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Sensing and Control for Underwater Vehicles and Road Marking Survey with Mobile Lidar Systems

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Title:
Sensing and Control for Underwater Vehicles and Road Marking Survey with Mobile Lidar Systems
Creator:
Xu, Yiming
Place of Publication:
[Gainesville, Fla.]
Florida
Publisher:
University of Florida
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Language:
english
Physical Description:
1 online resource (108 p.)

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering
Mechanical and Aerospace Engineering
Committee Chair:
CRANE,CARL D,III
Committee Co-Chair:
SCHUELLER,JOHN KENNETH
Committee Members:
DIXON,WARREN E
HAMMER,JACOB

Subjects

Subjects / Keywords:
auv -- carangiform -- control -- disturbance -- feedforward -- hydrodynamics -- lidar -- locomotion -- mls -- obstacle -- pavement -- sensor -- subcarangiform -- swimming -- uuv
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre:
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Mechanical Engineering thesis, Ph.D.

Notes

Abstract:
This dissertation aims at investigating the underlying physical principals while developing three engineering systems and utilizing the acquired insight to either achieve a desired function or improve the existing performance. The first part of the dissertation is focused on developing a distributed pressure sensory system for underwater vehicles. Inspired by the functionality of the fish lateral line that provides hydrodynamic information about the surrounding fluid, the prototype is to aid station keeping and accurate maneuvering by allowing the vehicle to react to flow changes before perturbation. The system can also detect obstacles by analyzing the pressure distribution. Particularly, the distance and angle of a wall may be inferred from the amplitude and phase of the Fourier components in the distribution. Experimental tests are conducted to estimate the hydrodynamic force and detect the presence of a wall. Furthermore, by incorporating the force estimation algorithm into a feedforward controller, an improved tracking performance is observed in simulation. The second part presents a fish-like locomotion model in a simulated ideal flow. A swimmer is geometrically defined based on the Joukowski hydrofoil that resembles the carangiform and sub-caragniform fish locomotion. Specifically, the swimmer body is constrained so that the length and volume remain constant. A transformation from the geometric model to a body-fixed frame guarantees that the linear and angular momenta are conserved during body deformation. A hydrodynamic model is developed from potential flow with a vortex shedding mechanism to represent the viscous properties. Actuation of the swimmer is defined in a cyclic manner to address the under-actuation problem, whereas the control algorithm is designed based on simulation data. Closed-loop simulation demonstrates satisfactory path following performances. The third part discusses the development of a mobile lidar system for road mark surveying. A lidar is mounted on a vehicular platform with an integrated positioning system. Position and orientation of the lidar is calculated to minimize the gap between consecutive scans while allowing a reasonable vehicle speed. Points on the curbs, obstacles, and the reflective paint on the road surface are identified, before a global survey map is formulated. Survey tests are conducted with satisfactory performance. ( en )
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In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Thesis:
Thesis (Ph.D.)--University of Florida, 2017.
Local:
Adviser: CRANE,CARL D,III.
Local:
Co-adviser: SCHUELLER,JOHN KENNETH.
Statement of Responsibility:
by Yiming Xu.

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UFRGP
Rights Management:
Applicable rights reserved.
Classification:
LD1780 2017 ( lcc )

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SENSINGANDCONTROLFORUNDERWATERVEHICLESANDROADMARKINGSURVEYWITHMOBILELIDARSYSTEMSByYIMINGXUADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2017

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c2017YimingXu

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Tomyparentsandfriends

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ACKNOWLEDGMENTSFirstly,IwouldliketoexpressmysinceregratitudetomyacademicadvisorProf.CarlD.Crane,IIIfortheimmensesupportofmyM.SandPh.D.study,andforhispatience,motivation,andguidance.IenjoyedtheencouragingandpassionateresearchenvironmenthehelpsnourishedattheCenterforIntelligentMachinesandRobotics(CIMAR)attheUniversityofFlorida.Besidesmyadvisor,Iwouldliketothanktherestofthesupervisorycommitteemembers:Prof.JohnK.Schueller,Prof.WarrenE.Dixon,andProf.JacobHammer,fortheirperceptivecomments,critics,andinspirationsthatenhancethequalityofthisdissertation.MygratitudealsogoestomyformeracademicadvisorProf.KamranMohseni,whograntedmetheopportunitytoparticipateinthefascinatingresearchprojectsattheInstituteforNetworkedAutonomousSystemsduringmyPh.D.study.Hisexceptionalinsightandenthusiasticpursuitforknowledgeinvigoratesmethroughoutmystudy.Inaddition,IgreatlyappreciatetheassistanceandsupportfrommycolleaguesDr.MichaelKrieg,Dr.XiXia,ZhengRen,SamuelNason,NicolaImponenti,andKevinNelsonontheunderwatervehicleprojects,andDr.MichaelGris,ShannonRidgeway,PatrickJ.Neal,andTimWilliamsonthemobilelidarsystem.Furthermore,myresearchstudywouldneverbecompletewithoutmyfellowteammembers:Dr.MatthewShields,Dr.DouglasLipinski,Dr.AdamC.DeVoria,Dr.LiqianPeng,RobertHodgkinson,JosephJ.Thalakkottor,PeterZhang,ZhuoyuanSong,RichardS.O'Donnell,MatthewSilic,ThomasLinehan,IsaacJ.Sledge,MatthewGriessler,AndrewGray,andDanielZ.Frank. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES LISTOFTABLES ..................................... 7 LISTOFFIGURES LISTOFFIGURES .................................... 8 ABSTRACT ABSTRACT ........................................ 10 CHAPTER 1INTRODUCTION 1INTRODUCTION .................................. 12 2LATERAL-LINE-INSPIREDUNDERWATERSENSINGANDCONTROL 2LATERAL-LINE-INSPIREDUNDERWATERSENSINGANDCONTROL ... 15 2.1UnderwaterSensingSetup 2.1UnderwaterSensingSetup ........................... 17 2.1.1DesignConcept 2.1.1DesignConcept ............................. 17 2.1.2PressureSensors 2.1.2PressureSensors ............................. 18 2.1.3TestingFacilities 2.1.3TestingFacilities ............................ 20 2.2HydrodynamicForceEstimation 2.2HydrodynamicForceEstimation ........................ 22 2.2.1PressureSurfaceFitting 2.2.1PressureSurfaceFitting ........................ 22 2.2.2EstimationAlgorithm 2.2.2EstimationAlgorithm .......................... 26 2.2.3ForceEstimationSetup 2.2.3ForceEstimationSetup ......................... 27 2.2.4ForceEstimationTestResults 2.2.4ForceEstimationTestResults ..................... 30 2.3UnderwaterWallDetection 2.3UnderwaterWallDetection .......................... 31 2.3.1DetectionModel 2.3.1DetectionModel ............................. 32 2.3.2FourierAnalysis 2.3.2FourierAnalysis ............................. 35 2.3.3WallDetectionSetup 2.3.3WallDetectionSetup .......................... 36 2.3.4WallDetectionTestResults 2.3.4WallDetectionTestResults ...................... 38 2.4HydrodynamicFeedforwardControl 2.4HydrodynamicFeedforwardControl ...................... 43 2.4.1VehicleDynamicModel 2.4.1VehicleDynamicModel ......................... 45 2.4.2HydrodynamicFeedforwardModel 2.4.2HydrodynamicFeedforwardModel ................... 46 2.4.3ControllerDesign 2.4.3ControllerDesign ............................ 48 2.4.4ControlSimulation 2.4.4ControlSimulation ........................... 50 3MODELINGANDCONTROLOFAFISH-LIKESWIMMER 3MODELINGANDCONTROLOFAFISH-LIKESWIMMER .......... 54 3.1GeometricModeloftheSwimmer 3.1GeometricModeloftheSwimmer ....................... 56 3.1.1JoukowskiTransformation 3.1.1JoukowskiTransformation ....................... 56 3.1.2SwimmerProle 3.1.2SwimmerProle ............................. 57 3.1.3DeformationParameter 3.1.3DeformationParameter ......................... 59 3.2SwimmerDeformationDynamics 3.2SwimmerDeformationDynamics ....................... 60 3.2.1BodyFrame 3.2.1BodyFrame ............................... 60 3.2.2InertialFrame 3.2.2InertialFrame .............................. 61 3.2.3InternalForces 3.2.3InternalForces .............................. 62 3.3HydrodynamicModel 3.3HydrodynamicModel .............................. 63 5

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3.3.1FlowFieldModel 3.3.1FlowFieldModel ............................ 63 3.3.2NumericalPanelMethod 3.3.2NumericalPanelMethod ........................ 65 3.4SwimmingControl 3.4SwimmingControl ............................... 66 3.4.1DeformationFunction 3.4.1DeformationFunction .......................... 66 3.4.2ActuationModel 3.4.2ActuationModel ............................ 67 3.4.3ControlStrategy 3.4.3ControlStrategy ............................. 68 3.4.4SwimmingSimulation 3.4.4SwimmingSimulation .......................... 70 4MOBILELIDARSYSTEMFORROADSURVEY 4MOBILELIDARSYSTEMFORROADSURVEY ................ 72 4.1LidarSystemDesign 4.1LidarSystemDesign .............................. 73 4.1.1LidarSensor 4.1.1LidarSensor ............................... 73 4.1.2ScanningResolution 4.1.2ScanningResolution ........................... 73 4.2LidarDataProcessing 4.2LidarDataProcessing ............................. 77 4.2.1DataParsing 4.2.1DataParsing ............................... 77 4.2.2CurbandObstacleIdentication 4.2.2CurbandObstacleIdentication .................... 78 4.2.3LaneMarkIdentication 4.2.3LaneMarkIdentication ........................ 81 4.3PointCloudProcessing 4.3PointCloudProcessing ............................. 86 4.3.1OccupancyFilter 4.3.1OccupancyFilter ............................ 86 4.3.2RoadSurveyTests 4.3.2RoadSurveyTests ........................... 87 5SUMMARYANDCONCLUSIONS 5SUMMARYANDCONCLUSIONS ......................... 90 APPENDIX APROOFOFTHEOREM1 APROOFOFTHEOREM1 .............................. 92 BUSEFULRESULTSFORFISH-LIKESWIMMERMODEL BUSEFULRESULTSFORFISH-LIKESWIMMERMODEL ........... 96 CHYDRODYNAMICMODELVALIDATION CHYDRODYNAMICMODELVALIDATION .................... 97 REFERENCES REFERENCES ....................................... 100 BIOGRAPHICALSKETCH BIOGRAPHICALSKETCH ................................ 108 6

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LISTOFTABLES Table page 2-1Summaryofforceestimationexperiments 2-1Summaryofforceestimationexperiments ..................... 32 2-2Comparisonofcontrolperformancewithandwithoutpressurefeedforward 2-2Comparisonofcontrolperformancewithandwithoutpressurefeedforward ... 52 7

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LISTOFFIGURES Figure page 2-1Schematicsofthelaterallinesysteminash. 2-1Schematicsofthelaterallinesysteminash. ................... 15 2-2Pictureoftheunderwatervehicleanddesignforthepressuresensorysystem. 2-2Pictureoftheunderwatervehicleanddesignforthepressuresensorysystem. .. 18 2-3Picturesofthedierentialpressuresensors. 2-3Picturesofthedierentialpressuresensors. .................... 19 2-4Voltageoutputsfromsensorsatvariouspressuredierences. 2-4Voltageoutputsfromsensorsatvariouspressuredierences. ........... 20 2-5Pictureofthetestingtankandloadingplatform. 2-5Pictureofthetestingtankandloadingplatform. ................. 21 2-6Drawingandpictureoftheslidingcart. 2-6Drawingandpictureoftheslidingcart. ....................... 21 2-7Geometricmodelfordescribingtheconvexvehiclesurface. 2-7Geometricmodelfordescribingtheconvexvehiclesurface. ............ 23 2-8Schematicsandpicturesoftheforceestimationexperimentalsetup. 2-8Schematicsandpicturesoftheforceestimationexperimentalsetup. ....... 29 2-9SchematicsofthestraingaugearrangementandtheWheatstonebridgecircuit. 2-9SchematicsofthestraingaugearrangementandtheWheatstonebridgecircuit. 30 2-10Hydrodynamicforceestimationtestresults. 2-10Hydrodynamicforceestimationtestresults. .................... 31 2-11Diagramofthewalldetectionmodel. 2-11Diagramofthewalldetectionmodel. ........................ 33 2-12Pressuredistributioninthefrontofacircularobjectapproachingawall. 2-12Pressuredistributioninthefrontofacircularobjectapproachingawall. .... 34 2-13Fouriercomponentsinthepressuredistributionversuswalldistanceandangle. 2-13Fouriercomponentsinthepressuredistributionversuswalldistanceandangle. 36 2-14Schematicsandpicturesofthewalldetectionexperimentalsetup. 2-14Schematicsandpicturesofthewalldetectionexperimentalsetup. ........ 38 2-15Walldetectionresultforangle==2. 2-15Walldetectionresultforangle==2. ...................... 39 2-16Walldetectionresultforangle==3. 2-16Walldetectionresultforangle==3. ...................... 40 2-17Walldetectionresultforangle==6. 2-17Walldetectionresultforangle==6. ...................... 41 2-18Comparisonbetweenthewalldetectionsimulationandexperimentalresults. 2-18Comparisonbetweenthewalldetectionsimulationandexperimentalresults. .. 42 2-19Walldistanceandangleestimationcomparedtothereference. 2-19Walldistanceandangleestimationcomparedtothereference. .......... 44 2-20Blockdiagramofpressurefeedforwardvehiclecontrol. 2-20Blockdiagramofpressurefeedforwardvehiclecontrol. .............. 45 2-21Trajectorytrackingsimulationresultswithoutpressurefeedforward. 2-21Trajectorytrackingsimulationresultswithoutpressurefeedforward. ....... 52 2-22Trajectorytrackingsimulationresultswithpressurefeedforward. 2-22Trajectorytrackingsimulationresultswithpressurefeedforward. ......... 53 2-23Hydrodynamicforceestimationwithandwithoutpressurefeedforward. 2-23Hydrodynamicforceestimationwithandwithoutpressurefeedforward. ..... 53 3-1Diagramofvariousshswimmingmodes. 3-1Diagramofvariousshswimmingmodes. ..................... 54 3-2SchematicsoftheJoukowskitransformation. 3-2SchematicsoftheJoukowskitransformation. .................... 57 8

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3-3InteriorareasbeforeandafterJoukowskitransformation. 3-3InteriorareasbeforeandafterJoukowskitransformation. ............. 59 3-4Deformationofthesh-likebodywithconstantlengthandarea. 3-4Deformationofthesh-likebodywithconstantlengthandarea. ......... 61 3-5Schematicsofthepanelmethodmodelwithdiscretevortex. 3-5Schematicsofthepanelmethodmodelwithdiscretevortex. ........... 65 3-6Deformationparameter0asapiecewisesinusoidalfunction. 3-6Deformationparameter0asapiecewisesinusoidalfunction. ........... 67 3-7Swimmingmotionsforvariousdeformationparameters. 3-7Swimmingmotionsforvariousdeformationparameters. .............. 68 3-8Arctrajectoriesforapproachingorconvergingtothedesiredpath. 3-8Arctrajectoriesforapproachingorconvergingtothedesiredpath. ........ 69 3-9Simulationresultsoftheswimmerfollowingthedesiredpaths. 3-9Simulationresultsoftheswimmerfollowingthedesiredpaths. .......... 71 4-1Lidarsensorandeldofview. 4-1Lidarsensorandeldofview. ............................ 74 4-2Scanningcoverageforthelidarsystem. 4-2Scanningcoverageforthelidarsystem. ....................... 75 4-3Simulatedscanningpointsonthegroundatmaximumsurveyingspeed. 4-3Simulatedscanningpointsonthegroundatmaximumsurveyingspeed. ..... 76 4-4Crosssectionoutlinesofvariouscurbtypes. 4-4Crosssectionoutlinesofvariouscurbtypes. .................... 80 4-5Illustrationofthegeometricmethodtoidentifycurbsandobstacles. 4-5Illustrationofthegeometricmethodtoidentifycurbsandobstacles. ....... 81 4-6Dierenttypesofpavementmarkinglines. 4-6Dierenttypesofpavementmarkinglines. ..................... 82 4-7Lanemarkidenticationfromlidardatapointsonroadsurface. 4-7Lanemarkidenticationfromlidardatapointsonroadsurface. ......... 83 4-8Flowchartsfororganizingandprocessinglidardata. 4-8Flowchartsfororganizingandprocessinglidardata. ............... 84 4-9Flowchartsforidentifyingcurbsandlanemarks. 4-9Flowchartsforidentifyingcurbsandlanemarks. ................. 85 4-10Occupancycategorizationalongasinglelaserbeam. 4-10Occupancycategorizationalongasinglelaserbeam. ................ 86 4-11Demonstrationofoccupancylterwithpassingtrac. 4-11Demonstrationofoccupancylterwithpassingtrac. .............. 87 4-12Pointcloudfromlidarroadsurvey. 4-12Pointcloudfromlidarroadsurvey. ......................... 88 4-13Identiedpointsoncurbsandlanemarksfromsurvey. 4-13Identiedpointsoncurbsandlanemarksfromsurvey. .............. 89 4-14Satellitemapofthesurveyedarea. 4-14Satellitemapofthesurveyedarea. ......................... 89 C-1Instantaneousthurstonthehydrofoilfromexperimenttest. C-1Instantaneousthurstonthehydrofoilfromexperimenttest. ........... 98 C-2Instantaneousthrustonthehydrofoilfromsimulationtest. C-2Instantaneousthrustonthehydrofoilfromsimulationtest. ............ 98 C-3Thrustcoecientscomparisonbetweenexperimentandsimulationtests. C-3Thrustcoecientscomparisonbetweenexperimentandsimulationtests. .... 99 9

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophySENSINGANDCONTROLFORUNDERWATERVEHICLESANDROADMARKINGSURVEYWITHMOBILELIDARSYSTEMSByYimingXuDecember2017Chair:CarlD.Crane,IIIMajor:MechanicalEngineeringThisdissertationaimsatinvestigatingtheunderlyingphysicalprincipalswhiledevelopingthreeengineeringsystemsandutilizingtheacquiredinsighttoeitherachieveadesiredfunctionorimprovetheexistingperformance.Therstpartofthedissertationisfocusedondevelopingadistributedpressuresensorysystemforunderwatervehicles.Inspiredbythefunctionalityoftheshlaterallinethatprovideshydrodynamicinformationaboutthesurroundinguid,theprototypeistoaidstationkeepingandaccuratemaneuveringbyallowingthevehicletoreacttoowchangesbeforeperturbation.Thesystemcanalsodetectobstaclesbyanalyzingthepressuredistribution.Particularly,thedistanceandangleofawallmaybeinferredfromtheamplitudeandphaseoftheFouriercomponentsinthedistribution.Experimentaltestsareconductedtoestimatethehydrodynamicforceanddetectthepresenceofawall.Furthermore,byincorporatingtheforceestimationalgorithmintoafeedforwardcontroller,animprovedtrackingperformanceisobservedinsimulation.Thesecondpartpresentsash-likelocomotionmodelinasimulatedidealow.AswimmerisgeometricallydenedbasedontheJoukowskihydrofoilthatresemblesthecarangiformandsub-caragniformshlocomotion.Specically,theswimmerbodyisconstrainedsothatthelengthandvolumeremainconstant.Atransformationfromthegeometricmodeltoabody-xedframeguaranteesthatthelinearandangularmomentaareconservedduringbodydeformation.Ahydrodynamicmodelisdevelopedfrom 10

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potentialowwithavortexsheddingmechanismtorepresenttheviscousproperties.Actuationoftheswimmerisdenedinacyclicmannertoaddresstheunder-actuationproblem,whereasthecontrolalgorithmisdesignedbasedonsimulationdata.Closed-loopsimulationdemonstratessatisfactorypathfollowingperformances.Thethirdpartdiscussesthedevelopmentofamobilelidarsystemforroadmarksurveying.Alidarismountedonavehicularplatformwithanintegratedpositioningsystem.Positionandorientationofthelidariscalculatedtominimizethegapbetweenconsecutivescanswhileallowingareasonablevehiclespeed.Pointsonthecurbs,obstacles,andthereectivepaintontheroadsurfaceareidentied,beforeaglobalsurveymapisformulated.Surveytestsareconductedwithsatisfactoryperformance. 11

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CHAPTER1INTRODUCTIONSincetheancienttimeswhenhumansdevisedfundamentaltoolssuchaslevers,wheels,andpulleysforvariouspracticalpurposes,thedisciplineofengineeringhasalwaysbeenfocusedonthecreativeapplicationofscienticprinciplesthatstemfromthecomprehensionofthephysicalworld.Fromthesimplestrecognitionofwaterowcomesforththeuseofwaterwheelstoharvestpower.Fromtheknowledgeofcombustion,modernengineersdevelopedcombustionenginesforpropulsion.Whetherrudimentaryorsophisticated,anengineeringsystemoftenoriginatesfromtheinsightofthephysicalphenomenainorderforittointeractwiththephysicalworldasintended.Inaddition,advancementsofsuchaman-madesystemmaycomefrominspirationsofthebiologicalsystems,orcomefromtechnologicalimprovementsoveritscomponents.Thisdissertationcoversbothaspectsinconcernwiththedevelopmentofafewengineeringsystems.Therstpartofthestudyisinspiredbytheshlateralline.Thebiologicalsensorysystemisbelievedtoplayanimportantroleinthecreature'sabilitytoschoolinahighlycoordinatedandsynchronizedmanner[ 1 1 2 2 ],topositionandorientitsbodyinavaryingoweld[ 3 3 ],andtodetectimpendingobstacles[ 4 4 ].Asensorysystemforanautonomousunderwatervehicle(AUV)isdevelopedandtested,basedontheknowledgethatinformationabouttheunderwaterenvironmentisembeddedinthehydrodynamicpressurefromthesurroundinguid.Itisfoundinthisstudythatthehydrodynamicinformationcouldimplytheforceinteractionbetweenthevehicleandtheoweld,andcouldalsoindicatetheexistenceandcertainpropertiesofanobstacle.Thisstudyfurtherinvestigatestheimplementationofthesensorysystemonimprovingtheaccuracyofvehicletrajectorycontrol.Thesecondpartofthestudyisfocusedondevelopingadynamicalmodelanddesigningacontrolalgorithmforasoft-body,sh-likeswimmer.Themotivationforthestudyistounderstandthephysicsbehindtheecientandagileshlocomotion,and 12

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hopefullytogainsomeinsightofhowtodesignandcontrolasoft-bodyroboticswimmer.Tothisend,asimpliedsh-likeswimmermodelisdevelopedintwodimensional(2D)space.Thegeometryoftheswimmerisdenedtoresemblethetopviewforthecarangiformandsub-carangiformlocomotiongroupofshthatonlybendthebodyandcaudalnsforpropulsion.Thesetwocategoriesofshlocomotionappeartobemorebasicthanthatintheanguilliformlocomotionwherebodywavespropagatefromtheheadtothetail,andyettheinteractionbetweenthedeformableswimmerbodyandtheuidisdistinctfromthatforarigidbody.Ontopoftheexistingdynamicalmodelsforash-likeswimmer,afewadjustmentsaremadetorealisticallydescribethedeformationdynamics.Additionally,toresolvetheinteractionbetweentheswimmerbodyandthesurroundinguid,amodiedpotentialowmodelisconstructedwithadiscretevortexsheddingmechanismcreatinganaccuratepresentationoftheswimmingbehaviors.Acycliccontrolalgorithmisdevelopedtocopewithunder-actuationandistestedinaseriesofsimulations.Theresultssuggestthatincreasingordecreasingthedeformationmagnitudeswillaccelerateordeceleratethesteadyswimming,andthattheasymmetryinthedeformationdirectionresultsinturningmaneuvers.Closed-loopcontrolsimulationsarealsocarriedoutwheretheswimmerfollowsdesignatedpaths.Thethirdandnalpartofthestudyisaimedatautomatingtheprocessofroadmarkingsurveywithamobilelidarsystem.Therecentadvancementsinscanningspeedandaccuracyofcompactlidarsensors,combinedwiththeintegratedglobalpositioningsystem(GPS)andinertialnavigationsystem(INS),allowsforhigh-resolutionscanningonvehicularplatformswithreal-timelocalization.Inthedesignofthemobilelidarsystem,thelidarsensorispositionedandorientedinawaytoimprovethescanningresolutionwhileallowingthevehicletotravelatspeed.Lidardatapointsarerstprocessedwithrespecttothemovingvehicleplatform.Pointsofinterestsuchascurbs,obstacles,andlanemarksareidentiedutilizingthegeometryofthescanningsequences.Aglobalsurveymapissubsequentlyconstructedasapointcloud.Toremoveoutliersandidentify 13

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temporaryobstructionfromthetrac,thepointcloudfromthecontinuousscanistransformedintoathree-dimensional(3D)gridspaceasvoxelsandregisteredwithdierentoccupancyproperties.Roadsurveytestsareconductedtovalidatethesystemdesign,dataprocessingalgorithms,aswellaslteringtechniques. 14

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CHAPTER2LATERAL-LINE-INSPIREDUNDERWATERSENSINGANDCONTROLThelaterallineisacommonmechanosensorysystemfoundinmostshandsomeotheraquaticorganisms[ 5 5 6 6 ](seeFigure 2-1 2-1 ).Considerableevidencesuggeststhatitservesanimportantroleinvariousbehaviorsincludingrheotaxis(i.e.,theunderwatercreatures'abilitytoorientthemselvesparalleltoaoweld)[ 3 3 ],schooling[ 1 1 ],preydetectionandcapture[ 7 7 { 9 9 ],andsocialcommunication[ 10 10 ].Theneuromast,amechanoreceptivestructure,isbelievedtoberesponsibleforthefunctionalityofthelateralline.Specically,asillustratedinFigure 2-1 2-1 ,supercialneuromastslocatedonthebodysurfaceandprotrudingintotheexternaluidrespondtosteadyandlow-frequencycomponentsintheowinproportiontothenetvelocity.Canalneuromastssituatedinsubdermalcanalsalongthelaterallinesrespondtohigh-frequencycomponents,andreactproportionallytothenetacceleration(orthepressuregradient)[ 9 9 11 11 12 12 ].Ineect,bydetectingwatermotionsandpressuregradientsinthesurroundingenvironment,thelaterallinesystemprovideshydrodynamicinformationthatinturnfacilitatesmanybehavioraldecisions. A B CFigure2-1. Schematicsofthelaterallinesysteminash,recreatedfrom[ 13 13 ].A)Typicallayoutofthelateralline.B)Schematicsofthesupercialneuromaststhatarelocatedonbodysurfaceandrespondtolow-frequencycomponentsproportionaltothenetvelocity.C)Schematicofthecanalneuromaststhatareinsidesubdermalcanalsandrespondtohigh-frequencycomponentsproportionaltothenetaccelerationoftheow. Todate,increasingresearcheortshavebeendevotedtoreplicatingthesensingcapabilitiesofthelaterallinesystem.Someresearchersdevelopdelicatesensorysystemswithmicrofabricatedarticialsensorstomimicthestructuralfeaturesofthebiological 15

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laterallinesystem,andstudythesensorybehaviorsinvariousowconditions.Forexample,in[ 14 14 ]and[ 15 15 ],miniaturelaterallinesensorsaredesignedbasedonthethermalhotwireanemometryprinciple,andaretestedforlocalizingdipolesourcesandidentifyingthehydrodynamicsignatureofwakes.Thetaskofdipolelocalizationisalsoachievedwithmicromachinedarticialhairsensors[ 13 13 ].Additionally,opticalowsensorsaredevelopedasin[ 16 16 ]todetectwatermotionsinsidearticiallateral-line-likecanalsandareutilizedtodetectthewakebehindmovingobjects.In[ 17 17 ],bio-inspiredmicroelectromechanicalcanalsensorsareimplementedtosensingvariousowvelocities.Ontheotherhand,someotherresearchersutilizeexistingsensorsintheirtests,aimingatimitatingthefunctionalityofthebiologicallaterallinesystems.Forinstance,in[ 18 18 ],pressuresensorsareusedtoidentifytheowsignaturefromstaticandmovingcylinderswithdierentcrosssections;andin[ 19 19 ],parallelarraysofpressuresensorsaredeployedinavonKarmanvortexstreettocharacterizethehydrodynamicfeatures;andin[ 20 20 ],apressuresensorarrayisusedtoidentifytheangleofattackofanunderwatervehiclewithrespecttoafreestreamowforrheotaxiscontrolfeedback.Inadditiontodiscoveringvariousfunctionalitiesoftheman-madelaterallinesensorysystems,studiescouldalsocontributetoovercomingsomeoftheexistingchallengesinAUVcontrol.ContrarytotheneedforaccuratepositioningtoestablisheectiveAUVcontrol,underwaterlocalizationremainsachallengingtaskasradiofrequencycommunications(usedbytheGPS)aresignicantlyattenuatedandacousticchannelsareaectedbylongpropagationdelays,limitedbandwidth,andhighbiterrorrates[ 21 21 ].Avarietyoflocalizationtechniqueshasbeendevelopedforunderwaterapplications(refertoasurveyin[ 22 22 ]),butthepositionsignalsaregenerallysubjecttolargeerrorsincomparisontothoseofthesurfacevehicles.ThisfurthermotivatestheintroductionofadditionalsensorysystemtofacilitateaccurateAUVcontrol.Inthischapter,alateral-line-inspiredhydrodynamicsensorysystemisdeveloped,utilizingcommerciallyavailablepressuresensorstoinvestigatethemechanismsof 16

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underwatersensing.Bycreatingdistributedarraysofpressuresensorsonthebodyofanunderwatervehicle,hydrodynamicinformationcouldbeobtainedforestimatingthehydrodynamicdisturbanceaswellasdetectingobstacles.Bothsimulationandexperimentaltestsareconducted,validatingthecapabilitiesoftheprototypesensorysystems.Additionally,thehydrodynamicforceestimationisintegratedasafeedforwardcomponentinacontrolalgorithmforAUVs.Accordingtoresultsfromaseriesofsimulationtests,thehydrodynamicfeedforwardcomponentbringsaboutanimprovementinvehiclecontrolperformance,especiallyinthepresenceoflocalizationerrorandmeasurementnoise.Resultfromthisstudyispublishedin[ 23 23 { 26 26 ].ThischapterrstintroducestheexperimentalsetupfortheunderwatersensingtestsinSection 2.1 2.1 ,thenpresentsthemethodsandtestresultsforhydrodynamicforceestimationinSection 2.2 2.2 aswellasunderwaterwalldetectioninSection 2.3 2.3 ,andnallydemonstratesthefeedforwardcontrolimplementationoftheforceestimationalgorithminSection 2.4 2.4 .ProofofthecontrolstabilityisprovidedinAppendix A A 2.1UnderwaterSensingSetup 2.1.1DesignConceptTheobjectiveoftheexperimentsistodevelopandtestthesensorysystemthatwilleventuallybeimplementedontheAUVprototypeCephaloBot[ 27 27 ],asshowninFigure 2-2A 2-2A .Thevehicleisequippedwithcephalopod-inspiredvortexringthrustersthatcanprovidequantizedpropulsiveforcebycreatingarraysofhigh-momentumvortexringswithsuccessiveingestionandexpulsionofwater[ 28 28 29 29 ].Theseactuatorsallowthevehicletoperformaccuratemaneuversatlowspeed,withoutsacricingitslow-dragstreamlineproleforecienthigh-speedtraveling[ 30 30 { 32 32 ].Thedesignconceptofthepressuresensorysystemistocreatedistributedarraysofsensorsonthevehiclebodyforhydrodynamicforceestimationaswellasalinear,densesensorarrangementatthefrontfordetectionofobstacles,asillustratedinFigure 2-2B 2-2B 17

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A BFigure2-2. Pictureoftheunderwatervehicleanddesignforthepressuresensorysystem.A)PictureoftheautonomousunderwatervehicleprototypeCephaloBot,courtesyofMichaelKrieg.Thevehicleisequippedwitharearpropellerforpropulsionandfourvortexringthrustersonbothsidesforturningmaneuvers.Thepressuresensorysystemunderdevelopmentwillbeinstalledandtestedonthisplatform.B)Designconceptofthepressuresensorysystem.Distributedarraysofpressuresensorsonthebodyofthevehicleprovidehydrodynamicforceestimation,whereasthelineararrangementofpressuresensorsatthefrontofthevehiclecouldaidobstacledetectionandavoidance. Theexperimentalsetupforthesensorysystemconsistsofthevehiclemock-upsastestsubjectswithintegratedpressuresensors,themechanicalandelectricalsystemsthatsupportthemotionsofthesubjects,andtheadditionalsensorysystemthatprovidestheindependentreference. 2.1.2PressureSensorsThesensingelementsofthesystemarecommerciallyavailablemonolithicsiliconpressuresensors,MPXV7002DP.Thesepiezoresistivetransducersprovidedierentialpressuremeasurementsbetweentheirtwoportswithasensingrangefrom)]TJ /F1 11.9552 Tf 9.298 0 Td[(2to2kPa.ThetransferfunctionfromthepressuremeasurementPtotheoutputvoltageVOUTcanbewrittenas VOUT=(0:2kPa)]TJ /F4 7.9701 Tf 6.587 0 Td[(1P+0:5)VS2:5%VFSS;(2{1)wherethenominalsupplyvoltageisVS=5:0Vandthefull-scalevoltagespanisVFSS=4:5V.PicturesofthesensorsareshowninFigure 2-3 2-3 .Duringthetests,theanalogsignalsarefedintothedataacquisitioncard(NIPCI-6229)viashieldedSubMiniature-A(SMA)cables.Thesignalsaresampledat1kHz,andconvertedwith16-bitprecision.Whilethe 18

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systemisinoperation,thenoiseinthepressuresignalsisabout6mV,correspondingtoamagnitudeofabout6Painpressure.Possiblesourcesofnoiseincludeacousticnoiseorvibrationsthatwouldaectthepiezoresistivetransducerandelectricalnoiseintroducedbythepowersupply,cableconnections,andthedataacquisitionprocess.Toeliminatethesignalosetduetothemechanicalstressandmountingpositionfrominstallation,theaveragezero-pressurevoltageissubtractedfromthesignalforeverysensorpriortoexperiments. A BFigure2-3. Picturesofthedierentialpressuresensors,courtesyoftheauthor.A)Dierentialpressuresensorusedinthesystem.B)Sensorconnections.Poweredby5VDC,thesensormeasurespressuredierenceupto2kPabetweenthetwoports.AnalogsignalsaresendthroughshieldedSubMiniature-A(SMA)cables. Thepressuremeasurementsarevalidatedbyplacingtheindividualsensorportsatvariousdepthsinwaterandcomparingthemeasuredpressuredierenceswiththeexpectedones.ThiscomparisonisshowninFigure 2-4 2-4 .Thepressureerrorbarsrepresentthestandarddeviationofthewaterdepthmeasurements.Thevoltageerrorbarsarefromthestandarddeviationofvoltagesamplesfrom20pressuresensors.Thesolidanddashedlinesdepictthenominaltransferfunctionandtheprecisionbound,respectively.Comparisonbetweenthesensorymeasurementandtheprecisionboundshowsthattheperformanceofthepressuresensorsissatisfactory. 19

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Figure2-4. Voltageoutputsfromsensorsatvariouspressuredierences.Thepressurevariationisobtainedfromdierentwaterdepths.Pressure(horizontal)errorboundsrepresentthestandarddeviationofthewaterdepthmeasurements.Voltage(vertical)errorboundsarefromthestandarddeviationofvoltagesamplesfrom20pressuresensors.Thesolidanddashedlinesdepictthenominaltransferfunctionandtheprecisionbound,respectively. 2.1.3TestingFacilitiesThepurposeofthetestingapparatusistocarrythetestingsubjects{cylindersintegratedwithpressuresensors{throughwateratadesignatedspeed,andtocollecttheirpositionandvelocityinformation.Thetestingcylindersaremadefrom6-inSchedule-40polyvinylchloride(PVC)pipeswithanouterdiameterof16.8cm(6.625in)andawallthicknessof7.54mm(0.297in).Beforebeingsubmergedinwater,thecylindersareloadedwithleadshotweightstoachieveneutralbuoyancy.Thepressuresensorportsareconnectedtotheopeningsonthecylindersurfacewith2.38mm(0.0937in)innerdiameterexiblevinyltubes.Twoseparatetestingcylindersaredesignedspecicallyfortheforceestimationandthewalldetectiontests,whosedesignswillbedetailedinSections 2.2.3 2.2.3 and 2.3.3 2.3.3 ,respectively.Thetestapparatusissetupinacylindricalwatertankwithadepthof4.6m(15ft),adiameterof8m(26ft),andacapacityof250m3(65,000gal),asshowninFigure 2-5 2-5 .AplatformI-beam(withaangewidthof20cmor8inandasectiondepthof20cmor8in)isutilizedasatrackforthelinearmotiondriver.Acarryingcartismanufacturedtosupportthetestingsubjects,whileclampingtightlyonandslidingalongtheI-beam,asshowninFigure 2-6 2-6 20

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Figure2-5. Pictureofthetestingtankandloadingplatform,courtesyoftheauthor.Thetankisa4.6m(15ft)tall,8m(26ft)diameter,and250m3(65,000gal)capacitycylindricalwaterreservoir.Theplatformspansontopofthetank.The6camerasforthemotioncapturesystemareinstalledatthebottomofthetank,xingtheeldofviewtowardstheareanexttotheplatform. A BFigure2-6. Drawingandpictureoftheslidingcart,courtesyoftheauthor.Thecarthasthreesetsofrubberwheelstoclampontotheangefromtopandbottom,fourgroovedwheelstorestrictsidewaysmotions,andaconnectortosupportthetestingsubjects.TheclampingmechanismallowsforeasyattachmentanddetachmentofthecarttoandfromtheI-beam. Theslidingcartiseitherpulledmanuallyoractuatedbyamotorizedpulleysystem.PositionedateachendoftheI-beam,thepulleysystemdrivesthecartatacontrolledspeedwithsteelcablewires.Onepulleyisconnectedtoamotor.Themotorisabrush-commutateddirect-current(DC)motor(PittmanID33005-SP)thatproducesacontinuousoutputtorqueof0.85Nm(120ozin)at6000rpm.Therotationofthemotorismonitoredbyanencoderatthemotorshaft,andtherotationalspeediscontrolledbyaproportional-integral-derivative(PID)feedbackcontroller. 21

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Thepositionofthetestingsubjectsismeasuredwithamotioncapturesystem,wheresixunderwatercameras(Oqus5-seriesfromQualisys)providethe3Dpositionsofreectivemarkersplacedonthetestingsubjects.Thecamerasystemrecordsthepositionsofthemarkersat100framespersecond,andhasaspatialresolutionofabout1mmaftercalibration. 2.2HydrodynamicForceEstimationThepressuresensorysystemisdevelopedtoobtainhydrodynamicinformationaboutthesurroundingowbymeasuringthepressuredistributionaroundtheunderwatervehicle.Asoneofthetwofunctionsoftheprototypesensorysystem,estimatingthehydrodynamicforcerequiresspatialintegrationofthepressuredistribution.Analgorithmisderivedtorapidlyestimatethehydrodynamicforce.Inthebody-xedcoordinatesystem,abiparametricsurfacedescribestheboundaryofthevehicle.Thehydrodynamicforcesandmomentscomefromthewaterpressureappliedonthesurfaceofthevehicle.TheshearforcesareminimalandnegligiblebecauseofthelowReynoldsnumber.Usingttingtechniques,thepressuredierencemeasurementsfromsensorsatmultiplelocationscanbeusedtoreconstructthepressuredistributionovertheentirevehiclebody.Thus,thetotaldampingforceandmomentexertedonthevehiclecanbeestimatedbyintegratingthepressuredistributionoverthevehicleprole(excludingthelocationsoftheactuators).Theresultantforceestimationwilltaketheformoflinear,xedweightcombinationsofthepressuremeasurements. 2.2.1PressureSurfaceFittingAsillustratedinFigure 2-7 2-7 ,theproleofthevehicleisdescribedinthebody-xedcoordinatesystem.Forapointonthevehicle'ssurface,thepositionvectorr2E3andthenormalvectorn2E3canbewrittenas r=rxryrz>;n=nxnynz>;;(2{2) 22

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whererx,ry,andrzarecomponentsinralongthex-,y-,andz-axes,respectively;similarlyfornx,ny,andnz. Figure2-7. Geometricmodelfordescribingtheconvexvehiclesurface. Ingeneral,theboundaryofthevehiclecanberepresentedwithabiparametricsurface,andthus,anypositiononthesurfaceisuniquelydenedbyspecifyingapairofparameters.Inthisstudy,allextrudingpartsonthevehicleareignoredforsimplicity,whichgivesaconvexvehiclesurfaceonwhichpositionsareconvenientlydeterminedbyangles2[)]TJ /F3 11.9552 Tf 9.299 0 Td[(;)Rand2[)]TJ /F3 11.9552 Tf 9.299 0 Td[(=2;=2)R.Specically,forpositionr,theazimuthalangleincoordinatesystemOxyisdesignatedas,whichsubtendsfromthepositivexaxistotheorthogonalprojectionofrontheOxy-plane;anddenotestheazimuthincoordinatesystemOyz.Asaresultoftheparameterization,vectorsrandnareexpressedasfunctionsinand.Supposeanumberofp=pp2Nsensorsarelocatedonthesurfaceofthevehicle(pandpineachofthecorrespondingdirections).EachsensortakesmeasurementofthenormalpressurePs2Ratpositions;s2R(s=1;2;:::;p).SurfacettingoverthepressuremeasurementswillgiveanestimateofthepressuredistributionbP(;)2R.AB-splinesurfaceisusedtomodelthepressuredistributionduetoitsexibilityinthesplinedegreeandsmoothness,anditslinearpropertythatwillbecomehelpfulforonlinecomputation.ForCk)]TJ /F4 7.9701 Tf 6.587 -.001 Td[(2andCl)]TJ /F4 7.9701 Tf 6.587 -.001 Td[(2continuityinthe-and-directions,respectively,aclosedperiodicB-splinesurface(see[ 33 33 34 34 ]fordetail)isusedastheapproximationfunction,withordersofkandl(degreek)]TJ /F1 11.9552 Tf 12.043 0 Td[(1;l)]TJ /F1 11.9552 Tf 12.043 0 Td[(12N)inthe-and-directions.Thus, 23

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theestimateddistributionbP(;)canbewrittenas bP(;)=N>()BM();(2{3)whereentriesinmatrixB2RnmdenotethecontrolverticesoftheB-splinesurface, B=2666666664B1;1B1;2B1;mB2;1B2;2B2;m............Bn;1Bn;2Bn;m3777777775:(2{4)ThevectoroftheB-splinebasisfunctionsinthe-direction,N()2Rn,isdenedas N()=N1()+N2();(2{5)inwhichN1();N2()2Rnare N1()=N0;k()N1;k()Nn)]TJ /F4 7.9701 Tf 6.587 0 Td[(1;k()>; (2{6a)N2()=Nn;k()Nn+1;k()Nn)]TJ /F4 7.9701 Tf 6.586 0 Td[(1+dk=2e;k()00N1bk=2c;k()N2bk=2c;k()N)]TJ /F4 7.9701 Tf 6.586 0 Td[(1;k()>: (2{6b)ThebasisfunctionNi;k()2Risexpressedwiththerecurrenceformuladueto[ 35 35 { 37 37 ] Ni;1()=8>><>>:1;ifhi
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ThedenitionforbasisfunctionvectorM()2RmisanalogoustoN(),andthereforeomitted.BasedonthepropertyfortheKroneckerproduct(see[ 38 38 ]),thepressureestimationin( 2{3 2{3 )isequivalentto bP(;)=K>MN(;)vec(B);(2{9)whereKMN(;)2RmnistheKroneckerproduct KMN(;)=M()N();(2{10)andvec()denotesvectorizationofamatrixasin[ 38 38 ].Persurfacetting,thecontrolverticesareapproximatedintheleastsquaressense,i.e.,foragivensetofmeasuringpoints,s,s,andPs,s=1;2;:::;p,thefollowingcostfunctionisminimized: pXs=1bP(s;s))]TJ /F3 11.9552 Tf 11.955 0 Td[(Ps2:(2{11)Substituting( 2{3 2{3 )into( 2{11 2{11 )andapplyingstandardlinearleastsquaresapproximationtechniques(referto[ 39 39 40 40 ])yieldsm-by-nequations,whichinturnareformulatedas KGHK>GHvec(B)=KGHP;(2{12)whereKGH2RmnpdenotestheKhatri-Raoproductforpartitionedmatricesfrom[ 41 41 ](refertoanoverviewin[ 42 42 ]) KGH=GH;(2{13)andP2Rpisthevectorofpressuremeasurements P=P1P2Pp>:(2{14)In( 2{13 2{13 ),G2RmpandH2Rnparecolumnwisepartitionedmatricesdenedas G=M(1)M(2)M(p);H=N(1)N(2)N(p):(2{15) 25

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Inordertoobtainthecontrolverticesvec(B)from( 2{12 2{12 ),thematrixKGHK>GHneedstobeinvertible.Thisimpliesthatwithintheinuencingregionforeveryvertex(i.e.,inthepatchwherethebasisfunctionassociatedwiththevertexisnonzero),thereshouldexistatleastonepressuresensor.Sinceavertexaectskorlneighboringintervalsdividedbythecontrolknotsalongthe-or-direction,thepressuresensorsshouldbespreadacrossthevehicleprole.Byprescribingasensordistributionsuchthateverycontrolregionwillcontainatleastonesensor,thematrixKGHK>GHisalwaysnonsingular.Solving( 2{12 2{12 )forthecontrolverticesvec(B)gives vec(B)=KPP;(2{16)whereKP2Rmnpisdenedas KP=(KGHK>GH))]TJ /F4 7.9701 Tf 6.587 0 Td[(1KGH:(2{17)Substituting( 2{16 2{16 )intothepressureestimatesin( 2{9 2{9 )yieldsthettingresult bP(;)=K>MN(;)KPP:(2{18) 2.2.2EstimationAlgorithmBasedonthettingresult,thedampingforceF2E3andmomentMO2E3relativetotheoriginOactingonthevehicleareestimatedbybF;cMO2E3,whichcanbewrittenasdoubleintegralsoverthe2DdomainT=[)]TJ /F3 11.9552 Tf 9.298 0 Td[(;)[)]TJ /F3 11.9552 Tf 9.299 0 Td[(=2;=2)R2 bF=ZZT)]TJ /F8 11.9552 Tf 9.298 0 Td[(nbP(;)r2dd;cMO=ZZT)]TJ /F8 11.9552 Tf 9.299 0 Td[(rnbP(;)r2dd;(2{19)wherer=krk2Risthenormofthepositionvectorr,andtheminussigncomesfromthefactthatthepressureisconsideredpositivetowardsthevehiclesurface. 26

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Forplanarmotions,thevectorofestimateddampingforcesandmomentsbfD2R3consistsoftheforcesalongthex-andy-directions,andthemomentaboutthez-axis: bfD=bFxbFycMOz>:(2{20)Combinedwith( 2{18 2{18 )and( 2{19 2{19 ),theforceestimatebfDcanbeexpressedas bfD=ZZTbK>MN(;)r2ddKPP;(2{21)whereb2R3isdenedas b=)]TJ /F10 11.9552 Tf 11.291 16.857 Td[(nxnyrxny)]TJ /F3 11.9552 Tf 11.955 0 Td[(rynx>:(2{22)With( 2{21 2{21 ),thedampingforcesandmomentscanbeestimatedasthepressuresignalvectorPpremultipliedbyamatrixthatisafunctionofthelocationsforthepressuresensors.Oncethesensorlocationsaredened,thematrixcanbeobtainedapriori.Sinceonlymatrixmultiplicationisrequiredforonlinecalculation,theforceestimationcanberenderedeortlesslybytheonboardembeddedsystem. 2.2.3ForceEstimationSetupThesystemprototypeistestedforhydrodynamicforceestimation.Theconceptofthetestisthatforanobjectmovinginwater,thelinear(orangular)accelerationmultipliedbymass(ormomentofinertia)oftheobjectisequaltotheresultantexternalforce(ortorque)includingthehydrodynamicforce(ormoment)andtheforce(ormoment)fromthestructuresupportingtheobject.Ontheonehand,thehydrodynamicforceandmomentcanbeestimatedwithpressuresensorsonthesurfaceoftheobject;andontheotherhand,thesamequantitiescanbecalculatedbasedontheobject'saccelerationandothersupportingforcesandmomentsactingontheobject,whicharemeasuredbythemotioncapturesystemandthestraingauges,respectively.Thespecicexperimentalsetup,asillustratedinFigure 2-8A 2-8A ,consistsofahorizontalcylinder,averticalrod,andanattachingstructuretotheslidingcart.Thecylinderis 27

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madefromaPVCpipewhichis81.3cm(32in)longandisclosedatbothendswithroundedcaps,sothatitresemblestheshapeofanunderwatervehicle.Inthetest,thecylinderissubmergedunderwater,andtheslidercarriesthecylinderwiththerod.Hydrodynamicpressureismeasuredonthesurfaceofthecylinder,theforceandmomentactingonthecylinderastransmittedthroughtheconnectingstructureareobtainedwithstraingaugesontherod,andtheaccelerationofthecylinder(usedtocalculateinertialforces)iscalculatedfromthepositionmeasurementswiththemotioncapturesystem.Thereareatotalof20sensorsinthepressuresensorysystem,asshowninFigure 2-8B 2-8B .Generally,thepressuresensorsneedtobedistributedaroundthecylinderinordertoreconstructthepressuredistributionforforceestimation.Inthisparticulartest,thedierentialpressuresensorsarearrangedinanarraythatcovershalfofthecylindersurface,basedontheassumptionthatthepressuredistributionissymmetricwhenthecylinderismovingperpendiculartoitscentralaxis.Thesensorsaregroupedinpairsoftwo;onemeasuresthepressuredierencealongthelongitudinaldirection,whiletheothermeasuresthedierencealongthecircumferentialdirection.Together,theyformsa52array.Theforceandmomentactingonthecylinderbytheconnectingrodismeasuredbystraingauges.Therodismadefromanaluminumpipewitha2.54cm(1in)diameter.Atotalof16straingaugeelementsformfourWheatstonebridgesonthesurfaceofthepipe,asillustratedinFigure 2-9 2-9 .Twobridges(AandB)measurethebendingstrainalongtwoperpendiculardirections,whiletheothertwogroups(incircuitsCandD)areplacedatanangleof45fromtheaxialdirectionandmeasurethetorsionalstrain.Oncecalibrated,thestraingaugecircuitsmeasuretheforceandmomentactingonthecylinderbytherod.Furthermore,toreducethedeviationfromthecylindricalshape,thesensorpowerandsignalcablesarethreadedthroughthealuminumpipebeforebeingconnectedtothedataacquisitionsystem.Whilethecylinderismovingalongtheslideway,itspositionis 28

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A B C DFigure2-8. Schematicsandpicturesoftheforceestimationexperimentalsetup,courtesyoftheauthor.A)Drawingoftheforceestimationexperimentalsetup.B)Drawingofsensorarrangement.C)Pictureoftestingcylinderontheslider.D)Pictureofsensorsinsidethetestingcylinder.Intotal,20pressuresensorsareinstalledwiththeportsconnectedtothesurfaceofthecylinder.Thesensorsaregroupedintopairs;onesensormeasuresthepressuredierencealongthelongitudinaldirection,whiletheothermeasuresthedierencealongthecircumferentialdirection.Eachgroupoftwoconnectedcirclesrepresentsasensorwithitstwoports.Therodsupportsthecylinderandprotectthesignalcableswithin.Ontherodtherearestraingaugesthatmeasuresthestrain,whichrelatestotheforceandmomentactingonthecylinderbytheroditself. 29

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recordedwiththemotioncapturesystem,andtheaccelerationcanbeobtainedthroughsignalprocessing. A BFigure2-9. SchematicsofthestraingaugearrangementandtheWheatstonebridgecircuit.A)Straingaugearrangementdrawing.B)Wheatstonebridgecircuit.The16straingaugesformfourWheatstonebridgecircuitslabeledfromatod.Aftercalibration,circuita(b)measuresthehorizontalforcealong(perpendicularto)thetraveldirection,whereascircuitscanddmeasurethehorizontaltorquewithstraingaugesplacedat45fromtheaxialdirection. 2.2.4ForceEstimationTestResultsThetestingsystemwastranslatedacrossthetankwithmultipletrajectorieswhileindependentlycollectingdatafromthepressuresensorsandthestraingauges,aswellasrecordingtheglobalpositionofthecylinderfromthemotioncapturesystem.Ineachtest,thesystemstartsfromrestandacceleratestoaconstantspeedbeforeitdeceleratesbacktoastop.Thepressuredistributionisassumedtobesymmetricbetweenthetwoendsofthecylinder.FilteredandcalibratedsignalstogetherwiththeforceestimationresultsfromtwotestsareshowninFigure 2-10 2-10 .Thevelocityisroughlymaintainedaround0:1m=swithintentionalvariationstoachievevaryingacceleration,whichresemblesthetypeofmotionsperformedbytheunderwatervehiclewhiledocking.Oncethecontrolledmotionstops,thecylinderstartsadampedoscillationduetothemotionofthewaterandtheelasticityintherod.Asshownintheresults,theestimatedhydrodynamicforcegenerallycapturesthevariationsinthemeasurement,whichveriestheestimationalgorithm.TheestimationresultsaresummarizedinTable 2-1 2-1 .Infoursetsoftests,thestandarddeviationoftheestimationerrorisabout0.8N.Notethatinthisparticular 30

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test,thegeometryandthemotionofthesetuparesymmetric,hencethesymmetryinthepressuredistribution.Forageneralcaseonanunderwatervehicle,pressuresensorsneedtobedistributedacrossthevehiclesurfaceforacorrectestimationofthehydrodynamicforceandmomentinalldirections.Inaddition,adensersensorarrangementmaybenecessaryinordertoaccuratelyresolveamorecomplexpressuredistributionduetoowseparationandvortexshedding. A B C D E FFigure2-10. Hydrodynamicforceestimationtestresults.A{C)Timevariationsofcylinderposition,velocity,andforceestimationinTest1.D{F)TimevariationsinTest2.Ineachtest,thecylinderstartsfromrestandismanuallypulledalongtheslidewaybeforeitdeceleratestoastop.Pressuremeasurementsarecollectedaroundthesurfaceofthecylinderandareformulatedintothehydrodynamicforceestimation.Theestimatedforceiscomparedtothemeasurementbasedontheforcefromthestraingaugesandtheaccelerationfromthemotioncapturesystem. 2.3UnderwaterWallDetectionBesidethehydrodynamicforceestimation,anothercapabilityofthesensorysystemisalsoinvestigated.Thebiologicallaterallinesystemisbelievedtobeabletosensethe 31

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Table2-1. Summaryofforceestimationexperiments TestEstimationerror(N)Referenceforce(N) MaximumvalueStandarddeviationMaximumvalueStandarddeviation 12.161.036.822.3622.970.868.422.1633.510.985.972.0041.050.634.601.42 oweldalteredbythepresenceofnearbyobjects,andthereforeenablestheshtodetectimpendingobstacles[ 4 4 ].Unliketheforceestimationwherethepressuredistributionisgloballyintegrated,obstacledetectionfocusesinsteadonthelocalcharacteristicsofthepressuredistribution.Thepresenceofanobstacleconnesandacceleratestheescapingowandresultsinahigh-pressureregiontowardsthedirectionoftheobstacle,andthemagnitudeofthepressureisrelatedtothedistancetotheobstacle.Bycomparingthepressuredistributiontothatofanopenenvironment,informationabouttheobstaclecouldbeobtained.Thissectionrstsummarizesatestcaseina2Dspacefornumericalsimulation,thendescribestheexperimentaltestthatrealizesthe2Dtestcaseinthewatertank,andnallyconcludeswithillustrationandanalysisofthetestresults. 2.3.1DetectionModelGenerally,detectingobstaclesusinghydrodynamicsensorysystemsdependsontheoweldgeneratedbythemotionofthesystemandthewaythisoweldisalteredbythepresenceoftheobstacles.Forthepurposeofdemonstration,asimple2Dcaseisdened:thesensorysystemisdistributedonacircularsurfaceandismovingalongastraightlineinanambientuidtowardsastraightwallastheobstacle.Itisworthnotingthatalthoughthiscircularmodelissimplerthanthesh-shapedbodystudiedinsimulationin[ 43 43 ],manyofthepressuredistributionfeaturesaresimilarandtheexperimentalresultsinthispapercouldaidfurtherdevelopmentofawalldetectionalgorithm.AsillustratedinFigure 2-11 2-11 ,theradiusofthecircleisdenedtober.Theanglebetweenthevelocityvectorandthewallboundaryisdenotedasandthedistanceto 32

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thewallfromthecenterofthecircleisdenotedbyd.Asthecirclemovesataspeedofu,theowpropertiesarounditscircumferencewillbeaectedbytheexistenceoftheobstacle.Therefore,withtheassumptionthatthehydrodynamicpressureismeasurableonthecircle,thepressuredistributionmaybeanalyzedtoobtaininformationaboutthewallincludingitsexistence,thedistanced,andthewallangle. Figure2-11. Diagramofthewalldetectionmodel.Acircularsensingsystemwithradiusrapproachesthewallataspeedofu.Circumferentialpositiononthecircleisdenotedby.Thedistancetothewallandthewallanglearedenedasdand,respectively. Assumingthattheowisinviscid,incompressible,andirrotational,a2Dpotentialowmodelissetuptostudythepressuredistributionaroundthecircle.Theanalyticalsolutionforthepressuredistributioninthecasethatthedistancetothewallapproachesinnity,i.e.,d!1,istheclassicalpotentialowaroundacircularcylinder.ThepressurePatcircumferentialpositioncanbeexpressedas P()=u2cos(2))]TJ /F1 11.9552 Tf 13.15 8.088 Td[(1 2u2+P1;(2{23)whererepresentsthedensityoftheuid,andP1denotesthestagnationpressure.Thepressurereachesthemaximumatthefrontandrearstagnationpointsofthecirclewhen=0and,andarrivesattheminimumonbothsideswhen==2.However,ndingtheanalyticalsolutionforthenon-trivialcasesisalmostintractable.Therefore,numericaltechniquesareusedtocalculatethepressuredistributionforseveraldierentcases,while( 2{23 2{23 )isusedasareferencefortheopenenvironmentcasewithoutobstacles. 33

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Specicallyinthenumericalcomputation,continuousvortexsheetsareintroducedtotheoweldontheboundariesofthecircularbodyandthestraightwallinordertoenforcetheno-penetrationcondition.Discretizingthevortexsheetsintoindividualvortexpanelswithuniformstrengthsyieldsapanelmethodformulationoftheproblem.Asaresult,theoweldcanbeobtainedbysolvingforthevortexpanelstrengthsundertheboundarycondition.Additionally,thepressuredistributionaroundthecircleiscalculatedwiththeBernoulliequation.Figure 2-12 2-12 showsthenumericalresultsofthepressuredistributionforvariouswalldistancesandangles.Inthiscase,400and800vortexpanelsareplacedontheboundariesofthecircleandthestraightwall,respectively.Thepressurevalueisnormalizedbythequantityu2,andtheaveragecomponentissubtractedfromtheresult.Thepresenceofthewallforcestheowtoacceleratearoundthecircleandresultsinahigh-pressureregiontowardsthewall.Thecloserthecirclecomestothewall,thehigherthepeakpressurevaluebecomes.Ontheotherhand,asthewallangledeviatesfrom==2,thehigh-pressureregioninclinestowardsthesideofthewall.Thesearethetwomajorfeaturestobeveriedintheexperimentaltests. Figure2-12. Pressuredistributioninthefrontofacircularobjectapproachingawall.Theresultscomefromnumericalcomputationswithdierentwallangles.Thepressureisnormalizedbythequantityu2aftersubtractionbythemeanpressurevalue.Asthecirclecomesclosertothewall,thepressureinthefrontbecomeshigher,andthehigh-pressureregionshiftstowardsthewallside,ifthewallisnotperpendiculartothemovingdirection,i.e.,6==2. 34

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2.3.2FourierAnalysisSincethehydrodynamicpressurevariesaroundthecircumferenceofthecylinder,thefeaturesofthepressuredistributionmayalsobeexaminedintheFourierdomain.Intheopenenvironmentcasewithoutobstaclesasin( 2{23 2{23 ),thereisonlyoneFouriercomponentwithawavenumberof2.PerformingtheFouriertransformationofthepressuredistributionforthegeneralcaseyieldsaFourierspectrumwithonedominantcomponentatthewavenumber2.Theamplitudesofothercomponentsdrasticallydecreaseasthewavenumberdepartsfromthisdominantcomponent.Whenthecircleapproachesthewall,theamplitudesofallcomponentsincrease,whichcorrespondstothepressureincrease.Inaddition,thephaseanglesoftheFouriercomponentsvarywiththewallangle,exceptforthedominantcomponentwhosephaseanglebarelychanges.Thiscorrespondtotheshiftofthehigh-pressureregionduetothepresenceofthewall,whilethephaseofthedominantcomponentisunaectedbecausethemotionofthecircleremainsthesame.BycorrelatingthefeaturesintheFourierspectrumtothewalldistancedandangle,theamplitudeofthewavecomponentsakrevealthewalldistancedandthephase kinferthewallangle.Inpractice,thereisonlyanitenumberofsensorscoveringthefrontsectionofacircle.Therefore,theFourierseriescanbeusedinsteadofthecontinuoustransformation.ThepressurefunctionP()canbewrittenas P()=a0+1Xk=1akcos(!k+ k);2[)]TJ /F3 11.9552 Tf 9.299 0 Td[(=2;=2];(2{24)wherea0denotestheDCcomponentofthepressurefunction,andakand kdenotetheamplitudeandphaseoftheperiodiccomponentwithwavenumber!k=2k,respectively.Inthisway,thepeakpressuremagnitudeandtheshiftingofthepressurepeakarereectedbytheamplitudeakandthephase kofeachFouriercomponent.AccountingfortheinevitablenoiseinthemeasurementandtheamplitudesoftheFouriercomponents,usefulsignalswiththelargestmagnitudesarepreferredforanalysis. 35

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Theamplitudeofwavenumber!1=2andthephase 2oftheneighboringwavenumber!2=4canbeconsideredforestimatingthewalldistancedandanglesincetheyhavethemostsignicantsignalmagnitudescomparedtothenoiselevel.Figure 2-13 2-13 illustratesthattherelativeamplitudea1isapproximatelyinreciprocalproportiontothewalldistanced;andthatthephaseangle 2isalmostamonotonicfunctionofthewallangle,whichcanbeapproximatedby a10:27=d+0:9; 2)]TJ /F1 11.9552 Tf 21.918 0 Td[(1:81+2:8:(2{25)Theserelationshipsfromthesimulationwillbeusedasreferencesintheexperiment.However,theprecisionofthisestimationdependsonthatofthesensors,whichwillbefurtherdiscussedinSection 2.3.4 2.3.4 A BFigure2-13. Fouriercomponentsinthepressuredistributionversuswalldistanceandangle.A)Relativeamplitudea1ofwavenumber!1=2versuswalldistanced.Comparedtothecasewithoutthewall,theamplituderoughlyvariesinreciprocalproportiontothewalldistance.B)Phaseangle 2ofwavenumber!2=4versuswallangle.Thephaseanglealmostmonotonicallychangeswiththewallangle. 2.3.3WallDetectionSetupThe2Dhydrodynamicmodelforwalldetectioncanberealizedinexperimentaltests.Thesetupincludesaverticalcylinderandawallstructure,asdepictedinFigure 2-14B 2-14B .Thecylinderisa76cm(30in)longPVCpipewithsensorportsaroundthemiddlecircumferencefor20dierentialpressuresensors,seeFigure 2-14A 2-14A .Whenthecylinderis 36

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installed,theportsareabout32cm(12.5in)bothfromthebottomofthecylinderandtothewatersurface,inordertoreducesurfaceinuenceand3Deects.Thesensoropeningsarefacingthefrontofthecylindertoavoidtheowseparationandcomplex(andpossiblyturbulent)wakes.Theinterlacedsensorconnectionensuresthatthedierentialsensorsarereceivingstimulationofsucientmagnitudes,whilemaintainingareasonablenumberofsamplingpoints.Thewallismadefrom1.2m1.2m(48in48in)PVCplates,withsupportingstructuresthatcanbeattachedtotheplatformatvariousangles.PicturesofthesensorysystemandthetestsetupareshowninFigure 2-14 2-14 .Threegroupsoftestsareconductedwithdierentwallangles==2,=3,and=6,respectively.Ineachgroup,thecylinderistowedinacontrolledmotiontowardsthewallandisstoppedbeforecontactwiththewallstructure.Aftereachgroup,thesamemotionisrepeatedwithoutthewallstructureforreference.Signalsfromthedierentialpressuresensorsaswellasthecylinderpositionisrecordedandanalyzed,asshowninFigures 2-15 2-15 to 2-17 2-17 .Foreachtest,thedistancefromtheaxisofthecylindertothesurfaceofthewalliscomputedwiththepositiondatafromthemotioncapturesystem.Thecylinderacceleratestowardsthewallanddeceleratesabruptlybeforerunningintoastopperinfrontofthewallstructure.Atotalofvetestswiththewallandvetestswithoutthewallareconductedforeachwallangle.Onepairoftestswiththeminimaldierencesinthevelocityprolesisselectedforanalysisineachgroup.DierentialpressuredataislteredtemporallyandttedtoaFourierseriesfunctionalongthecircumferentialdirectionasin( 2{24 2{24 ).Thepressuredistributionduringeachtestisdepictedusingcontourplots.Betweenneighboringcontourlevelsthereisapressureincrementof20Pa,whichisabovetheaveragenoiselevelof6Pa.Sincethepressuredistributionbeyondtheangularposition=4maybeaectedbyowseparationandttingerror,onlythemiddlesectionwillbeanalyzed. 37

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A B C DFigure2-14. Schematicsandpicturesofthewalldetectionexperimentalsetup,courtesyoftheauthor.Thecylinderispositionedvertically.Atotalof20pressuresensorsareinstalledwiththesenorportsconnectedtothefront-facingsurfacealongthehorizontalcircumference.A)Sensorarrangementforwalldetection.Eachsensormeasuresthepressuredierencebetweenitstwoports,depictedasapairofcirclesconnectedbyanarc.Thesensorsareconnectedinaninterlacedmannertoensuresucientstimulationforeachsensorandanabundantnumberofsamplingpoints.B)Drawingofthetestingcylinder.C)Pictureofwalldetectionsetup.Thewallstructurecanbepositionedatvariousangles.Ineachtest,thecartcarriesthetestcylindertowardsthewallinacontrolledmotionandstopsbeforecontactwiththewallstructure.D)Pictureofthesensorsinsidecylinder. 2.3.4WallDetectionTestResultsInFigure 2-15 2-15 ,thetestresultswithwallangle==2(i.e.,wallperpendiculartomotion)isillustrated.ThedistancetothewallandthecylindervelocityintheselectedpairoftestsareshowninFigure 2-15A 2-15A ,toshowcasetheconsistencybetweenthetesting 38

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A B C D E FFigure2-15. Walldetectionresultforangle==2.A)Cylinderdistancefromthewallanditsvelocityasafunctionoftime.B)Pressuredistributionwiththewall.C)Pressuredistributionwithoutthewall.D)Pressurecontributionbytheexistenceofthewall.E)Asymmetricpressurewiththewall.F)Asymmetricpressurewithoutthewall.Ignoringthepressuredistributionbeyondangularposition=4(whichmaybeaectedbyowseparation,etc.)andafterthecylinderstops(asindicatedbydottedline),theexistenceofthewallincreasesthepeakpressureasthecylinderapproaches.Thepressuredistributionismoreorlesssymmetricwhilethecylinderisinmotion.Thereisapressureincrementof20Pabetweenneighboringcontourlevel. cases.Bycomparingthepressuredistributionsbetweenthecasewithwallangle==2inFigure 2-15B 2-15B andthecasewithoutwallinFigure 2-15C 2-15C ,thedierenceinthepressuredistributionisshowninFigure 2-15D 2-15D .Beforethecylinderstopsinfrontofthewall(asmarkedbythedashedlineinthecontourplot),thepressureisrelativelyhigherwiththewallforcingtheowtoacceleratearoundthecylinder,whichagreeswiththepredictionfromnumericalsimulation.Also,itcanbefoundthatthepressuredistributioninbothtestsaremoreorlesssymmetricabouttheangularposition=0whencomparingthe 39

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A B C D E FFigure2-16. Walldetectionresultforangle==3.A)Cylinderdistancefromthewallanditsvelocityasafunctionoftime.B)Pressuredistributionwiththewall.C)Pressuredistributionwithoutthewall.D)Pressurecontributionbytheexistenceofthewall.E)Asymmetricpressurewiththewall.F)Asymmetricpressurewithoutthewall.Thepeakpressureslightlyincreasesasthecylinderapproachesthewall,andthepositivepressureslightlyinclinestowardsthewallsideascomparedtothereference. pressurebetweentheleftandtherightsides,asshowninFigure 2-15E 2-15E forthewallangle==2caseandinFigure 2-15F 2-15F forthereference(nowall)case.Similarconclusioncanbereachedforthegroupswithwallangle==3and==6,asinFigures 2-16 2-16 and 2-17 2-17 .Inadditiontothechangein(relative)pressuremagnitude,thepositionofthepressurepeakforthesetwogroupsisslightlyinclinedtowardsthesideofthewall,becausethepresenceofthewallincreasesthepressurebyacceleratingtheowbetweenthecylinderandthewall.Asthewallangledeviatesawayfromthesymmetricconguration==2,theasymmetricinthepressuredistributionbecomesmoreobvious,asdepictedinFigures 2-16E 2-16E and 2-17E 2-17E .Thisalsocoincideswiththetrendfromthenumericalcomputation. 40

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A B C D E FFigure2-17. Walldetectionresultforangle==6.A)Cylinderdistancefromthewallanditsvelocityasafunctionoftime.B)Pressuredistributionwiththewall.C)Pressuredistributionwithoutthewall.D)Pressurecontributionbytheexistenceofthewall.E)Asymmetricpressurewiththewall.F)Asymmetricpressurewithoutthewall.Thepeakpressureincreasesasthecylinderapproachesthewall,andthepressuredistributionisobviouslyleaningtowardsthewallsideascomparedtothereference. Theresultsfromtheexperimentaltestsimplythat,asthecylindermovesinwater,theexistenceofawallcanbeinferredbycomparingthepressuredistributionwiththatofa`nominal'distributioninanopenenvironment,andthattheangleofthewallrelativetothecylindermotioncanbeobtainedbyanalyzingtheasymmetryofthepressuredistribution.TheexperimentandsimulationresultsarecomparedintheFourierdomaininFigure 2-18 2-18 .Specically,Figure 2-18A 2-18A showstherelationshipbetweentherelativeamplitudea1andthewalldistancedforwallangle==2fromonepairoftestswiththebestvelocityprolematchbetweenthecaseswithandwithoutwall.Theexperimentaldatagenerallyfollowsthetrendpredictedbythesimulation,exceptforaregion(coloredingray)wherethevelocityprolesofthecylinderhaveaslightdiscrepancy.Sincethe 41

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A BFigure2-18. Comparisonbetweenthewalldetectionsimulationandexperimentalresults.A)Relativeamplitudea1versuswalldistanced.Therelativeamplitudeisobtainedfromonepairoftestsanditgenerallyfollowsthetrendfromthesimulation,exceptfortheregionwherethevelocityproleshaveslightdiscrepanciesbetweenthecaseswithandwithoutthewall(whereforetherelativeamplitudeislessaccurateascoloredingray).B)Phaseangle 2versuswallangle.Thephaseangleistheaverageamongvepairsoftestsanditroughlyagreeswiththepredictionfromsimulation.Theanglecorrespondenceislesspreciseforthewallangle==6and=3becausethemagnitudeofthecorrespondingcomponenta2isclosetothesignalnoiselevel. pressuremagnitudeisroughlyquadraticinthecylindervelocity,largerdierencebetweentheestimationandthereferencemaybeexpectedwhenthevelocityprolesarenotaligned.Figure 2-18B 2-18B depictsthecorrespondencebetweenthephaseangle 2andthewallangle.Theexperimentaldataisobtainedfromtheaverageofvepairsoftestsandlooselyfollowsthesimulationresults,whichisreasonablebecausethewavenumber!2componentsnormallyhaveasmallermagnitudes(thereforelowerprecision)ascomparedtothoseofwavenumber!1.Additionally,theamplitudea2ofthewavenumber!2componentbecomessmallerasthewallangledeviatesawayfrom==2.Infact,itcomesaroundthesensornoiselevelforthedatapointswithwallangle==6and=3,whichmightexplainthedatapointsbeingfurtherawayfromthereferencethanthewallangle==2case.Applyingtheapproximationfunctionsin( 2{25 2{25 ),thewalldistanceandanglecouldbeinferredfromtherelativeamplitudea1andphaseangle 2.Theestimationduringve 42

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pairsoftestsiscomparedwiththereferenceinFigure 2-19 2-19 .Particularly,inFigure 2-19A 2-19A ,thewalldistanceestimationdataisbasedontheaverageamongvepairsoftestsinordertoaccommodatethediscrepancyinthevelocityproleforeachindividualpairoftests.Asaresult,thewalldistanceestimation(includingthevelocityprolemismatch)hasastandarddeviationof0.83r(asillustratedbythegraydashedlines).InFigure 2-19B 2-19B ,datapointsforthewallangleestimationareobtainedfromtheaverageamongvepairsoftestsfordierentwallangles.Basedonthesensornoiseintheexperiment,anvaryingerrorboundisalsoprovidedwithrespecttodierentwallangles(illustratedingraydashedlines).Thisalsoconrmsthattheestimationuncertaintyincreasesasthewallangledeviatesawayfrom==2,becausethesignalmagnitudebecomessmallerwithrespecttothesensornoise.Fromthecomparison,thesameconclusioncanbearrivedthatthisprototypesensorysystemisabletoestimatethewalldistance(ifthenominalpressureamplitudeisprovided)anddeterminethegeneralorientationofthewall(withrespecttotherelativemovingdirectionintheuid). 2.4HydrodynamicFeedforwardControlTraditionally,thecontrolperformanceofunderwatervehiclesisanalyzedinstaticowconditionswithperturbationsaboutsomenominaltravelingspeed[ 44 44 ].Hydrodynamicforcesduetoaccelerationandvelocityofthevehiclearemodeledasaddedmasstermsandviscousdampingterms,respectively.Coecientsofthesetermsareusuallyobtainedbasedonlinearizationaroundanominaloperationstateofthevehicle.Inuencesfromthenon-staticbackgroundowareoftenconsideredasadditionaldisturbances.Thisconventionaltreatmentisundoubtedlylimitedinmodelingaccuracyforcontrolpurposes,especiallyforunderwatervehicleswithhighmaneuverabilityinanunsteadyowenvironment.Withthemotivationtoimprovethevehicle'scontrolperformance,thehydrodynamicforceestimationisimplementedasafeedforwardcomponentinthevehiclecontroller. 43

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A BFigure2-19. Walldistanceandangleestimationcomparedtothereference.A)Walldistanceestimation.B)Wallangleestimation.Thewalldistanceisprovidedbythemotioncapturesystemandtheangleisobtainedbydesignofthesetup.TheestimationofthewalldistanceandangleisbasedontheFourieranalysisofthepressuredistribution.Thedataisobtainedfromtheaverageofvepairsoftests.Theaveragedistanceestimationincludingvelocityprolediscrepanciesgenerallycapturesthemeasurementwithastandarddeviationof0.83r(asillustratedbythegraydashedlines).Theestimatedangleroughlyagreeswiththeactualvalue,especiallyconsideringthemodestsignalmagnitudeforthecaseswiththewallangles==6and=3.Theestimationerrorhasavaryingerrorboundduetothedierentsignalmagnitudeswithrespecttothesensornoise(asillustratedbythegraydashedlines). Strategically,asillustratedinFigure 2-20 2-20 ,theproposedcontrolschemeincludesinadditiontothestandardfeedbackstructure,afeedforwardpathwaythatsendssignalsfromthepressuresensorstothecontroller.Usingthepressuremeasurements,anapproximationofthepressuredistributionisobtained.Thisgivesanestimateofthetotalpressureforceactingonthevehicle.Consequently,modelingfortheaddedmassandhydrodynamicdampingcoecientsbecomesunnecessaryforthecontroldesign;andpreviouslyinaccessibleinformationonthebackgroundowisnowavailablesothatbettercontrolperformancemaybeachieved,especiallyinthepresenceoflocalizationuncertainty.TheAUVmodelinthisstudyisbasedontheprototypeCephaloBotasdetailedinSection 2.1.1 2.1.1 .Itisworthmentioningthatthefeedforwardcontroldesigndescribedinthisstudygenerallyappliestoallvehicles,yetitespeciallysuitstheneedforimprovingmaneuveringaccuracyonthisparticulartypeofunderwatervehicle. 44

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Figure2-20. Blockdiagramofpressurefeedforwardvehiclecontrol.Inadditiontotheconventionalpositionalfeedbackcontrolloop,apressuresensorysystemprovideshydrodynamicforceestimationtoimprovetrajectorytrackingperformanceagainsthydrodynamicdisturbances. 2.4.1VehicleDynamicModelTodescribethetranslationalandrotationalmotionsofthevehicle,acoordinatesysteminthebody-xedreferenceframeisdenedwithitsoriginatthegeometriccenterofthevehicle;thex-axispointsforward,thez-axisisdirectedfromtoptobottom,andthey-axissatisestheright-handrule.Forthemotioninthehorizontalplane,therearethreedegreesoffreedom,namely,translationalmotionsalongx-andy-directions(surgeandsway),androtationalmotionaboutz-axis(yaw).Atatimeinstantt,thevehicle'svelocityisdesignatedasvector(t)2R3.Theearth-xedreferenceframeisconsideredtobeinertial,inwhichtheearth-xedcoordinatesystemisdenedwithitsx-andy-axesinthehorizontalplane,andz-axispointingdownward.Positionandorientationofthevehicleatatimeinstanttcanbedescribedintheearth-xedframeasvector(t)2R3.Thevelocityofthevehicleintheearth-xedreferenceframecanbeobtainedbythefollowingtransformation: _=J();(2{26)wherethematrixJ()2R33isdenedas J()=2666664cos(3))]TJ /F1 11.9552 Tf 11.291 0 Td[(sin(3)0sin(3)cos(3)00013777775:(2{27) 45

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Thevariable3(t)2Rdenotesthethirdcomponentinthevector(t),i.e.,theangleofrotationaboutz-axis.Thedynamicequationforthevehiclecanbewritteninthebody-xedframeas[ 44 44 ] =M_+C()+fD+fN;(2{28)where(t)2R3denotesthevectorofcontrolforcesandmomentsfromtheactuators;matricesM2R33andC()2R33denotetheinertialtermsandtheCoriolisandcentripetalterms,respectively;fD(t)2R3representsthevectorofhydrodynamicdampingforcesandmoments;andfN(t)2R3representstheunmodeledforcesandmoments. 2.4.2HydrodynamicFeedforwardModelInthetraditionalmodelingprocess,thehydrodynamicforcesduetotheaccelerationofthevehiclearemodeledasaddedmassterms,asifsomevolumeofuidismovingtogetherwiththevehicleandcausinganequivalentdissipativeeectfromthefactthatthewaterismovingaroundit.Similarly,viscousdampingforcesareexpressedasfunctionsofthevehicle'svelocity,andinuencesfromthenon-staticbackgroundowareoftenconsideredasadditionaldisturbances.Thus,thehydrodynamicforcesandmomentsfD(t)andtheunmodeledtermsfN(t)canbewrittenas fD+fN=MA_+CA()+D()+efN;(2{29)whereMA2R33andCA()2R33denotetheinertiamatrixandtheCoriolisandcentripetalmatrixduetotheaddedmass,D()2R33representsthedampingmatrix,andefN(t)2R3representsthecombinationofthehydrodynamicforcesandmomentsfromthenon-staticbackgroundowandtheunmodeledterms.Consequently,thedynamicsin( 2{28 2{28 )canbeexpressedas =(M+MA)_+[C()+CA()]+D()+efN:(2{30) 46

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Everymatrixin( 2{29 2{29 )canbeestimatedfromrecordeddatainexperimentaltests,assumingthatMAisconstantandthatallentriesinCA()andD()haveconstantcoecientsinfrontofthevehicle'svelocity(t).Linearornonlinearcontrollerscanbedevelopedforthesystemaccordingly.However,itshouldbepointedoutthattheaccuracyofthemodelreliesheavilyonthesetofdatathatareusedinthemodelingprocess.Theactualvaluesofcoecientsinthematricesmaydeviatefromthenominalvaluesespeciallywhenthevehicleisoperatingatadierentstatefromthoseonwhichthemodelisbased.Moreover,thehydrodynamicforcesandmomentsduetothemotionofthebackgrounduidisunknowntothecontrollerandtheyactasadditionaldisturbancestothesystem.Theseconcernsmotivatethedevelopmentofasystemthatwillestimatethehydrodynamicforcesforimprovementofthecontrolperformance.Toreiterate,thepurposeoftheproposedhydrodynamicfeedforwarddesignistoobtainanestimationofthehydrodynamicforcebfD(t)2R3.Accordingtothefeedforwardconguration,thepropulsiveforce(t)combinesthefeedforwardelementbfD(t)withafeedbacksignalB(t)2R3fromanycontroldesign, =B+bfD:(2{31)DeningefD(t)2R3tobethemismatchbetweenthevectorfD(t)anditsestimationbfD(t): efD=fD)]TJ /F10 11.9552 Tf 11.026 3.155 Td[(bfD:(2{32)Then,theequationofmotionbecomes B=M_+C()+efD+fN;(2{33)whichpresumablyreducesthescaleofuncertaintiesinthesystemascomparedwiththatin( 2{30 2{30 ). 47

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2.4.3ControllerDesignAccordingtothedynamicmodelin( 2{33 2{33 ),thesystemissubjecttoestimationmismatchinthehydrodynamicdisturbancesandunmodeledforcesandmoments,bothofwhichareassumedtobeC2continuousandupperboundedbyknownconstants.Thecontroldesigninthisworkisthusbasedonthe`robustintegralofthesignoftheerror'(RISE)technique,see[ 45 45 46 46 ].BecausetheintegralsignumtermintheRISEcontrollerisabletocompensatethesmooth,boundeddisturbancesandyieldanasymptoticallystableclosed-loopsystem,despitetheuncertainties[ 47 47 ].Inconjunction,backstepping(dueto[ 48 48 49 49 ])isutilizedtobridgethecontroldesignbetweenthereferenceframes.Thepositionandvelocityvectors(t)and_(t)areassumedtobemeasurable.Thevelocityvector(t)inthebody-xedframecanbeobtainedbyusingthetransformationin( 2{26 2{26 ).Thecontrolobjectiveistotrackadesiredtrajectoryd(t)2R3describedwithrespecttotheearth-xedframe.Toquantifythetrackingperformance,positiontrackingerrore1(t)2R3isdenedas e1=d)]TJ /F14 11.9552 Tf 11.955 0 Td[(:(2{34)Takingtimederivativeof( 2{34 2{34 )givestheopen-loopsystemforpositionerrore1(t) _e1=_d)]TJ /F1 11.9552 Tf 14.138 .166 Td[(_=_d)]TJ /F6 11.9552 Tf 11.955 0 Td[(J():(2{35)Usingbackstepping,thepositionerrorsystemin( 2{35 2{35 )istranslatedintothebody-xedreferenceframeforcontroldesignofthemotiondynamicsin( 2{33 2{33 ).Avirtualdesiredvelocitysignald(t)2R3isdesignedtobe d=J)]TJ /F4 7.9701 Tf 6.586 0 Td[(1()(_d+1e1);(2{36)where12Rdenotesapositiveconstantcontrolgain. 48

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Thebacksteppingerrore2(t)2R3isdenedtobethemismatchbetweenthevirtualdesiredvelocityd(t)andtheactualvelocity(t)inthebody-xedframe e2=d)]TJ /F14 11.9552 Tf 11.955 0 Td[(:(2{37)Substituting( 2{36 2{36 )and( 2{37 2{37 )into( 2{35 2{35 )yieldsthe`closed-loop'systemforpositionerrore1(t) _e1=J()e2)]TJ /F3 11.9552 Tf 11.955 0 Td[(1e1:(2{38)TofacilitateRISE-basedcontroldesign,alteredtrackingerror[ 50 50 ]e3(t)2R3isdenedas e3=_e2+2e2;(2{39)where22Risapositiveconstantcontrolgain.Substitutingthedenitionsfrom( 2{33 2{33 ),( 2{36 2{36 ),and( 2{37 2{37 )into( 2{39 2{39 )yieldstheopen-looperrorsystem Me3=+efD+fN)]TJ /F14 11.9552 Tf 11.955 0 Td[(B;(2{40)where(t)2R3isdenedas =M_J)]TJ /F4 7.9701 Tf 6.587 0 Td[(1(;)(_d+1e1)+MJ)]TJ /F4 7.9701 Tf 6.586 0 Td[(1()(d+1_e1)+C()+2Me2:(2{41)ThecontrolinputB(t)isdesignedasacombinationofafeedbacklinearizationtermandaRISE-basedfeedbackterm. B=+;(2{42)where(t)2R3denotestheRISEtermas =3e2)]TJ /F3 11.9552 Tf 11.955 0 Td[(3e2(0)+;(2{43)andsignal(t)2R3isdesignedtobe _=23e2+sgn(e2)+e2;(0)=031:(2{44) 49

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Positiveconstants3;2Rarecontrolgains.Fromtheaforementioneddesignofthecontrolsignal,thefollowingtheoremcanbeestablished. Theorem1. Thecontrollergivenin( 2{42 2{42 ),( 2{43 2{43 ),and( 2{44 2{44 )ensuresthatallsignalsareboundedandthatthetrackingerrorisregulatedinasensethat limt!1e1(t)=031;(2{45)providedthatthecontrolgains1,2,3,and(introducedin( 2{36 2{36 ),( 2{39 2{39 ),( 2{43 2{43 ),and( 2{44 2{44 )respectively)aredesignedtobesucientlylarge.ProofofthetheoremandfurtherrequirementsforthecontrolgainscanbefoundinAppendix A A .Inthefollowingsections,aseriesofsimulationtestsareconductedinregardtotheproposedfeedforwardcontrolstructure. 2.4.4ControlSimulationThevehicle'saccelerationrelativetothebackgroundowwillaectthetotalhydrodynamicdampingforceandmomentactingonthevehicle.Thisdoesnotimposeanycomplicationsinanactualsystemaslongasthepressuresensorscanprovidetrustworthyreadings,butnevertheless,itcreatesdicultiesforthesimulationtests.Sincethetotaldampingforcecontributestotheresultantforceactingonthevehicle,basedonwhichtheaccelerationofthevehicleiscalculated,thefactthatthedampingforceisafunctionoftherelativeaccelerationproducesacomputationalloop.Inordertoavoidsolvinghydrodynamicequationsfortheaccelerationterm,theeectfromtherelativeaccelerationonthedampingforceisignoredinthissimulation.Althoughinaccuraciesinthehydrodynamicforcecalculationmayberesultedfromthetreatment,thesimulationtestsarestillvalidintermsofinvestigatingtheideaofusinghydrodynamicforceestimationtoimprovecontrolperformance. 50

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TheinertiamatrixMisexpressedas M=2666664p1000p1p20p2p33777775;(2{46)whereparametersp1;p2;p32Raredenedtobe p1=20kg;p2=2kgm;p3=4kgm2:(2{47)Correspondingly,thecentripetal-CoriolismatrixC()equals C()=266666400)]TJ /F3 11.9552 Tf 9.299 0 Td[(p12)]TJ /F3 11.9552 Tf 11.955 0 Td[(p2300p11p12+p23)]TJ /F3 11.9552 Tf 9.299 0 Td[(p1103777775;(2{48)where1;2;32Rarecomponentsinvelocityvector.Localizationerrorisaccountedforwithdeadbandzonesandsinusoidalnoises(withspansof0:5m,=180rad,1m/s,and=90rad/s).Velocitiesofthebackgroundowaredenedas0:2m/salongthex-directionand0:3cos(0:2t)m/salongthey-directionintheearth-xedcoordinatesystem.Thecontrolgainsaredesignedtobe 1=2=3=2;=30:(2{49)Desiredtrajectoryd(t)isdesignatedas d(t)=26666645sin(0:15t)m5)]TJ /F1 11.9552 Tf 11.955 0 Td[(5cos(0:15t)m0:15t+0:06rad3777775;(2{50)whichrepresentsahorizontalcircularorbitwitharadiusof5m,andatimeperiodofabout42s. 51

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Simulationresults,withandwithoutthepressurefeedforward,togetherwiththehydrodynamicdampingforceareshowninFigures 2-21 2-21 to 2-23 2-23 ,respectively.Thecontrolperformancesbetweenthetimeintervalfrom20to60sarecomparedinTable 2-2 2-2 Table2-2. Comparisonofcontrolperformancewithandwithoutpressurefeedforward UnitsWithoutfeedforwardWithfeedforward MeanMaximumMeanMaximum Absolutem0.5251.3300.3250.657positionm0.5130.9820.3370.720errorrad0.0290.2040.0100.035 Absolutem/s1.1332.7870.7871.994velocitym/s0.9322.0650.6011.753errorrad/s0.1480.6940.0790.196 AbsoluteN31.873142.73023.910155.071controlN24.16782.58514.587101.744inputNm4.23416.0942.59413.002 A B CFigure2-21. Trajectorytrackingsimulationresultswithoutpressurefeedforward.A)Positionerror.B)Velocityerror.C)Controlinput. Duetotheexistenceoflocalizationerror,inwhichthecontrollerisunabletoacquiretheactualposition,theerrordoesnotconvergetozeroinanyofthetests,butiscontractedwithinsomeboundingintervalgovernedbythedeadbandspansandthecontrolgains.However,sincethesystemwiththefeedforwardcomponentcanrespondtohydrodynamicforcesfromthebackgroundow,theonlymajordisturbanceaectingthecontrolperformanceisthelocalizationerror.Thismayexplaintheabsenceoflargedeviationsinthetrackingerrorscomparedtothesystemwithoutthefeedforward. 52

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A B CFigure2-22. Trajectorytrackingsimulationresultswithpressurefeedforward.A)Positionerror.B)Velocityerror.C)Controlinput. A B CFigure2-23. Hydrodynamicforceestimationwithandwithoutpressurefeedforward.A)Hydrodynamicforcewithoutfeedforward.B)Hydrodynamicforcewithfeedforward.C)Estimationofhydrodynamicforcewithfeedforward. Repeatingthesimulationusingdierentsensornumbersdemonstratessimilarresults.Generally,aslongasthealgorithmgeneratesafairestimationofthehydrodynamicforce,thefeedforwardsystemexhibitsabout20%to50%lesslineartrackingerrorthanthestandardfeedbacksystem. 53

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CHAPTER3MODELINGANDCONTROLOFAFISH-LIKESWIMMERThestudyoftheswimmingmechanicsofshhasalonghistory.Manyoftheworksareoftenmotivatedtounderstandthecomplexfunctionaladaptationsinshthatallowsforecientlocomotionincomparisontotheunderwaterpropulsionmethodsimplementedonman-madevehicles.Forexample,earlyresearchofswimmingbiomechanicsisreportedin[ 51 51 { 54 54 ].Somerecentreviewpaperscanbefoundin[ 55 55 { 57 57 ].Generally,shadoptdierentmodeswhenswimmingwiththeirbodyandcaudalns(ortails):fromundulatorymotionswherethebodywavespropagatefromtheheadtothetail,tooscillatorymotionswherethecaudalnsimplyoscillatestocreatethrust[ 58 58 ],asillustratedinFigure 3-1 3-1 .Thisstudyismainlyfocusedonthecarangiformandsub-carangiformlocomotion,notonlybecausetheseswimmingmechanismsinvolvetheinteractionbetweentheuidandadeformablesolidbody{whichisconceivablydierentfromthatbetweentheuidandarigidbody,butalsoowingtothefactthebodydeformationinquestionisevidentlymorebasicthanthatintheanguilliformlocomotion.Nevertheless,themodelingmethodandanalysisinthisresearchcouldbebenecialforstudiesofmorecomplexswimmingmaneuvers. Figure3-1. Diagramofvariousshswimmingmodes,rangingfromundulaorymotionswithbodywavespropagatefromheadstotails,tooscillatorymotionswithoscillatingcaudalns.Areasthatcontributetopropulsionareindicatedbyshading.Theillustrationisadaptedfrom[ 58 58 ]. Ineortstoinvestigatetheunderlyingmechanicsofsh-likelocomotion,avarietyofnumericalmodelshavebeendevelopedtosimulatesh-likeswimmersperformingvariousmaneuvers[ 59 59 { 67 67 ].Forinstace,in[ 61 61 ],a3D,nonlinearnumericalmethodisutilizedtoidentifytheowandvortexfeaturesarounddierentsh-likebodiesastheyswiminaninvisciduid.Duetothecomplexityofthe3Duidsimulation,manyoftheexisting 54

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worksconsiderinsteadthe2D,simpliedcasesinwhichtheswimmerbodyisrepresentedwithaplanarcontourandthebodymotionsandtheuiddynamicsarerestrictedinsidethehorizontalplane.Forinstance,arigid-bodyswimmerisconsideredin[ 60 60 ],usingatrailingedgevortextorepresentthehydrodynamiceectfromthecaudalntorotateandpropelthebody.In[ 62 62 ]and[ 63 63 ],themodelingandanalysisforaswimmerbodyconsistingofthreeidenticalellipsesisexamined;byperiodicallychangingtheanglesofjointsbetweentheellipticalbodyparts,theswimmerisabletosteerandpropelitselfthroughanidealuid.Moreover,theswimmingproblemisalsoinvestigatedfordeformingJoukowskihydrofoilsin[ 65 65 68 68 ],whichapparentlybearsmoreresemblancetothecarangiformorsub-carangiformlocomotion.Similartothatin[ 65 65 ],thesh-likeswimmerunderconsiderationinthisstudyisgeometricallydenedasaJoukowskihydrofoil.Apotentialowmodelisalsodevelopedinconjunctionwithadiscretevortexsheddingmechanismtodescribetheinteractionbetweentheswimmerbodyandtheuid.However,themodelinthisstudyundergoesacoupleofdistinctivetreatmentsthatarephysicallysoundratherthanarbitrarilydenedforsimplicity.Firstly,thedeformationoftheswimmerbodyisconstrainedsothatboththelengthandtheareaofthebodyremainconstant.Secondly,abody-xedframeisdenedindistinctiontothegeometriccoordinatesystemsothatthecenterofmassandtheangularmomentumareconservedinthebodyframeduringdeformation.Furthertowardsthegoalofexploringthemechanismofsh-likelocomotion,afewclosed-loopcontroldesignsareproposedalongsidethesimulationmodelsintheliterature.Forexample,in[ 69 69 ],sinusoidalfunctionsareappliedtothelinkanglesofathree-linksh-likeswimmer.Largeramplitudesandhigherfrequenciesofthesinusoidalfunctionincreasetheswimmingspeed;andabiasinthefunctionchangestheswimmingdirection.Also,aproportional-integral-derivative(PID)controllerisusedin[ 68 68 ]tosteeraJoukowskihydrofoilswimmer.Itisfoundthatstepchangesinthedesiredswimming 55

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directioncanbedirectlyfedtotheempiricallytunedcontrollerandcreateadampedoscillationinthebodydeformationforturning.Itmaybereasonabletoarguethattheexistingcontroldesignsaremoreheuristicthansystematic,possiblythankstothecomplexityofthedynamicalinteractionbetweentheswimmerbodyandtheuid.Tothisend,theswimmingcontrolinthisstudyisdevelopedintwostages.Intherstplace,anactuationfunctionisdenedforasetofmotionprimitives.Subsequently,theactuationcommandsareissuedinacyclicmannerbasedonthetrajectorytrackingerrorforeachcontrolcycle.Closed-loopswimmingsimulationshowssatisfactorypathfollowingperformance.Resultfromthisstudyispublishedin[ 70 70 71 71 ].Thischapterisorganizedasfollows.Section 3.1 3.1 introducesageometricmodelthatdescribestheshapeofthesh-likeproleusingJoukowskitransformation.Section 3.2 3.2 developsthephysicalrepresentationforthedeformationtheswimmerbody.Section 3.3 3.3 providesadynamicalmodelfortheinteractionbetweentheswimmerandthesurroundinguid.Section 3.4 3.4 illustratesthecontrolstrategyandpresentsresultsfromtheclosed-loopsimulation.UsefulequationsandvalidationforthemodelarepresentedinAppendices B B and C C ,respectively. 3.1GeometricModeloftheSwimmerThegeometricmodeldenesthe2Dshapeoftheswimmerbody.Inthehorizontalplane,thebodyofthesh-likeswimmerisgeometricallyrepresentedbyahydrofoildenedbytheJoukowskitransformation.Thebodyundulationisdescribedbydeformingtheprolewhilekeepingitscamberlinelength(correspondingtothebodylength)andenclosingarea(correspondingtothebodyvolume)constant. 3.1.1JoukowskiTransformationTheJoukowskitransformationisaconformalmappingwidelyusedtocreatehydrofoilprolesfromcircularcontoursinthecomplexplane.Thepointsz2Conthehydrofoilcontourinthez-planeisobtainedfromthepoints2Conacircleinthe-plane 56

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employingthetransformationdenedas z=+a2=;(3{1)wheretheparameterofthetransformation,a2R,denesthepointwherethecirclemustpassinthe-plane.Thetransformationisaone-to-onemappingbetweentheexteriorofthecontours. 3.1.2SwimmerProleTocreatethesh-likeswimmerprolethatwillbesubsequentlyusedinthisstudy,theJoukowskitransformationissetupinaspecicmanner.Intherstplace,bydenotingthecircleinthe-planeasC1,thecenterasc12C,andtheradiusasrc12R,onemayexpressthecircularcontouras C1:=rc1ei+c1;2[0;2)R:(3{2)SincethecircleC1mustpassthroughpointainthe-plane,theparametersmustsatisfytheequation rc1=jc1)]TJ /F3 11.9552 Tf 11.956 0 Td[(aj:(3{3)Inthisanalysis,theparameteraischosentobenegativesothatthesharpedgeofthefoilpointstotheleft-handsideofthez-plane. A BFigure3-2. SchematicsoftheJoukowskitransformation.A)Circularcontoursin-plane.B)Joukowskihydrofoilinz-plane. 57

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Withthetransformationin( 3{1 3{1 ),ash-likeproleS1inthez-planemaybeobtainedastheimageofthecircleC1inthe-plane,asshowninFigure 3-2 3-2 .Itisobviousthattheshapeofthesh-likeprolecanbeuniquelydenedbytheparametersa,c1x,andc1y,wherec1x2Randc1y2Rcorrespondtotherealandimaginarypartofthecirclecenter,c1,respectively.Thecamberline1S00inthez-planeisdenedastheimageofanarcC00inthe-plane.ThearcispartofacircleC0inthe-plane,andhasacenteratc02Candaradiusofrc02R.TheequationforthecircleC0canbewrittenas C0:=rc0ei+c0;2[0;2)R:(3{4)ThecirclesC0andC1aretangentatpointa,hence c0=ic1y=1;rc0=rc1=1;(3{5)where12Risdenedas 1=1)]TJ /F3 11.9552 Tf 11.955 0 Td[(c1x=a:(3{6)ThearcC00maybedenedintheupperhalf-planeas C00:=rc0ei+c0;2[)]TJ /F3 11.9552 Tf 9.299 0 Td[(0;+0];(3{7)where02Rcanbeobtainedas 0=tan)]TJ /F4 7.9701 Tf 6.587 0 Td[(1(ic0=a)2()]TJ /F3 11.9552 Tf 9.299 0 Td[(=2;=2):(3{8)Consequently,thesh-likeswimmerproleisdenedgeometrically.Theinterioroftheprole,i.e.,theregionDSCenclosedbyS1inthez-plane,ismappedfromthe 1Duetoitsdenition,thecamberlineinthiscaseiseitherastraightlinesegmentwhenc0=0,oranarcthatpassesthroughpoints2a,)]TJ /F1 11.9552 Tf 9.298 0 Td[(2a,and2ic0whenc06=0. 58

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regionDCCinthe-planeas DC:=rc0ei+(1)]TJ /F3 11.9552 Tf 11.955 0 Td[()a+c0;2(1;1]R;2[0;2)R:(3{9)Themapping( 3{9 3{9 )betweenthetworegionsDCandDSisillustratedinFigure 3-3 3-3 ,withameshgridobtainedfromtheparametersand. A BFigure3-3. InteriorareasbeforeandafterJoukowskitransformation.A)Interiorareain-plane.B)Interiorareainz-plane. 3.1.3DeformationParameterThesh-likeproledescribedbytheJoukowskitransformationhasthreedegreesoffreedom,i.e.,anycombinationofthreeindependentparameterswilluniquelydeterminetheshapeoftheprole.Inthisstudy,thegeometricmodelisdenedsuchthattheprolebendsitselfwhilemaintainingitscamberlinelengthl02RanditsareaA12R.Thelengthl0ofthecamberlineS00is l0=8>><>>:)]TJ /F1 11.9552 Tf 18.164 8.088 Td[(8a0 sin(20);06=0;)]TJ /F1 11.9552 Tf 9.299 0 Td[(4a;0=0:(3{10)TheareaA1oftheregionDScanbewrittenas A1=ZZDSdA=4r2c131(1)]TJ /F1 11.9552 Tf 11.955 0 Td[(1) (21)]TJ /F1 11.9552 Tf 11.956 0 Td[(1)2:(3{11)Imposingtheseconstraintsreducesthedegreesoffreedominthegeometricmodeltoone.Forconvenience,theangle0isdesignatedasthedeformationparameterinthe 59

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geometricmodel,withwhichallotherparametersandtheirderivativescanbederived.Infact,theangle0equalshalftheanglebetweenthecamberlineandtherealaxisattheirpointofintersection.Positiveornegative0anglemakestheprolebendtowardsthepositiveornegativeimaginarydirection,whereaszero0angleyieldsanuncambered,symmetricprole.Theresultinghydrofoildeformationinthez-planeisillustratedinFigure 3-4A 3-4A .Thismodelmaintainsaconstantcamberlinelengthl0andbodyareaA1,whichisarguablyanaccurateandrealisticrepresentationofthesh-likeswimmer. 3.2SwimmerDeformationDynamicsWhilethegeometricmodeldenestheshapeanddeformationofthesh-likeprole,theundulatorymotionmustsatisfythefundamentaldynamicalprinciples.Abody-xedframeisintroducedtoseparatethedeformationdynamicsfromtheinteractionbetweenthesh-likebodyandtheuidenvironment.Specically,withrespecttothebody-xedframethedeformablesolidbodyoftheswimmershouldbehavethesameasinadynamicallyisolatedenvironment,withbothlinearandangularmomentumconservedduringdeformation.Thebodyframetranslatesandrotateswithrespecttotheinertialframeasaresultoftheexternalforcesandmomentsoriginatedfromthehydrodynamicinteractions. 3.2.1BodyFrameIndistinctionfromthegeometricmodel,thephysicalmodelofthesh-likebodytakestheformofadeformablesolidinabody-xedreferenceframe,denotedasFB.Insuchaframe,thebody'scenterofmassisxedattheoriginandtheangularmomentumalwaysequalzeroduringbodydeformation.Foranypointintheprolez2DS,thecorrespondingposition2CinthebodyframeFBcanbewrittenas =(z)]TJ /F3 11.9552 Tf 11.955 0 Td[(zc1)eiB;(3{12)wherezc12Cdenotesthecenterofmassinthegeometricz-plane,andB2[0;2)RdenotestheangleofbodyrotationwithrespecttoFBthatconservestheangular 60

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momentumLc12Raboutthecenterofmass.TherateofchangeintheangleBsatises Lc1= 2iZZD1( z)]TJ /F3 11.9552 Tf 11.955 0 Td[(zc1)(_z)]TJ /F1 11.9552 Tf 13.965 0 Td[(_zc1))]TJ /F1 11.9552 Tf 11.955 0 Td[((z)]TJ /F3 11.9552 Tf 11.956 0 Td[(zc1)( _z)]TJ /F1 11.9552 Tf 13.965 0 Td[(_zc1)dA+Ic1_B0;(3{13)where2Rdenotesthedensityoftheprole,andIc12Rrepresentsthemomentofinertiaaboutthecenterofmass.ThedeformationinthebodyframeFBisillustratedinFigure 3-4B 3-4B .Equationsforzc1andIc1canbefoundinAppendix B B A BFigure3-4. Deformationofthesh-likebodywithconstantlengthandarea.A)Bodycontoursandcenterofmasstrajectoryunderdeformationinz-plane.B)BodycontoursunderdeformationinthebodyframeFB. 3.2.2InertialFrameTheinertialframe,FI,isdenedwithrespecttotheearth.Thepositionofapointq2ContheswimmerprolecanbewritteninFIas q=eiI+q0;(3{14)whereI2[0;2)RistheanglebetweenthebodyframeFBandtheinertialframeFI,andq02CrepresentspositionoftheoriginofbodyframeFBintheinertialframeFI.TheresultantexternalforceFext2Candmomentext2Raboutthecenterofmassactingonthesh-likeproleinducesthelinearandangularaccelerationsofthebodyframeFBrelativetotheinertialframeFI: Fext=M1q0;ext=Ic1I+_Ic1_I:(3{15) 61

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TherelativemotionbetweenthetwoframesFBandFIhasthreedegreesoffreedom,namely,thetranslationalmotionswithq0x;q0y2R(q0=q0x+iq0y)andtherotationalmotionwithI.Inthisstudy,allforcesandmomentsexternaltotheshcomefromthedynamicsoftheuid,whosemodelwillbedevelopedinSection 3.3 3.3 .Oncetheexternalforcesandmomentsareobtained,thevariablesq0andImaybesolvedforusing( 3{15 3{15 ). 3.2.3InternalForcesThedeformationoftheswimmerbodyiscontrolledbytheinternalforces.2Atanypointqontheswimmerprole,theforcedensityf2C(forceperunitarea)consistsofbothinternalandexternalcomponentsandcanbeobtainedfromNewton'ssecondlaw: f=fint+fext=q;(3{16)wherefint2Candfext2Cdenotetheinternalandexternalforcedensity,respectively.Basedontheassumptionthatthelinearandangularmomentumareconservedinthebodyframeduringdeformation,thecombinedinternalforceFint2Candmomentint2Rmustalwaysequalzero,whichcanbeexpressedas Fint=ZZD1fintdA0;int=ZZD1( finteiI)]TJ /F3 11.9552 Tf 11.955 0 Td[(fint e)]TJ /F11 7.9701 Tf 6.587 0 Td[(iI)dA0:(3{17)Intheinterestofquantifyingtheswimmingeort,thepowerP2Rofforcesactingontheswimmerbodycanbecalculatedfrom P=1 2ZZD1( f_q+f _q)dA;(3{18) 2Inthisstudy,theinternalforcesaredenedwithoutconsideringtheelasticityofthebody.Therefore,inapplicationswheretheswimmerbodyismadefromelasticmaterials,thetotalinternalforcesmayalsoincludetheadditionalcomponentsthatcounterbalancethedeformationstress. 62

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wherethevelocity_qincludetherateofbodydeformationaswellaslinearandangularmotions: _q=_eiI+_q0+i_IeiI:(3{19)Theenergyobtainedbytheswimmerfromexternalsources(e.g.,thebackgroundow)canbecalculatedfromthepowerofexternalforces,Pext2R.Furthermore,theswimmingeortcanbeevaluatedwiththepoweroftheinternalforcesPint2Raftersubstituting( 3{17 3{17 )and( 3{19 3{19 )as Pint=1 2ZZD1( fint_eiI+fint _e)]TJ /F11 7.9701 Tf 6.587 0 Td[(iI)dA;(3{20)whichonlydependsontherateofbodydeformation. 3.3HydrodynamicModelInordertoresolvethedynamicalinteractionbetweenthesh-likeswimmerandthesurroundinguid,a2Dhydrodynamicmodelisdeveloped,generatingthehydrodynamicpressuredistributionontheboundaryoftheswimmer.Thepressuredistributionissubsequentlyusedtocalculatetheexternalforcesandmoments,whichinturndeterminethemotionoftheprole.Conversely,theswimmermayundulateitsbodytogeneratethedesiredpropulsiveforces.Assumingtheuidtobeideal(i.e.,incompressible,irrotational,andinviscid),theoweldcanbemodeledasauniformowwithanitenumberofsingularities,sincethesuperpositionprincipleissatised.Inparticular,avortexsheetisplacedattheboundaryoftheswimmertoaccountfortheno-penetrationcondition,whilediscretevorticesareplacedinthenearowregiontoresolvetheunsteadyvortexsheddingandwakeeects.Thenumericalcomputationofthehydrodynamicmodelfollowstherecentmethodsdevelopedin[ 72 72 ]. 3.3.1FlowFieldModelThemodeloftheoweldissetupinthebodyframeFB.ThevelocityeldconsistsofauniformowU12Ratanangleofattack2[0;)R,acirculationdueto 63

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thebodyrotation_I,aswellastheoweldduetoacontinuousvortexsheetalongtheswimmer'sbodyboundary(inordertohandletheno-penetrationcondition)andaseriesofdiscretepointvorticesinthewake.ThecomplexowvelocityU2Catposition2Ccanbeexpressedas U=U1ei)]TJ /F3 11.9552 Tf 11.955 0 Td[(i_I+UP+UV;(3{21)wherethevelocitiesUP;UV2CcomefromthevortexsheetonthebodyboundaryandtheNV2Npointvortices,respectively.EquationsforUPandUVcanbewrittenas UP=1 2ZS1(s) )]TJ /F3 11.9552 Tf 11.955 0 Td[(&@s @&d&;UV=)]TJ /F3 11.9552 Tf 15.955 8.087 Td[(i 2NVXv=1v )]TJ /F3 11.9552 Tf 11.956 0 Td[(v;(3{22)inwhich(s)2Rdenotesthevortexstrengthperunitlengthonthevortexsheet,andv2Rrepresentsthestrengthofthediscretevortexatpositionv2C(v=1;2;:::;NV2N).Providedthatthebodydeformationisgivenbytheswimmingcontroller(thusdeningthecontourofthevortexsheet),theunknownvariablesin( 3{21 3{21 )includesthevorticitystrength(s)onthevortexsheetaswellasthelocationsvandstrengthsvofthediscretevortices.Thetrailingedgevorticesareintroducedintotheowaccordingtothepreviousstudyin[ 73 73 ],andthepositionsoftheleadingedgevorticesaredeterminedusingtheowseparationcriterionfrom[ 74 74 ].Ateachtimeinstant,atotalofNV2Nvorticesarepresentintheowatpositionv2Cwithstrengthsv2R(v=1;2;:::;NV2N).Thetrailingedgevorticesareplacedbasedonpreviousstudy[ 73 73 ],whereasthepositionsoftheleadingedgevorticesaredeterminedusingtheStratford'sseparationcriterion[ 74 74 ].Oncethelocationsofthevorticesaredened,thestrengthofthevorticesandthevortexsheetcanbesolvedforsimultaneouslybyimposingtheboundaryconditionsuchthatthevelocitycomponentnormaltotheswimmerbodyshouldbeidenticaltothenormalvelocityatbodyboundaryduetodeformation.However,thesolutioniselusiveduetothecomplexityofthecomputation.Instead,theresultisobtainednumerically. 64

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3.3.2NumericalPanelMethodThepanelmethodmodelissetupfornumericalcomputationbasedontheoweldmodelin( 3{21 3{21 ).Thesh-likeproleisdividedintoNP2Nlinesegmentsaspanels,segregatingthecontinuousvortexsheetintolinepanelswithuniformvorticitystrengths.AsillustratedinFigure 3-5 3-5 ,thep-thpanelhastwoendpointsp)]TJ /F4 7.9701 Tf 6.586 0 Td[(1;p2C,alengthlp2R,andauniformstrengthp2R.Hence,theowvelocityUPin( 3{22 3{22 )canberewrittenas UP=NPXp=1p 2ln)]TJ /F3 11.9552 Tf 11.955 0 Td[(p)]TJ /F4 7.9701 Tf 6.586 0 Td[(1 )]TJ /F3 11.9552 Tf 11.955 0 Td[(plp p)]TJ /F3 11.9552 Tf 11.955 0 Td[(p)]TJ /F4 7.9701 Tf 6.587 0 Td[(1:(3{23) Figure3-5. Schematicsofthepanelmethodmodelwithdiscretevortex. Theboundaryconditionforthepanelmethodrequiresthatthevelocitycomponentnormaltothepanelequalstothenormalvelocityofthecontrolpointateverycontrolpointonthebody.Furthermore,theKelvin'scirculationtheoremshouldbesatisedsuchthatthetotalcirculationdiminishes: NPXp=1plp+NVXv=1v=0:Thesystemofequationsforthenumericalmethodturnsouttooverdetermined,withmoreconstraintsthanthenumberofunknowns.Theproblemmaybesolvedinaleastsquaressense,whichyieldsthepanelstrengthspandthevortexstrengthsv.Finally,thepressuredistributionaroundthehydrofoilprolecanbeobtainedusingtheunsteadyBernoulliequation.Itshouldbenotedthatalthoughthepanelmethodmayprovidesimilarresultsasthepotentialowmodel,itdoesallowforthecomputationofarbitrarydeformationthatmaynotbeeasilydenedbyconformaltransformations.Detailsaboutthenumericalmodelcanbefoundin[ 72 72 ]. 65

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3.4SwimmingControlUptothispoint,thedynamicalsystemofthesh-likeswimmerhasbeencompletelydened.ThedeformingswimmerbodyisrstcreatedbythegeometricmodelinSection 3.1 3.1 beforebeingtransformedintothephysicalbodyframeasdenedinSection 3.2 3.2 .TheinteractionbetweentheswimmerbodyandtheuidisresolvedusingthehydrodynamicmodeldevelopedinSection 3.3 3.3 .Theresultoftheinteraction{theforcesandmomentsexertedontheswimmerbytheuid{dictatesthemotionofthebodyframewithrespecttotheinertialframe.Inordertomanipulatetheswimmingbehaviors,acontrollerisdevelopedtoregulatetheswimmer'smotionwithitsbodydeformation.Themotionisdenedinthehorizontalplane;therefore,thestatevariableofthecontrolsystemhasthreecomponents:positionsq0x,q0y,andorientationIasdenedin( 3{14 3{14 ).Thecontrolinputisdesignatedasthebodydeformationandhasonlyonecomponent0.Sincethenumberofcomponentsinthestatevariableisgreaterthanthatinthecontrolinput,thesystemisunder-actuated,whichgenerallycannotbecommandedtofollowarbitrarytrajectoriesinthecongurationspace.However,byoperatingtheactuationinacyclicmannerinwhichthedeformationfunctionisdesignatedfortheentirecycleatthebeginningofeachcycle,thesystembecomesfullyactuatedbecausethecontrolinputineachcyclehastheoreticallyinnitedegreesoffreedom.Apiecewisesinusoidalfunctionischosenasthedeformationfunction.Theactuationperformanceofvariousparametersinthedeformationfunctionaresystematicallytestedinsimulation,fromwhichanactuationmodelisdevelopedcapableofmanagingaccelerating,decelerating,andturningmaneuvers. 3.4.1DeformationFunctionThedeformationfunctionisdenedasapiecewise,sinusoidalfunctionoftime.Deningthetimeinterval[tj;tk)asanactuationcyclewiththefollowingpartitions: tj=t0
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thedeformationfunction0(t)fort2[tn)]TJ /F4 7.9701 Tf 6.587 0 Td[(1;tn)(n=1;2;3;4)canbewrittenasapiecewisesinusoidalfunction(asillustratedinFigure 3-6 3-6 ): 0(t)=nsin!n(t)]TJ /F3 11.9552 Tf 11.955 0 Td[(tn)]TJ /F4 7.9701 Tf 6.586 0 Td[(1)+n)]TJ /F1 11.9552 Tf 11.956 0 Td[(1 2;(3{25)wheren2Rdenotesthedeformationamplitude,and!n2Rdenotestheangularfrequencydenedas !n= 2(tn)]TJ /F3 11.9552 Tf 11.955 0 Td[(tn)]TJ /F4 7.9701 Tf 6.586 0 Td[(1):(3{26)Theamplitudenandtheangularfrequency!nsatises 1=2=13=14;1 !1=2 !2=3 !3=23 !4;(3{27)where1;2;32Rarethreeadjustableparametersthatdictatethetrajectoryofthebodydeformation. Figure3-6. Deformationparameter0asapiecewisesinusoidalfunction. 3.4.2ActuationModelToinvestigatethebehaviorofthedeformationfunction( 3{25 3{25 ),aseriesofsimulationtestsarecarriedoutusingdierentvaluesfortheparameters1,2,and3.AsillustratedinFigure 3-7 3-7 ,itisfoundthatincreasingordecreasingthedeformationamplitude=1+32RwillchangethemagnitudeanddirectionofthesteadyswimmingdisplacementinonecycleT=tk)]TJ /F3 11.9552 Tf 11.987 0 Td[(tj2R(correspondingtochangingthesteadyswimmingvelocity).Inaddition,thechangeoforientationIinonecycle(correspondingtoturning)isroughlylogarithmicallyrelatedtotheparameter3,whichisthetimeratioofdeformingtowards 67

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onesidethantheother.Inotherwords,thedeformationamplitudecontrolsswimmingspeedandtheparameter3createsturningmaneuvers. A B CFigure3-7. Swimmingmotionsforvariousdeformationparameters.Deformationamplitudeaectsthemagnitudeanddirectionofswimmingspeed,andparameter3changestheorientationI,showninonecycle. Forsimplicity,thedeformationamplitudeandthetimeperiodTarenormalizedsothattheswimmermaintainsasteadyspeedofabout2l0=Twhilethecontrolparametersarenominal1=2=3=1.ItisfurtherassumedthatduringeachcontrolcycleT,theswimmeriseectivelyturningwithaconstantradius.Thus,thecontrolparameter3islogarithmicallyrelatedtotheturningcurvature2RbasedonthelineartrendinFigure 3-7 3-7 3.4.3ControlStrategyThedeformationfunctionisdenedinacyclicmannerinwhichthecontrolcommandisissuedatthebeginningofeachcycleandcannotbealteredduringthecycle.Therefore,thecontrolstrategyistomatchthedesiredswimmingtrajectorywithadeformationfunctionthatgeneratesasimilarsetofmovements,onecycleafteranother.Inthisspeciccasewheretheactuationmodeldependsonthecontrolparameter3togenerateturningcurvature,thedesiredtrajectoryisdenedasaconnectedsetoftargetlinesandarcs.Thecontrolobjectivethenbecomesobtainingthecontrolparameter3foreachcyclebasedonthedierencebetweentheswimmer'scurrentposition(andswimmingdirection)andthedesiredtrajectory. 68

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A BFigure3-8. Arctrajectoriesforapproachingorconvergingtothedesiredpath.Thearcsconnectthecurrentpositionq0(withvelocityu0)anddesiredtrajectorydenedbyqiandqi+1.A)Illustrationofanapproachingarc.B)Illustrationofaconvergingarc.Thechoicebetweenthetwoarcsdependsonthedistancefromthecurrentpositiontothelineconnectingthewaypoints.Thethresholdisdepictedbytheshadedareas. AsillustratedinFigure 3-8 3-8 ,thedesiredtrajectoryisdenedasaseriesoflinesegmentsconnectingthetargetpointsqi=[qix;qiy]>2R2.Aimingatthedesiredlinesegmentdenedbypointsqiandqi+i,theswimmerstartsfromthecurrentpositionq0=[q0x;q0y]>2R2andswimswithavelocityu0=[u0x;u0y]>2R2thathasthesamemagnitudeasthedesiredvelocityui=[uix;uiy]>2R2.Twodierentcontrolstrategiesaredenedbasedonthedistancefromthecurrentpositionoftheswimmertothelineconnectingthewaypoints.Whentheswimmerisrelativelyfarawayfromthetargetline,theapproachingarcisdenedsuchthatitistangenttothecurrentanddesiredvelocitiesu0andui.Astheswimmergetsclosertothetargetline,theconvergingarcisdenedsuchthatitistangenttothecurrentvelocityu0andpassesthroughpointqi+1.Therefore,theapproachingandconvergingcurvature1;22Raredenedas 1=u20x+u20y)]TJ /F3 11.9552 Tf 11.955 0 Td[(u0xuix)]TJ /F3 11.9552 Tf 11.955 0 Td[(u0yuiy [(q0x)]TJ /F3 11.9552 Tf 11.955 0 Td[(qix)uiy)]TJ /F1 11.9552 Tf 11.955 0 Td[((q0y)]TJ /F3 11.9552 Tf 11.955 0 Td[(qiy)uix]ku0k;2=u0x(qiy)]TJ /F3 11.9552 Tf 11.955 0 Td[(q0y))]TJ /F3 11.9552 Tf 11.955 0 Td[(u0y(qix)]TJ /F3 11.9552 Tf 11.955 0 Td[(q0x) [(q0x)]TJ /F3 11.9552 Tf 11.955 0 Td[(qix)2+(q0y)]TJ /F3 11.9552 Tf 11.955 0 Td[(qiy)2]ku0k;(3{28)wherekkdenotestheEuclideannormofavector.Itisworthnotingthatthecontrolstrategyinquestiondoesnotguaranteeconvergenceofswimmingtrajectoryexactlyontothetargetline,butonlyguidestheswimmerreaching 69

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towardsit.Also,overshootingmayappearsincethecontrolcommandcannotbeadjusteduntiltheendofeachactuationcycle.Nevertheless,satisfactorycontrolperformancecanbeachievedbycarefulplacementofthewaypointsandadjustingthethresholdbetweentheapproachingandconvergingstrategyaccordingly. 3.4.4SwimmingSimulationTotesttheeectivenessofthecontrolalgorithm,twosetsofdesiredpathsaredenedbytargetpoints: i:q1=[4l0;0]>;q2=[4l0;4l0]>;q3=[)]TJ /F1 11.9552 Tf 9.298 0 Td[(100l0;4l0]>; (3{29a)ii:q1=[5l0;0]>;q2=[105l0;)]TJ /F1 11.9552 Tf 9.298 0 Td[(100l0]>: (3{29b)Setirepresentsacounter-clockwiseturnof180,andsetiirepresentsaclockwiseturnof45.Theswimmerstartsfromtheoriginwithasteadyswimmingvelocitydirectedtotheright-handside,andfollowsthedesiredtrajectoryforseveralcycles.Thethresholdfortheapproachingandconvergingarcsarechosentobetwobodylengths2l0.SnapshotsofthedesiredandactualtrajectoriesareillustratedinFigure 3-9 3-9 .Theswimmergenerallyapproachesandfollowsthedesiredpath.Specically,inFigure 3-9A 3-9A itappearsthattheswimmerovershootstowardstheendoftheturnandcorrectsitselfafterwards;andinFigure 3-9D 3-9D theswimmerfollowsthedesiredarcnicely.Overall,theswimmerisabletostayclosetothedesiredpath(withinonebodylengthl0attheendofeverycycle),andthepathfollowingperformanceissatisfactory. 70

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A B C D EFigure3-9. Simulationresultsoftheswimmerfollowingthedesiredpaths.A)Desiredtrajectoryiandactualswimmingpath.B)Snapshotoftheswimmeranditswakeattime2Tfortrajectoryi.C)Snapshotoftheswimmeranditswakeattime4Tfortrajectoryi.D)Desiredtrajectoryiiandactualswimmingpath.E)Snapshotoftheswimmeranditswakeattime4Tfortrajectoryii.Allaxesarescaledtothebodylengthl0.Thedesiredpathshownasasolidlineandtheactualtrajectoryshownwithblackandgreyalternatingbodysnapshotsat0:25Ttimeintervals.Theinitialpositionoftheswimmerismarkedwitharrowheadsontheaxes.Redandbluedepictvorticesofpositiveandnegativestrengths,respectively. 71

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CHAPTER4MOBILELIDARSYSTEMFORROADSURVEYLightdetectionandranging(lidar)technologyisalaserapplicationtoremotesensingthatprovidesdistanceestimationbyilluminatingobjectswithpulsedlaserbeamsandmeasuringthereectedlaserpulses.Initiallyimplementedformeteorology[ 75 75 ]andatmosphericstudies[ 76 76 ],lidarsystemshavebeenutilizedinabroadrangeofapplicationsinresearchandindustry[ 77 77 ].Thelidarsystemscouldrapidlycreatedense,3Dpointclouddataandsurveythesurroundingenvironmentwithsuperioraccuracy,precision,andexibilitywhencomparedtoconventionalmeasurementmethods.Particularly,mobilelidarsystemsonvehicularplatforms(oftenreferredtoasmobilelaserscanning,orMLS)havereceivedincreasingattentioninrecentresearchstudies[ 78 78 ].Thescanningspeedandaccuracyareimproved,andtheintegratedGPSandINSoerreal-timelocalizationandorientationinformation.Themobilelidarsystemshavebecomeaneectivesolutionforrapidenvironmentalmappingandroadinventorysurveying.Athoroughreviewoftheseapplicationscouldbefoundin[ 78 78 79 79 ].Thisstudyaimsatdevelopingamobilelidarsystemforsurveyingthereectivemarkingsonroadsurfaces.Thesystemincludestypicalcomponentssimilartoothermobilelidarsystems;however,acoupleofdesignchoicesaremadetoimproveperformance.First,thelidarsensorispositionedandorientedtominimizethegapbetweenconsecutivescanswhileallowingthevehicletotravelatareasonablespeedintrac.Second,pointsofinterestinthelidardataareidentied,utilizingthescanninggeometryrelativetothevehicleplatform,beforebeingcongregatedintoaglobalpointcloudwherethescanninginformationislost.Additionally,theconceptofoccupancygridsisutilizedtoregisterthescannedspaceasempty(free)oroccupied,suchthatoutliersandtemporaryobstructionscouldbeeasilyidentiedbyexaminingtheaccumulatedregistrations. 72

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4.1LidarSystemDesignThemobilelidarsystemconsistsofacompactlidarsensor,anintegratedGPSreceiver,adigitalgyroscopeorinclinometer,andanonboardcomputerfordataprocessingandstorage.Mountedontopofavehicleplatform,therear-facinglidarcollectspointclouddatafromtheroadsurfaces.Relativedistance,togetherwithreectanceofthepointsontheroad,areobtained.Real-timelidarscanpointsareregisteredinthevehicleandworldreferenceframeforsubsequentprocessing. 4.1.1LidarSensorInthisstudy,thelidarsensor(VelodynePUCKVLP-16)isacompactdirectenergydetectionlidardeviceasshowninFigure 4-1A 4-1A .Ithasarelativelylowpowerconsumption(about8W)andasmallfootprint(acylinderofabout103mmdiameterand72mmheight).Thelaseroperatesat903nmwavelength.Duringoperation,thelaserpulsesswitchamong16evenlyspacedelevationangleswithina15range,astheysweeparound360azimuthally.AsillustratedinFigure 4-1B 4-1B ,everylaserbeamemittedfromthecenterofthelidarcouldbedescribedusinganazimuthangleandanelevationangle.Theelevationanglechangesevery2.3sduringtheringsequenceofeachsetof16laserbeams,whereastherotationspeed(orrateofchangeforangle)isadjustablefrom5to20rotationspersecond.Providedthatthedistancefromthescannedobjectcouldbeinferredbasedontheamplitudeofthereturninglight,pointsontheobjectcouldberegisteredwithrespecttothereferenceframethatisxedonthelidarsensor.Datapointsupto100minrangecanbedetectedwithmeasurementsoftheirreectance. 4.1.2ScanningResolutionSincethelidarsystemistobemountedonboardavehicleplatformmovingintrac,areasonablechoicewouldbeonthefrontorthebackofthevehiclewheretheroadsurfacesareexposedforscanning.Assumingthelidarismountedonthebackwithoutlossofgenerality,thegeometryforthelidarscanningeldcouldbedepictedasinFigure 4-2A 4-2A 73

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A BFigure4-1. Lidarsensorandeldofview.A)Pictureoflidarsensor,printedwithpermissionfromVelodyneLiDARInc.B)Illustrationoflidarscanningeld.Thescanningeldisdenedby16evenlyspacedelevationanglesbetween15fromthexy-planeandanazimuthalanglethatcontinuouslychangesinafull360rotation.Theelevationangleshiftsevery2.3sina55-sringsequencewhiletherateofrotationisadjustablebetween5and20rotationspersecond. Asthevehicletravelsforwardalongthex-axis,thesetof16laserbeamswithin15separationfromthecenterline(dash-dotlineinFigure 4-2 4-2 )formsacircularsector,whichinturnsweepsaroundfollowingahelixcurve.Spacingbetweentheadjacentlaserbeamscouldbereducedwhentheyhittheground,ifthelidarismountedlowerinheightand/orpitchedfurtherdown.However,thisdoesnotnecessarilyresultinhigherscanningresolutionbecauseitmayalsoincreasethegapbetweenconsecutiverotations.Tofurtherinvestigatethescanninggeometry,anapproximationismadethatall16laserbeamsareredsimultaneouslyandreachthegroundalongthex-axisaftereveryrotation.1TheapproximatedscanningmodelisillustratedinFigure 4-2B 4-2B ,inwhichthelaserbeamsmakecontacttothegroundalonglinesegmentBCandsubsequentlyB0C0onthenextrotation,whilethelidarcentertravelsfrompointAtoA0.Ideally,consecutive 1Thisisavalidapproximationbecausethetimeperiod(55s)forthelaserringsequenceof16laserbeamsisconsiderablysmallerthanthatoftheazimuthalrotation(whichisadjustablebetween0.05to0.2s).All16laserrayscannothitexactlyonthex-axissimultaneously,buttheirintersectionswiththegroundarerelativelyclosetothex-axis. 74

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A BFigure4-2. Scanningcoverageforthelidarsystem.A)Illustrationoflidarscanningcoverage.Thelidarsensorismountedonthebackofavehicleplatformthattravelsalongthex-axis.Asetof16laserbeamsformsa30circularsectorandsweepsalongahelixcurve.B)Consecutivescanningrotationsinthexz-plane.Thegroundcoverageinthexz-planecanberepresentedbythelinesegmentBCandB0C0asthecenterofthelidarproceedsfrompointAtoA0.Themountingheightandthepitchangleofthesensoraredenotedbyhand,respectively. rotationsdonotoverlapwhenthevehicleismovingatadesignatedmaximumsurveyingspeed.Grounddistancesbetweentheadjacentscanningpoints(themostsignicantdistancecomesfromthesegmentbetweenABanditsadjacentlaserray)areminimized.Atthesametime,thegap(CB0)betweenconsecutivesweepsdoesnotexceedthescanningresolutioninasinglesweep(alongBCorB0C0).Asaresult,thelidarpitchangleandmountingheighthconstituteanoptimizationproblem: argmin2[m;90)]TJ /F11 7.9701 Tf 6.587 0 Td[(n]R;h2R+h[cot()]TJ /F3 11.9552 Tf 11.955 0 Td[(m))]TJ /F1 11.9552 Tf 11.955 0 Td[(cot()]TJ /F3 11.9552 Tf 11.956 0 Td[(m+)];subjectto:umaxTroth[2cot()]TJ /F3 11.9552 Tf 11.955 0 Td[(m))]TJ /F1 11.9552 Tf 11.955 0 Td[(cot()]TJ /F3 11.9552 Tf 11.955 0 Td[(n))]TJ /F1 11.9552 Tf 11.956 0 Td[(cot()]TJ /F3 11.9552 Tf 11.955 0 Td[(m+)];(4{1)whereumaxdenotesthemaximumsurveyspeedandTrotrepresentstheazimuthalrotationtimeperiod.Theanglesm,n,andstandforthemaximumandminimumelevationangles(m=)]TJ /F3 11.9552 Tf 9.298 0 Td[(n=15),andtheangularelevationdierencebetweenadjacentlaserrays(=2). 75

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Itisdiculttondtheoptimalsolutionanalytically.However,thetrigonometricfunctionscouldbereplacedwiththeirestimatesat=75,sincetheexpressionsinbothbracketsaremonotonicallydecreasingfunctions.Subsequently,theminimalvalueforlidarheighthisobtainedbasedonthemaximumsurveyingspeedumax.Forexample,deningthemaximumspeedumaxtobe80km/hor50mphyieldsaminimalheighthofaround1.8mor6ft.Insimulation,theresultinglaserintersectionpointsonthegroundareillustratedinFigure 4-3 4-3 .Consequently,thescanswillcontinuouslycovertheroadsurfaceifthevehicleismovingnofasterthanthemaximumspeed.Inaddition,thelidarmayalsoprovidesucientmeasurementsontheneighboringlaneswhentherearenoobstructions. Figure4-3. Simulatedscanningpointsonthegroundatmaximumsurveyingspeed.Thelidarpitchangleis75,themountingheightissetaround1.8mor6ft,andthesurveyingspeedisat80km/hor50mph.Theseparametersgrantsatisfactoryscanningresolutionuptotheadjacentlaneswithminimaloverlappingbetweenrotations. 76

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4.2LidarDataProcessingAsvisuallydemonstratedbyFigure 4-3 4-3 ,thelidarsystemcanrapidlyproducealargenumberofdatapoints{almost200,000pointspersecondforthisparticularmodel.Thelidardataisorganizedinadatastructurethatincludesthetimestamps,azimuthalandelevationangles,distancesandreectances(basedonreturnintensities),instantaneouspositionandorientationinformation(fromGPSandINS),aswellasthe3Dpointcoordinateswithrespecttothevehicleandtheearth.Toreducethecomputationload,thedataisprocessedandthepointsofinterestsareextractedforeveryscanrotationpriortocastingthemintoapointcloudandundergoingfurtherconversions.Curbsandobstacles,roadsurfaceregions,andlanemarksareidentiedduringthisprocess. 4.2.1DataParsingThedatacollectedfromthemobilelidarsystemisarrangedinadatastructurethatcontainsinformationdirectlyfromthelidar,GPS,andINS,aswellasintermediatedataprocessingresultsasthemeasurementsarebeingrelayedthroughvariousstages.Filtersareappliedandinterpolationaremadeatthisstagetoprepareforsubsequentprocessing.Particularly,thelidar(VelodynePUCKVLP-16)providesonetime-stampforeverynetworkpacketincluding24ringsequencesof16laserpulsesofdierentelevationangles.Individualtime-stampforeachlaserringiscalculatedaccordingtotheringprogramfromthemanufacture.Furthermore,theazimuthalanglesaremeasuredforeveryotherringsequenceandtheremainingvaluesarelinearlyinterpolatedbasedonthederivedtime-stamps.Combiningtheazimuthalandelevationangles2[0;360)and2[)]TJ /F1 11.9552 Tf 9.299 0 Td[(90;90]withthelaserreturndistanced2R+,theCartesiancoordinatesLp2R3ofthedatapoints,withrespecttothelidarcoordinatesystemL,canbeobtainedby Lp=dcos()sin()cos()cos()sin()>:(4{2)ThepointcoordinatesarethentransformedtothevehiclecoordinatesystemVas Vp=VLRLp;(4{3) 77

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wheretherotationmatrixVLR2R33isdenedas VLR=26666640)]TJ /F1 11.9552 Tf 11.291 0 Td[(cos())]TJ /F1 11.9552 Tf 11.291 0 Td[(sin()1000)]TJ /F1 11.9552 Tf 11.291 0 Td[(sin()cos()3777775;(4{4)anddenotesthepitchangleofthelidarmount.Atalaterstage,thedatapointswillbeconvertedtotheearthreferenceframe,usinglteredandinterpolatedpositionandorientationdatafromGPSandINS.A3Dpointcloudwillalsobeformedinwhichtheroadsurveyresultsarepresented.However,beforetheconversion,pointsofinterestareidentiedinthevehiclereferenceframe.Datapointsareanalyzedinbatcheseverytimethelasersequencesof16dierentelevationanglescompleteafullrotation,duringwhich,roadfeaturessuchascurbs,obstacles,roadsurface,andlanemarksarerecognizedandlabeled.TheowchartsfororganizingandprocessinglidardataareshowninFigure 4-8 4-8 4.2.2CurbandObstacleIdenticationTherehavebeenextensivestudiesfocusingonthegeneraltopicofterraintraversabilityanalysisforgroundvehicles(seesurveysin[ 80 80 81 81 ]).Someoftheexistingmethodsconstruct2Dtraversabilitymapsbycomputingtheelevationstatisticssuchasrange,varianceofheight,andslope[ 82 82 83 83 ].Othersanalyzetheenvironmentbydetectingbasicshapefeaturessuchasedges,planes,orpointclusters[ 84 84 ].Thegeometricfeaturesarethencomparedtothelimitationsandstabilitiesofthevehiclesforpathplanning[ 85 85 86 86 ].Particularly,roadandlanedetectionhasbeenanactiveeldofresearch(refertoasurveyin[ 87 87 ]).Manystudiesextractroadpositionfromairbornedata[ 88 88 ].Otherresearchers,whilecollectingdatawithgroundvehicleplatforms,utilizethescangeometrytoalleviatethecomputationloadduringthepreliminaryidentication[ 89 89 { 91 91 ].Thisstudyadoptssimilarstrategiesinordertoachieverapidprocessing. 78

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Inthisstudy,theinitialtaskofroadfeatureidenticationistodenetheroadsurfacebylocatingcurbsandobstacles.Assumingthatthemobilelidarsystemistravelingalongastreetwiththerear-facinglidarpitchingdownwards,thescanpointswillformseverallateralstripes(16forthisparticularmodel)thatswipeacrossthepavement,revealingthecontoursoftheroadsurface.Sincecurbsandobstaclesaregeometricallycharacterizedbytheabruptchangesfromthestreetelevationthatimpedecrossingtrac,areasonablewayofidentifyingthemisexaminingthecrosssections.Accordingtotheroadwaydesignstandard[ 92 92 ],thecrosssectionoutlinesofvarioustypesofcurbssharesimilargeometrywithdierentdimensions,asshowninFigure 4-4 4-4 .Inparticular,thetracseparatorcurbinFigure 4-4A 4-4A andtheroundaboutcentralcurbhavethesameshapetowardstrac,andthesamegoesfortheTypeDcurbinFigure 4-4C 4-4C andtheasphalticconcretecurb.Othercurbtypesalsosharethesameoutline,despiteconstitutingdierentparts.TypeEandFcurbshaveslightlyslopedtransitionstothedriveway,depictedasdashedlinesinFigures 4-4B 4-4B and 4-4C 4-4C .Furthermore,inletsandguttersmayalsoappearalongcurbs,sometimeswithsupportbarsand/orgratesasinFigure 4-4D 4-4D .Asidefromthesimilar,butdiverse,curbgeometrythataddscomplexitytotheiridenticationprocess,distributionofthedatapointsalsoincreasesthediculty.Thepointsonthescanlinesarealmostevenlyspacedintheazimuthalanglesandaregenerallynotuniformlydistributedalongeitherlateralorverticaldirection.Forthisreason,simplyusingnitedierence,heightaverage,andvariancecannotprovideaconsistentcharacterizationofthecurbsandobstacles.Inaddition,advancedtechniquesusingcurveandsurfacettingcouldbeeasilydisruptedbycurbinletsandgutters.Torapidlyidentifycurbsandobstaclesinarobustway,thephysicalinteractionwithavehicle{specicallywheels{isinvestigated.AsillustratedinFigure 4-5A 4-5A ,thetwoshadedrectanglesrepresentthecross-sectionsofwheel-likeobjectswithequallateralwidth.Alsoshownintheplotisthefrontviewprojectionofasamplescanlineovera 79

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A B C DFigure4-4. Crosssectionoutlinesofvariouscurbtypes.A)Tracseparatorcurbandroundaboutcentralislandcurb(TypeRA).B)TypeA,B,andEcurbs.C)TypeD,Fandasphalticconcretecurb.TypeEandFcurbsslopeslightlytotthedriveway,asindicatedbythedashedlines.D)Curbinletwithorwithoutsupportbarsanddraingrates. curbsection.Placingthetwowheelobjectsabreastontopofthescanlinerevealsthegroundheightsifanimaginaryvehicleistodriveoverthetwosegments.Thus,iftheheightdierenceoftwoadjacentsegmentsreachesbeyondathresholdforastableride,thesegmentsmayincludeobstacles.Likewise,curbscanbeidentiediftheheightdierencelieswithinapossiblerange(e.g.,from5to20cm).Becausetheidenticationprocessisbasedontheinteractionbetweentheroadsurfaceandwheels,complexgeometryfromthecurbinlets,grates,orotherobjectswillnotaecttheresults.Withtheassumptionthatthemobilelidarsystemistravelingalongadriveway,itisexpectedthatthesectioninfrontoftherear-facinglidarispartoftheroadsurface.Therefore,theidenticationofcurbsandobstaclescanbesimpliedintosearchingfromthemiddleofthescanfortherstsegmentswithanabruptchangeinrelativeheight.Theprocessisfurtherstreamlinedbydividingthescanlineintoequal-widthsegments 80

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A BFigure4-5. Illustrationofthegeometricmethodtoidentifycurbsandobstacles.A)Wheelobjectsoverasamplecurbscan.Placingtwowheel-likeobjectssidebysideoverthetopofalidarscanlineprovidesameasurementofthegroundheightdierenceforadjacentroadsegments.B)Lateralsegmentationandheightdierencesearch.Animprovedsearcheciencymaybeachievedbydividingthescanlineintoequal-widthsegmentsandcomparethemaximumheightsofdatapointsbetweenadjacentones.Curbsandobstaclescanbeidentiedbysearchingforthedatapointsthatareabovethresholdsandclosesttothemiddleofthedriveway. andcomparingtheneighboringheightdierences,asdemonstratedinFigure 4-5B 4-5B .Onceacurborobstaclesegmentisfound,thedatapointonthecurborobstacleisidentiedastherstpointfromthemiddlewiththesignicantheightchange.Alongeachofthescanlines,theroadsurfaceisdenedbythepointsbetweencurbsandobstacles.TheowchartforidentifyingcurbsandobstaclesisillustratedinFigure 4-9A 4-9A 4.2.3LaneMarkIdenticationPavementmarkingsincludestripes,shapes,symbols,andlettersontheroadsurfacecoatedwithretroreectivepaint.Atthisstage,theroadsurveyisfocusedonidentifyingthelinemarksthatdenelaneboundaries.ShowninFigure 4-6 4-6 areacollectionofdierenttypesofpavementmarkinglines,amongwhichthelane-deninglinesareabout13.2cmor6inwide.Fromthelidardatapointsontheroadsurface,retroectivepavementmarkingsarerecognizedaccordingtothereectancemeasurements.LanemarkscanbeidentiedwithalinedetectionmethodderivedfromtheHoughtransform.TheHoughtransformisafeatureextractiontechniqueusedindigitalimageprocessing[ 93 93 ].Theclassicaltransformismainlyconcernedwithlineidentication,andislaterextendedforarbitraryshapes.Thealgorithmessentiallygroupsimagepointsinto 81

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Figure4-6. Dierenttypesofpavementmarkinglines.Thelane-dividinglinesare15.2cmor6inwide,whichhelpstodistinguishthemfromthechannelizingandpedestriancrosswalklines. asetofobjectcandidatesbyperforminganexplicitvotingprocedureoveraparameterspace.Forexample,whendetectingstraightlines,theimagepointsaretransformedintoHoughspaceandthecandidatelineparametersoftheHessenormalformarecollected.Lineparameterswithmostlikelihoodcanbedeterminedbylocalmaximafromtheaccumulatorspace.However,directapplicationoftheHoughtransformoverthelidardataisproblematic.Informationonthelinewidthswillbelostintheprocess,andthevotingprocedurecanbebiasedalongthelateraldirectionduetothenon-uniformscanningpattern.Toavoidtheseissues,onlythelinesalongthelongitudinaldirectionarecollected,withtheassumptionthatthevehicleplatformisfollowingadriveway.Also,thelinewidthsareassignedasthesecondparameter. 82

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A B CFigure4-7. Lanemarkidenticationfromlidardatapointsonroadsurface.A)Reectivepointsonroadsurface.High-reectancepointsbetweenthecurbs(markedbytriangles)arehighlightedafterpassingthroughamedianlter.B)Positionsandwidthsofconnectedreectivesegmentsonroadsurface.Connectedsegmentsalongeachscanlinearegroupedtogetheriftheyhaveoverlappinglateralpositionsandwidths.C)Identiedlanemarksandlanewidths.Lanemarksareidentiedfromgroupswithadequatenumbersofregisteredsegments,whosemedianpositionsandaveragewidthsareassignedaspositionsandwidthsofthemarkinglines.Lanewidthsbetweenthelinesarealsocalculated.Curbpositionisrepresentedwithdashedlines. Figure 4-7 4-7 illustratesthelanemarkidenticationprocess.First,reectivepointsontheroadsurfacearedistinguishedusingareectancethreshold.Amedianlteristhenappliedalongthescanlinestoremovenoise,whichyieldsanumberofconnectedsegmentsofhigh-reectancepointsoneachofthescanlines,asinFigure 4-7A 4-7A .Subsequently,thelateralpositionsandwidthsofeveryreectivesegmentsareregistered,seeFigure 4-7B 4-7B .Segmentsofcomparablewidthsaregrouptogetheriftheyarelocatedinsidethewidthofacentralmember.Finally,thegroupswithsucientmembersareidentiedaslongitudinallinemarkswiththeircorrespondinglateralpositionsandwidths,asillustratedinFigure 4-7C 4-7C .TheowchartforthisprocessisshowninFigure 4-9B 4-9B 83

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A BFigure4-8. Flowchartsfororganizingandprocessinglidardata.A)Organizinglidardata(P1).B)Lidardataprocessing(P2). 84

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A BFigure4-9. Flowchartsforidentifyingcurbsandlanemarks.A)Curbandobstacleidentication(P3).B)Reectivelanemarkextraction(P4). 85

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4.3PointCloudProcessingAfteridentifyingthepointsofinterestinthelidardata,thedatapointsareconvertedintotheworldreferenceframe,formingapointcloud.Toreducedatasizeandcomputationload,thepointclouddataisconvertedintodiscretevoxelspacewheredatapointsarecollectedinseparatecubes.Thus,thegeometryofthescannedscenecanberepresentedbyvoxelsthatcontainoneormoredatapoints.Outlierscanbereadilyeliminatedbysettingathresholdforthenumberofpointsinthevoxels.Undesiredpointsregistered,duetotemporaryobstructionbytrac,canbeidentiedbyutilizingtheconceptofoccupancygridstoregisterscannedpoints. 4.3.1OccupancyFilterApplicationoftheoccupancygridconceptinlidarscanisproposedin[ 94 94 ],wherethescannedsceneiscategorizedasfree,occupied,orhiddenalongthedirectionofeverylaserbeam,andaprobabilisticmodelisderivedtofacilitatefeaturedetection.Anon-parametricsolutionforoccupancyprobabilityestimationispresentedin[ 95 95 ]toimprovethecomputationperformance. Figure4-10. Occupancycategorizationalongasinglelaserbeam.Informationaboutthescannedsceneindicatesthatnotonlyisthedatapointoccupied,butthespacebeforethepointisemptyandthespacebehindthepointishidden. ThelteringtechniquecanbeillustratedinFigure 4-10 4-10 .Aseachdatapointonanobjectgetsregisteredbythelidar,thecorrespondinglaserbeampassthroughemptyspacebetweenthelidarcenterandtheobject.Theinformationaboutthescannedscenesuggeststhatnotonlyisthedatapointoccupied,butthespacebeforethepointisemptyandthespacebehindthepointishidden.Therefore,byregisteringthevoxelsalongthelaserrayasemptyoroccupiedandcomparingtheaccumulatedregistrationaftermultiple 86

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scans,temporaryobstructionscanbeidentiedbythevoxelsthatareregisteredasbothoccupiedandempty. A B C DFigure4-11. Demonstrationofoccupancylterwithpassingtrac.A)Pointcloudfromthestartofastationarylidarscanwhichcoversanemptyroad.B)Pointcloudbytheendofthelidarscanafteronevehiclepassedbyfromoppositelaneandanothervehicleenteredthescanningeldonadjacentlane.C)Voxelizingtheaccumulatedpointcloudrevealstracesfrombothvehicles.D)Voxelizedpointcloudaftertheoccupancylter.Thetemporaryobstructionfrombothvehiclescanberemovedwithlittleresidue. Asanexample,thelidarsystemissetstationaryinaroadandcapturespointclouddataastwovehiclespassbyonneighboringlanes.Figures 4-11A 4-11A and 4-11B 4-11B showthepointcloudfromtwodierenttimeintervals.Onedepictstheroadbeingemptyandtheothershowsoneofthevehicle.AsdemonstratedinFigures 4-11C 4-11C and 4-11D 4-11D ,directlyvoxelizingtheaccumulatedpointclouddatagivesa3Dscenethatcontainsthetracesofbothofthepass-byvehicleswhilethevoxelsrepresentingtheroadsurfacearehiddenunderneath.Applyingtheoccupancylterremovestheobstructionwithlittleresidue. 4.3.2RoadSurveyTestsAseriesofroadsurveytestswereconductedtovalidatethedesignofthemobilelidarsystemandthelteringtechniques.Thesystemismountedonavehiclethattraversesthecampusareaintrac.PointcloudfromlidarscanisshowninFigure 4-12 4-12 .TheidentiedpointsoncurbsandreectivelanemarksareillustratedinFigure 4-13 4-13 .AsatellitemapfromGoogleofthesameareaisprovidedinFigure 4-14 4-14 forreference.Geometricfeatures 87

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ofthescene{includingtrees,buildings,powerlines,etc.{canbeeasilyrecognizedinthepointcloudmap(Figure 4-12 4-12 );whereascurbsandroadsurfacemarkings(Figure 4-13 4-13 )matchthesatelliteimage.Inthetest,theprocessingtime(P2)isaround10%ofthedatarateonthecomputerplatform2. Figure4-12. Pointcloudfromlidarroadsurvey.Grayscalerepresentselevation. 2Thecomputerisequippedwitha6th-generation,4-coreIntelRCoreTMi5-6500centralprocessingunit(CPU)operatingat3.20GHz,16GBrandom-accessmemory(RAM),anda256GBsolid-statedrive(SSD).ItrunsontheUbuntuoperatingsystemversion16.04.3LTS. 88

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Figure4-13. Identiedpointsoncurbsandlanemarksfromsurvey. Figure4-14. Satellitemapofthesurveyedarea,obtainedfromGoogleEarthPro[ 96 96 ]. 89

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CHAPTER5SUMMARYANDCONCLUSIONSIntherstpartofthisdissertation,alaterallineinspiredpressuresensorysystemisdevelopedforautonomousunderwatervehicles.Thesystemisabletoobtainpressuredistributionthatreectsthehydrodynamicinformationaboutthesurroundingow.Therstorderofthedistribution{thespatialintegration{representsanestimationofhydrodynamicforceandmomentsthataretraditionallycategorizedasunknowndisturbancetothesystem.Hence,thesensorysystemmayserveasanimportantguidanceforcontrolmaneuversespeciallywhenlocalizationisinaccurate.Ontheotherhand,higherordersofthedistributionreectlocalpressurevariationsthatallowforthedetectionofowpatternsandobstacles.Particularlyinthisstudy,estimatingthedistanceandangleofawallstructureisinvestigatedbyanalyzingthevariationsinthepressuredistributionontheFourierdomain.Bothexperimentalandsimulationtestsareconductedtovalidatethesystemdesign.Incorporatingthesensorysystemwithanautonomousvehiclecontrollercouldpotentiallyimprovetheperformanceofstationkeeping,docking,andtrajectorytracking;whereasthewalldetectingcapabilitycouldbehelpfulforobstacleavoidanceandnavigation.Thesecondpartofthedissertationpresentsash-likelocomotionmodelbasedonJoukowskitransformation,aimingatinvestigatingtheswimmingmechanismofthecarangiformandsub-carangiformshlocomotioninthe2Dspace.Theswimmerproleandbody-xedframearedenedtomaintainconstantbodylengthandareaandtoconservelinearandangularmomentaduringdeformation.Inaddition,toresolvetheunder-actuationproblem,acycliccontrolstrategyisdenedandcontrolcommandsareissuedatthebeginningofeachcycleaimingtowardsreducingtrackingerrorattheendofthecycle.Thisessentiallyincreasesthemanipulabledegreesoffreedominthecongurationspace.Subsequently,aseriesofsimulationtestsareconductedtoobtainasimplecontrolfunction.Closed-loopcontrolsimulationsyieldsatisfactorypathfollowing 90

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results.Nonetheless,basedontheexistingmodelarchitecture,furtherstudyonthehydrodynamicinteractionscouldpotentiallyuncoverothercontrolfunctionswithanimprovedenergyeciency.Inthethirdpartofthedissertation,amobilelidarsystemisdevelopedforroadmarkingsurvey.Incorporatedwithapositioningsystem,alidarsensorismountedonavehicularplatformandperformslaserscansasthevehicleisbeingdrivenalongthestreets.Thelidarpositionandorientationaredesignedtominimizegapsbetweenconsecutivescansandguaranteeanacceptablesurveyingspeed.Utilizingthescanninggeometry,pointsofinterestinthelidarscanareidentiedandasurveymapisformulated.Curbs,obstacles,roadsurfaces,andreectivepavementmarkingsareextracted.Surveyingtestsdemonstratessatisfactoryresults.Withthesurveymap,furtherdataprocessingandfeatureextractionsmaybedevelopedtoretrieveadditionalinformation.Throughoutthedissertation,understandingofthegoverningphysicsissoughtafterandisthenutilizedtosolveeachoftheproblems{whetheritistoimitatethefunctionalityofthebiologicallaterallinesystemwithapressuresensorysystem,tomodelandcontrolash-likeswimmer,ortodevelopamobilelidarsystemforroadmarksurveying.Howeverapparentthismayseem,itisoftentimesignoredandevenforgottenasoverwhelmingmathematicalequationsandexperimentaldataareaccumulatedduringresearchstudies.Simplicationsofmathematicalmodelsandmanipulationsofnumericaldatashouldneverbeimplementedwithoutconsultingtotheirunderlyingphysicalinterpretation.Ultimately,suchaseeminglytediouspracticewillbenetthedevelopmentofengineeringsystemswithwell-understoodbehaviorsandperformances. 91

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APPENDIXAPROOFOFTHEOREM1Tofacilitatesubsequentanalysis,fromthedenitionsin( 2{43 2{43 )and( 2{44 2{44 ),thetimederivativefortheRISEfeedbacksignal(t)iswrittenas _=3e3+sgn(e2)+e2:(A{1)Substitutingthecontrolinputfrom( 2{42 2{42 )into( 2{40 2{40 )yieldstheclosed-looperrorsystem Me3=efD+fN)]TJ /F14 11.9552 Tf 11.955 0 Td[(;(A{2)whosetimederivativecanbeexpressedas M_e3=NB)]TJ /F3 11.9552 Tf 11.955 0 Td[(3e3)]TJ /F3 11.9552 Tf 11.955 0 Td[(sgn(e2))]TJ /F8 11.9552 Tf 11.955 0 Td[(e2;(A{3)whereNB(t)2R3isdenedas NB=_efD+_fN:(A{4)Severalpropertiesandassumptionsareusefulfortheproof. Property1. ThetransformationmatrixJ()isorthogonal,anditsEuclideannormequals1,i.e., J)]TJ /F4 7.9701 Tf 6.587 0 Td[(1()=J>();kJ()k=kJ>()k=1:(A{5) Property2. TheinertiamatrixMissymmetricandpositivedenite.ThereexistspositiveconstantscM1;cM22Rsuchthat8"2R3, cM1">"">M"cM2">":(A{6) Assumption1. ThesignalNB(t)anditstimederivativeareboundedbyknownpositiveconstantsc1;c22R kNB(t)kc1;k_NB(t)kc2:(A{7) 92

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Proof. DeneanauxiliaryfunctionQ(t)2Rtobe Q=ke2(0)k1)]TJ /F8 11.9552 Tf 11.955 0 Td[(e>2(0)NB(0))]TJ /F3 11.9552 Tf 11.955 0 Td[(L;(A{8)whereL(t)2Risdenedas _L=e>3[NB)]TJ /F3 11.9552 Tf 11.955 0 Td[(sgn(e2)];L(0)=0:(A{9)Substituting( 2{39 2{39 )intoexpressionofLgivesL(t)=Zt0_e>2()NB()d)]TJ /F10 11.9552 Tf 11.956 16.272 Td[(Zt0_e>2()sgn(e2())d+Zt02e>2()[NB())]TJ /F3 11.9552 Tf 11.955 0 Td[(sgn(e2())]d=[e>2()NB())]TJ /F3 11.9552 Tf 11.956 0 Td[(ke2()k1]t=0)]TJ /F10 11.9552 Tf 11.955 16.272 Td[(Zt0e>2()_NB()+Zt0[e>2()2NB())]TJ /F3 11.9552 Tf 11.955 0 Td[(2ke2()k1]dke2(0)k1)]TJ /F8 11.9552 Tf 11.955 0 Td[(e>2(0)NB(0))]TJ /F1 11.9552 Tf 11.955 0 Td[(()]TJ /F3 11.9552 Tf 11.955 0 Td[(c1)ke2(t)k)]TJ /F10 11.9552 Tf 11.955 16.273 Td[(Zt0(2)]TJ /F3 11.9552 Tf 11.955 0 Td[(2c1)]TJ /F3 11.9552 Tf 11.956 0 Td[(c2)ke2()kd: (A{10)Thus, Q(t)()]TJ /F3 11.9552 Tf 11.955 0 Td[(c1)ke2(t)k+Zt02()]TJ /F3 11.9552 Tf 11.955 0 Td[(c1)]TJ /F3 11.9552 Tf 14.354 8.088 Td[(c2 2)ke2()kd:(A{11)Ifisdesignedsuchthat c1+c2 2;(A{12)then Q(t)0;8t0:(A{13)Denesignalu(t)2R10as u=e>1e>2e>3p Q>:(A{14) 93

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LetDR10beadomaincontainingu(t)=0101,andletV(u;t):D[0;1)!Rbeacontinuouslydierentiable,positivedenitefunctionas V=1 2e>1e1+1 2e>2e2+1 2e>3Me3+Q;(A{15)whichsatises W1(u)V(u;t)W2(u):(A{16)FunctionsW1(u);W2(u)2Rarecontinuous,positivedenite,radiallyunboundedfunctionsonDdenedas W1(u)=1 2minf1;cM1gkuk2;W2(u)=1 2maxf1;cM2gkuk2:(A{17)Thetimederivativeof( A{15 A{15 )canbewrittenas _V=e>1_e1+e>2_e2+e>3M_e3+_Q=e>1J()e2)]TJ /F3 11.9552 Tf 11.955 0 Td[(1ke1k2)]TJ /F3 11.9552 Tf 11.956 0 Td[(2ke2k2)]TJ /F3 11.9552 Tf 11.955 0 Td[(3ke3k2)]TJ /F3 11.9552 Tf 21.918 0 Td[(W3(u):(A{18)wherethefunctionW3(u)2Risdenedas W3(u)=minf1)]TJ /F1 11.9552 Tf 13.15 8.088 Td[(1 2;2)]TJ /F1 11.9552 Tf 13.151 8.088 Td[(1 2;3gkqk2;(A{19)andq(t)2R9isdenedas q=e>1e>2e>3>:(A{20)Providedthat1>1=2and2>1=2,anychoiceofthedomainDR10willensurethefunctionW3(u)tobecontinuousandpositivesemi-deniteonD.Theinequalitiesin( A{16 A{16 )and( A{18 A{18 )canbeusedtoshowthatV(u;t)2L1inD;hence,e1(t);e2(t);e3(t)2L1inD.Duetotheboundednessofthedesiredtrajectoryanditsderivatives,onecanshowfrom( 2{34 2{34 ),( 2{36 2{36 ),( 2{37 2{37 ),( 2{38 2{38 ),and( 2{39 2{39 )that(t);d(t);(t);_e1(t);_e2(t)2L1inD;thus,e1(t)ande2(t)isuniformlycontinuousinD.With( 2{42 2{42 ),( 2{43 2{43 ),and( 2{44 2{44 ),itisobviousnowthatthecontroltorque(t)2L1inD.Therefore,using( A{3 A{3 ),onecanshowthat_e3(t)2L1inD;hence,e3(t)isuniformly 94

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continuousinD.Fromdenitionsin( A{19 A{19 )and( A{20 A{20 ),functionW3(u)isuniformlycontinuousinD.InvokingTheorem8.4in[ 97 97 ]gives limt!1W3(u(t))=0;8u(0)2D:(A{21)FromthefactthatW3(u)asymptoticallyconvergestozero,theglobaltrackingresultdescribedin( 2{45 2{45 )canbeobtained. Remark1. Thedierentialequationsin( A{3 A{3 )and( A{9 A{9 )havediscontinuousrighthandsides.However,theexistenceanduniquenessofthesolutioncanstillbeshownaccordingto[ 98 98 ]and[ 99 99 ],andissummarizedin[ 100 100 ]forRISE-basedcontrollers. Remark2. Althoughthestabilityanalysishasprovedaglobalresult,itisoftentruethattheunmodeledforcesandmomentsaredependentonthesystemstates,andhencecertainupperboundsfor( A{7 A{7 )mightnotholdglobally,inwhichcasetheresultreducestobesemiglobal. 95

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APPENDIXBUSEFULRESULTSFORFISH-LIKESWIMMERMODELListedbelowaresomeresultsfromthegeometricmodelthatareimportantforthedynamicsofthesh-likeprole.Thelengthl02RofthecamberlineS00canbeobtainedasl0=ZS00jdzj=40ic0+a2 ic0: (B{1)TheareaA12RoftheregionDSis A1=ZZDSdA=1 2iIS1zdz=4r2c131(1)]TJ /F1 11.9552 Tf 11.955 0 Td[(1) (21)]TJ /F1 11.9552 Tf 11.955 0 Td[(1)2:(B{2)Assumingthattheprolehasauniformdensity2R,themassM12Roftheprolecanbeexpressedas M1=A1:(B{3)ThemomentofinertiaI012Rabouttheoriginis I01=ZZDSjzj2dA= 4iIS1z2zdzr2c1(r2c1+2c1c1)[(r2c1)]TJ /F1 11.9552 Tf 13.012 3.155 Td[(c1c1)4)]TJ /F3 11.9552 Tf 11.955 0 Td[(a8] 2(r2c1)]TJ /F1 11.9552 Tf 13.012 3.155 Td[(c1c1)4:(B{4)Furthermore,thegeometriccenterzc12CofDSsatises zc1A1=ZZDSzdA=)]TJ /F1 11.9552 Tf 13.487 8.088 Td[(1 4iIS1z2dz=r2c1c1+a6c1 (r2c1)]TJ /F1 11.9552 Tf 13.012 3.155 Td[(c1c1)3:(B{5)Sincethedensityisuniformlydistributed,pointzc1isalsothecenterofmass,whichcanbewrittenas zc1=1+a2 2(2c1x)]TJ /F3 11.9552 Tf 11.955 0 Td[(a)c1xc1x+i1+a2 2(2c1x)]TJ /F3 11.9552 Tf 11.955 0 Td[(a)(c1x)]TJ /F3 11.9552 Tf 11.955 0 Td[(a)c1y:(B{6)ThemomentofinertiaIc12Raboutthecenterofmassis Ic1=ZZDSjz)]TJ /F3 11.9552 Tf 11.955 0 Td[(zc1j2dA=I01)]TJ /F3 11.9552 Tf 11.955 0 Td[(M1zc1zc1:(B{7) 96

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APPENDIXCHYDRODYNAMICMODELVALIDATIONThehydrodynamicmodelemployedinthisstudyisvalidatedbycomparingtoresultsfromexperimenttestsin[ 101 101 ].Theexperimentisrecreatedwiththesamehydrodynamicsimulationmodelforthesh-likeswimmer.Referto[ 72 72 ]forfurtherdetailsonthedevelopmentofthenumericalmodel.Intheexperiment,arigidhydrofoil(NACA0012)istowedacrossawatertankataconstantspeedU02Rwhilebeingactuatedfortime-varyingpitchandheavemotions.Thechordlengthofthefoilis0:1mandthespanis0:6m.Themotionattimet2Rcanbedescribedinthecrosssectionplane(x;y)2R2as x=U0t;y=y0sin(!t);=0sin(!t+ );where2[0;2)Rdenotesthepitchangle,!2Rdenotestheangularfrequencyofthemotion,y0;02Rarethemagnitudesofheaveandpitchmotions,and 2Risthephaselagbetweenthetwo.Theparametersofthemotionarefurtherdescribedbytheangleofattack2RandtheStrouhalnumberas =)]TJ /F1 11.9552 Tf 11.956 0 Td[(tan)]TJ /F4 7.9701 Tf 6.587 0 Td[(1_y U0;St=!y0 U0:Inthetests,thefollowingparametersareused: U0=0:4m=s;y0=0:1m; ==2:Withdierentmaximumanglesofattackmax2RandStrouhalnumbersSt,experimenttestsarecarriedoutmeasuringtheinstantaneousthrustcreatedbythemotionofthehydrofoil,asshowninFigure C-1 C-1 .Thesamesetofmotionsareproducedonthesamerigidhydrofoilinsimulationusingthehydrodynamicmodeldevelopedforthesh-likeswimmer.AsillustratedinFigure C-2 C-2 ,theinstantaneousthrustfromsimulation 97

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generallyagreeswiththeexperimentresults.Inaddition,thethrustcoecientsforvariousmaximumangleofattackandStrouhalnumberarealsoprovidedin[ 101 101 ].Figure C-3 C-3 showsthecomparisonbetweentheexperimentandthesimulation,whichfurthervalidatesthehydrodynamicmodel. A B C DFigureC-1. Instantaneousthurstonthehydrofoilfromexperimenttestin[ 101 101 ].ThethrustvectorsareobtainedforvariousmaximumanglesofattackmaxandStrouhalnumberSt.A)max=15,St=0:4.B)max=35,St=0:4.C)max=15,St=0:6.D)max=35,St=0:6. A B C DFigureC-2. Instantaneousthrustonthehydrofoilfromsimulationtest.ThethrustvectorsareobtainedforvariousmaximumanglesofattackmaxandStrouhalnumberSt.A)max=15,St=0:4.B)max=35,St=0:4.C)max=15,St=0:6.D)max=35,St=0:6. 98

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A BFigureC-3. Thrustcoecientscomparisonbetweenexperimentandsimulationtests.ThecontourplotsarepresentedwithvariousmaximumanglesofattackmaxandStrouhalnumberSt.A)Experimentresultsfrom[ 101 101 ].B)Simulationresults. 99

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BIOGRAPHICALSKETCHYimingXureceivedtheB.S.degreeinmechatronics,robotics,andautomationengineeringfromZhejiangUniversity,Hangzhou,Chinain2010.In2012,hereceivedtheM.S.degreeinmechanicalengineeringfromtheUniversityofFlorida,Gainesville,FL,USA,whereheiscurrentlyworkingtowardthePh.D.degree.Hiseldsofresearchincludecomputervision,dynamicalsystemmodelingandanalysis,nonlinearcontroldesignandstabilityanalysis,anddataacquisitionandprocessing. 108