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外文翻译--设计及建模的一个多余全方位机器人杯守门员 英文版.pdf

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外文翻译--设计及建模的一个多余全方位机器人杯守门员 英文版.pdf

DesignandModelingofaRedundantOmnidirectionalRoboCupGoalieLanceWilson,CraigWilliams,JustinYance,JaeLew,RobertL.WilliamsIIDepartmentofMechanicalEngineeringOhioUniversity,Athens,Ohio,USAPaoloGallinaDepartmentofInnovationinMechanicsandManagementUniversityofPadova,ItalyAbstract.ThispapercoversthemechanicaldesignandmodelingofaredundantomnidirectionalmobilerobotdevelopedfortheOhioUniversityRoboCupgoalie.Thegoalierobotisactuatedredundantlywithfourwheelsforgoodmobility.Inthepaper,firsttheoverallmechanicaldesignofthesystemisdiscussed.Second,theinversekinematicssolutionisobtainedusingtheprincipleofvirtualwork.Third,dynamicequationsofmotionofthesystemarederivedinasymbolicformresultingincouplednonlineardifferentialequations.Finally,asimulationdemonstratestheinversekinematicssolutionandsimpleindependentPDwheelcontrolofourredundantomnidirectionalgoalierobot.1.INTRODUCTIONOmnidirectionaldriveistheabilitytomoveinanydirection0to360degreesatanygivenorientation.Usingthistypeofdrivesystemenablesarobottomoveinagivendirectionwhilebeingabletorotateduringlineartravel.TimeissavedbyeliminatingtheneedtorotatetherobotbeforetranslatingfrompointAtopointB.Omnidirectionaldrivegivesthegoalierobottheabilitytoalwaysfacetheballwhilebeingabletomoveinanydirection.Inaddition,itprovidessimplerinversekinematicssolutionforpathplanning.Forthesereasons,manyresearchgroupsarestudyingomnidirectionalholonomicmobilerobotsandvehicles15.TheOhioUniversityOURoboCupTeamincorporatestheomnidirectionaldriveintotheirmobilerobots.TheOURoboCupTeamconsistsof4playersand1goalietheplayersandgoalieeachhaveseparatemechanical,electrical,andsoftwaredesigninordertomeetdifferentperformancespecifications.Forexample,theplayersaredesignedtooptimizeforwardmotion,whilethegoalieisdesignedtooptimizesidetosidemotion.Thispaperwillfocusonthemechanicaldesign,dynamicmodeling,andsimulationoftheredundant,omnidirectionalRoboCupgoalie.2.DESIGNThedesignforthegoaliehastwomainfunctions.Themajorfunctionistohavetheabilitytoquicklymovesidetosidetoguardthegoal.Thishasbeenaccomplishedbyhavingthewheelsalignedhorizontallyforquickmovement.Theotherfunctionisthekickingoftheball.Thecurrentdesignnotonlyallowsforastrongkickbutalsotheabilitytocatchingballundercontrol.2.1ConstraintsInordertocompeteintheRobocuptournament,robotshavetomeetspecifiedsizeconstraints.Thegoalierobotcanbenotallerthan22.5cmiflocalvisionistobeused,andmustfitwithina18cmdiametercylinder.Anypartthatmayextendoutwardontherobotmustbefullyextendedwhenplacedinsidethe18cmcylinder.Thesesizeconstraintsgreatlylimitthearrangementofdriveandkickingsystems.Kickinganddrivesystemsarerectangularinshapeanddesigningalayouttomeettherobotsizeconstraintsresultsinwastedspacearoundthesesystems.2.2.PerformanceSpecificationThroughtestingvariousradiocontrolledtoycars,experimentswereperformedtobettervisualizewhatkindofperformancewedesireforthegoalierobot.Highvaluewasplacedonmakingtherobotzippywhichmeansitcanmoveorchangedirectionquicklybutdoesnthaveahighmaximumvelocity.Anaccelerationof2m/sec2andamaximumvelocityof1m/secweretheperformancespecificationsdecideduponforthegoalieslocomotion.Thekickingmechanismusedonthegoalieneededtobepowerfulenoughtopropeltheballatleasthalfthelengthoftheplayingfield.Controllingthekickingpowerisaccomplishedbyusingavariablespeedmotoronthekickingmechanism.Oneadvantageofthegoalieistheabilitytocapturetheballandcompletelyencloseit.Enclosingtheballandhidingitfromopposingrobotsoperatingontheglobalvisionsystemcanleadtoconfusioniftheycannotlocatetheball.2.3LayoutThegoalielayoutconsistsofthedrivesystemandkickingmechanismFigure1.Tomaintaintractiononthedrivewheels,therobotcenterofmassshouldbelocatedonthecentralaxesofthedrivewheels.Fourwheelsarebeingusedtodrivetherobotomnidirectionally.Keepingthegoaliescenterofmassneartheseaxesbecomesdifficultoncethekickermechanismisaddedtothesystem.Thekickermechanismshiftsthecenterofmasstowardthecenteroftherobot,whichcancausetherearwheeltoslip.Shiftingthecenterofmasstocompensatefortheweightofthekickercanbeaccomplishedthroughshiftingbatterypositionstowardtherearoftherobot.Figure1OUGoalieaCADmodelbHardwarePhotographThereare6motorsutilizedintherobotassembly.Fourareplacedinthewheelassemblytodrivewheels.Oneisinkickerassemblyandrotatesthedrivebar.Thereisalsoaservomotorassociatedwiththekickerassembly.2.4OmniDirectionalDriveTheKornylakCorporationmanufacturestheOmniwheelthatappearsinFigure2a.Tominimizewheelwidth,theoriginalOmniwheelismodifiedbyremovingmaterialfromthecenterandouterfaces.Removalofmaterialalsoallowedroomtoinsertafabricatedhubtobeusedforgearmounting.Figure2bshowsthemodifiedwheelmountedtoanaluminumhub.Figure2aKornylakOmniwheelbModifiedOmniwheel2.5Kicking/Dribbling/CapturingMechanismThekickingmechanism,Figure3,isstructuredaroundonebasicprinciple,capturingtheball.Ithastheabilitytorotatearoundapivotpointwiththisrockingmotioncontrolledbyaservomotor.Theservomotorislocatedonthegoaliebaseandthusisstationarywithrespecttothekicker.Duringthegamethegoaliewillbelocatednearthegoalwithitsdrivebarrotatingbackwards.Thedrivebarwillbeencasedinrubbertubing.Initiallythekickingmechanismwillbeatitshighestpointinthearc.Whentheballgetsnearthekickerthedrivebarwillcapturetheballviabackspin.Atthistimetheballwillberotatingbetweenthedrivebarandtheidlerbar,locatedunderneaththerobot.Beingunderneaththerobotwillcausetheballtobehiddenfromtheglobalcamera.Thedrivebarwillthenreversedirectionandcausetheballtospinintheoppositedirectionbetweenthetwobars.Aftertheballgainsasufficientamountofforwardrotationthekickingmechanismwillberockedbackedtheservomotor.Thiswillallowtheballtobereleasedwhilehavingtopspin.Afterreleasingtheballthekickingmechanismwillbebroughtuptoitshighestpositionintherotatingarcbytheservomotortowaitforthenextball.Figure3CloseupofKickerAssembly3.ModelingThedynamicequationsforthefourwheeledOhioUniversityRoboCupgoalieisderivedfromthemodelshowninFigure4,similarto1.Itisassumedthemobilerobotismovingonahorizontalplayingfield.Asitisshown,theinertialcoordinateframeXwYwisfixedontheplaneandthemovingcoordinateframeXmYmisattachedtothemasscenterofthemobilerobot.Liisthedistancefromthemasscentertothecenterofthecorrespondingwheel.fistheorientationofthemobilerobotwithrespecttowS.Aspreviouslystatedthisrobotisomnidirectional,givingusnononholonomicconstraintequations.Also,itisimportanttopointoutthattheOURoboCupgoaliehasthreedegreesoffreedom,buthasfouractuatorsmeaningthatthesystemisredundantlyactuated.First,wedefinethepositionandforcevectorsofthemasscenterfortheOURoboCupGoalieintheabsolutecoordinateframeas{}{}TGyxwTwwwMFFFyxSf1Figure4Kinematic/FreeBodyDiagramwhereMGisthetorqueappliedtotherobot.ThefollowingtwoequationsrelateCartesianposeandwrenchforthemovingandinertialframesfRFsRSmwmwmwmw2,3wherethecoordinaterotationmatrixRwmrepresentstheinertialframewithrespecttotheorientationofthemovingframe.Theposeandwrenchvectorsofthegoalieintermsofthemovingcoordinatesare{}{}TGyxmTmmmMfffyxsfApplyingNewtons2ndLawSMFww4whereMisapositivedefinitediagonalmatrixwiththemobilerobotsmassMonthediagonal.Equation4canberewrittenintermsofthemovingcoordinatesusingEquations13fssRRMmmmwmTwm5SimplifyingEquation5,thedynamicequationsoftherobotareGmymmxmmMIfxyMfyxM−fff6,7,8whereImisthemassmomentofinertiaforthemobilerobot.TocomputetherelationshipbetweentherobotCartesiancoordinatesandthewheelangles,theprincipleofvirtualworkisused.Summingtheforcesandmomentsgives9whereQistheJacobianmatrixbaseduponthesystemgeometry,andTiisthetractionforcefromeachwheel.SincethevirtualworkdoneissameforthewheelandCartesiancoordinates,wewritesfqTmTmT10whereisthevelocityofthewheelrollingcontactpointassumingthatthereisnoslipinthewheelspindirection.ie.{}Trrrq321www.Thus,wecanobtaintheinversekinematicssolutionoftheOURoboCupgoaliefromEquations9and10.GiventheCartesianvelocity,wemayfindthewheelangularvelocities1144332211LxrLyrLxrLyrmmmm−−fwfwfwfw12,13,14,15whereristhewheelradiusandwiisthewheelrotationalrate.Thewheeldynamicsforeachassemblyasgivenby1areasfollowsiiiiwrTkucI−wwi1,2,3,416WhereIwisthemassmomentofinertiafortheOmniwheel,cistheviscousfrictionfactoroftheOmniwheel,kisthedrivinggainfactororthegearratio,anduiisthedrivinginputtorqueThencombiningEquations616wehavethefollowingequationsofmotionwritteninmatrixvectorformsQqmTTQfTTTTLLLLMffmGyxor0101101043214321−−

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