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Research on Flexible Joint Stiffness Test and Trajectory Planning of Space Manipulator

HindawiPublishingCorporationAdvancesinMechanicalEngineeringVolume2013,ArticleID280453,7pageshttp://www.wenkuxiazai.com/10.1155/2013/280453

ResearchArticle

ResearchonFlexibleJointStiffnessTestandTrajectoryPlanningofSpaceManipulator

YongtaiYang,1JiliRong,1JianLi,2andLingTang3

1

DepartmentofMechanics,SchoolofAerospaceEngineering,BeijingInstituteofTechnology,Beijing100081,China

AutomotiveandTransportationEngineeringInstitute,GuangxiUniversityofScienceandTechnology,Liuzhou545006,China3

ChinaAcademyofSpaceTechnology,Beijing100094,China

2

CorrespondenceshouldbeaddressedtoJiliRong;rongjili@http://www.wenkuxiazai.comReceived23August2013;Revised15October2013;Accepted23October2013AcademicEditor:XiaotingRui

Copyright©2013YongtaiYangetal.ThisisanopenaccessarticledistributedundertheCreativeCommonsAttributionLicense,whichpermitsunrestricteduse,distribution,andreproductioninanymedium,providedtheoriginalworkisproperlycited.BothNaturalCoordinateFormulationdescribingrigidbodiesandAbsoluteNodalCoordinateFormulationdescribingflexiblebodiesareusedtomodelaflexiblemanipulatorwithflexiblejointandflexiblelink.Thetorsionalstiffnessofflexiblejointistestedusingaspecializedstiffnesstestequipment,andthenthenonlineartorsionalstiffnessisdeterminedbyfittingtheexperimentaldata.Anewtrajectoryplanningfunctioncalledthecosine-basedfunctionisproposedtodesignthejointtrajectory,whichissmootherthanthefifth-polynomialandcycloidalmotionfunctions.Finally,aone-linkmanipulatorwithflexiblejointandflexiblelinkisusedtocomparetheperformanceofthethreetrajectoryplanningfunctions.Resultsshowthatresidualvibrationcanberemarkablyreducedbytheproposedcosine-basedfunction,whichexhibitsasignificantlybetterperformancethanthefifth-polynomialandcycloidalmotionfunctions.

1.Introduction

Aspacemanipulatorundertakestasksofcabintranslocation,transfer,andinstallationofequipment,aswellasservesasanastronautauxiliaryinastationsystem.Itservesanimportantfunctioninspaceengineering,withtheadvantagesoflighterstructure,lowerlaunchingcost,higheroperationalspeed,greaterpayload-to-manipulator-weightratio,smalleractuators,lowerenergyconsumption,andbettermaneu-verability.However,thegreatestdisadvantageofthespacemanipulatoristhevibrationproblemduetotheflexibilityofthejointandlink.Forinstance,ittookmanycumulativehoursinordertodampdowntheresidualvibrationintheremotemanipulatorsysteminaSpaceStation-assemblyShuttleflight,whichoccupied20%to30%ofthetotaltime[1].Theresidualvibrationsignificantlyreducestheend-pointaccuracyofthemanipulator.Therefore,thebestschemeisinwhichtheflexiblemanipulatorcompletestherequiredmovewithminimalresidualvibration.

Jointflexibilityandlinkflexibilityarebasicreasonsofmanipulatorvibration,whichcannotbeneglectedinthedynamicmodeling.Spong[2]firstmodeledtheflexiblejoint

asalinearspring,andthismodelingtechniquewasadoptedbymostresearchers[3,4].However,simplelinearspringisnotcapableofdescribingtheflexiblejointprecisely.Inthedynamicmodelingofflexiblelink,theassumedmodemethodistypicallyusedbymostresearchers.Martinsetal.[5]andTsoetal.[6]studiedaflexiblemanipulatorusingtheLagrangianequationandtheassumedmodemethod.Inassumedmodemodelformulation,thelinkflexibilityisusuallyrepresentedbyatruncatedfinitemodalseriesintermsofspatialmodeeigenfunctionsandtime-varyingmodeamplitudes.Themaindrawbackofthismethodisthatthereareseveralwaystochooselinkboundaryconditionsandmodeeigenfunctions.Moreover,theassumedmodemethodisonlycapableofdescribingsmalldeformation,notlargedeformation.Thepreviousworkssolelyfocusedoneitherjointflexibilityorlinkflexibility.

Severaldifferentapproacheshavebeensuggestedtoreduceresidualvibration,whichcanbecategorizedasactivecontrol,passivecontrol,andtrajectoryplanningmethods.Differenttrajectoriesofjointspace,significantlyaffectthevibrationofaflexiblemanipulator.Thefifth-polynomialfunctioniswidelyusedtoplanthejointtrajectory,butit

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