Haptic teleoperation system control design for the ultrasound task A loopshaping approach - PDF document

Haptictele-operationsystemcontroldesignfortheultrasoundtask:Aloop-shapingapproachC.J.Zandsteeg,D.J.H.Bruijnen,M.J.G.vandeMolengraftEindhovenUniversityofTechnology,DepartmentofMechanicalEngineering,Postbus513,5600MBEindhoven,TheNetherlandsPhilipsAppliedTechnologies,HighTechCampus7,5656AEEindhoven,TheNetherlandsarticleinfoMedicalsystemsControlsystemdesign Correspondingauthor.Tel.:+30631042913.E-mailaddresses:(C.J.Zandsteeg), Mechatronics20(2010)767…777 ContentslistsavailableatScienceDirectMechatronicsjournalhomepage:www.elsevier.com/locate/mechatronics oflineartele-operationsystems,isthehybridmatrixnotationnotation.Thisnotationisthebaseforthegeneralbilateraltele-operatorsys-temblock-diagramasproposedinin.Anextensiontotheblock-diagramofLawrenceLawrenceisgiveninin,wheretwo(local)forcecontrollersareadded.Theextracontrollersresultinextradesignfreedom,whichenablesidealtransparencywhileusingonlythreecommunicationchannels.Thehybridmatrixnotationisapowerfultoolforcontrolarchi-tecturedesign.Inthelastdecadesnumerouscontrolarchitecturesaredevelopedfromthispointofview.Arecentoverviewofseveralcontrolarchitecturesusingthisnotationisgiveninin.However,thecurrentliteraturedoesnotprovideaclearframeworkforro-bust,performance-driven,data-basedcontrollerdesignoftele-operationsystemcontrollersinthefrequencydomain.A“rstfrequencydomainloop-shapingapproachforcontrolde-signforatwo-channelposition…forcearchitectureisintroducedinin.Inthisapproach,classicalcontroltheorycanbeusedtoenableasimultaneousincreaseintransparencyandstabilityrobustnessfortheforce…positionschemewithoptionallocalforcefeedbackcontrolloops.ThisapproachisextendedtoMIMOsystemsinin.Inbothpapersanextra“lterisplacedinoneofthecommu-nicationchannels.Theincrementinperformanceandstabilityrobustnessisachievedbyshapingthisextra“lter,buttheactualcontroldesignoftheseveralothercontrollersisnotdiscussed.Fur-thermore,theresultsarebasedonidealrigidbodydynamicswith-outmode-shapes.Thispapercontributestothehaptictele-operationsystemcontroldesign,byintroducingastepbystep,frequencydomain,data-based,loop-shapingapproachforusewithwell-knownhaptictele-operationsystemcontrolarchitectures.Theadvantagesoftheproposedframeworkarethatnoparametricmodelofthehardwareisnecessaryduetothedata-basedapproachandclassicloop-shap-ingtechniquescanbeusedtodesignforperformanceandstabilityrobustness.Hence,themodelingerrorsinthedynamicsofmasterandslavearereducedbecauseallresonancesaretakenintoac-countinthecontroldesign.Incontrastwiththeworkinin,thispaperdiscussesthecontroldesignofthecompletetele-operationsystemcontrollerandtheexperimentalresultsarebasedatrealsystemdynamicswithresonances.Theapproachisexplainedfromapragmaticpointofview,thatistheapplicationattheTOUPtele-operationsystem.Theapproachisillustratedbythe”owchartinFig.3.TheprocedurebeginsbyanalyzingtheFrequencyResponseFunctions(FRF)ofthemasterandtheslaveandbycreatingmodelsoftheenvironment(Section).TheseFRFsareusedforfurtheranalysis.Furthermore,theper-formancerequirementisspeci“edapriori(Section).Thenacon-trolarchitectureisselected.Thecontrolarchitectureselectionisbasedonthesystemdynamics,thesystemcon“gurationandtheperformancerequirement.Animportantstepinthecontroldesignprocedureproposedinthispaperisthesimpli“cationofthecontrolproblembyexpress-ingthesystemdynamicsintermsofwell-knownclosedlooptrans-ferfunctions.Thesimpli“edcontrolproblemgivesinsightinthein”uenceofthecontrollerparametersatstabilityrobustnessandperformance,whichenablesintuitivecontroldesignusingclassicloop-shapingtechniques.TheselectionofthecontrolarchitectureandthecontroldesignmethodarediscussedinSection.Further-more,anadaptedtele-operationsystemblockschemeisproposed,whichisbasedontheblock-schemeofHashtrudi-ZaadandSalcu- Fig.1.5-DOFtele-operatedultrasoundprobeforultrasoundecho-cardiography. Fig.2.Simpli“edrepresentationofthecontrollayoutofTOUPincludingthemaster(left)andtheslave(right).C.J.Zandsteegetal./Mechatronics20(2010)767…777 ThedesignedcontrollerisanalyzedforstabilityinSectionwherethesystemisanalyzedforpassivityandstabilityrobustnessforoperatorimpedances.Finally,theperformanceofthesystemisanalyzedusingtheoryandexperimentsinSections6and8.DespitethefactthatthecontroldesignmethodologyiselaboratedusingtheEFCcontrolarchitecturearchitecture,theproposedcontroldesignproce-durecanalsobeusedfortheSharedComplianceControl(SCC)(SCC)sinceitsstructureissimilartotheEFCcontroller.Furthermore,thisframeworkcanalsobeinspiringforcontrolde-signforothercontrolarchitecturesthatcanbedescribedbythegeneraltele-operationsystemblock-schemeofHashtrudi-ZaadandSalcudeanSalcudean.2.ExperimentalmodelingAhaptictele-operationsystemconsistsoffourdynamicalsub-systems,whicharetheMasterŽ,theSlaveŽ,theEnvironmentŽandtheOperatorŽ.Theoperatorinteractswiththemaster,whiletheslaveinteractswiththeenvironment.Atele-operationsystemcontrollerisplacedinbetween,whichvirtuallyconnectsallsub-systemsinthecontrolloop.The“rststepinthedesignofthiscon-trolleristoobtaintheFRFsandtoanalyzethedynamicalbehaviorofthesubsystemsinthetele-operationsystemtocreateinsightinthelimitationsbythehardwareinthecontroldesign.Themea-suredFRFsofthemasterandtheslave,whicharediscussedinthissection,areusedintherestofthecontroldesignframework.2.1.MasterandslaveThemaster(Fig.2)isthecommerciallyavailable6-DOFForceDimensionOmega.6Omega.6.ThethreetranslationalDOFs,,areconstructedviaaclosedkinematicshape.Threerotations,,aremountedontopofthisstructure.Thepositioninalldirectionsismeasuredbyencoders,whileonlythedirectionsareactuated.Therefore,thetele-operationsystemisonlybilaterallycoupledinthethreetranslationalDOFs.Further-isnotusedinthetele-operationsystem.Incontrasttothemaster,the5-DOFslavemanipulator)isespeciallydesignedfortheultrasoundtask.The5-DOFpositionismeasuredbyencodersinalljointsandalljointsareactuated.Furthermore,a3-DOFforcetransducerisplacedclosetotheultrasoundprobeandmeasurestheforcesinthetranslationalDOFs, .Thisenablestheuseofdirectforcefeedbackinthetele-operationsystemcontroller.ThetranslationalDOFsarebilaterallycoupledwiththeDOFsofthemaster,whiletherotationalDOFsoftheslaveareinpositioncontrolonly.Forcefeedbackintherotationaldegreesoffreedomisnotnec-essaryfortheultrasoundtask,becausethetorquesappliedbytheoperatoraresmall.Lubricantisusedbetweentheprobeandthehumanskin,whicheliminatesfriction.Anadvantageofprovidingforcere”ectioninthetranslationalDOFsonlyisthattheforcesen-sorcanbeplacedanywhereneartheultrasoundprobe.Asimpli“edrepresentationoftheinteractionbetweenmasterandslaveinthehaptictele-operationsubsystemsisgiveninFig.2.Inthis“gure,thearrowsrepresentmulti-dimensionalsig-nalscommunicatedfromoneperipheraltoanother. Xmx;y;z; Xsx;y;zand representthemeasuredpositionofthemaster,themea-suredpositionoftheslaveandthemeasuredforceattheend-effec-toroftheslave,respectively,indirections.Moreover,representtheforcegeneratedbythebilateralcon-,forthemasterandtheslave,respectively.representtheorientationoftheend-effectorofthemasterandtheslave,respectively,around.Furthermore, ,representstheforcegeneratedbythe(non-bilateral)controllerBoth,themasterandtheslavearenon-linearroboticmanipula-tors,sincebothinertiaandgravityforcesarefunctionofthegener-alizedcoordinates.However,modelbasedgravitycompensationisappliedtocompensatethestaticgravityforces.Furthermore,itisassumedthatthechangeininertiaisalsoverysmallbecausetheworkspaceofbothmanipulatorsissmall.Hence,itisassumedthatthenon-linearitiesarenegligibleandthatbothmasterandslavearedominatedbyLinearTime-Invariant(LTI)dynamics.First,theassumptionoflinearityisvalidatedforthemaster.Therefore,the3MIMOFRFismeasuredin27evenlydistributedoperatingpointswithintheusedworkspaceofthemanipulator.TheFRFfromtheactuatorforcein[N], ,tothecartesianpositionoftheend-effectorin[m], ,ismeasuredineachoperatingpoint.There-sultsareillustratedinFig.4.Itcanbeseenthatthedifferencesbe-tweenoperatingpointsaresmallforthediagonalterms,uptothe“rstmode-shapeatapproximately20[Hz],inalldirections.Thismode-shapeisthedecouplingoftheend-effector,whichcausesnon-collocatedactuationbytheoperator,whiletheactuatorsarecollocated.Belowthisfrequency,rigidbodydynamicsarepresent.Differencesbetweenoperatingpointsarenoticedbetweentheoff-diagonaltermsintheFRFofthemaster.However,theoff-diag-onaltermscanbeneglectedifthesystemisdecoupled.TheamountofcouplingforthemasterisanalyzedbycomputingtheRelativeGainArray(RGA)(RGA).TheRGAaddressesthedynamicalbehaviorofeachdirection,whenthecontrollersintheotherdirec-tionshavein“nitebandwidth.WhentheRGAofasystemisuni-tary,eachinputonlyin”uencesoneoutputanddecentralizedcontrolcanbeusedtostabilizethesystem.TheRGAofthemasterisshowninFig.5.ItcanbeseenthattheRGAisnearlyunitaryuptothefrequencyofthe“rstmode-shapeat20[Hz].Hence,thediagonaltermsdominatethedynamicsofthemasterandtheoff-diagonaltermsdonotsigni“cantlycontrib-utetothedynamicsofthediagonalterms.Therefore,decentralizedcontrolisallowedifthebandwidthiskeptwithintherigidbodydynamics.Ifso,themulti-DOFtele-operationsystemcanbecon-sideredasmultipleSISOloops.Asimilarapproachisusedforthe Fig.3.Flowchartcontainingthestepstakeninthehaptictele-operatorcontroldesignmethodology.C.J.Zandsteegetal./Mechatronics20(2010)767…777