FORCE
CHINESEJOURNALOFMECHANICALENGINEERnG
;Vo1.21,No.6,2008
;DOI:1O.3901/CJME.2008.06.001.availableonlineatwww.cjmenet.com;www.cjmenet.com.an
;GONGMingde
;ZHAODingxuan
;ZHANGHongyan
;JIACuiling
;CollegeofMechanicalScienceand
;Engineering,
;JUinUniversity,
;Changchun130022.China
;FORCEFEEDBACKMODELOF
;ELECTRO.HYDRAULICSERVO
;TELE.OPERATlONROBOTBASED
;ONVELOCITYCONTROL木
;Abstract:etele.operationroboticsystemwhichconsistsofa玎
excavatorastheconsU‟uctionroboL
;andtwoioysticksforoperatingtherobotfromasafeplaceareusefu1forperformingrestorationin
;damagedareas.Inordertoaccomplishaprecisetask.theoperatorneedstofee1arealisticsenseof
;taskforcebroughtaboutfromafeedbackforcebetweentheforkgloveofslaverobotandanfamiliar
;environment.Anovelforcefeedbackmode1isproposedbasedonvelocitycontrolofcylinderto
;determineenvironmentforceactingonforkglove.Namely,thefeedbackforceisformedbytheerror
;ofdisplacementofjoystickwithvelocityanddrivingforceofpiston,andthegainiscalculatedbyfhe
;drivingforceandthresholdofdrivingforceofhydrauliccylinder.Moreover,thevariablegain
;improvedalgorithmisdevelopedtoovercomethedefectforgraspingsoftobject.Experimentalresults
;f0rf0rkglovefreedomofroboticsystemareprovidedtodemonstratethedevelopedalgorithmis
;availableforgraspingsoftobject.
;Keywords:ConstructionrobotTele.operationB订
ateralelectro—hydraulicservocontro1
;Velocitycontro1Forcefeedbackmode1
;aD一一Cr0ss-sectionalareaofpiston,m
;b——Dampcoefficientofjoystick,N?s/m
;G(s)——nansferfunctionofjoystick(Input:torqueto ;joystickandoutput:displacementofjoystick) ;—
;Gainofservoamplifier,mA/V
;——
;Difrerentia1gainofmaster,N?m
;——
;F1owrategain,mZ/s
;一—
;GainofseI‟vovalve.m/mA
;m——Massofpiston,kg
;——
;PressuresinBchambersofcylinder,Pa
;一一
;Loadpressure,Pa
;——
;Timeconstantofmaster,s
—COntmlinputtoslave,V ;“s一
;Ym——Displacementsofmasterside,m
;V——Vel0cityofpiston,m/s
;v0——Nominalquantityofv(v0m=0.10),m/s
;——
;Nondimensionalquantityofv(=Vm/V0)
;——
;Nondimensionalquantityofy.(s0s)
;fm——Inputtorquetojoystick,N?m
;n——Naturalangularfrequency,rad/s
;0INTRoDUCTIoN
;NoTATIoNS
;Atele-operationroboticsystembasedonbilatera1controlis ;usefulforperformingrestorationindamagedareas.andalsoin ;extremeenvironmentssuchasspace,seabed,anddeep ;undergroundL”.Theworld‟sfirstremotecontrolsystemwasa
;mechanica1master-slavemanipulatorcalledANL(Argonne ;NationalLaboratory)ModelMldevelopedbvGOERTZ【.
;Sinceitsintroduction.thefieldoftele.operationhasexpandedits
;seope.Forexample.tele.operationhasbeenusedinthehandling
;ofradioactivematerials,sub.seaexploration.andservicing.Its
;appliancehasalsobeendemonstratedinspace,construction, ;forestry,andmining.Asanadvancedformoftele—operation.the
;conceptof”tele.presence”wasproposedbvMINSKY【jJ.
;Tele.presenceenablesahumanoperatortoremotelyperformtasks ;ThisprojectissupposedbyNationalNaturalScienceFoundationofChina ;(No.50475011).ReceivedFebruary13,2007;receivedinrevisedform ;October20;acceptedOctober24,2008
;b...........——Viscousdampingcoefficient
;ofpiston,N?s/m
;——
;DriVingforcetoslave,N
;——
;Pr0portiona1anddifferentialcoe街cient
;ofmaster,N
;ktm——T0rquegainofmaster,N?m
;——
;Pressuregain,m/kg
;——
;Delaytimeofjoystick,s
;P——PressuresinAchamberofcylinder.Pa
FlOwrate,m/s ;qL——
;——
;Gain
;——
;N0ndimensionalquantityof(=Tr/f0r)
;——
;Displacementofspool,m
;s——Displacementsofslaveside,m
;肋——N0mina1quantityofy(.vom=0.06),m
;ym——Nondimensionalquantityofy(YmYo)
;)——Nominalquantityofy.(yos=0.3),m
;——
;Dampingratio
;——
;Reactiontorquetojoystick,N?m
;withdexterity,makingtheuserfee1thatshe/heispresentinthe ;remotelocation.Almostatthesametime.”tele.existence”.a
;similarconceptwasproposedbyTACHI,etalLqJ.
;Intllisstudy,weinvestigatedatele.roboticssystemfora ;constructionmachine.Thesystemconsistsofaservo.con仃oiled
;constructionrobot,andtwoioysticksforoperatingtherobotfrom ;aremoteplace.Aforkgloveisequippedwiththefrontendofthe ;excavatorasahandforgraspingtaskonects.Themasterandthe ;slaveinthissystemcorrespondtothejoysticksandtheforkglove ;controlledbilaterallybyanoperator.
;Asanapplicationforexcavatorcontro1.bilateralmatched—
;impedancetele.operationwasdevelopedattheUniversityof
;BritishColumbiaL.Thevalsohavedevelopedavirtual ;excavatorsimulatorsuitableforexperimentationwithuser ;interfaces.controlstrategies.andoperatortrainingt”.This
;simulatorcomprisesmachinedynamicsasanimpedancemodel,a ;ground-bucketinteractionmodel,andagraphicaldisplay ;sub-system.Intheirexperiment.anactualexcavatorisoperated ;bybilateralcontrolmethod,andtheforcefeedbackcanbewell ;feltbytheoperator.
;„2GONGMingde.etal:Forcefeedbackmodelofelectro—hydraulicservotele-operationrobotbasedonvelocitycontrol
;Inorder幻improvethecontrollabilityofthesystem.we
;examinedthemasterandslavecon仃o1methodbetweenjoysticks
;androbotarmst,Refs.『8-91bothdiscussedtheforce
;presentationofthetaskfieldforalloperatorL….Becausetheforce
;presentationistheessentialinforrnationofslavesidetothe ;operator,thosestudiesmainlyfocusedonpositioncontrolof ;master.slavesideanddevelopedforcefeedbackmodels.Namely, ;theoperatorcontrolsthedisplacementofpistonofslavesideby ;thedisplacementofoystick.Thesemethodscanrealizehi2h1y ;sensualforcefeedbacktoioystickt.Butthestrangesensingwill ;befeItwhentheoperatormovedthe{oystickusing
;position.positioncontro1.Manyoperatorsgetusedto ;position—velocitycontro1becausethismethodisastandard ;practiceforbilateralcontro1.Soweapplythisnorma1methodthat ;theoperatorcontrolsthevelocityofpistonofslavesidebythe ;displacementofioystick.Moreover,thenewforcefeedback ;modelisdeveloped.Experimenta1resultsforforkglovefreedom ;ofroboticsystemareprovidedtodemonstratethedeveloped ;algorithmisavailableforgraspingsoRobject.
;1MATHEMATICALMoDELoFMASTER.-
;SLAVESYSTEM
;Experimentalapparatusconsistsoftheioystickandthe ;tele.operatedconstructionrobot.Thejoystickf‟‟SideWinderForce
;Feedback2”,MicrosoRCo.,Ltd.)canbeoperatedtotheX.axis
;andY—axisdirections.Displacementsofthejoystickaredetected ;bypositionsensors.ADCmotorisconnectedundertheioystick, ;andthereactionforcefromtheforkgloveisfedbacktothe ;operatorthroughareducerconnectedtotheDCmotor~The ;hydrauliccylindersfordrivingtheconstructionrobotare ;controlledbytheservovalves.Thedisplacementsofthecylinders ;aredetectedbymagneticstrokesensorswhichareembeddedin ;thepistons.Thedrivingforcesaredetectedbyapairofpressure ;sensorsattachedtothecylinders.
;1.1Mathematicalmodelofmastersystem
;Inordertogetthemathematicalmodelofthemastersystem. ;weperformedaparameteridentificationoftheioystick.The ;identificationresultshowedastepresFIprisecurveofthe ;displacementYmtotheinputtorqueoftheioystick.Fromthis ;result,the仃ansferfunctionofthe{oystickwasestimatedasoneof ;thefirstorderlagsystem(=O.125s,=0.18N)withatime ;lagelement(上=O.08s).Transferfunctionofjoystickisas ;?)=exp()(1)
;1.2Mathematicalmodelofslavesystem
;Inthisstudythesameslavesystemastheoneinprevious ;pal:}erswasused.Therefore.themathematicaImodeltusedfor ;thisslavesystemisalsothesameasinthepreviousone. ;Experimentalresultsforonedegree.of-freedomaregivento ;demonstratetocylinderoff0rkglove.
;ThemotionequationoftheservovalveisasEq.(2)
;戈+2i+:x=kakco:”(2)
;TheequationofmotionofthepistonisasEq.(3)
.PI ;my+=口
;PlPa—pb
;TherelationsforflowrateqLareasfollows
;qt:kxx—kpPL
;qI=ap
;(3)
;(4)
;(5)
;Astheresult,themathematicalmodeloftheslavesystemis ;representedbyEq,(2)toEq.(5).
;2FoRCEFEEDBACKMoDELBASEDoN
;VELoCITYCoNTRoL
;2.1Constantthresholdofdrivingforcefeedbackmodel ;Inthjs口art,wecomparedpositioncontrolmethodand
;developedvelocityeontro1method.Thedifferenceof山ismethod
;isthatthefeedbackvalueisthenon.dimensiona1valueofvelocity ;ofpistoninsteadofthenon.dimensiona1valueofdisplacementof ;piston.Thecon仃o1erroristhedifferencebetweenthe
;non.dimensionalvalueofvelocityofpistonandthe ;non—dimensionalvalueofdisplacementof{oystick.Theposition ;ofioystickreachesmiddleposition(zeroposition),theveloeityof ;pistonequalstozero.Themorethedisplacementofioystickis, ;themorethevelocityofpistonis.Sowegotthevelocityofpiston ;trackingonthedisplacementofioystick.ThecontrollerisalsoPD ;controller.Theblockdiagramforrepresentingthecontrolmethod ;isillustratedinFig.1.Inthisstudy,thedampofioystickbis ;consideredtobezerobecausethevalueofitrelativelyverysmal1.
;ThereactiontorquetothejoystickisgivenbyEq.f6) ;=
;Tr=[(ym—)+t】(6)
;Masterside
;3c?)?)t
;)t,
;f<
;Fig.1Schematicdiagramofmaster—slavesystemofforce
;feedbackmodelbasedonvelocitycontrol
;InEq.(7),theparameters/thataresummationoffriction, ;inertialforceandweightofpistonarecalledexpanding/ ;contractingmotionsthresholdofdrivingforces.Thevaluecannot ;beeasilygotandberegardedasconstantvalueinthisresearch. ;Whenanexternalforcegeneratedforgraspingataskobjectbythe ;fbrkgloveisabsent,thevalueis=2.0kN,=一1.4kN).
;Furthermore.themaximumdrivingfcIrcetothecylinderin ;expandingandcontractingmotionsisdefinedasma)【andm”
;11.7kN,mi=-6.8l(N).Therefore,thegainTis
;determinedbydrivingforceofpiston.
;Theexperimentalresultsformovingioysfickin行eespace
;withoutgraspingobjectareshowninFig.2.InFig.2athesolid ;lineisthedisplacementofioystickandthebroken1ineisthe ;velocityofpiston.Wecanfindtheerroroftwo1inesisverysmal1. ;ThereactionforcetoioystickcanbeinferredfromEqs.(61and ;(7).AsshowninFig.2bdrivingforceisintherangeofthreshold ;ofdrivingforces,Tequalstozero.Thereactionforcetooystick ;equalstozero.
;Fromtheexperimentalresults,whentheexternalforceis ;absentintheforkglove,meioystickbecomessmoothbecausethe ;reactionforcetoioystickiszero.Theresultcanbeseenflr0mFig. ;2d,thatis,theactLIa1fbrceinf-0m1atiOnofslavesidecanbewel1 ;feltbytheopemt0r.
;一一一一
;CHINESEJOURNALOFMECHANICALENGINEERING?3?
;1.0
;1O
;010203040506065
;Timet/s
;(a)Displacementofjoystickandvelocityofpiston ;Timet/s
;1Drivingforceofpiston
;Timet/s
;(c)Displacementofpiston
;10203040506O65
;Timet/s
;(d)Reactionforcetojoystick
;Fig.2Movejoystickinfreespace
;Ontheotherhand,whentheforkglovegraspssoftobiect ;stepbystep,especiallywithslowspeed,thereactionforceto ;joystickisnotsatisfactory.Theexperimentalresultsmovingthe ;joysticktograspsoftobjectareshowninFig.3.InthepartAof ;Fig.3a,thejoystickdoesn‟tmove;inthepartB,movingthe
;joystickgraspsthetire;inthepartC,thetireisgrasped,andinthe ;partD,thetireisunlocked.Thereactionforcetojoystickcanbe ;inferredfromEq.(6)andEq.(7).Fig.3bshowsthedrivingforce ;isnotintherangeofthresholdofdrivingforcesandTdoesnot ;equaltozero.Thereactionforcetooystickisnotzero.Fromthe ;experimentalresults,wecanfindtheresultfromFig.3d,ivthe ;partC.operatorcanfee1reactionforcebutitissosmal1that ;operatorcannotfee1theactualforcestepbysteDtof0rkglove. ;Whentheexternalforceisexistandchangesslowlyinthefork ;glove.theactua1forceinformationofslavesidecannotbewell ;feltbyoperator.
;Themainlyreasonisthatthedrivingforcedoesnot
;necessarilyexceedtheregionof??.n1isunsatisfa.
;ctorysituationoccursinataskwhenthefbrkglovegraspsasoft ;objectinaslowvelocity.First,displacementsofthejoystickand ;velocityofthefbrkglovepiston,rmand,areshowninFig.3 ;againsttimetintheabscissa.TheshortverticallinemarkedinFig. ;3indicatesthestartingpointofthetask.AtierstartingthepartC. ;asisshowninFig.3.thetaskofgraspingthetirecontinuesinthis ;mannerinwhichthedisplacementofpistonreachesgrasping ;maximalpositionandunlocksitstepbystepandthen.atabout ;90s,thetireiscrushedcompletely.Fromthedrivingforceand ;reactionforcefigure.itisobservedthatthedrivingforceand ;reactionarealsomaxima1.Butinthepictureofthedrivingforce ;totheforkgloveisshowninFig.3b.ThebrokenlinesinFig.3 ;denotethethresholdofdrivingforces,.AsisseeninFig.3, ;thedrivingf0rceisinrangeofthresholdofdriving ;forces?fs?,whenthedrivingforceissmallatbeginningof
;grasping.InEqs.(6)and(7),thegainTequalstozero,andthe ;reactionforceto1oysfickalsoequalstozero.Thereforethe ;proposedalgorithmcannotreflectthefactua1forcetoforkglove. ;Inmisstudy,wefoCUSonsuchaproblemasisseenhereandaim ;atovercomingtheproblembyusingvelocitycontrolmethod. ;譬
;盘
;>
;舌
;.一
;g
;E
;譬
;一?
;凸
;——
;„
;8B.(
;1
;『[
;…
;I
;i
;0Timet/s130
;(a)Displacementofjoystickandvelocityofpiston ;Timet/s
;(b)Drivingforceofpiston
;2
;&
;C
;宴
;芑
;Timet/s
;(C)Displacementforceofpiston
;Timet/s
;(d)ReactionforcetoJoystick
;Fig.3Graspingatirewithconstantthresholdofdrivingforces
;Thisproblemisconsideredtobeoriginatedfromthenext ;reasons.InthecontrolmethodbasedonEq.(7),eachvalueof ;505
;OO
;50一
;E,{芒量uBIds一(】
;OO0
;00
;2岔口0l18
;„4‟GONGMingde.etal:Forcefeedbackmodelofelectro一
~draulicservotete-operationrobotbasedonvelocitycontrol ;thresholdofdriivingf0rces,istreatedasconstant.Forthis ;reason,thereactiontorquecanappearasseenjtnFig.3whenthe
;drivingfo)rceofthef0rkglovefsexceedsthethresholdasseenin
;Fig.6.Ontheotherhand.intheregionof??sincethe
;gainTbecomeszerointhdssituation.thereactionforcedoesnot ;appearthoughtheforkgloveisgraspingataskobject. ;2.2Improvedthresholdofdrivingforcefeedbackmodel ;Inordertoovercometheprobleminthepreviousmexhod.in ;thebeginning,thedrivingforceofthehydrauliccylinderwas ;measuredaltongwiiththepistonvelociItyv,thustoobtainv—
;character]istics.
knownthatthedrivingforceisindicatedasa ;Itiswell【
;functionofthevelocityv.Soiitiisbettertoadoptavariable ;thresholdofdrivingfc)rcechangingwitththevelocityv.j~nsteadof ;fixedthresholds,.Intheimprovedmethod,.therefore,we ;adoptthevariablethreshold厂Dre.Fromtheexperimental,the
;thresholdfpisdescribedbyEq.(8)
;18v6v:m10.0?l/=
;(一9.+5.一0.4)×y<
;ByapplyingEq.(8),itisexpectedthatthenewmethodis ;abletodealwithagraspingmotionoftimedependence,e.g., ;slow—movinggrasping,andalsotofeedbacksensitivelyareaction ;fo:)rceofanextemallfo:)rce,.moreoverjncreasingmaneuverabilitty ;throughcontrollingvelocil[,,ofpiston.
;Invelocitycontrolmet1)od,thereactionforcetojoysticksf, ;isshownjtnEq.f61.desoribedbytherelationdependingonthe ;differencebetweenthtedisplacementofioystickandthevelocity ;ofpistonaswellasthedrivingfo.rce.Atthesametime.theinertia ;fo:rceandfrictionofpistonarenotconsidered.Asaresult,the ;reactionforcetoioystickfoftheimprovedalgori(thmis ;writtenbyEq.(9)andthegainTisdeterminedbyEq.(10) ;T=
;O
;『r=丁【(ym—)+](9)
;0<二盘
;…一.
;0二
;一
;…一
;?If
;?l0nfl0)
;?1<0n<
;AsisshowninEq.(9),thegainTchangesiItsvaluewith ;thechangeinthedrivingforcethreshold
;ThefeaturesoftheimprovedmethodbasedonEqs.f91and ;(10)alestatedasfollows.ifthedrivingforcetopistonfisbigger ;thanthethresholdregivenbyEq.(10),thedifferencebetween ;themitsregardedastheexternalforcetothepiston,andthusthe
;correspondingreactionfolrcecanbegenerated.Itistherefcpre ;expectedinthismethodthattheoperatorcanfeelthegrasping ;forcetothefolgloveverywel1.evenift‟tisdoingaslow—move
;ingraspingofsoftobject.
;AItierapplydngtheimprovedmethodtothemaster.slave ;system,.weconfirmtheavailab41ityofthemethodbyexperiment. ;CorrespondingtotheexperimentalresultsshowninFig.4,a ;taskofgraspingatirewithslowvelo@tywastestedbythe ;velocitycontrolmethodstepbystep.InFig.4athepartA.the ;joystickdoesn‟tmove;inthepartB,movingthejoystickgrasps
;thetire;inthepartC,thetireisgrasped,andinthepartD.thetire ;:isunlocked.
;A,fterstartingthepartC,asisshowninFig.4.operatorcan ;feelreactionfo)teeverywell,thetaskofgraspingthetire ;continuesinthdsmann