1、外文翻译译文题目一种与移动机械臂的局部零件所受载荷相协调的运动结构(2)原稿题目AkinematicallyCOmPatibleframeworkforCOoPeratiVePaylOadtransportbySonholonomicmobilemanipulators(2)原稿出处AUtOnRobot(2006)21:227-242Akinematicallycompatibleframeworkforcooperativepayloadtransportbynonholonomicmobilemanipulators(2)M.Abou-Samah1,C.P.Tang2,R.M.Bhatt2
2、andV.Krovi2(1) MSCSoftwareCorporation,AnnArbor,Ml48105,USA(2) MechanicalandAerospaceEngineering,StateUniversityofNewYorkatBuffalo,Buffalo,NY14260,USAReceived:5August2005Revised:25May2006Accepted:30May2006Publishedonline:5September2006AbstractInthispaper,weexaminethedevelopmentofakinematicallycompati
3、blecontrolframeworkforamodularsystemofwheeledmobilemanipulatorsthatcanteamuptocooperativelytransportacommonpayload.Eachindividuallyautonomousmobilemanipulatorconsistsofadifferentially-drivenWheeledMobileRobot(WMR)withamountedtwodegree-of-freedom(d.o.f)revolute-jointed,planarandpassivemanipulatorarm.
4、Thecompositewheeledvehicle,formedbyplacingapayloadattheend-effectorsoftwo(ormore)suchmobilemanipulators,hasthecapabilitytoaccommodate,detectandcorrectbothinstantaneousandfiniterelativeconfigurationerrors.Thekinematica11y-compatib1emotion-planning/controlframeworkdevelopedhereisintendedtofacilitatema
5、intenanceofallkinematic(holonomicandnonholonomic)constraintswithinsuchsystems.Givenanarbitraryend-effectortrajectory,eachindividualmobi1e-manipu1ator,sbi-levelhierarchicalcontrollerfirstgeneratesakinematically-feasibledesiredtrajectoryfortheWMRbase,whichisthentrackedbyasuitablelower-levelposturestab
6、ilizingcontroller.Twovariantsofsystem-levelcooperativecontrolschemesleader-followeranddecentralizedcontrolarethencreatedbasedontheindividualmobi1e-manipuIatorcontrolscheme.Bothmethodsareevaluatedwithinanimplementationframeworkthatemphasizesbothvirtualprototyping(VP)andhardware-in-the-loop(HIL)experi
7、mentation.Simulationandexperimentalresultsofanexampleofatwo-modulesystemareusedtohighlightthecapabilitiesofareal-timelocalsensor-basedcontrollerforaccommodation,detectionandcorectionofrelativeformationerrors.KeywordsCompositesystem-Hardware-in-the-loop-MobilemanipuIator-Physicalcooperation-Redundanc
8、yresolution-VirtualprototypingKinematiccollaborationoftwomobilemanipulatorsWenowexaminetwovariantsofsystem-levelcooperativecontrolschemes-leader-followeranddecentralizedcontrol-thatcanbecreatedbasedontheindividualmobi1e-manipu1atorcontrolscheme.1.eader-followerapproachThefirstmethodofmodelingsuchasy
9、stemconsidersthemidpointofthemobilebase(MPB)ofthemobi1e-manipuIatorBtoberigidlyattachedtotheend-effectorofmobilemanipulatorA,asdepictedinFig.4.Figure4(b)depictshowtheend-effectorframe用ofMPAisrigidlyattachedtotheframeatMPB(separatedbyaconstantrotationangle).co0anj3Xg0Yt(15)Fig.4Schematicdiagramsofthe
10、leader-followerscheme:(a)the3-linkmobilemanipulatorunderanalysis,and(b)thetwo-modulecompositesystem(*),玦),g(2),MPBnowtakesontheroleoftheleaderandcanbecontrolledtofollowanytrajectorythatisfeasibleforaWMR.Hence,givenatrajectoryoftheleaderMPBand the preferred manipulator configuration of( M(e)(5) can b
11、e rewritten as:X，_co8XYi=sin/5cob0Y；三inco-rfcc4-in,rfLj+LcosLjco空1.ISm%+三nC0Sinyc07-smqi323-Lsin11.11三)Ljc03Ljcott0|彳(16)andcorrespondinglyEqs.(6)-(8)as:(17)(部三(2)+M)xi-jx(%7rco也Thus,thetrajectoryofthevirtual(reference)robotforthefollowerMPA(Xf,F,CIvf).u4C),andthederivedvelocitiescannowbedetermined.
12、Thisformstheleader-followerschemeusedforthecontrolofthecollaborativesystemcarryingacommonpayload.DecentralizedapproachThesecondapproachconsiderstheframeattachedtoapointofinterestonthecommonpayloadastheend-effectorframeofboththeflankingmobilemanipulatorsystems,asdepictedinFig.5.Thus,adesiredtrajector
13、yspecifiedforthispayloadframecanthenprovidethedesiredreferencetrajectoriesforthetwomobileplatformsusingthesimilarframeworkdevelopedintheprevioussectionbytaking人工3=and0*),wherek=A,B.ThispermitsEq.(5)toberewrittenas:气4AilkYieo4-4coV一mVsin/cosFig. 5 Decentralizedcontrolschemeimplementationpermitsthe(a)
14、compositesystem;tobetreatedas(b)twoindependent2-linkmobilemanipulatorsS=慧)，=(), (tvi),kd v 上 W * Yd(kiVandcorrespondinglyEq.(6)-(8)as:(19)Eachtwo-linkmobilemanipulatornowcontrolsitsconfigurationwithreferencetothiscommonend-effectorframemountedonthepayload.However,thelocationsoftheattachmentsofthephy
15、sicalmanipulatorswithrespecttothepayloadreferenceframemustbeknownapriori.ImplementationframeworkWeexaminethedesignanddevelopmentofatwo-stageimplementationframework,showninFig.6,thatemphasizesbothvirtualprototyping(VP)basedrefinementandhardware-in-1he-1oop(HIL)experimentation.Fig. 6 Paradigmforrapidd
16、evelopmentandtestingofthecontrolschemeonvirtualandphysicalprototypesVirtualprototypingbasedrefinementInthefirststage,weemployvirtualprototyping(VP)toolstorapidlycreate,evaluateandrefineparametricmodelsoftheoverallsystemandtestvariousalgorithmsinsimulationwithinavirtualenvironment.3Dsolidmodelsofthem
17、obileplatformsandthemanipulatorsofinterestarecreatedinaCADpackage,andexportedwiththeircorrespondinggeometricandmaterialpropertiesintoadynamicsimulationenvironment.Figure7(a)showsanexampleoftheapplicationofsuchframeworkforsimulatingthemotionofamobileplatformcontrolledbyanalgorithmimplementedinSimulin
18、k.However,itisimportanttonotethattheutilityofsuchvirtualtestingislimitedby:(a)theabilitytocorrectlymodelandsimulatethevariousphenomenawithinthevirtualenvironment;(b)thefidelityoftheavailablesimulationtools;and(c)ultimately,theabilityofthedesignertocorrectlymodelthedesiredsystemandsuitablyinterpretth
19、eresults.Fig. 7 AsingleWMRbaseundergoingtestingwithinthe(a)virtualprototypingframework;and(b)hardware-in-the-loop(HIL)testingframeworkHardware-in-the-loopexperimentationWeemployahardware-in-the-loop(HIL)methodologyforrapidexperimentalverificationofthereal-timecontrollersontheelectromechanicalmobilem
20、anipulatorprototypes.EachindividualWMRisconstructedusingtwopoweredwheelsandtwounactuatedcasters.Conventionaldisc-typerearwheels,poweredbygear-motors,arechosenbecauseofrobustphysicalconstructionandeaseofoperationinthepresenceofterrainirregularities.Passiveballcastersarepreferredoverwheelcasterstosimp
21、lifytheconstraintsonmaneuverabilityintroducedbythecasters.Themountedmanipulatorarmhastwopassiverevolutejointswithaxesofrotationparalleltoeachotherandperpendiculartothebaseofthemobileplatform.Thefirstjointisplacedappropriatelyatthegeometriccenterontopframeoftheplatform.Thelocationofthesecondjointcanb
22、eadjustedtoanypositionalongtheslottedfirstlink.Thesecondlinkitselfisreducedtoaflatplatesupportedbythesecondjoint.Eachjointisinstrumentedwithopticalencoderthatcanmeasurethejointrotations.Thecompletelyassembledtwo-linkmobilemanipulatorisshowninFig.1.(c).Thesecondmobilemanipulator(seeleftmoduleofFig.1(
23、b)and(d)employsthesameoveralldesignbutpossessesamotoratthebasejointofthemountedtwo-linkarm.Themotormaybeusedtocontrolthejointmotionalongapredeterminedtrajectory(whichcanincludebraking/holdingthejointatapredeterminedposition).Whenthemotorisswitchedoffthejointnowrevertstoapassivejoint(withmuchgreaterd
24、amping).Themotorisincludedforpermittingfutureforce-redistributionstudies.Inthispaper,however,themotorisusedsolelytolockthejointpreventself-motionsofthearticulatedlinkageforcertainpathologicalcases(Bhattetal.,2005;TangandKrovi,2004).PWrM-OUtputmotordrivercardsareusedtodrivethegearmotors;andencodercar
25、dsmonitortheencodersinstrumentingthevariousarticulatedarms.ThisembeddedcontrollercommunicateswithadesignatedhostcomputerusingTCP/IPforprogramdownloadanddatalogging.ThehostcomputerwithMATLAB/Simulink/RealTimeWorkshopprovidesaconvenientgraphicaluserinterfaceenvironmentforsystem-levelsoftwaredevelopmen
26、tusingablock-diagrammaticlanguage.Thecompiledexecutableisdownloadedoverthenetworkandexecutesinreal-timeontheembeddedcontrollerwhileaccessinglocallyinstalledhardwarecomponents.Inparticular,theabilitytoselectivelytestcomponents/systemsatvariouslevels(e.g.individualmotors,individualWMRsorentiresystems)
27、withoutwearingoutcomponentsduringdesigniterationswasveryuseful.Figure7(b)illustratestheimplementationofsuchasystemononeoftheWMRs.Numerouscalibration,simulationandexperimentalstudiescarriedoutwiththisframework,attheindividual-levelandsystem-level,arereportedinAbou-Scimah(2001).ExperimentalresultsFort
28、hesubsequentexperiments,2weprescribetheinitialconfigurationofthetwo-modulecompositesystem,asshowninFig.8.Specifically,wepositionthetwoWMRSsuchthatMPAislocatedatarelativepositionof工一O.OOjdjOin.)y=0.61m124in.,ancjwt1arelativeorientationdifferenceof=0.00owithrespecttoMPB.Forfixedlink-lengthsthisinheren
29、tlyspecifiesthevaluesofthevariousconfigurationanglesasshowninTable1.Table1Parametersfortheinitialconfigurationofthetwo-modulecompositewheeledsystem(seeFig.8fordetails)LinklengthsofthearticulationL10.28m(11in)L20.28m(11in)RelativeanglesoftheconfigurationofthearticulationL30.28m(11in)1333.982280.07o33
30、37.36oOffsetbetweenthewheeledmobilebases1128.59o0.00oObOax0.00m(0in)0.61m(24in)Fig.8Initialconfigurationofthetwo-modulecompositewheeledsystem1.eader-followerapproachAstraightlinetrajectoryatavelocityof0.0254m/sisprescribedfortheleader,MPB.Givenadesiredconfigurationofthemanipulatorarm,thealgorithmdes
31、cribedinSection4.1isusedtoobtainadesiredtrajectoryforMPA.AlargedisruptionisintentionallyintroducedbycausingoneofthewheelsofMPAtorunoverabump,toevaluatetheeffectivenessofthedisturbanceaccommodation,detectionandcompensation.Theresultsareexaminedintwocasescenarios-CaseA:MPAemploysodometricestimationfor
32、localizationasseeninFig.9,andCaseB:MPAemployssensedarticulationsforIocalizationasseeninFig.10.Ineachofthesefigures,(a)presentstheoveral1(Xu,u)-trajectoryofMofMPAwithrespecttotheend-effectorframe(thatisrigidlyattachedtothe.ofMPB)while(b),(c)and(d)presenttherelativeorientationdifference,differenceandd
33、ifferenceasfunctionsoftime.Furtherinbothsetsoffigures,theDesired(-line)isthedesiredtrajectorytypicallycomputedoffline;and*Actual,(-o-line)thesystem,asdeterminedbypost-processingthearticulations.is the actual trajectory followed by measurements of the instrumentedHowever,inFig.9,the(-x-line)represent
34、stheodometricestimatewhileinFig.10itFig.9 Ca se A: Odom etric Estim ation ofFrame M, used in the controI of MP A followi(which therefore coincides with the Actualstands for the articulation based estimate后恐Iused for control of MPA J with respect to MP B in a leader-follower approach is able to detec
35、t and correct non-systematic errors suchFig. 10ArticulationEstimation ofCase B: based Frame M,g MPBin a leader -follow(d)erapproach,isunabletodetectnon-systematicerrorssuchaswheel-slip,(a)XYtrajectoryofFrameM;(b)OrientationversusTime;(c)XpositionofFrameMversusTime;and(d)YpositionofFrameMversusTimeas
36、wheel-slip,(a)XYtrajectoryofFrameM;(b)OrientationversusTime;(c)XpositionofFrameMversustime;and(d)YpositionofFrameMversustimeInCaseA,theintroductionofthedisruptioncausesadriftintherelativeconfigurationofthesystemwhichremainsundetectedbytheodometricestimation.Further,asseeninFig.9,thisdrifthasatendenc
37、ytogrowifleftuncorrected.However,asseeninFig.i0,thesystemcanusethearticulation-basedestimation(CaseB)tonotonlydetectdisturbancestotherelativeconfigurationbutalsotosuccessfullyrestoretheoriginalsystemconfiguration.DecentralizedcontrolapproachInthisdecentralizedcontrolscenario,astraightlinetrajectoryw
38、ithavelocityof0.0254m/sispresentedforthepayloadframe.Asintheleader-followerscenario,alargedisruptionisintroducedbycausingoneofthewheelsofMPAtorunoverabump.ThealgorithmistestedusingtwofurthercasescenariosCaseC:BothmobiIeplatformsemployodometricestimationforlocalizationasshowninFig.1_1,andCaseD:Bothmo
39、bileplatformsemploysensedarticulationsforlocalizationasshowninFig.2.化、小Fig.11CaseC:OdometricestimationofframesMofMPAandMPB,usedinthecontrolofMPAwithrespecttoMPBinthedecentralizedapproach,isagainunabletodetectnon-systematicerrorssuchaswheel-slip.(a)XYtrajectoryofframeMofMPA;(b)XYtrajectoryofframeMofM
40、PB;(c)Relativeorientation,betweenMPAandMPB,versustime;(d)Xdistance,betweenMPAandMPB,versustime;and(e)Ydistance,betweenMPAandMPB,versustime.(f)Sequentialphotographsofthecorrespondingcompositesystemmotion(astimeprogressesfromlefttorightalongeachrow)Fig.of MP A and MP B with respect to a payload-fixed
41、frame is able to detect and correct non-systematic errors such as wheel-slip, (a) XY trajectory of frame M of MP A; (b) XY trajectory of frame M of MP B; (c) Relative orientation, between MP A and MP B, versus time; (d) X distance, between MP A and MP B, versus time; and (e) Y distance, between MP A
42、 and MP B, versus time. (f) Sequential photographs of the corresponding composite system motion (as time progresses from left to right along each row)12CaseD:ArticulationbasedestimaIneachofthesefigures,subplots(a)and(b)presentstheoverall(viVtrajectoriesofframesMofMPAandMPBrespectivelywithrespecttoth
43、eirinitialposes.Subplots(c),(d)and(e)presenttherelativeorientationdifference,differenceanddifferenceofframes册ofMPAandMPBrespectivelyasfunctionsoftime.Furtherinbothsetsoffigures,theDesired(-line)isthedesiredtrajectorytypicallycomputedoffline;and4Actual,(-o-line)istheactualtrajectoryfollowedbythesyste
44、m,asdeterminedbypost-processingthemeasurementsoftheinstrumentedarticulations.However,inFig.LI,the(-x-line)representstheodometricestimatewhileinFig.12itstandsforthearticulationbasedestimate.InCaseC,bothmobileplatformsusetheodometricestimationforlocalization-henceasexpected,Fig.reflectsthefactthatthes
45、ystemisunabletodetectorcorrectforchangesintherelativesystemconfiguration.HoweverthedataobtainedfromthearticulationsaccuratelycapturestheexistenceoferrorsbetweentheframesofreferenceofMPBandMPA.Thus,usingthearticulation-basedestimationofrelativeconfigurationforcontrolasinCaseDallowsthedetectionofdistu
46、rbancesandsuccessfulrestorationoftheoriginalsystemconfigurationasshowninFig.12.Note,however,whiletherelativesystemconfigurationismaintained,errorsrelativetoaglobalreferenceframecannotbedetectedifbothWMRSundergoidenticalsimultaneousdisturbances.Detectionofsuchabsoluteerrorswouldrequireanexternalrefer
47、enceandisbeyondthescopeoftheexistingframework.ConclusionInthispaper,weexaminedthedesign,developmentandvalidationofakinematicallycompatibleframeworkforcooperativetransportofacommonpayloadbyateamofnonholonomicmobilemanipulators.Eachindividualmobilemanipulatormoduleconsistsofadifferentiallydrivenwheele
48、dWMRretrofittedwithapassivetworevolutejointedplanarmanipulatorarm.Acompositemultidegree-Of-freedomvehiclesystemcouldthenbemodularIycreatedbyattachingacommonpayloadontheend-effectoroftwoormoresuchmodules.Thecompositesystemallowedpayloadtrajectorytrackingerrors,arisingfromsubsystemcontrollererrorsorenvironmentaldisturbances,tobereadilyaccommodatedwithinthecomplianceofferedbythearticulatedlinkage.TheindividualmobilemanipulatorscompensatedbymodifyingtheirWMRbases,
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