1、Full-PoseCalibrationofaRobotManipulatorUsingaCoordinate-MeasuringMachineMorrisR/Driels/LtW/SwayzeUSNandLtS/PotterUSNDepartmentofMechanicalEngineering/NavalPostgraduateSchool/Monterey/California/USTheworkreportedinthisarticleaddressesthekinematiccalibrationofarobotmanipulatorusingacoordinatemeasuring
2、machine(CMM)whichisabletoobtainthefullposeoftheend-effector/Akinematicmodelisdevelopedforthemanipulator/itsrelationshiptotheworldcoordinateframeandthetool/Thederivationofthetoolposefromexperimentalmeasurementsisdiscussed/asistheidentificationmethodology/Acompletesimulationoftheexperimentisperformed/
3、allowingtheobservationstrategytobedefined/Theexperimentalworkisdescribedtogetherwiththeparameteridentificationandaccuracyverification/Theprincipalconclusionisthatthemethodisabletocalibratetherobotsuccessfully/witharesultingaccuracyapproachingthatofitsrepeatability/Keywords/Robotcalibration；Coordinat
4、emeasurement；Parameteridentification；Simulationstudy；Accuracyenhancement1/IntroductionItiswellknownthatrobotmanipulatorstypicallyhavereasonablerepeatability(0/3ram)/yetexhibitpooraccuracy(10/0mm)/Theprocessbywhichrobotsmaybecalibratedinordertoachieveaccuraciesapproachingthatofthemanipulatorisalsowel
5、lunderstood1/Inthecalibrationprocess/severalsequentialstepsenabletheprecisekinematicparametersofthemanipulatortobeidentified/leadingtoimprovedaccuracy/Thesestepsmaybedescribedasfollows/1/Akinematicmodelofthemanipulatorandthecalibrationprocessitselfisdevelopedandisusuallyaccomplishedwithstandardkinem
6、aticmodellingtools2/Theresultingmodelisusedtodefineanerrorquantitybasedonanominal(manufacturers)kinematicparameterset/andanunknown/actualparametersetwhichistobeidentified/2/Experimentalmeasurementsoftherobotpose(partialorcomplete)aretakeninordertoobtaindatarelatingtotheactualparametersetfortherobot/
7、3/Theactualkinematicparametersareidentifiedbysystematicallychangingthenominalparametersetsoastoreducetheerrorquantitydefinedinthemodellingphase/OneapproachtoachievingthisidentificationisdeterminingtheanalyticaldifferentialrelationshipbetweentheposevariablesPandthekinematicparametersKintheformofaJaco
8、bian/andtheninvertingtheequationtocalculatethedeviationofthekinematicparametersfromtheirnominalvaluesAlternatively/theproblemcanbeviewedasamultidimensionaloptimisationtask/inwhichthekinematicparametersetischangedinordertoreducesomedefinederrorfunctiontozero/Thisisastandardoptimisationproblemandmaybe
9、solvedusingwell-known3methods/4/Thefinalstepinvolvestheincorporationoftheidentifiedkinematicparametersinthecontrolleroftherobotarm/thedetailsofwhichareratherspecifictothehardwareofthesystemunderstudy/Thispaperaddressestheissueofgatheringtheexperimentaldatausedinthecalibrationprocess/Severalmethodsar
10、eavailabletoperformthistask/althoughtheyvaryincomplexity/costandthetimetakentoacquirethedata/Examplesofsuchtechniquesincludetheuseofvisualandautomatictheodolites4/5/6/servocontrolledlaserinterferometers7/acousticsensors8andvidualsensors9/Anidealmeasuringsystemwouldacquirethefullposeofthemanipulator(
11、positionandorientation)/becausethiswouldincorporatethemaximuminformationforeachpositionofthearm/Allofthemethodsmentionedaboveuseonlythepartialpose/requiringmoredatatobetakenforthecalibrationprocesstoproceed/2/TheoryInthemethoddescribedinthispaper/foreachpositioninwhichthemanipulatorisplaced/thefullp
12、oseismeasured/althoughseveralintermediatemeasurementshavetobetakeninordertoarriveatthepose/Thedeviceusedfortheposemeasurementisacoordinate-measuringmachine(CMM)/whichisathree-axis/prismaticmeasuringsystemwithaquotedaccuracyof0/01ram/Therobotmanipulatortobecalibrated/aPUMA560/isplacedclosetotheCMM/an
13、daspecialend-effectorisattachedtotheflange/Fig/1showsthearrangementofthevariouspartsofthesystem/Inthissectionthekinematicmodelwillbedeveloped/theposeestimationalgorithmsexplained/andtheparameteridentificationmethodologyoutlined/2/1KinematicParametersInthissection/thebasickinematicstructureofthemanip
14、ulatorwillbespecified/itsrelationtoauser-definedworldcoordinatesystemdiscussed/andtheend-pointtoilmodelled/Fromthesemodels/thekinematicparameterswhichmaybeidentifiedusingtheproposedtechniquewillbespecified/andamethodfordeterminingthoseparametersdescribed/Thefundamentalmodellingtoolusedtodescribethes
15、patialrelationshipbetweenthevariousobjectsandlocationsinthemanipulatorworkspaceistheDenavit-Hartenbergmethod2/withmodificationsproposedbyHayati10/Mooring11andWu12toaccountfordisproportionalmodels13whentwoconsecutivejointaxesarenominallyparallel/AsshowninFig/2/thismethodplacesacoordinateframeoneachob
16、jectormanipulatorlinkofinterest/andthekinematicsaredefinedbythehomogeneoustransformationrequiredtochangeonecoordinateframeintothenext/ThistransformationtakesthefamiliarformTheaboveequationmaybeinterpretedasameanstotransformframen-1intoframenbymeansoffouroutofthefiveoperationsindicated/Itisknownthato
17、nlyfourtransformationsareneededtolocateacoordinateframewithrespecttothepreviousone/Whenconsecutiveaxesarenotparallel/thevalueof/3/isdefinedtobezero/whileforthecasewhenconsecutiveaxesareparallel/d/isthevariablechosentobezero/WhencoordinateframesareplacedinconformancewiththemodifiedDenavit-Hartenbergm
18、ethod/thetransformationsgivenintheaboveequationwillapplytoalltransformsofoneframeintothenext/andthesemaybewritteninagenericmatrixform/wheretheelementsofthematrixarefunctionsofthekinematicparameters/Theseparametersaresimplythevariablesofthetransformations/thejointangle0//thecommonnormaloffsetd//thelinklengtha//theangleoftwista//andtheangle/3/Thematrixformisusuallyexpressedasfollows/
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