape is maintained in the image plane and (2)

a small rotation to change the depth results with a small distortion. Therefore, if the

distance between the object and the camera is increased to where it's much larger than

the distance in depth, the object's shape is retained in the image plane. Figure 5-6,

demonstrates this by increasing the relative distance from the camera to the grid points

with the same rotation.

The relative distance from the camera to the horizon line is much larger than the

depth of the horizon and therefore can be approximated as a planar line in 3D space.

This approximates the G function to a linear mapping from inertial space to the image

plane.

The lens distortion due to curvature still remains a nonlinearity in the system and

is depicted in Figure 5-7 for a horizon example. The image on the left is of a MAV

in flight at straight and level and contains the horizon roughly in the center, which

correlates to little distortion. The image on the right now shows a MAV in banked

flight which lowers and rises the horizon line in the image. The resulting horizon has











0 08







-004~




9 (mm)

(a) 70 ft


0 02


-0 02






4 (mm)

(b) 120 ft


Figure 5-6: Image Plane Depth Comparison


warping effects associated with both sides. Depending if the horizon is above or below

the centerline, the warping will be either concave or convex. With the horizon at such

a far distance the warping has little effect until the sides are approached.











Figure 5-7: Lens Curvature for a Horizon


A better study of the horizon detection algorithm may reveal a similar simplifi-

cation for the function L. The horizon line is determined by characterizing each pixel

to a known sky or ground color distribution. For example, shades of blue would be a

common feature for the sky while shades of green and brown would model the ground.

Some structure is added to the algorithm that checks the neighboring pixels to add

robustness. This accounts for any misclassified shades of blue in the ground or greens

and browns in the sky. A decision boundary is the found when the pixel distribution is

shifted from sky to ground in the image and is approximated by the linear line through

statistical regression. This linear line represents the determine horizon from which










roll and pitch percentage are calculated. Figure 5-8 shows an overlay of the horizon

algorithm onto the images given Figure 5-7.

















Figure 5-8: Lens Curvature with Horizon Approximation


When applying a linear regression curve fit, the warped ends of the horizon are

statistical outliers compared to the overall distribution and are not represented. The

resulting linear fit therefore, loses this nonlinearity and approximations can be made to

neglect this distortion for this particular case.















CHAPTER 6
CLOSED-LOOP LATERAL CONTROL

6.1 Controller Implementation

This section will interface the controls system with the hardware described in

Chapter 5. The architecture describes a close interaction between RC and autopilot

modes. The ground station code allowed easy implementation of the controller by

summing the determined control deflections around a trim condition. The commands

are then over-written when the signal is transferred to RC mode, giving the pilot

complete control of the MAY.

This transition from RC mode to the autopilot requires some consistent deflection

during this period. An offset deflection was then coded for the initial servo positions

which matched the RC trim. This offset helped remove any transition bias sent to

the servos when the autopilot is activated. Therefore, Equation 4. 1 now becomes

Equation 6.1, with the additional offset deflection.



So =- 6a,,,,, +- 6n +- 6., (6.1)

The on-board sensors that provide the roll and heading angles include the horizon

detection algorithm and GPS. The horizon detection calculates the roll angle made by

the horizon in the image plane and is updated at 35 Hz. Meanwhile, the GPS sensor

determines the course heading angle, relative to North, from past and present GPS

location and is available at 1 Hz. At this sample rate, the aircraft will potentially

exhibit oscillations around a given heading command.

In Chapter 5.3, the nonlinearities associated with the camera were assumed

to have little effect on the horizon because of the relative distance in depth. With










this information, the roll angle determined from the horizon detection sensor can be

approximated as the MAV's body axis roll angle and is used directly in feedback. The

control systems for both roll and heading commands now reduce to the block diagrams

shown in Figures 6-1 and 6-2.

6aoffset


Figure 6-1: Roll Control Block Diagram


Figure 6-2: Heading Control Block Diagram


The sample rate of this outer loop is 1 Hz, in Figure 6-2, causing the performance

of the heading tracker to diminish. For fast moving vehicle, the low sampling rate will

cause overshoot oscillations in the heading response due to a low time constant. The

response of the MAV during a heading command should be expected to fall within

a threshold value above and below the required heading, even when the controller is










designed properly. Commercial GPS sensor are also known to have a large degree of

uncertainty with some reliability issues. Some issues include interference or even loss

of satellite coverage. With the loss of data due to dropouts, the performance of the

controller can decrease tremendously. Drifting off course and large sudden maneuvers

will result due to these types of dropouts.

6.2 Flight Testing and Results

6.2.1 Gain Tuning

As mentioned earlier, a limited amount of MAV models have been generated for

control synthesis so little is known for implementation. Typically, when a dynamic

model is known of the aircraft, a rough estimation of the gains can be made using a

theoretical approach such as root locus. Without a model, as in this case, flight test

iterations are required to adjust the gains for the desired response.

For the roll controller, two gains need to be determined, the proportional gain and

the integral gain, K4 and KI. For the first few flights, these gains were set very small to

effectively eliminate the controller. Once the trim of the aircraft was found for straight

and level flight, using RC mode, adjustments were made to the offset deflections for

autopilot transition. When a rough estimate of trim is then found for the autopilot, the

gains in the controls systems are increased .

The first controller gain that was increased was the proportional gain. This gain

determines the transient portion of the controller by rolling the MAV to within a steady

state offset of the command. Some interesting responses occurred while increasing

this gain. When the gain was too high a noticeable oscillation about the command was

observed. This oscillation could have been cause by several different factors. The gain

could be too large resulting in a low damping ratio in Dutch roll for the closed-loop

system. The other factor under consideration is the wind gust. A MAV traveling at

25 mph can experience wind gust on the same order, which would drastically change

the flight characteristics and most importantly the trim conditions. By decreasing this










gain, the response of the MAV would maintain a bank angle. When this gain was

slightly large the bank angle response would settle down above the desired command.

Likewise, when the gain was slightly lower than the final value, the response would

center around a value less than the desired command.

Final flight iterations were done to acquire a response that is centered about

the desired roll angle with some steady state offset. The gain is then determined

through more flight iterations, where the response of the aircraft was used to determine

the direction in which the gain should be changed. When the response oscillates or

overshoots to a larger roll angle the gain should be decreased and increased when

the response has some undershoot and settles to a smaller roll angle. Finally, the

proportional gain that achieved a response centered around the desired command was

determined to be K4 =- 0.75.

The integral gain was then increased to make small corrections around the desired

command for steady state conditions. Some aggressive maneuvers were observed

when the integral gain was set to a large value. This integral gain is proportional to

the integral of roll error, so, when the MAV was straight and level and a 0 deg roll

command is given, a high integral gain has a smaller effect on the response because

of the small error. Although, the aggressive maneuvers occurred when the MAV was

placed at an initial bank angle, making the roll error large and the integral to roll

error increase, when the autopilot is activated the resulting aileron deflection is large.

Wind gust also had an effect on the integral loop by creating oscillations to correct

for the offset. When this gain was large the wind gust would be corrected by a large

deflection causing an overshoot in the opposite direction resulting in a correction for

the overshoot. This behavior describes a limit cycle oscillation caused by the controller

interacting with the physical flow. Some additional blocks or other control methods can

be used for disturbance rejection from wind gust.










The integral gain also helps limit the rate at which the maneuver is performed. A

slow response with some delay occurred when the gain was set too small. Therefore,

by slowly increasing this gain the desired rate and steady state condition can be

acquired. The integral gain that generated a reasonable response to commands was

determined to be KI =- 0. 19.

With these gains coded in the control loop, flight test were then documented to

record the data for a range of commands at various initial conditions.

6.2.2 Lateral Response

Using the gains found in the previous section, the data recorded from the flight

test will be analyzed. The sampling rate of the data-logging was being sampled at

25 Hz while the controller was operating at 5 Hz. This means for roughly every fifth

data sample a control is send up to command the airplane. A control systems for an

aircraft commanding on 5 Hz is unreasonable to expect a high level of performance.

These sampling frequencies are an estimate and therefore every fifth data point cannot

be plotted against the command. So to try and give an estimate of the response of

the MAV during the command an average of the measured roll angle between control

changes was used to plot the response, and is shown in Figure 6-3.

This figure shows the response of the MAV during a human commanded roll

doublet. From this response plot, one can see reasonable transient response during

the command from level to roughly +1t8deg. A steady state offset is shown for the

first bank command and for the level command, which can be adjusted by slightly

increasing the integral. For both bank commands of +rt18deg, there exists some

oscillations which could be caused from several different factors. This oscillation

could be a dutch roll mode being excited, a resolution issue, or a response to wind gust

corrections. If these oscillations are caused by the dutch roll mode, a yaw damper can

be used to control this mode.



















Is 0 510 52
tim (s
Fiur 6-3 RolRsos
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Ther wa somen difcut tetn h haigcnrolraddtemnn
The GPS ha frqetdoot ttets ieadee a ifcull okn nt
satllte tacurdaaSo esmlatrtion a emdsc spaigcpe
tapearoud th senor o inreas theantena r etoaqieasrn rsgalTh
GPS will thnb sdfrwyon rcig heelniueadlttd r sda






an alttude old were te innr loo commands lm ae obnn hs w






sens rs with th e sadardct inertiasnsors. Theais could b leusdfr inc treasing the










sampling rate, sensor bias corrections, and state estimation. The modeling of MAVs

will be conducted through flight data acquired from testing and wind tunnel data in the

lab. In the future, the models will aid in the control design process through simulation.















CHAPTER 7
CONCLUSION

In conclusion, this thesis has demonstrated that Micro Air Vehicles (MAVs) are

a reasonable platform for vision-based autonomous research. The military describes

many scenarios where this technology can be applied to save lives and help protect our

country from possible terrorist attacks.

A final relation was derived between the dynamics of a MAV and the motion of

feature points viewed by a camera attached to this vehicle. These equations, being

nonlinear, then gave some insight into how objects are viewed as the MAV passes

around them. This revealed how depth could change the shape of an object when its

mapped into the focal plane. Another nonlinearity related to the camera was described

as lens curvature. This mapping effected the outside portion of the image by warping

feature points into a convex and concave pattern.

A physical feature was then extracted from the images to control the MAV, where

the horizon line was determined. The image processing used a linear fit to track the

horizon line. Using the horizon also allowed the camera nonlinearities to be neglected

in the control design therefore, making the horizon's roll angle an estimate of the

aircraft's roll angle.

Controller designs for the lateral states using roll and heading angle feedback

were described using a classical proportional/integral control approach. With the

design and fabrication of a 24 in MAV, a test-bed was constructed along with the

required hardware and software to test the autopilot controls system. Due to some

GPS dropouts, data was only taken for the roll controller. A response to a roll doublet

was plotted and verified several issues. First, some steady state offset occurs during

a bank hold with some oscillations possibly due to a dutch roll mode. Second, the










synchronization between data-logging and the controller was inconsistent with the data

sampling a 25 Hz and the control working at 5Hz. To get an approximate response of

the MAV during the doublet, an average measured roll angle was taken over the course

of a control pulse.

The roll response acquired from the data, was tracking with a reasonable per-

formance for a 5 Hz controller. For future works, the data-logger and the control

should be operating at the same frequency to avoid any uncertainty in how the MAV

is responding. Once this issue is resolved, flight test for the heading controller will

preclude to determine the proportional gain. Finally, implementing a longitudinal con-

troller to track altitude to complete the aircraft states. Further research will then lead

onto implementing these controls systems into a fully autonomous waypoint tracker.















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BIOGRAPHICAL SKETCH

Ryan Scott Causey was born in Miami, Florida, on May 10, 1978. He grew up

in a stable family with one brother in a typical suburban home. During his teenage

years and into early adolescence, Ryan built and maintained a small business providing

lawn care to the local neighborhood. The tools acquired from this work carried over

into his college career. After graduating from Miami Killian Senior High School, Ryan

attended Miami Dade Community College for two years that commenced with an

Associate in Arts degree in engineering. A transfer student to the University of Florida,

Ryan was prepared to tackle the stresses of a university aside from the poor statistics.

A few years later, he received a Bachelor of Science in Aerospace Engineering degree

with honors and was considered in the top three of his class. During his summers

before and after graduation, he worked for Honeywell Space Systems in Clearwater,

Florida, as an intern applying his education to guided defense missiles. Ryan soon after

chose to attend graduate school back at the University of Florida under Dr. Andrew

Kurdila and Dr. Richard Lind in the Dynamics and Controls Laboratory. Vision-based

control of air-vehicles became his interest and he is now pursuing a doctorate degree

on this topic.