DESIGN,DEVELOPMENT,ANDMODELINGOFAWIRELESSLYCHARGED ROBOTICFISH By HusseinNaeemHasan ATHESIS Submittedto MichiganStateUniversity inpartialentoftherequirements forthedegreeof MechanicalEngineering-MasterofScience 2015 ABSTRACT DESIGN,DEVELOPMENT,ANDMODELINGOFAWIRELESSLY CHARGEDROBOTICFISH By HusseinNaeemHasan Inthepasttwodecades,robotichavereceivedtinterestduetotheirvarious perceivedapplications.Designingroboticisachallengingtask,partlyduetothedelicate needofwaterproInaddition,oneneedstooptimizethehydrodynamicperformance whileaccommodatingtheconstraintsonsize,cost,andfeasibilityofmanufacturing. Inthiswork,twobio-inspiredroboticprototypespropelledbyapairofpectoral andacaudalhavebeendeveloped.Theprototypehasbeenusedasatoolformod- eling,control,andeducationalpurposes.Thesecondonewillbeusedforamuseumexhibit attheMSUMuseum.Fortheserobots,anoveldesignforpectoralispresented,which hasdemonstratedexcellenthydrodynamicperformance.Theroboticismathematically modeledbyincorporatingtherigidbodydynamicswithhydrodynamicsofthecaudaland pectoralwhicharecapturedwithLighthill'selongated-bodytheoryandbladeelement theory,respectively.Themathematicalmodelisvalidatedexperimentally. Forthesecondroboticsh,awirelesschargingsystemhasbeendeveloped.Amathe- maticalmodelforthewirelesschargingsystemispresentedandvalidatedbyexperimental results.Anautomaticdockingsystemisalsodeveloped,whichliftstheroboticoutof waterforwirelesschargingandplacesitbackinwaterafterwards. Finally,awebcam-basednavigationsystemfortheroboticispresented.Thesystem isdesignedtoallowinteractionsbetweenauserandtherobot.Theusercanassignatarget pointanywhereintheworkingareaofthetank,andtheroboticwilltrackthattarget. Copyrightby HUSSEINNAEEMHASAN 2015 ToeverymartyrwhohassacindefenseofIraq,tomyparents,andmyfamily... iv ACKNOWLEDGMENTS Iwouldliketoexpressmybestgratitudetomyadvisor,Prof.XiaoboTan,forhisenthusiastic encouragementandwonderfulguidanceduringmymaster'sstudy.Iamverygratefulforhis time,advices,andformetopursuemyacademicstudy. IwouldliketothankProf.GuomingZhuandProf.JongeunChoi,forkindlyconsenting tojoinmythesiscommittee.IwouldliketothankMr.CraigGunn,fortakingthetime toeditmywork.IamgratefultomylabmatesinSmartMicrosystemsLabatMichigan StateUniversitywhohavehelpinvariousways:OsamaEn-Nasr,SanazBehbahani, MohammedKhalid,MontassarSharif,CodyThon,andmanyothers.Iwouldliketogive specialthankstoJohnThon,forhishelptoputtouchesonbalancing,sealing,and paintingoftheroboticprototypes,whichenablesmetofocusonotherpartsofmy projectdevelopment.Also,IwouldliketoacknowledgeLexieRobertsforherworkonthe softwarepartofthemuseumrobotic.Ialsowouldliketothankthetechnicaland administrativeofbothMEandECEDepartmentsfortheirassistanceduringmystudy atMichiganStateUniversity,inparticular,BrianWright,GreggMulder,RoxannePeacock, andAlainaBurghardt.IwouldliketoacknowledgetheHigherCommitteeForEducation DevelopmentinIraq(HCED)forgivingmethewonderfulopportunityofscholarshipto completemystudy.AlsoIwanttoacknowledgethesupportofmyresearchby NationalScienceFoundation(CCF1331852,IIS1319602,IIP1343413,andECCS1446793). Last,butnotleast,Iamforemostthankfulformyfamilyfortheirsupportandpatience duringmystudy.Iwouldliketoexpressmyultimategratitudetomyparents,brothers, sistersfortheireverlastingsupporttopursuemydreams.Iamgratefultomywifeand daughtersfortheirlove,supportandencouragement. v TABLEOFCONTENTS LISTOFTABLES .................................... viii LISTOFFIGURES ................................... ix Chapter1Introduction ............................... 1 1.1Motivation.....................................1 1.2LiteratureReview.................................2 1.3ThesisContributions...............................4 1.3.1RoboticFishDevelopment........................4 1.3.2DynamicModelfortheRoboticFish..................5 1.3.3TheWirelessChargingandtheDockingMechanism..........5 1.3.4Webcam-basedAutonomousNavigationSystem............8 1.4Organization...................................8 Chapter2DesignandImplementationoftheRoboticFish ......... 10 2.1TheFirstRoboticFishPrototype........................10 2.1.1MechanicalStructure...........................11 2.1.1.1PectoralFinDesign......................12 2.1.1.2TailFinDesign.........................14 2.1.2ElectricalSystem.............................16 2.1.2.1Hardware............................16 2.1.2.2SoftwareArchitecture.....................18 2.1.3SystemAssembly.............................19 2.2RoboticFishforMuseumExhibit........................19 2.2.1MechanicalStructure...........................21 2.2.2ElectricalSystem.............................21 2.2.3WirelessChargingSystem........................23 2.2.3.1TheTransmitterandReceiverCircuits............23 2.2.3.2ChargingStation........................23 2.2.4NavigationSystem............................25 2.3EducationandOutreachActivitiesUsingthe RoboticFish....................................26 Chapter3MathematicalModel .......................... 28 3.1Introduction....................................28 3.2RigidBodyDynamics..............................29 3.3HydrodynamicForcesandMoments.......................32 vi 3.3.1BladeElementTheory..........................32 3.3.2Lighthill'sLargeAmplitudeElongated-bodyTheory..........35 3.3.3DragandLiftontheRobotBody....................39 3.4ExperimentalValidationoftheDynamicModel................40 3.4.1ParameterIden.........................43 3.4.2SimulationandExperimentalResults..................45 3.5ComparisonofMulti-SegmentVersusRigidPectoralFins...........47 Chapter4AWirelessChargingSystemforRoboticFish .......... 49 4.1Introduction....................................49 4.2MathematicalModel...............................51 4.3TheChargingStation...............................54 4.4SimulationandExperimentalResults......................55 4.4.1SystemParameters............................55 4.4.2Results...................................57 Chapter5Webcam-basedAutonomousLocalization,NavigationandDock- ingforRoboticFish ........................... 62 5.1Introduction....................................62 5.2SystemComponentsandAlgorithms......................63 5.2.1ImageProcessingUnit..........................64 5.2.2UserInterfaceUnit............................65 5.2.3NavigationUnit..............................66 5.2.4TemperatureMappingUnit.......................67 5.2.5AutonomousDockingUnit........................70 5.3Discussion.....................................72 Chapter6ConclusionandFutureWork ..................... 73 6.1Conclusion.....................................73 6.2FutureWork....................................74 BIBLIOGRAPHY .................................... 75 vii LISTOFTABLES Table2.1Listofcomponentsusedintheroboticprototype.........17 Table3.1Parametervaluesofthebodyforsimulation..............42 Table4.1Mechanicalandelectricalcomponentsofthechargingstation.....55 Table5.1Listoftheroboticnavigationsystemcomponents.........72 viii LISTOFFIGURES Figure1.1ofswimmingmethods:(a)BCFpropulsionand(b) MPFpropulsion(Adaptedfrom[1,2])..................3 Figure1.2RoboticprototypedevelopedintheSmartMicrosystemsLabat MichiganStateUniversity:(a)themainpartsoftherobotic prototype;(b)aswimmingtestinanindoortank...........6 Figure2.1Thedesignoftheshelloftheroboticbody..........12 Figure2.2Thefourbasicmotionsofthepectoral[3]..............13 Figure2.3Thedesignofthepectoral.....................15 Figure2.4Designofthe3D-printedtail....................15 Figure2.5Thelayoutofthemaincircuitboard..................17 Figure2.6Thesoftwarearchitecture........................18 Figure2.7Assembledroboticprototype:(a)fourviewsoftheassembled prototypeanditscomponentsbeforesealingandpainting,(b)the roboticaftersealingandpainting...............20 Figure2.8ThemuseumroboticprototypedevelopedintheSmartMicrosys- temsLabatMichiganStateUniversity.................21 Figure2.9Museumrobotic(a)circuitboardlayout,(b)thesoftwarearchi- tecture...................................22 Figure2.10Thechargingstation:(a)thechargingstationwiththerobotic (b)theelectricalcircuitryofthechargingstationwiththewireless chargingmodule(ModelNo.(18579694)fromShenzhenTaidaCen- turyTechnologyCo.)...........................24 Figure2.11Aschematicrepresentationofthetrackingsystem...........25 ix Figure2.12Participationoftheroboticprototypeinthe2015MSUSci- enceFestival................................27 Figure3.1Schematictopviewoftheroboticsh'sbodywithapairofpectoral andatail............................30 Figure3.2oftheroboticwithpectoralandtaila)Schematic representationoftheroboticwithpectoralandtail b)Sideandtopviewsoftheentirepectoralandbladeelementof thepectoralwithassociatedforcesandanglesrespectively.....33 Figure3.3ExperimentalsetupwiththeMotionCaptureSystems........42 Figure3.4Simulationandexperimentalresultsoftheforwardvelocity......45 Figure3.5Simulationandexperimentalresultsoftheturningperiod.......46 Figure3.6Simulationandexperimentalresultsoftheturningradius.......46 Figure3.7Experimentalresultsonthecomparisonoftheturningperiodofthe roboticwhenusingmulti-segmentpectoralandrigidpectoral respectively..............................48 Figure3.8Experimentalresultsonthecomparisonoftheturningradiusofthe roboticwhenusingmulti-segmentpectoralandrigidpectoral respectively..............................48 Figure4.1Schematicrepresentationofthewirelesschargingsystem.......51 Figure4.2Magneticresonantsystemequivalentcircuit,adaptedfrom[4]....52 Figure4.3Thedevelopedwirelesschargingstation.(a)chargingstationholding therobotic(b)thereceivercoilinsidethebodyoftherobotic (ModelNo.(18579694)fromShenzhenTaidaCenturyTechnologyCo.).56 Figure4.4vs.separationdistance....................58 Figure4.5Mutualinductanceandcouplingfactorvs.separationdistance....59 Figure4.6Simulationandexperimentalresults:(a)inputpowervs.separation distance;(b)outputpowervs.separationdistance...........60 x Figure4.7Simulationandexperimentalresults:(a)inputcurrentvs.separation distance;(b)outputcurrentvs.separationdistance..........61 Figure5.1Schematicrepresentationofthelocalizationandnavigationsystemof theroboticwiththetargetpoint..................64 Figure5.2Theuserinterfacelayout.........................66 Figure5.3Targettracking:(a)plotofthetrajectorywiththeinitialandtarget points,(b)snapshotsoftheroboticswimminginthetank....68 Figure5.4Thewchartofthecontrolalgorithm.................69 Figure5.5Dockingtrajectory:(a)2-Dplotofthetrajectorywiththeprescribed targetpoints,(b)snapshotsoftheroboticautonomousdocking.71 xi Chapter1 Introduction Inthepastfewdecades,eunderwaterrobots,namelyrobotichavebeengiven tattentionduetothehighdemandforunderwaterapplications.Thewiderange ofunderwaterapplications,suchas,aquaticsystemsmonitoring,underseaexploration,and defenseapplications,providetpotentialopportunitiesforresearch[5{10].Inspired bytheamazingswimmingabilities/attributesoflivebiologists,mathematicians,and engineershaveconductedvastresearchtryingtounderstand,model,design,andcontrol roboticinantomimicreal[11{29].Theseroboticshtendtohavehigher andmaneuverabilitycomparedwithrotarypropeller-actuatedunderwatervehicles usingthesamelevelofpowerconsumption[11]. 1.1Motivation Fishareveryimpressivecreaturesandtswimmers.Theypropelthemselvesbya harmonicmotionoftheirbodies,tails,andTherefore,theyhaveveryentpropulsion mechanismsandhighmaneuveringabilities;thatmakestheroboticaveryattractive researchsubjectforbothbiologicalandrobot-designengineeringcommunities[12].Re- searchershavecarriedoutmanysuccessfulattemptsindesigningandcontrollingrobotic Manymodelsandmethodshavebeendevelopedtomimictheswimmingpatternsof realIntheearlierresearch,rotarypropellerswereusedtoactuatetheunderwater 1 roboticvehicles[13].Propellerswerearguablythemostcommonactuatorsthatresearchers coulduseinunderwaterrobots.Whileitwasasuccessfulstepintheusingthepro- pellersinunderwaterrobotsmadethemlessetandhavelessmaneuverability.Inorder todesignmoretandmaneuverablerobotsthatmimicrealconsiderableresearch hasbeendonetotwaystoactuatetherobotic[14{32]. 1.2LiteratureReview Inrecentyears,tinteresthasbeengivenfordevelopingbionicrobots.Robotic havebeenoneofthemostinterestingbiomimeticrobotsintheSupportedby therapidprogressintechnology,robotichavepassedverysuccessfulstepsintermsof mechanicaldesign,modelingmethods,andcontrollingalgorithms.Withthisfastprogress, researchersarefocusingonminiaturizingthebodyandaddingmultiplesensingfeaturesto therobotictoserveasaversatileplatformthatcanbeusedinmanyapplicationssuch asaquaticsystemsmonitoring. Giventhedrawbacksoftherotarypropellers,researchersstartedseekingquiet,feasible toimplementinthedesignandcontrol,andmorerealisticactuationmethods.Theyhave developedroboticthatcanpropelthemselvesbytailpectoralorboth[13{29]. Mostoftheroboticprototypeswereaimedtomimicthemorphologicalfeaturesof realRealusebodyand/orcaudal(tail)n(BCF),mediumand/orpaired (MPF)locomotion,orbothforpropulsion.Breder[1]proposedaofreal swimmingmethods.Figure1.1showsthemainswimmingmethods.TheBCFlocomotion isusedforhighforwardthrustandaccelerationwhiletheMPFlocomotionisusedfor maneuverabilityandlowspeedpropulsion[11].Whilemuchoftheliteratureresearchhas 2 focusedoninvestigatingeithertheBCForMPFlocomotionoftheroboticsomeresearch groupshavedevelopedprototypeswithbothBCFandMPFpropulsion.RoboTunawasthe successfulerobotthatwaspropelledbythetail[26,27].Sixbrushlessmotors andanassemblyofstringsandpulleyswereusedtoproducethetailoscillatorymovement todrivearelativelylarge,49-inchbodyoftherobot.ZhouandLow[28,29]designeda roboticthatcanpropelitselfbyundulatorythataredrivenbyasetofservomotors. Undulatoryshavetheabilitytopropelroboticforwardandbackwardbychanging thepatternofwaves.Yang etal. [30]usedpectoraltopropeltheirrobotic whichwascomposedofabodyandtwolateralswithoutatail Exploitingthetremendousdevelopmentintheengineeringresearchershavealso usedsmartmaterialsasnoiselessactuationmethods.Rossi etal. [31]usedshapemem- oryalloys(SMAs)toactuatetheirmotor-lessroboticIonicpolymer-metalcomposite Figure1.1:ofswimmingmethods:(a)BCFpropulsionand(b)MPF propulsion(Adaptedfrom[1,2]). 3 (IPMC)wasalsousedtoactuaterobotic[19,32,33]. 1.3ThesisContributions Mostoftheresearchintheliteraturehasfocusedondevelopingroboticthatcan closelymimicthemotionofrealwhichoftenleadstoincreasedsizeandcostofthe robots.Inthisthesiswepresentfourcontributionsasfollows. 1.3.1RoboticFishDevelopment ThetworoboticprototypespresentedinthisthesisutilizeboththeBCF(tail)and MPF(pectorallocomotionforachievingactuationandmaneuverability.Eachrobotuses onlythreeactuators(servomotors):oneservomotorforthetailandtwoservomotorsfor thepectoralTherefore,thesizeandcostarekeptlowandtherobotsrequirelowpower consumption.Toachievegoodhydrodynamicperformanceforthepectoraloftherobotic researchershaveexploredmanydesigns,suchasrigidpectoralpectoral andpectoralwithiblejoints[3,11,34].Inthiswork,anoveldesignforthepectoral ispresented.Thepectoralis3D-printedandmadeofarigidplasticmaterialonly; however,ithasdemonstratedexcellenthydrodynamicperformance.Figure1.2(a)showsa roboticprototypedevelopedintheSmartMicrosystemsLab(SML)atMichiganState University.Thisroboticisusedformodeling,control,andeducationalpurposeswhile thesecondroboticprototypewillbeusedforanexhibitattheMichiganStateUniversity Museum.Figure1.2(b)showsthesameroboticswimminginatestingtank.The roboticisequippedwithaninertialmeasurementunit(IMU),atemperaturesensor, afuelgaugesensor,andawirelesscommunicationmodulewhilethesecondrobotic 4 prototypeisequippedwithextrafeatures,suchasawirelesschargingsystemandanIR switch. 1.3.2DynamicModelfortheRoboticFish Theroboticprototypehasbeenusedasatoolformodelingandcontrol.The roboticismathematicallymodeledbyincorporatingtherigidbodydynamicswithhy- drodynamicsofthepectoralnsandthecaudalwhicharecapturedwithbladeelement theoryandLighthill'slarge-amplitudeelongated-bodytheory,respectively.Toreducethe modelcomplexity,thecaseofrigidcaudalandpectoralisconsidered.Inaddition,to verifythehydrodynamicperformanceoftheproposeddesignforpectoralacomparison betweenitsperformanceandthatofplain,rigidisprovided.Themathematicalmodel isvalidatedexperimentally. 1.3.3TheWirelessChargingandtheDockingMechanism Foralmostallapplicationsofroboticrechargeablebatterieshavebeenusedasa powersupply.Forarobotictofunction,thebatterieshavetoberoutinelyrecharged. Rechargingbatterieswithregularcordchargersisachallengingtaskwhentheroboticis requiredtobeautonomousandstayintheInthiswork,weproposeawirelesscharging stationforanindoorroboticWhentherobotneedstoberecharged,itwillswim autonomouslytothechargingstationandtherechargingprocesstakesplacewirelessly.The principleofwirelesspowertransferuseselectromagneticinduction.Wirelesspowertransfer waspioneeredbyNikolaTeslaintheearly19thcentury.Heperformedsomeexperimentsto lightlampsseveralkilometersaway[35].Duetothelowofwirelesspowertransfer 5 (a) (b) Figure1.2:RoboticprototypedevelopedintheSmartMicrosystemsLabatMichigan StateUniversity:(a)themainpartsoftheroboticprototype;(b)aswimmingtestin anindoortank. 6 andsomeproblems,Tesla'sexperimentsweresuspendedwithoutbeingexploited commercially.Afteralmosttwocenturies,Aristeidis etal. [36,37]conductedresearchto achievewirelesspowertransferof60wattsover2metersusingstronglycoupledmagnetic resonance(SCMR).Thistresultprovedthefeasibilityofwirelesspowertransfer overamid-rangedistanceusingarelativelysmallapparatus.Benjamin etal. [38]investigated wirelesspowertransferusingmagneticresonancecouplingforsingleandmultiplereceivers, where50%ofpowertransferwasachieved.Basset etal. [39]proposedwireless poweringandcontrolofamicrorobotbyusinginductivecoupling.Inductivecouplingutilizes theresonancecouplingbetweenthetransmitterandthereceiver,whichareboth LC circuits.Theresonancehappensbetweentheinductorandthecapacitorataparticular frequencycalledtheresonancefrequency ! .Thetransmitterandreceiverhavetofaceeach otherwithashort-to-mediumseparationbetweenthemtohighinpower transfer.Thisprincipleisutilizedtobuildthewirelesschargingsystemfortherobotic presentedinthisthesis. Thewirelesschargingsystemoftheroboticfacestwochallenges.Thechallenge isthat,therobotichasnobrakes,thusitwillnotstopexactlyataparticularposition andwilldriftawayduetothecontinuityofmotioninthewater.Therefore,itishardtoput thereceiver,whichisinsidetheroboticandthetransmitter,whichisoutside,faceeach other.Thesecondchallengeisthat,puttingthereceiverinthewaterstheinductance ofthecoil;thus,theresonancefrequencywillbechangedandthatwilldecreasethe ofthesystem.Inordertosolvethesetwochallenges,anovelliftingsystem(chargingstation) isproposedtoholdtheroboticinaproperwayandliftitoutwater,makingthe transmitterandreceiveralignedtogivemaximumofwirelesspowertransfer.The liftingsystemconsistsofalinearsliderandactuator,aholdingbox,andacontrolcircuit 7 featuredwithwirelesscommunicationandIRswitching. 1.3.4Webcam-basedAutonomousNavigationSystem Todrivetherobotictothechargingstation,awebcam-basedautonomouslocalization andnavigationsystemhasbeendeveloped.Thesystemutilizesanoverheadcamera(we- bcam)andimageprocessingtechniquestotracktwomarkersplacedonthebodyofthe roboticTheoverheadcameraisusedtocapturealivevideofortheroboticand itsenvironmentandsendittothemainstation(aPC).Theimageprocessingtechniques areusedtoanalyzethevideotodetectandextractthepositionandorientationofthetwo markers,basedonwhichthepositionandorientationofroboticaredetermined.By obtainingthepositionandorientationoftheroboticthelattercanbecontrolledto swimtodockatthechargingstation.Inadditiontothat,theautonomouslocalizationand navigationsystemfurtherallowstherobottotrackanyassignedtargetpointwithinthe swimmingareaofthetank.Inparticular,ausercanchangethetargetpointbytouching ascreen,whichshowsthelivevideooftheroboticanditsenvironmentasmentioned above;andtheroboticwillautonomouslyswimtothattargetpointintheswimming tank.Theextractedpositionandorientationdataoftheroboticareusedasinputsto thetargettrackingandnavigationalgorithmtoachievethetask. 1.4Organization Thisthesisisorganizedasfollows.InChapter2,thedesignanddevelopmentofthe proposedroboticprototypesarediscussed.InChapter3,adynamicmodelforthe roboticactuatedbytailandpectoralispresented.InChapter4,theproposed 8 wirelesschargingsystemfortheroboticisdescribed.Chapter5focusesonthewebcam- basedlocalizationandnavigationsystemwithautonomousdocking.Conclusionsandfuture workarepresentedinChapter6. 9 Chapter2 DesignandImplementationofthe RoboticFish Duringthepastfewdecades,roboticdevelopmenthaspassedveryimportantsteps.In additiontothencyandmaneuverability,cost,size,powerconsumption,andfeasibility ofmanufacturingarealsocriticalfactorsthathavetobeoptimizedduringthedevelopment process.Thechapterisorganizedasfollowing.InSection2.1,adetaileddescriptionof theroboticprototypeisgiven.InSection2.2thesecondroboticbuiltforthe museumexhibitispresented.InSection2.3educationandoutreachactivitiesusingthe roboticarepresented. 2.1TheFirstRoboticFishPrototype Theroboticisdesignedtoserveasaplatformforstudyingmodeling,control,and mobilesensingofroboticinanindoorenvironment.Cost,size,andpowerconsumption playcriticalrolesindesigningsuchasimple,miniature,androbustroboticsystem.The prototypehasatotallengthof0.28m(includingthetailThebody'slengthis0.2m whilethetaillengthis0.08m.Inadditiontothat,theprototypehasapairofpectoral Thepectoralaremadeonlyfromrigidplasticmaterial,buttheyaredesignedto changetheirshapesspanwisetoproducesmoothhydrodynamicperformance.Therobotic 10 prototypeisequippedwithawirelesscommunicationmodulefordatatransmission andremotecontrol,atemperaturesensor,apowermeasurementunit,and10degree-of- freedom(DOF)inertialmeasurementunit(IMU).Allthetailandpectoralareactuated byservomotors. 2.1.1MechanicalStructure Inordertodesignandbuildabiomimeticroboticoneneedstoaccommodatethe followingchallengingrequirementsforthebody: Itneedstobedesignedinastreamlinedshapetoprovidegoodhydrodynamicperfor- mance; Itmustbewaterproofedtoprotecttheelectricalcircuitsinsidetheshell; Itshouldberelativelysmallandcompacttoserveasaminiaturemobilesensingplat- form; Ithastobeaccessibleforserviceandmaintenanceoftherobotic Itneedstoprovideconvenientaccommodationoftheelectricalparts,actuators,sen- sors,andwiringconnections. Inordertoimplementalloftheabovelistedfeaturesinthebodyoftheroboticcomputer aideddesign(CAD)softwarewasusedtodesignthebody.Solidworkssoftwarewaschosen fordesigningtheprototypebecauseithaslotsofprofessionaltoolstobuild3Dmechanical parts.Figure2.1showsthedesignoftheshelloftheroboticbody. AfterthebodydesignwasanObjetConnex350Multi-Material3Dprinterwas utilizedtoprototypeit.Duringthedesignprocessweaccommodatedthebuoyancyand 11 Figure2.1:Thedesignoftheshelloftheroboticbody. balancingissuesbyaddingsomeemptycapsulesinsidethebody,whichcouldbeusedto houseleadbeadsforadjustmentofballastandbalance. 2.1.1.1PectoralFinDesign Biologicalusethepectoralinfourbasicmotionsthatcanbeas[11] Flappingmotion, Featheringmotion, Rowing(lead-lag)motion, Spanningmotion. Themotionofthepectoralissimilartothemovementofthebird'swing beating.Inthemotion,thepectoralpsintheverticalplaneasshowninFigure 2.2(a).Inthefeatheringmotion,thepectoralrotatesaboutthehorizontalaxisneartothe bodyasshowninFigure2.2(b).Rowing(lead-lag)motionhappensinthehorizontalplane. 12 Therowingmotionincludestwoparticularmovementsthatcalledthepowerstrokeand recoverystrokeasshowninFigure2.2(c).Inthespanningmotion,thepectoralshape changesspanwiseinboththepowerandrecoverystrokes.Inthepowerstroke,thepectoral extendswhileitcontractsintherecoverystrokeasshownin2.2(d).Accordingto Wang[11]andBlake[40,41],theandrowingmotionsareoscillatoryandtheyare modeledaslift-basedanddrag-basedlabriformmodes,respectively.Thelift-basedmode ismoretandsuitableforhigherspeedswhilethedrag-basedmodeismoret forslowerspeeds[11,42].Forhighhydrodynamicperformance,theshapeofthehas tobeoptimized.Theshapeofthehasatontheproductionofthrust. AccordingtoBlake[43],forthedrag-basedpropulsionmode,awedge-shapedbluntis moretthanarectangular-shapedduetothelowinterferencedragnearthebody. (a)Flapping (b)Feathering (c)Rowing (d)Spanning Figure2.2:Thefourbasicmotionsofthepectoral[3]. 13 Inthiswork,weproposeanoveldesignofapectoralthatemploysboththerowing andspanningmotionsusingonlyoneservomotorforactuation.Theproposedpectoral ismadeofarigidplasticmaterialonly.ItwasdesignedusingSolidworkssoftwareand3D- printedbythe3Dprinter.Forhydrodynamic,thepectoralwasdesignedasa wedge-shapedbluntwiththeapexofthewedgeconnectedtotheservomotorarmnear thebody.Thepectoralconsistsofesegments,theone(apexofthewedge)is thebasesegmentwhichisdirectlyconnectedtothearmoftheservomotor,whiletheother segmentsformthebody(bluntedge).Alloftheesegmentsareconnectedtogether byhingeswithrestrictionlocks,andthustheshapeisrestrictedtochangespanwiseonly. Inthepowerstroketheismechanicallyrestrictedbythehingesandlockstobehaveasa single-straightrigidplate,movingposteriorlynormaltothew,thusprovidingmaximum thrust.Ontheotherhand,thepectoralbendsinaparticularangleforeachsegment relativetothewintherecoverystroke.Eachsegment'sanglecontributestomakethe pectoralmovestangentiallytothew,whichtlyreducesthedragonthe Asaresult,theroboticgainspositivethrustoverthepectoralentirebeatcycle (bothpowerandrecoverystrokes).Figure2.3showsthethedesignofthepectoral 2.1.1.2TailFinDesign Thetailcanbemadefromarigidormaterial.Accordingto[44],theble tailismoretthantherigidone,butitismorecomplicatedtobemathematically modeled.Exploitingthecapabilitiesofthe3D-printingtechnology,wedesignedandprinted thetailwithbothrigidandmaterials.Figure2.4showsthedesignofthe3D- printedtail 14 Figure2.3:Thedesignofthepectoral Figure2.4:Designofthe3D-printedtail 15 2.1.2ElectricalSystem Forthecompactness,onesmallcircuitboardwasdesignedwithonemicrocontroller responsibleforhandlingallthecomputation,sensing,andactuationfunctionalitiesofthe roboticTheelectricalsystemconsistsoftwoparts,hardwareandsoftwarearchitecture. 2.1.2.1Hardware Asinglecircuitboardisusedtodoalloftheprocessingandcontroltaskswithone microcontroller.Thesetasksinclude,acquiringdatafromsensors,processingtherawdata, producingtheactuationsignals,andcoordinatingwiththemainstation(aPC).Themain circuitboardconsistsofseveralmodules.Eachmoduleisresponsibleforoneoftheafore- mentionedtasks.Amicrocontroller(dsPIC30f6014afromMicrochip)isusedasaprocessing unit.Thereisadigitaltemperaturesensor(DS18B20fromMaxim/DallasSemiconductor) andasmartbatterymonitoringsensor(DS2438fromMaxim/DallasSemiconductor),which bothworkwithone-wirecommunicationprotocol.Theunique1-wireinterfacerequiresonly oneportpinforcommunicationforallone-wiredevices,whichhavea64-bitaddressspace, allowingupto75devicestobefoundpersecond[45].Threewaterproofservomotorsfrom Hitectwo(HS-5086WP)forthepectoralandone(HS-5645WP)forthetailn,areused asactuators.AnXBeePro60mWWireAntenna(802.15.4)modulefromDigiisusedfor wirelesscommunication.Twovoltageregulatorsareusedforsupplyingpowertovarious onboardelements.A10DOFIMU(VN-100fromVectorNav)isadopted,whichincludes 3DOFaccelerometer,3DOFgyroscope,3DOFmagnetometer,and1DOFbarometer. Figure2.5showsthelayoutofthemaincircuitboard.Table2.1liststhedetailsofabove components. 16 Figure2.5:Thelayoutofthemaincircuitboard. Table2.1:Listofcomponentsusedintheroboticprototype. No. Componentname Componentmodel 1 Microcontroller Microchip,dsPIC30f6014a 2 Temperaturesensor MaximDS18B20,digitaltemperaturesensor 3 Batterymonitoringsensor MaximDS2438,smartbatterymonitor 4 Servomotors HS-5086WPandHS-5645WP,Hitecwaterproofservos 5 Wirelessmodule Digi,XBeePro60mWWireAntenna(802.15.4)module 6 Battery Batteryspace7.4V(1800mWh)Li-ionPolymerBatteryPack 7 Voltageregulators 3.3Vand5Vlinearregulators 8 IMU VectorNav,(VN-100)IMU 17 2.1.2.2SoftwareArchitecture Thesoftwarearchitectureconsistsofanembeddedwarelayerandauserinterface layer.Theembeddedwarelayerincludesadataacquisitionunit,aprocessingunit,an actuationunit,andacoordinationunit.Eachunitisresponsibleforaparticulartask.The dataacquisitionunitisresponsibleforacquiringthedatafromthesensors,toobtainall oftheinformationneededforthemaintask.Theacquiredrawdataaredeliveredtothe processingunit.Thelatter,hastheresponsibilityofprocessingtherawdataandgenerating theappropriateactuationsignals.Theactuationunitisresponsiblefortranslatingtheactu- ationsignaltomechanicalmovements.Thecoordinationunithasthetaskoftransmitting andreceivingtheprocesseddatabetweenthemobileplatformandthemainstation(PC). Figure2.6showsthesoftwarearchitecture. Figure2.6:Thesoftwarearchitecture. 18 2.1.3SystemAssembly Toconstructtheentireroboticsystem,everycomponentisdesignedseparately. Thentheassemblyprocessisstartedbyattachingtheservomotorstotheshell.Theshell containsawaterproofedchambertoaccommodatetheelectricalparts.Afterplacingevery componentinitsparticularlocation,thebodyisbalancedtobestablybuoyantatthe surfaceofthewater.Finally,thebodyissealedpermanentlyforwaterprowithsome accessibleportsforprogramming,recharging,andswitchingFigure2.7(a)shows fourviewsoftheassembledroboticprototypeanditscomponentsbeforesealingand painting.Figure2.7(b)showstheroboticaftersealingandpainting. 2.2RoboticFishforMuseumExhibit Theroboticformuseumexhibit(referredtoas\museumroboticfromhereon) involvestargettrackingsystemwithaninterfaceforrobot-userinteractions.Theusercan assignttargetpointsonatouchscreen,whichshowsalivevideofortherobotic andtheswimmingtankenvironment.Thesystemanalyzesthevideowithimageprocessing techniquestoidentifythepositionandorientationoftheroboticcomputesthedistance andrelativeorientationbetweentherobotandthetarget,calculatesthecontrolinputstothe robot,andsendthosetotheroboticthroughthewirelesscommunicationmodule.The museumroboticshisequippedwithaZigbeewirelesscommunicationmodule,aninfrared (IR)remotecontrolswitch,atemperaturesensor,apowermeasurementunit,andawireless chargingsystem. 19 (a) (b) Figure2.7:Assembledroboticprototype:(a)fourviewsoftheassembledprototype anditscomponentsbeforesealingandpainting,(b)theroboticaftersealingand painting. 20 Figure2.8:ThemuseumroboticprototypedevelopedintheSmartMicrosystemsLab atMichiganStateUniversity. 2.2.1MechanicalStructure Themuseumroboticusesthesamedesignofthebodyasfortheprototype,with someimprovementsandmodtoaccommodatetheaddedparts,theIRswitchand thewirelesschargingsystem.Thelocationsofthetailandpectoralarealsomo tooptimizethesizerequirementswhileprovidingproperaccommodationsforallelectronics andtheadditionalpartsmentionedabove.Figure2.8showsthedevelopedmuseumrobotic 2.2.2ElectricalSystem TheelectricalsystemissigtlymobyaddingtheIRswitchandthewireless chargingsystem.Inadditiontothat,theinertialmeasurementunit(IMU)isremovedand replacedbyanoverheadcamerasystemforindoorapplicationstosavecostandsize.Figure 2.9(a)showsthemainboardlayoutofthemuseumroboticFigure2.9(b)showsthe softwarearchitecture. 21 (a) (b) Figure2.9:Museumrobotic(a)circuitboardlayout,(b)thesoftwarearchitecture. 22 2.2.3WirelessChargingSystem Thewirelesschargingsystemconsistsoftwoparts,thetransmitterandreceivercircuits andthechargingstation. 2.2.3.1TheTransmitterandReceiverCircuits Forwirelesscharging,twocoilsareusedtotransferthepowerwirelesslybasedonthe electromagneticinductionprinciple.Thereceivercoilisplacedinsidetheroboticwhile thetransmittercoilisoutside.Forfurtherdetailsonthewirelesschargingsystem,see Chapter4. 2.2.3.2ChargingStation Oneofthechallengingtasksinthewirelesschargingsystemishowtoalignthetransmitter andreceivercoils.Duetothenatureofhydrodynamicinteractionsbetweentherobotic andwater,itishardtomaketheroboticstaystillatasplocationtoachievethe requirementofmaximumpowertransfer.Toaddressthischallenge,wehaveproposeda chargingstationfortheroboticThechargingstationconsistsof(1)docking/holding boxwhichisdesignedtocaptureandholdtheroboticupwardtoensurethealignmentof thetransmitterandreceivercoils,(2)linearsliderandanactuatorforautomaticallylifting up/downboththeholdingboxandtherobotic(3)mechanicalframetoattachthe entiresystemtothewalloftheswimmingtank,and(4)theassociatedelectricalcircuitry. Thechargingstationiswirelesslycontrolledbythemainstation(PC)throughawireless communicationmodule(XBeeProfromDigi).Figure2.10(a)showsthechargingstation holdingtheroboticFigure2.10(b)showstheelectricalcircuitryofthechargingstation withthetransmittercoilinsidethechargingandcontrolbox. 23 (a) (b) Figure2.10:Thechargingstation:(a)thechargingstationwiththerobotic(b)the electricalcircuitryofthechargingstationwiththewirelesschargingmodule(ModelNo. (18579694)fromShenzhenTaidaCenturyTechnologyCo.). 24 2.2.4NavigationSystem Thetargettrackingsystemconsistsofanoverheadcamera(webcam),atouchscreen tabletcomputer,andawirelesscommunicationmodule.Theoverheadcameraisresponsible forcapturingalivevideooftheroboticandtheswimmingtankenvironmentandsending ittothecomputer.Thelatterisresponsibleforthreemaintasks.First,itperformsonline processingandanalyzesthevideotoextractthepositionandorientationdataoftherobotic Second,itanalyzestouchesonthescreentoidentifythetargetpoint.Third,itcomputes andsendsactuationcommandsbacktoaroboticthroughthewirelesscommunication module.Withthesecommands,theroboticwillswimtotheparticulartargetpoint. Figure2.11showsaschematicrepresentationofthetrackingsystem.Furtherdetailsofthe trackingsystemcanbefoundinChapter5. Figure2.11:Aschematicrepresentationofthetrackingsystem. 25 2.3EducationandOutreachActivitiesUsingthe RoboticFish Roboticprovidenotonlycantpotentialresearchopportunities,butalsooppor- tunitiesforengagingyoungstudentsandthegeneralpublic.Roboticandotherbionic robotshaveparticipatedinmanyexhibitionsaroundtheworld[46,47].Therobotic prototypehasbeendemonstratedatthe2015MSUScienceFestival(seeFigure2.12). Atthisevent,theMSUSmartMicrosystemsLabpresentedvariousroboticprototypes whilethevisitorshadanopportunitytowatchandinteractwiththeroboticThemu- seumroboticisscheduledtobedeployedattheMSUMuseuminSpring2016,whichis expectedtohavepositiveimpactonlocalschools,students,andthegeneralpublic. 26 Figure2.12:Participationoftheroboticprototypeinthe2015MSUScienceFestival. 27 Chapter3 MathematicalModel 3.1Introduction Researcherhaveshownatinterestindynamicmodelingandcontrolofrobotic [14,19,20,34,44,48,49].Manymodelingmethodsandtheorieshavebeenutilizedto capturetheodyinteractionsandtheforcesandmomentsontheroboticbody. Computationaldynamics(CFD)modelinghasbeenutilizedtocapturesuchinteractions [44,50{52];however,itisnotamenabletocontroldesign.Airfoiltheoryhasbeenusedto applythequasi-steadyliftanddragtoevaluatetheforcesonbodyandsurfacesof underwatervehicles[20,53].J.Wang[44]usedLighthill'slargeamplitudeelongated-body theorytocapturethehydrodynamicforcesinducedbytheinteractionsbetweenthe andacaudalroboticSanaz etal. [3,34]modeledaroboticactuated byapairofpectoralusingbladeelementtheorytocalculatethehydrodynamicforces. Inthiswork,weincorporatetherigidbodydynamicswiththebladeelementtheory[48] andLighthill'slargeamplitudeelongated-bodytheory[49]tomodelourroboticwhich isactuatedbyacaudal(tail)andapairofpectoral Formathematicalmodeling,weconsidertheactuationmodulesandtheactuatedbody. Theactuationmodulesarethetailandpectoralwhicharethedeformablepartsofthe roboticThebodyistheundeformablepart,anditsmotionisgovernedbyrigidbody dynamicsincorporatingtheadded-massTheinteractionofthedeformable(actuation) 28 moduleswiththerigidbodyandtheenvironment(water),andtheresultinghydrodynamic forcesareevaluatedusingbladeelementtheoryandLighthill'slargeamplitudeelongated- bodytheoryforthepectoralnsandtailrespectively.Thepectoralaredesignedto performrowingandspanningmotionsonly.Thetailisassumedtohavenoabruptchange onitsdepthalongthelengthdirection,andthusitmeetstherequirementofanelongated- body[49].Theproposedmodelingapproachisamenabletogeneralizationtofor easeofdiscussion,however,wefocusonthecaseofrigidactuatedatthebasepoint.To providethebackgroundofourwork,briefreviewsoftherigidbodydynamics,bladeelement theory,andLighthill'slargeamplitudeelongated-bodytheoryarepresented 3.2RigidBodyDynamics Figure3.1showsaschematictopviewoftheroboticbodywithtwopectoraland tailFollowingtheliterature[19,34,44]ondescribingtherigidbodydynamics,[ XYZ ] denotestheglobal(inertial)coordinatesystemwhile[ xyz ]denotesthelocal(bo coordinatesystemwithunitvectors[^ x; ^ y; ^ z ].The^ p and ^ t aretheperpendicularandparallel unitvectorsrespectivelyforeachofthepectoralns.Also,^ a and ^ b aretheperpendicularand parallelunitvectorsrespectivelyforthetailTheentireroboticbodyincludingthe pectoralandtailisassumedtobeneutrallybuoyant.Furthermore,itisassumedthatthe centerofmassandthecenterofgeometryofthebodycoincideatpoint C b .Thelinearand angularvelocitiesofthebodyatthepoint C b areexpressedinthelocalcoordinatesystem. Thelinearvelocity ~ V C b =[ u;v;w ] T comprisesofthe x -directioncomponent( u ), y -direction component( v ),and z -directioncomponent( w ),whicharerespectivelycalledsurge,sway, andheave.Also,theangularvelocity ~ =[ r;p;q ] T consistsofthreecomponents,whichare 29 Figure3.1:Schematictopviewoftheroboticbodywithapairofpectoralanda tail theroll( r ),pitch( p ),andyaw( q ),respectively.Inaddition, isusedtodenotetheangle ofattackoftheroboticbody,whichismeasuredfromthe x -axistothedirectionof ~ V C b , ' denotestheangleofthepectoralwithrespectto x -axis, denotesthe angleofthetailwithrespecttothenegative x -axis,anddenotestheheading angleoftheroboticbody,formedbythelocal x -axiswithrespecttotheglobal X -axis. Thelinearmomentumandangularmomentum ~ P and ~ H ofthebodyarerespectively expressedinthelocalcoordinatesystemas ~ P = M b ~ V C b + K T ~ ; (3.1) ~ H = K ~ V C b + J ~ ; (3.2) 30 where M b isthemassmatrix, J istheinertialmatrix,and K istheCoriolisandcentripetal matrix.TheKirc'sequationsofthemotionforarigidbodyinaninviscid,irrotational expressedinthelocalcoordinatesystem,aregivenby[44,54,55] _ ~ P = ~ P ~ + ~ F; (3.3) _ ~ H = ~ H ~ + ~ P ~ V C b + ~ M E ; (3.4) where ~ F =[ f x ;f y ;f z ] T denotestheexternalforcesonthebodycenterofmass C b , ~ M E = [ M x ;M y ;M z ] T denotestheexternalmomentsabout C b ,and( )denotesthecrossproduct. Inthiswork,wefocusontheplanar(surface)motionoftheroboticPlanarmotion accompaniedwiththeassumptionofneutralbuoyancyaswellasthebodysymmetryabout the xz -plane,impliesthattheroboticbodyhasonlythreedegreesoffreedom,whichare thesurge( u ),sway( v ),andyaw( q ).Therefore,theheave( w ),roll( r ),andpitch( p )are allzeros.Furthermore,weassumethattheinertialcouplingbetweenthesurge,sway,and yawisnegligible[19,34,44],whichimpliesthat K vanishesaswell.Withtheseassumptions, Eq.(3.4)canbereducedto[55] m x _ u = m y vq + f x ; (3.5) m y _ v = m x uq + f y ; (3.6) I z _ q =( m x m y ) uv + M z ; (3.7) where m x = m b m xx ;m y = m b m yy ; and I z = I b I zz , m b denotesthemassofthe body, I b denotesthemomentofinertiaofthebodyaboutthe z -axis, m xx and m yy are theaddedmassesinthe x -and y -directions,respectively,and I zz istheaddedinertial 31 aboutthe z -axis. 3.3HydrodynamicForcesandMoments Inthedynamicmodel(3.5)-(3.7),theexternalforces f x and f y andthemoment M z are generatedduetotheinteractionbetweentheactuationparts(pectoralandtailwith thesurroundingThegeneratedforcesandmomentaretransmittedtotherigidbody (roboticbody). Tocompleteourmodel,weneedtoevaluatethesehydrodynamicforcesandmoments. AsmentionedinSection3.1,weusebladeelementtheoryandLighthill'selongated-body theorytoevaluatethehydrodynamicforcesgeneratedbythepectoralandthetail respectively. 3.3.1BladeElementTheory Accordingtobladeelementtheory,therowingmovementofthepectoralcanbe modeledbydividingtheintoaseriesofsmallparts(bladeelements)andthenevaluating theforcesoneachofthesebladeelements.Afterthat,thetotalforceoftheentirepectoral canbedeterminedbyintegratingtheseforcesalongitsspanlength.Intherowing movementofthepectoraltherearetwotsub-movementsduringtheeat cycle,powerandrecoverystrokes.Inordertogainthrust,realtendtochangethe shapeoftheirpectoralinacertainwayineachstroke.Inthepowerstroke,thepectoral extendstohavethemaximuminteractionareawiththesurroundingtoproduce maximumthrust.Ontheotherhand,theisinclinedandcontracteddowntoreducethe dragintherecoverystroke.Asaresult,thegainsthrustandmovesforward.Inspired 32 Figure3.2:oftheroboticwithpectoralandtaila)Schematicrepre- sentationoftheroboticwithdpectoralandtailb)Sideandtopviewsofthe entirepectoralnandbladeelementofthepectoralwithassociatedforcesandangles respectively. bythisbiologicalfeature,wehavedesignedthepectoralofourrobotictochange theirshapesinboththepowerandrecoverystrokes(forfurtherdetailseeSection2.1.1.1). However,asmentionedinSection3.1,wefocusontherigidcaseofthepectoralforthe modelingpurpose,andthusitisconsideredasarectangle-shapedplatewithlength(span) S anddepth(cord) C .Figure3.2(a)showsaschematicrepresentationofthetopviewofthe roboticwithpectoralandtailFigure3.2(b)showsasideviewoftheentire pectoralandatopviewofabladeelementofthepectoralwithassociatedforcesand angles. 33 AsshowninFigure3.2(b),theperpendicularforce dF p ( s;t )andthetangentialforce dF t ( s;t )canbecalculatedoneachsmallbladeelement ds attime t as[3,34,48] dF p ( s;t )= 1 2 C p ( ( s;t )) ˆCV p 2 i ( s;t ) ds; (3.8) dF t ( s;t )= 1 2 C t ( ( s;t )) ˆCV p 2 i ( s;t ) ds; (3.9) where V p ( s;t )isthevelocityofthe i -thbladeelementofthe ˆ isthedensityofthe surrounding C isthedepth(cord)ofthepectoral ( s;t )istheangleofattackof the i -thbladeelementwhichisgivenby[48], tan i = _ ' i r V C b sin ' i V C b cos ' i (3.10) where ' i and_ ' i aretheangularpositionandvelocityofthe i -thbladeelementofthe respectivelyand V C b isthevelocityofthebodyatthecenterpoint C b .Notethathere,for simplicityofdiscussion,weassumethattheangleofattackforthebodyiszero. C p and C t aretheperpendicularandtangentialforcecotswhichcanbeevaluated usingthefollowingformula[3,56] C p ( ( s;t ))=3 : 4sin ( s;t ) ; (3.11) C t ( ( s;t ))= 8 > > > < > > > : 0 : 4cos 2 (2 ( s;t )) ; for0 ( s;t ) ˇ= 4 0 ; otherwise (3.12) Byintegratingalongtheentirepectoralthetotalhydrodynamicforcesforeachcan 34 bedeterminedas F p ( t )= Z S 0 dF p ( s;t ) ds; (3.13) F t ( t )= Z S 0 dF t ( s;t ) ds; (3.14) Thetotalforce F P hx and F P hy exertedonthecenterofmass( C b )canbedeterminedby addinguptheforcesfrombothpectoral ~ M pL and ~ M pR arethehydrodynamicmomentsinducedbytheleftandrightpectoral respectively,withrespecttothecenterpointoftherobotbody C b . ~ M pL canbeevaluated bymultiplyingthetotalforcegeneratedbytheleftpectoral ~ F pl withthepositionvector ~r pc whichismeasuredfromthepoint C b tothebasepointoftheleft p bl ,anditisgiven by ~ M pL = ~ F pl ~r pc (3.15) Themoment ~ M pR canbeevaluatedinthesameway.Thetotalhydrodynamicmoment inducedbybothleftandrightpectoralisgivenby ~ M pT = ~ M pL + ~ M pR (3.16) 3.3.2Lighthill'sLargeAmplitudeElongated-bodyTheory Anelongated-bodyinLighthill'stheory[49]couldmeanaliveroboticora tail[44].Inourwork,weapplythetheorytothetailFollowingour assumptionofplanarmotionoftheroboticthemovementofthetailwillbeinthe XY -plane.AsshowninFigure3.2(a)(inthedetailpart)andfollowingtheelongated- 35 bodytheory,areferenceframeisconsideredsuchthatthewaterfarawayfromthebodyisat rest.Thecenterlineoftheelongated-bodyisparameterizedby l ,anditisassumedtoremain inextensible.Thetailbasepointisrepresentedwith l =0,whiletheposteriorendofthetail is l = L ,where L denotesthetotallengthoftheelongated-body(tailThetrajectory ofanypoint l alongthetailattime t isgivenby( X ( l;t ) ;Y ( l;t )),where0 l L .The time-dependenceofthecoordinatescouldbecausedbyoscillation/undulationofthetailor asaresultofrotational/translationalmotionofthebody[44]. Forthehydrodynamicforceevaluation,theissetinacoordinatesystemsuchthat animaginaryverticalplaneperpendiculartothetailattheposteriorendseparates betweenthewakeandthetail.Therefore,thetailiscontainedinahalfplane < asshownin Figure3.2(a).Forthissituation,therearethreecomponentsofforceinplay:theconvection ofmomentumoutof < acrossthepressureforceactingonandtheforcesactingonthe tailwhicharethereactiveforces[49].Thesehydrodynamicforcesactasaconcentrated forceatthetailtip( l = L )andareactiveforcealongthetail( l