外文翻译--应用坐标测量机的机器人运动学姿态的标定 原版.PDF

IntJAdvManufTechnol(1993)8:34-4191993Springer-VerlagLondonLimitedTheInternationalJournalofRdvancedmanufacturingTechnoloouFull-PoseCalibrationofaRobotManipulatorUsingaCoordinate-MeasuringMachineMorrisR.Driels,LtW.SwayzeUSNandLtS.PotterUSNDepartmentofMechanicalEngineering,NavalPostgraduateSchool,Monterey,California,USATheworkreportedinthisarticleaddressesthekinematiccalibrationofarobotmanipulatorusingacoordinatemeasuringmachine(CMM)whichisabletoobtainthefullposeoftheend-effector.Akinematicmodelisdevelopedforthemanipulator,itsrelationshiptotheworldcoordinateframeandthetool.Thederivationofthetoolposefromexperimentalmeasurementsisdiscussed,asistheidentificationmethodology.Acompletesimulationoftheexperimentisperformed,allowingtheobservationstrategytobedefined.Theexperimentalworkisdescribedtogetherwiththeparameteridentificationandaccuracyverification.Theprincipalconclusionisthatthemethodisabletocalibratetherobotsuccessfully,witharesultingaccuracyapproachingthatofitsrepeatability.Keywords:Robotcalibration；Coordinatemeasurement；Par-ameteridentification；Simulationstudy；Accuracyenhance-ment1.IntroductionItiswellknownthatrobotmanipulatorstypicallyhavereasonablerepeatability(0.3ram),yetexhibitpooraccuracy(10.0mm).Theprocessbywhichrobotsmaybecalibratedinordertoachieveaccuraciesapproachingthatofthemanipulatorisalsowellunderstood1.Inthecalibrationprocess,severalsequentialstepsenabletheprecisekinematicparametersofthemanipulatortobeidentified,leadingtoimprovedaccuracy.Thesestepsmaybedescribedasfollows:1.Akinematicmodelofthemanipulatorandthecalibrationprocessitselfisdevelopedandisusuallyaccomplishedwithstandardkinematicmodellingtools2.Theresultingmodelisusedtodefineanerrorquantitybasedonanominal(manufacturers)kinematicparameterset,andanunknown,actualparametersetwhichistobeidentified.Acceptedforpublication:21October1991Correspondenceandoffprintrequeststo:Prof.MorrisR.Driels,DepartmentofMechanicalEngineering.NavalPostgraduateSchool,Monterey,California93943,USA.2.3.Experimentalmeasurementsoftherobotpose(partialorcomplete)aretakeninordertoobtaindatarelatingtotheactualparametersetfortherobot.Theactualkinematicparametersareidentifiedbysystemati-callychangingthenominalparametersetsoastoreducetheerrorquantitydefinedinthemodellingphase.OneapproachtoachievingthisidentificationisdeterminingtheanalyticaldifferentialrelationshipbetweentheposevariablesPandthekinematicparametersKintheformofaJacobian,P=JK(1)andtheninvertingtheequationtocalculatethedeviationofthekinematicparametersfromtheirnominalvalues8K=jrj-,jrp(2)Alternatively,theproblemcanbeviewedasamultidimen-sionaloptimisationtask,inwhichthekinematicparametersetischangedinordertoreducesomedefinederrorfunctiontozero.Thisisastandardoptimisationproblemandmaybesolvedusingwell-known3methods.4.Thefinalstepinvolvestheincorporationoftheidentifiedkinematicparametersinthecontrolleroftherobotarm,thedetailsofwhichareratherspecifictothehardwareofthesystemunderstudy.Thispaperaddressestheissueofgatheringtheexperimentaldatausedinthecalibrationprocess.Severalmethodsareavailabletoperformthistask,althoughtheyvaryincomplexity,costandthetimetakentoacquirethedata.Examplesofsuchtechniquesincludetheuseofvisualandautomatictheodolites4,5,6,servocontrolledlaserinterferometers7,acousticsensors8andvidualsensors9.Anidealmeasuringsystemwouldacquirethefullposeofthemanipulator(positionandorientation),becausethiswouldincorporatethemaximuminformationforeachpositionofthearm.Allofthemethodsmentionedaboveuseonlythepartialpose,requiringmoredatatobetakenforthecalibrationprocesstoproceed.Full-PoseCalibrationofaRobotManipulator352.TheoryInthemethoddescribedinthispaper,foreachpositioninwhichthemanipulatorisplaced,thefullposeismeasured,althoughseveralintermediatemeasurementshavetobetakeninordertoarriveatthepose.Thedeviceusedfortheposemeasurementisacoordinate-measuringmachine(CMM),whichisathree-axis,prismaticmeasuringsystemwithaquotedaccuracyof0.01ram.Therobotmanipulatortobecalibrated,aPUMA560,isplacedclosetotheCMM,andaspecialend-effectorisattachedtotheflange.Fig.1showsthearrangementofthevariouspartsofthesystem.Inthissectionthekinematicmodelwillbedeveloped,theposeestimationalgorithmsexplained,andtheparameteridentifi-cationmethodologyoutlined.2.1KinematicParametersInthissection,thebasickinematicstructureofthemanipulatorwillbespecified,itsrelationtoauser-definedworldcoordinatesystemdiscussed,andtheend-pointtoilmodelled.Fromthesemodels,thekinematicparameterswhichmaybeidentifiedusingtheproposedtechniquewillbespecified,andamethodfordeterminingthoseparametersdescribed.ThefundamentalmodellingtoolusedtodescribethespatialrelationshipbetweenthevariousobjectsandlocationsinthemanipulatorworkspaceistheDenavit-Hartenbergmethod2,withmodificationsproposedbyHayati10,Mooring11andWu12toaccountfordisproportionalmodels13whentwoconsecutivejointaxesarenominallyparallel.AsshowninFig.2,thismethodplacesacoordinateframeonJointn/Joint.n+1L/Linkn+1.L-/ZnnX.-Y/Yn-1X,-IFig.2.Linkcoordinateframeallocation.eachobjectormanipulatorlinkofinterest,andthekinematicsaredefinedbythehomogeneoustransformationrequiredtochangeonecoordinateframeintothenext.ThistransformationtakesthefamiliarformA.=rot(z,O.)trans(z,d,)trans(x,a.)rot(x,t.)rot(y,fl.)(3)Theaboveequationmaybeinterpretedasameanstotransformframen-1intoframenbymeansoffouroutofthefiveoperationsindicated.Itisknownthatonlyfourtransformationsareneededtolocateacoordinateframewithrespecttothepreviousone.Whenconsecutiveaxesarenotparallel,thevalueof/3.isdefinedtobezero,whileforthecasewhenconsecutiveaxesareparallel,d.isthevariablechosentobezero.WhencoordinateframesareplacedinconformancewiththemodifiedDenavit-Hartenbergmethod,thetransformationsgivenintheaboveequationwillapplytoalltransformsofoneframeintothenext,andthesemaybewritteninagenericmatrixform,wheretheelementsofthematrixarefunctionsofthekinematicparameters.Theseparametersaresimplythevariablesofthetransformations:thejointangle0.,thecommonnormaloffsetd.,thelinklengtha.,theangleoftwista.,andtheangle/3.Thematrixformisusuallyexpressedasfollows:An=Ce.CO.-SO.Sa.SO.-Se.Ca.CO.SO.+Se.Sa.CO.a.CO.SO.CO.+CO.Sa.SO.CO.Ca.SO.SO.-CO.Sa.CO.a.Se.(4)-Ca.SO.Sot.Ca.CO.d.0001Fig.1.Calibrationequipment.Foraseriallinkage,suchasarobotmanipulator,acoordinateframeisattachedtoeachconsecutivelinksothatboththeinstantaneouspositiontogetherwiththeinvariantgeometryaredescribedbythepreviousmatrixtransformation.The36M.R.DrielsetaL9%82)/4.Z41-,.X4Fig.3.PUMAframeallocation.transformationfromthebaselinktothenthlinkwillthereforebegivenbyTn=A1A2.An(5)Fig.3showsthePUMAmanipulatorwiththeDenavit-Hartenbergframesattachedtoeachlink,togetherwithworldcoordinateframeandatoolframe.Thetransform-ationfromtheworldframetothebaseframeofthemanipulatorneedstobeconsideredcarefully,sincetherearepotentialparameterdependenciesifcertaintypesoftransformsarechosen.ConsiderFig.4,whichshowstheworldframexw,y,z,theframeXo,Yo,z0whichisdefinedbyaDHtransformfromtheworldframetothefirstjointaxisofthemanipulator,frameXb,Yb,Zb,whichisthePUMAJe4ZlxbYb/1/do9.Yw.xwZwFig.4.Basetransformations.manufacturersdefinedbaseframe,andframexl,Yl,zlwhichisthesecondDHframeofthemanipulator.Weareinterestedindeterminingtheminimumnumberofparametersrequiredtomovefromtheworldframetotheframex,Yl,z.Therearetwotransformationpathsthatwillaccomplishthisgoal:Path1:ADHtransformfromx,y,z,tox0,Yo,zoinvolvingfourparameters,followedbyanothertransformfromxo,Yo,z0toXb,Yb,ZbwhichwillinvolveonlytwoparametersbanddinthetransformTob=rot(z0,4)trans(zo,d)(6)Finally,anotherDHtransformfromxb,Yb,ZbtoXt,y,ZwhichinvolvesfourparametersexceptthatA01and4arebothabouttheaxiszoandcannotthereforebeidentifiedindependently,andAdlanddarebothalongtheaxiszoandalsocannotbeidentifiedindependently.Itrequires,therefore,onlyeightindependentkinematicparameterstogofromtheworldframetothefirstframeofthePUMAusingthispath.Path2:Asanalternative,atransformmaybedefineddirectlyfromtheworldframetothebaseframeXb,Yb,Zb.Sincethisisaframe-to-frametransformitrequiressixparameters,suchastheEulerform:Ab=rot(z,Cb)rot(y,0b)rot(x,bb)trans(Pxb,Pyb,Pzb)(7)ThefollowingDHtransformfromxb,Yb,zbtOXl,Yl,zlwouldinvolvefourparameters,butA0mayberesolvedinto4,0b,andAdresolvedintoPxb,Pyb,Pzb,reducingtheparametercounttotwo.Itisseenthatthispathalsorequireseightparametersasinpathi,butadifferentset.EitheroftheabovemethodsmaybeusedtomovefromtheworldframetothesecondframeofthePUMA.Inthiswork,thesecondpathischosen.ThetooltransformisanEulertransformwhichrequiresthespecificationofsixparameters:As=rot(z,b6)rot(y,04)rot(x,/6)(8)trans(Px6,Py6,P,6)Thetotalnumberofparametersusedinthekinematicmodelbecomes30,andtheirnominalvaluesaredefinedinTable1.2.2IdentificationMethodologyThekinematicparameteridentificationwillbeperformedasamultidimensionalminimisationprocess,sincethisavoidsthecalculationofthesystemJacobian.Theprocessisasfollows:1.Beginwithaguesssetofkinematicparameters,suchasthenominalset.2.SelectanarbitrarysetofjointanglesforthePUMA.3.CalculatetheposeofthePUMAend-effector.4.MeasuretheactualposeofthePUMAend-effectorforthesamesetofjointangles.Ingeneral,themeasuredandpredictedposewillbedifferent.5.Modifythekinematicparametersinanorderlymannerinordertobestfit(inaleast-squaressense)themeasuredposetothepredictedpose.Table1.NominalparametersforthePUMArobot.0bP*bP,bPzb(o)(o)(o)(mm)(mm)(mm)180.00.090.0-394.0-383.0474.0Link(50,d,a,/3,(o)(mm)(mm)(1000.0-90.0020.00431.850.00.030.0149.09-20.3390.0040.0433.00.0-90.0050.00.00.090.00(mm)(mm)(ram)90.00.00.00.00.0134.0Theprocessisappliednottoasinglesetofjointanglesbuttoanumberofjointangles.Thetotalnumberofjointanglesetsrequired,whichalsoequalsthenumberofphysicalmeasurementmade,mustsatisfyKp.NDt(9)whereKpisthenumberofkinematicparameterstobeidentifiedNisthenumberofmeasurements(poses)takenDrrepresentsthenumberofdegreesoffreedompresentineachmeasurementInthesystemdescribedinthispaper,thenumberofdegreesoffreedomisgivenbyDt=6(10)sincefullposeismeasured.Inpractice,manymoremeasure-mentsshouldbetakentooffsettheeffectofnoiseintheexperimentalmeasurements.TheoptimisationprocedureusedisknownasZXSSO,andisastandardlibraryfunctionintheIMSLpackage14.2.3PoseMeasurementItisapparentfromtheabovethatameanstodeterminethefullposeofthePUMAisrequiredinordertoperformthecalibration.Thismethodwillnowbedescribedindetail.Theend-effectorconsistsofanarrangementoffiveprecision-toolingballsasshowninFig.5.Considerthecoordinatesofthecentreofeachballexpressedi