外文翻譯--混合位置力控制SCORBOT-ER4支機(jī)械手與神經(jīng)網(wǎng)絡(luò)的非線性補(bǔ)償 英文版.pdf

HybridPosition/ForceControloftheSCORBOT-ER4pcManipulatorwithNeuralCompensationofNonlinearitiesPiotrGierlakRzeszowUniversityofTechnology,DepartmentofAppliedMechanicsandRobotics8PowstancowWarszawySt.,35-959Rzeszow,P.plAbstract.Theproblemofthemanipulatorhybridposition/forcecon-trolisnottrivialbecausethemanipulatorisanonlinearobject,whoseparametersmaybeunknown,variableandtheworkingconditionsarechangeable.Theneuralcontrolsystemenablesthemanipulatortobe-havecorrectly,evenifthemathematicalmodelofthecontrolobjectisunknown.Inthispaper,thehybridposition/forcecontrollerwithaneu-ralcompensationofnonlinearitiesfortheSCORBOT-ER4pcroboticmanipulatorispresented.Thepresentedcontrollawandadaptivelawguaranteepracticalstabilityoftheclosed-loopsysteminthesenseofLyapunov.Theresultsofanumericalsimulationarepresented.Keywords:NeuralNetworks,RoboticManipulator,TrackingControl,ForceControl.1IntroductionRoboticmanipulatorsaredeviceswhichfinddierentapplicationsinmanydo-mainsoftheeconomy.Therequirementsinrelationtoprecisionofmotionandautonomyofmanipulatorsareincreasingaswellasthetasksperformedbythemaremoreandmorecomplex.Incontemporaryindustrialapplicationsitisdesiredforthemanipulatortoexertspecifiedforcesandmovealongaprescribedpath.Manipulatorsareobjectswithnonlinearanduncertaindynamics,withunknownandvariableparameters(masses,massmomentsofinertia,frictioncoecients),whichoperateinchangeableconditions.Controlofsuchcomplexsystemsisveryproblematic.Thecontrolsystemhastogeneratesuchcontrolsignalsthatwillguaranteetheexecutionofmovementalongapathwithasuitableforceandwithdesiredprecisioninspiteofthechangeableoperatingconditions.Inthecontrolsystemsofindustrialmanipulators,thecomputedtorqueme-thod1,2fornon-linearitycompensationisused.However,theseapproachesrequirepreciseknowledgeaboutthemathematicalmodel(thestructureofmo-tionequationswithcoecients)ofthecontrolobject.Moreover,insuchanapproach,parametersinthecompensatorhavenominalvaluessothecontrolL.Rutkowskietal.(Eds.):ICAISC2012,PartII,LNCS7268,pp.433441,2012.cSpringer-VerlagBerlinHeidelberg2012434P.Gierlaksystemactswithouttakingintoaccountthechangeableoperatingconditions.Intheliteratureexistsmanyvariationofalgorithms,inwhichparametersofthemathematicalmodelofmanipulatorareadapted1,2.Howevertheseapproachesdonoteliminatetheproblemwithstructuraluncertaintyofthemodel.Inconnectionwiththepresentdiculties,neuralcontroltechniqueswerede-veloped3,4,5,6.Inthesemethodsthemathematicalmodelisunnecessary.Thesetechniquesareusedinhybridposition/forcecontroller.Inworks7,8suchcon-trollershavebeenpresented.Butinthefirstoftheworksonlyforcenormaltothecontactsurfaceistakingintoaccount,andinthesecondworksomeassumptionishardtosatisfyinpracticalapplications,namelysomestinessmatrixwhichcharacterizesfeaturesofenvironmentandallowstocalculatecontactforces,mustbeknown.Inpreviousauthorspaperonlypositioncontrollershavebeenconsidered.Inpresentpaperhybridposition/forceneuralcontrollerisshown.Thisapproachtakesintoaccountallforces/momentswhichactsontheend-eector.Theseforces/momentsaremeasuredbysensorlocatedintheend-eector.2DescriptionoftheSCORBOT-ER4pcRoboticManipulatorTheSCORBOT-ER4pcroboticmanipulatorispresentedinFig.1.Itisdrivenbydirect-currentmotorswithgearsandopticalencoders.Themanipulatorhas5rotationalkinematicpairs:thearmofthemanipulatorhas3degreesoffreedomwhereasthegripperhas2degrees.a)A1q3yzxOBCOOO=d1OA=lAB=lBC=lCD=d1235q1q223u2u1u3q4D4u4q5u5b)contactsurfacec108FEFig.1.a)SCORBOT-ER4pcroboticmanipulator,b)schemeThetransformationfromjointspacetoCartesianspaceisgivenbythefol-lowingequationy=k(q),(1)HybridPosition/ForceControloftheSCORBOT-ER4pcManipulator435whereqRnisavectorofgeneralizedcoordinates(anglesofrotationoflinks),k(q)isakinematicsfunction,yRmisavectorofaposition/orientationoftheend-eector(pointD).Dynamicalequationsofmotionoftheanalysedmodelareinthefollowingform7,9:M(q)q+C(q,q)q+F(q)+G(q)+d(t)=u+JTh(q)+F,(2)whereM(q)Rnxnisaninertiamatrix,C(q,q)RnisavectorofcentrifugalandCoriolisforces/moments,F(q)Rnisafrictionvector,G(q)Rnisagravityvector,d(t)Rnisavectorofdisturbancesboundedby|d|0,uRnisacontrolinputvector,Jh(q)Rm1xnisaJacobianmatrixassociatedwiththecontactsurfacegeometry,Rm1isavectorofconstrainingforcesexertednormallyonthecontactsurface(Lagrangemultiplier),FRnisavectorofforces/momentsinjoints,whichcomefromforces/momentsFERmappliedtotheend-eector(excepttheconstrainingforces).ThevectorFisgivenbyF=JbT(q)FE,(3)whereJb(q)RmxnisageometricJacobianinbody2.TheJacobianmatrixJh(q)canbecalculatedinthefollowingwayJh(q)=h(q)q,(4)whereh(q)=0isanequationoftheholonomicconstraint,whichdescribesthecontactsurface.Thisequationreducesthenumberofdegreesoffreedomton1=nm1,sotheanalysedsystemcanbedescribedbythereducedpositionvariable1Rn17.Theremainderofvariablesdependon1inthefollowingway2=(1),(5)where2Rm1,andarisefromtheholonomicconstraint.Thevectorofgeneralizedcoordinatesmaybewrittenasq=T1T2T.LetdefinetheextendedJacobian7L(1)=bracketleftbiggIn11bracketrightbigg,(6)whereIn1Rn1xn1isanidentitymatrix.Thisallowstowritetherelations:q=L(1)1,(7)q=L(1)1+L(1)1,(8)andwriteareducedorderdynamicsintermsof1,as:M(1)L(1)1+V1(1,1)1+F(1)+G(1)+d(t)=u+JTh(1)+JbT(1)FE,(9)whereV1(1,1)=M(1)L(1)+C(1,1)L(1).Pre-multiplyingeq.(9)byLT(1)andtakingintoaccountthatJh(1)L(1)=0,thereducedorderdyna-micsisgivenby:M1+V11+F+G+d=LTu,(10)whereM=LTML,V1=LTV1,F=LTF,G=LTG,d=LTbracketleftbigdJbTFEbracketrightbig.436P.Gierlak3NeuralNetworkHybridControlTheaimofahybridposition/forcecontrolistofollowadesiredtrajectoryofmotion1dRn1,andexertdesiredcontactforcedRm1normallytothesurface.Bydefiningamotionerrore,afilteredmotionerrors,aforceerrorandanauxiliarysignal1as:e=1d1,(11)s=e+e,(12)=d,(13)1=1d+e,(14)whereisapositivediagonaldesignmatrix,thedynamicequation(10)maybewrittenintermsofthefilteredmotionerrorasMs=V1s+LTf(x)+LTbracketleftbigdJbTFEbracketrightbigLTu,(15)withanonlinearfunctionf(x)=ML1+V11+F+G,(16)wherex=bracketleftBigeTeTT1dvT1dT1dbracketrightBigT.Themathematicalstructureofhybridposi-tion/forcecontrollerhasaformof7u=f(x)+KDLsJThbracketleftBigd+KFbracketrightBig,(17)whereKDandKFarepositivedefinitematrixesofpositionandforcegain,isarobustifyingterm,f(x)approximatesthefunction(16).Thisfunctionmaybeapproximatedbytheneuralnetwork.Inthisworkaty