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外文翻译--混合位置力控制SCORBOT-ER4支机械手与神经网络的非线性补偿 英文版.pdf

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外文翻译--混合位置力控制SCORBOT-ER4支机械手与神经网络的非线性补偿 英文版.pdf

HYBRIDPOSITION/FORCECONTROLOFTHESCORBOTER4PCMANIPULATORWITHNEURALCOMPENSATIONOFNONLINEARITIESPIOTRGIERLAKRZESZOWUNIVERSITYOFTECHNOLOGY,DEPARTMENTOFAPPLIEDMECHANICSANDROBOTICS8POWSTANCOWWARSZAWYST,35959RZESZOW,POLANDPGIERLAKPRZEDUPLABSTRACTTHEPROBLEMOFTHEMANIPULATORHYBRIDPOSITION/FORCECONTROLISNOTTRIVIALBECAUSETHEMANIPULATORISANONLINEAROBJECT,WHOSEPARAMETERSMAYBEUNKNOWN,VARIABLEANDTHEWORKINGCONDITIONSARECHANGEABLETHENEURALCONTROLSYSTEMENABLESTHEMANIPULATORTOBEHAVECORRECTLY,EVENIFTHEMATHEMATICALMODELOFTHECONTROLOBJECTISUNKNOWNINTHISPAPER,THEHYBRIDPOSITION/FORCECONTROLLERWITHANEURALCOMPENSATIONOFNONLINEARITIESFORTHESCORBOTER4PCROBOTICMANIPULATORISPRESENTEDTHEPRESENTEDCONTROLLAWANDADAPTIVELAWGUARANTEEPRACTICALSTABILITYOFTHECLOSEDLOOPSYSTEMINTHESENSEOFLYAPUNOVTHERESULTSOFANUMERICALSIMULATIONAREPRESENTEDKEYWORDSNEURALNETWORKS,ROBOTICMANIPULATOR,TRACKINGCONTROL,FORCECONTROL1INTRODUCTIONROBOTICMANIPULATORSAREDEVICESWHICHFINDDIffERENTAPPLICATIONSINMANYDOMAINSOFTHEECONOMYTHEREQUIREMENTSINRELATIONTOPRECISIONOFMOTIONANDAUTONOMYOFMANIPULATORSAREINCREASINGASWELLASTHETASKSPERFORMEDBYTHEMAREMOREANDMORECOMPLEXINCONTEMPORARYINDUSTRIALAPPLICATIONSITISDESIREDFORTHEMANIPULATORTOEXERTSPECIFIEDFORCESANDMOVEALONGAPRESCRIBEDPATHMANIPULATORSAREOBJECTSWITHNONLINEARANDUNCERTAINDYNAMICS,WITHUNKNOWNANDVARIABLEPARAMETERSMASSES,MASSMOMENTSOFINERTIA,FRICTIONCOEffiCIENTS,WHICHOPERATEINCHANGEABLECONDITIONSCONTROLOFSUCHCOMPLEXSYSTEMSISVERYPROBLEMATICTHECONTROLSYSTEMHASTOGENERATESUCHCONTROLSIGNALSTHATWILLGUARANTEETHEEXECUTIONOFMOVEMENTALONGAPATHWITHASUITABLEFORCEANDWITHDESIREDPRECISIONINSPITEOFTHECHANGEABLEOPERATINGCONDITIONSINTHECONTROLSYSTEMSOFINDUSTRIALMANIPULATORS,THECOMPUTEDTORQUEMETHOD1,2FORNONLINEARITYCOMPENSATIONISUSEDHOWEVER,THESEAPPROACHESREQUIREPRECISEKNOWLEDGEABOUTTHEMATHEMATICALMODELTHESTRUCTUREOFMOTIONEQUATIONSWITHCOEffiCIENTSOFTHECONTROLOBJECTMOREOVER,INSUCHANAPPROACH,PARAMETERSINTHECOMPENSATORHAVENOMINALVALUESSOTHECONTROLLRUTKOWSKIETALEDSICAISC2012,PARTII,LNCS7268,PP433–441,2012CSPRINGERVERLAGBERLINHEIDELBERG2012434PGIERLAKSYSTEMACTSWITHOUTTAKINGINTOACCOUNTTHECHANGEABLEOPERATINGCONDITIONSINTHELITERATUREEXISTSMANYVARIATIONOFALGORITHMS,INWHICHPARAMETERSOFTHEMATHEMATICALMODELOFMANIPULATORAREADAPTED1,2HOWEVERTHESEAPPROACHESDONOTELIMINATETHEPROBLEMWITHSTRUCTURALUNCERTAINTYOFTHEMODELINCONNECTIONWITHTHEPRESENTDIffiCULTIES,NEURALCONTROLTECHNIQUESWEREDEVELOPED3,4,5,6INTHESEMETHODSTHEMATHEMATICALMODELISUNNECESSARYTHESETECHNIQUESAREUSEDINHYBRIDPOSITION/FORCECONTROLLERINWORKS7,8SUCHCONTROLLERSHAVEBEENPRESENTEDBUTINTHEFIRSTOFTHEWORKSONLYFORCENORMALTOTHECONTACTSURFACEISTAKINGINTOACCOUNT,ANDINTHESECONDWORKSOMEASSUMPTIONISHARDTOSATISFYINPRACTICALAPPLICATIONS,NAMELYSOMESTIffNESSMATRIXWHICHCHARACTERIZESFEATURESOFENVIRONMENTANDALLOWSTOCALCULATECONTACTFORCES,MUSTBEKNOWNINPREVIOUSAUTHOR’SPAPERONLYPOSITIONCONTROLLERSHAVEBEENCONSIDEREDINPRESENTPAPERHYBRIDPOSITION/FORCENEURALCONTROLLERISSHOWNTHISAPPROACHTAKESINTOACCOUNTALLFORCES/MOMENTSWHICHACTSONTHEENDEffECTORTHESEFORCES/MOMENTSAREMEASUREDBYSENSORLOCATEDINTHEENDEffECTOR2DESCRIPTIONOFTHESCORBOTER4PCROBOTICMANIPULATORTHESCORBOTER4PCROBOTICMANIPULATORISPRESENTEDINFIG1ITISDRIVENBYDIRECTCURRENTMOTORSWITHGEARSANDOPTICALENCODERSTHEMANIPULATORHAS5ROTATIONALKINEMATICPAIRSTHEARMOFTHEMANIPULATORHAS3DEGREESOFFREEDOMWHEREASTHEGRIPPERHAS2DEGREESAA1Q3YZXOBCO’OO’D1O’ALABLBCLCDD1235Q1Q223U2U1U3Q4D4U4Q5U5BCONTACTSURFACEC108FEFIG1ASCORBOTER4PCROBOTICMANIPULATOR,BSCHEMETHETRANSFORMATIONFROMJOINTSPACETOCARTESIANSPACEISGIVENBYTHEFOLLOWINGEQUATIONYKQ,1HYBRIDPOSITION/FORCECONTROLOFTHESCORBOTER4PCMANIPULATOR435WHEREQ∈RNISAVECTOROFGENERALIZEDCOORDINATESANGLESOFROTATIONOFLINKS,KQISAKINEMATICSFUNCTION,Y∈RMISAVECTOROFAPOSITION/ORIENTATIONOFTHEENDEffECTORPOINTDDYNAMICALEQUATIONSOFMOTIONOFTHEANALYSEDMODELAREINTHEFOLLOWINGFORM7,9MQQCQ,˙Q˙QF˙QGQΤDTUJTHQΛΤF,2WHEREMQ∈RNXNISANINERTIAMATRIX,CQ,˙Q∈RNISAVECTOROFCENTRIFUGALANDCORIOLISFORCES/MOMENTS,F˙Q∈RNISAFRICTIONVECTOR,GQ∈RNISAGRAVITYVECTOR,ΤDT∈RNISAVECTOROFDISTURBANCESBOUNDEDBY||ΤD||B,B0,U∈RNISACONTROLINPUTVECTOR,JHQ∈RM1XNISAJACOBIANMATRIXASSOCIATEDWITHTHECONTACTSURFACEGEOMETRY,Λ∈RM1ISAVECTOROFCONSTRAININGFORCESEXERTEDNORMALLYONTHECONTACTSURFACELAGRANGEMULTIPLIER,ΤF∈RNISAVECTOROFFORCES/MOMENTSINJOINTS,WHICHCOMEFROMFORCES/MOMENTSFE∈RMAPPLIEDTOTHEENDEffECTOREXCEPTTHECONSTRAININGFORCESTHEVECTORΤFISGIVENBYΤFJBTQFE,3WHEREJBQ∈RMXNISAGEOMETRICJACOBIANINBODY2THEJACOBIANMATRIXJHQCANBECALCULATEDINTHEFOLLOWINGWAYJHQ∂HQ∂Q,4WHEREHQ0ISANEQUATIONOFTHEHOLONOMICCONSTRAINT,WHICHDESCRIBESTHECONTACTSURFACETHISEQUATIONREDUCESTHENUMBEROFDEGREESOFFREEDOMTON1N−M1,SOTHEANALYSEDSYSTEMCANBEDESCRIBEDBYTHEREDUCEDPOSITIONVARIABLEΘ1∈RN17THEREMAINDEROFVARIABLESDEPENDONΘ1INTHEFOLLOWINGWAYΘ2ΓΘ1,5WHEREΘ2∈RM1,ANDΓARISEFROMTHEHOLONOMICCONSTRAINTTHEVECTOROFGENERALIZEDCOORDINATESMAYBEWRITTENASQΘT1ΘT2TLETDEFINETHEEXTENDEDJACOBIAN7LΘ1BRACKETLEFTBIGGIN1∂Γ∂Θ1BRACKETRIGHTBIGG,6WHEREIN1∈RN1XN1ISANIDENTITYMATRIXTHISALLOWSTOWRITETHERELATIONS˙QLΘ1˙Θ1,7QLΘ1Θ1˙LΘ1˙Θ1,8ANDWRITEAREDUCEDORDERDYNAMICSINTERMSOFΘ1,ASMΘ1LΘ1Θ1V1Θ1,˙Θ1˙Θ1F˙Θ1GΘ1ΤDTUJTHΘ1ΛJBTΘ1FE,9WHEREV1Θ1,˙Θ1MΘ1˙LΘ1CΘ1,˙Θ1LΘ1PREMULTIPLYINGEQ9BYLTΘ1ANDTAKINGINTOACCOUNTTHATJHΘ1LΘ10,THEREDUCEDORDERDYNAMICSISGIVENBYMΘ1V1˙Θ1FGΤDLTU,10WHEREMLTML,V1LTV1,FLTF,GLTG,ΤDLTBRACKETLEFTBIGΤD−JBTFEBRACKETRIGHTBIG436PGIERLAK3NEURALNETWORKHYBRIDCONTROLTHEAIMOFAHYBRIDPOSITION/FORCECONTROLISTOFOLLOWADESIREDTRAJECTORYOFMOTIONΘ1D∈RN1,ANDEXERTDESIREDCONTACTFORCEΛD∈RM1NORMALLYTOTHESURFACEBYDEFININGAMOTIONERROREΘ,AFILTEREDMOTIONERRORS,AFORCEERROR˜ΛANDANAUXILIARYSIGNALΥ1ASEΘΘ1D−Θ1,11S˙EΘΛEΘ,12˜ΛΛD−Λ,13Υ1˙Θ1DΛEΘ,14WHEREΛISAPOSITIVEDIAGONALDESIGNMATRIX,THEDYNAMICEQUATION10MAYBEWRITTENINTERMSOFTHEFILTEREDMOTIONERRORASM˙S−V1SLTFXLTBRACKETLEFTBIGΤD−JBTFEBRACKETRIGHTBIG−LTU,15WITHANONLINEARFUNCTIONFXML˙Υ1V1Υ1FG,16WHEREXBRACKETLEFTBIGETΘ˙ETΘΘT1DV˙ΘT1DΘT1DBRACKETRIGHTBIGTTHEMATHEMATICALSTRUCTUREOFHYBRIDPOSITION/FORCECONTROLLERHASAFORMOF7UˆFXKDLS−JTHBRACKETLEFTBIGΛDKF˜ΛBRACKETRIGHTBIG−Ν,17WHEREKDANDKFAREPOSITIVEDEFINITEMATRIXESOFPOSITIONANDFORCEGAIN,ΝISAROBUSTIFYINGTERM,ˆFXAPPROXIMATESTHEFUNCTION16THISFUNCTIONMAYBEAPPROXIMATEDBYTHENEURALNETWORKINTHISWORKATYPICALFEEDFORWARDNEURALNETWORKFIG2BWITHONEHIDDENLAYERISASSUMEDTHEHIDDENLAYERWITHSIGMOIDALNEURONS,ISCONNECTEDWITHANINPUTLAYERBYWEIGHTSCOLLECTEDINAMATRIXD,ANDWITHANOUTPUTLAYERBYWEIGHTSCOLLECTEDINAMATRIXWTHEINPUTWEIGHTSARERANDOMLYCHOSENANDCONSTANT,BUTTHEOUTPUTWEIGHTSINITIALLYAREEQUALZERO,ANDWILLBETUNEDDURINGADAPTATIONPROCESSSUCHNEURALNETWORKISLINEARINTHEWEIGHTS,ANDHASTHEFOLLOWINGDESCRIPTION3,4FXWTΦXΕ,18WITHOUTPUTFROMHIDDENLAYERΦXSDTX,WHEREXISANINPUTVECTOR,SISAVECTOROFNEURONACTIVATIONFUNCTIONS,ΕISANESTIMATIONERRORBOUNDEDBY||Ε||ΕN,ΕNCONST0THEMATRIXWISUNKNOWN,SOANESTIMATIONˆWISUSED,ANDAMATHEMATICALDESCRIPTIONOFAREALNEURALNETWORK,WHICHAPPROXIMATESFUNCTIONFXISGIVENBYˆFXˆWTΦX19

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