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维普资讯 CHINESEJOURNALOFMECHANICALENGINEERING 92 v0118，No1，2005 SELFRECONFlGURATlONOF UNDERACTUATEDREDUNDANT HeGuangping MANIPULATORSWITHOPTIM亿lNG SchooIofMechanicaIand ElectricalEngineering， THEFLEXIBILITYELLlPSOlD木 NorthChinaUniversityofTechnology, Beijing100041，China LuZhen Abstract：Themultimodesfeature，themeasureofthemanipulatingflexibility,andself-reconfigurat ScheoIofAutomationScience ioncontro1methodoftheun deractuatedredun dna tmna ipulatorsareinvestigatedbasedontheopti andElectriacIEngineering mizingtechnologyTherelationshipbetweentheconfigurationofthejointspaceandthemnaipulating BejiingUniversityofAeronautics flexibilityoftheunderactuatedredun dna tmna ipulatorisna alyzedanew measureofmna ipulating andAstronautics， flexibilttyellipsoidfor出eunderactuatedredundantmanipulatorwithpassiveointsin】ockedmodejs Beijing100083，China proposed，which can be used to gethte optimal configuration for the realization of hte self-reconfiguration contro1Furthermoreatimevaryingnonlinera contro1methodbasedon har monic inputs is suggested ofr fulfillnig hte self-reconfigurationA simulation example ofa htreeD0Fsunderactuatedmnaipulatorwithonepassivejointfeaturessomeaspectsoftheinvestiga tjons Keywords：Underactuatedmanipulators Self-reconfiguration Optimization Nonlinearcontro1 deractuatedacrobotTheseresearchesontheconrtolofunderac 0 INTRoDUCTIoN matedsystem haverevealedhtatthesemethodsraenothingbut nonlinera,timevaryingand discreteinnatureThefactismat Underactuatedmechanism andmanipulatorcan beused in Brockett 【”haveprovedthatthereisnosmoothand satticstate somefieldssuch asspacetechnology,cooperationrobotand feedback 1aw htatstabilizesthesystem toagivenconfingration metamorphicmechanismInthespacefield，forthesakeofno asymptoticallyAnobviousfeatureofthenonholonomicsystem is losingtheusefulfunctionorrealizingthereconfigurationofthe tllatitisconrtollablein aconfiguration spacewithmoredimen systemthefaulttolerancebasedontheunderactuatedtechnology sionshtna htatofhteinputspaceS0matmuchattentionshavebeen isessentialwhensomeactuatedcomponentsrevealsometroubles paidonhteconrtolofhtenonholonomicsystem Anunderacmatedmnaipulatoralsocanbedesignedasacoopera Theunderactuatedmechna ism ormanipulatoralsoiSdisobe tionrobotthatistosayC0B0T ThedriversoftheCOBOTare dienttohtefundamenatlprincipleofthemechanism desing ing notforacreatingthemachinebutforprovidingaldnematicscon theorythatjsthenumberoftheacmatedcomponentsshouldequal straintthatisusuallynonholonomicTheC0B0Tneedsoutside t0 thatofhteDOFsofthemechanismTheunderactuatedma 1oteehtatisprovidedbyoperatorandcancompletesomeaccurate nipulatorhadbeensuggestedfirstly isnotbyreason thatithas apphcatlonssuchas in biologY englneenng，surgical，andsemi somemeritsdistinctly，butsomereserachesshow thattheunder- conductormanufactureand so onIn thefieldofmechanisms， actuatedmechanism desing edpurposelyalsoiSvaluableForex themetamoprhicmechanism hasmultimodesnad can bertans ma pleRivhter,etal141havemeasuredmultidimensionsofrceby formedfrom onemodetona other,hadbeenpresentedrecentlyt a flexibleunderactuated manipulator,Nakamuraetalt” have Thertansfomr ationbetweenhtedifferentmodesislikelytoresult desing edanonholonomicmanipulatorbasedonhtewheelrolling inchangeoftheDOFsorconsrtaintsofthemetamoprhicmecha conatctand conrtolled a four DOFs plnara manipulator by nismItisobviously thatconrtoltheunderactuatedredundant wtoinputsHeetal【 haveproposedacollisionrfeemotionplna actuatedna d flexiblemechanism cannotbe evadedThereofre。 algorithm ofrhteun deractuatedredundantmanipulatorBasedon hteunderacmated system becomesan attractiveresearch field theresultsthathavebeendiscussedabove。weCallconcludehtat gradually theinvestigationabouttheun deractuatedmanipulatordeliberately Th eresearchesontheunderacmatedmanipulatorsmanifest mayresultinsomenew phenom enontobediscovered，techniques thesystem cnanotbeconrtolledbykinematicsTh emotionofthe t0beproposedorhteorytobeofrmedhtereofrecouldbedevelop passiveiointcanbemovedbythedynamiccouplingonlyL4,3JJain， themechanicspotentially etal 【haveshown htatthedynamiccouplingissecondorder InthisPape weexplorethestaticfeamrenadself-reconfigu nonholonomic cons仃aints0fhteunderacmatedmanipulatorIn rationconrtolmethodofrhteunderactuatedredundna tmanipula conrtastwiththefacthtatnonholonomicsystem isstdiedexten t0rS sively aboutonehunrdedofyerasinmechna icsbutthemotion planningna d conrtolofthenonholonomicsystem iSno longer 1 FLEXIBILITYELLIPSoID htna wtodecadena dthestdieslimitedinthefirstordernon holonomicsystem (suchaswheelmovingrobottJ,hoppingrobott Themanipulating stiffnessisan importantpraameterofa nadspacerobotWJ)mainlyInhteaspectofhtereserachonhteun manipulator,whichcna beusedinhteofrceorimpedanceconrto1 deractuatedmanipulatorsAnthoneyetalt haveinvestigatedhte Amnaipulatorisopenchaininmechna ism generally,andhtelinks satbilityofhtemotionAraietalLIIJhaveproposedatime。scaling alwaysraerigidbodies，sothedeofmr ationonendeffectorresults mehtodnadachievedhtepositionconrtolofhtes3stemLeeetalLlZ from theiointsmainlyThestiffmodecanbewrittentotheofllow havepresentedseveralkindsofnonlinearconrtolmetbo dofrun equationapproximately M = i=1，2，。， (1) ThisprojectissupportedbyNali0nalNatura1scienceFoun血Ii0nofchim where ，T0rque0fj0int (No50375007，No50475177)ReceivedMarchl0，20o4；receivedinrevised f0INOvember23，2004；acc印tcdDecember2，2004 维普资讯 CHINESEJOURNALOFMECHANICALENGINEERING 93 Def0mationofjointi kiStiffhessconstantofjointi Ifthegravitationandthefrictioninthejointsareignored， supposinghtereisaforcevector F R on themanipulators endeffector，theequivalentjointtorquecanbewrittenas M =JF (2) where M R EquiVaIenttorqueofthejoints J R JacObianmatrix Itiswellknownthatthedeformationsonthejointsandthe endeffectorhavearelationshipasfollows Fig1 Planar2Rmanipulator Ax=JA0 (3) where Ax Microdisplacementoftheendeffector Micr0displacementofthejoints WewriteEq(1)asamatrixfomr andcombineitwithEqs(2) and(3)，bysomesimplecalculations，therelationshipbetween Ax na dFcanbewrittenas Ax=(以t，)F (4) where b ，i 11日一， a_力 b 一日 11B1 a_力 Singularity valueo1 0 0 0 0 k2 0 0 Fig2 GFEofafullactuatedplanar2Rmnaipulator (5) 0 0 0 L1：L2=10In 101=02=60。 2 = ：35。 3 ：o2：2o。 0 0 0 Ifwedefine C ：Jk J (6) Eq(6)istosaytheflexibilitymatrixoftheend-effectorWhereas C correspondstothestifinessmatrixinatskspaceTheflexibi1- itymatrix C cna beused tomeasurethesatticfeatureofMa nipulatorMatrix C isalsoafunctionoftheJacobina henceitis changeableinalargerangofritrelationstotheconfigurationand hteconstructionpraametersThevariablefeaturesofthemanipu latorinstaticcna beusedtocompletesomecomplinatandcom。 plexmna ipulationsuchasassemblage，polishingtreatmentandso Singularityvalue 1 onBasedonEqs(5)and(6)，wecanseemartix C issymmet- ric Fig3 GFEofaufll-acutatedplna ar2Rmna ipulator Ifwedefine LI：05inL2=10ni 165=82=60。 265=82=35。 301=02=20。 det() (7) Thesefiguresshow thatthemeasuredependsonthe con figurationandthestructureprama etersW hereasaufllactuated anddecomposematrix C bythesingulravalue，fromEq(7)we manipulator1sunabletobechangedtothestructurepraam eters have generallyTherefore，theGFEcna bechangde bydifferentcon。 figuration(Fig2)butnotthestructurepraameters(chnagefrom = 丌 (8) Fig2toFig3)Whensomepassiveiointsraeinrtoducedintothe fu11acutatedmanipulator,forsomeconveniencesupposingthat where o-i， i=l，2， ， ，denotesthesingulra valueofmartixC thepassivejointsraeequippdewithbrakesandpositionsensorso mat the brka es cna switch the passive ioints bewt een hte Thereforetheexpression c isapositivedefinitesymmertic rfeeswingmodeand也elockedmodethustheunderacutated matrix，na dna equationcanbedefinedas rdeundnatmnaipulatorrevealssomeredundantDOFsinkinemat xT(cc)=1 (9)icsbutcannotbeshown in “self-motion”forthatthedimension oftheinputsspaceisnotmorethanhtatofthetaskspacetypically Ontheotherhand，switchingthemodeofthepassiveioinscan Eq(9)describestheequationofageneralizde ellipsoidThis reconfiRalretheun deracutatde manipulator，andthesystem reveals ellipsoidistosaythegeneralizedflexibilityellipsoid(GFE)The somedexterousnessinadaptingtodifferentworks principalaxesoftheellipsoidareequaltothesingularvaluesof matrixC respectivelyForsomeintuitionisticsake，aplanarwt o 2 FLEXIBILITY M ATIUX linksmanipulatorthatthelengthoflink s L =10m ， i=1，2，is regradedasanexample(Fig1)，andsomeGFEsareshownin Supposedthathtereraespassivejointsinanunderacut- Fig2nadFig3 atedredundantmnaipulator,andthepassivejointsraeequipped 维普资讯 HeGuangping，etal：Self_rec0nfigurati0nofunderactuatedredundantmanipulators 94 withoptimizingtheflexibilityellipsoid withbrakesWhenthepassivejointsarefreeswingmode，the workinginthefu11actuatedmodeonecancontrolittomanipula micromotionequationsofthemanipulatorcanbewrittenas tionSubstantivelythemanipulatorworking in underacutated modecna realizesomemnail：、ulationsuchas positionconrtolp or = Ja +JpA0p (10) discretepointtopointmotionL41Butthisisnothtecenrtalofhtis PaDerWepayattentiontohtestaticfeaturena dself-reconfiguration where AxR _ Microdisplacementoftheendeffector conrtolmethodoftheunderacutatedredundantmna ipulator R Submatrix oftheJacobian ofthema Thekinematicalequationsofthewtomodesoftheunderac nipulatorcorrespondingtotheactuated utatedmanipulatorcanbeestablishedbymanymethods(suchas joints DenavitHartenbergmethod)butthereisadifficultyinthestruc tureparametertobedefinedoframultiDOFmanipulatorthatis J一R _submatrixoftheJacobian ofthema complicatedinmechna ismToresolvethisproblemnextweana nipulatorcorrespondingtothepassive lyzetherelationshipbewt eenhtewtomodesoftheunderacutated joints redundnatmanipulator R， R Microdisplacementinactuatedjoints Givena specialconfiguration ofthemanipulator,and sup andthepassivejointsrespectively posing thathas , m thedeofmr ationsofthe end effector Whenthepassivejointsarelocked，themicromotionequa underthewtomodesofthemechna ism willbethesameThiscan tioncanbedescribedas beexpressedas Ax=J1碍 (11) -，IAq=J + p (12) where R Micr0一displacementoftheendeffector JIR Jacobianofhtemnaipulatoraspassivejoints Jaaaa Je=0 (13) locked Thatmenasthemicromotionoccurredinjointspacedoesnot AqR Microdisplacementinhteactuatedjoints changehtepositionoftheendeffectorFromEq(13)，na expres ItisobviouslythatEqs(11)and(3)havethesameforms sioncanbewrittenas Eqs(10)and(11)indicatethatnaunderacutatedmanipulatorhas twodifferentmodelinkinematicsInotherwords，thesystem has 8=一JJa8a (14) thefeatureofmultimodesinkinematicsA planar3Rmanipula torshown inFig4canberegardedasanexampleofthisThe where ()denotestheMoorePenrosepseudoinverseSubstiutt secondjointofthemanipulatorispassive，andtheothersareactu ingEq(14)intoEq(12)，weobatin atedWhenhtepassivejointisrfee，0R canbechosenasthe -，I=(，一JpJ；)JalAOa (15) generalizedcoordinatesIfthepassivejointislocked，theDOFsof themanipulatorchna gestowto，nadthegeneralizedcoordinates Eq(15)describesthesameconfigurationofhtewtomodesof cna beselectedas qR Forthereasonof q0 obviously hteun deracutatedmanipulatorThereforethemicromotion de thus hte Jacobian matrix satisfies the relationship of notedbythewtokindsofgeneralizedcoordinateswillbesame -，Il I LetAq=AOa，afomr ulationisobtainedas -，I=(，一Jos；)s (16) Eq(16)showstherelationshipofhteJacobianinhtewto modes，which cna beused to predicttheperfomr anceofthe fullactuatedmodeSubstitutingEq(16)intoEq(5)，anewflexi bilitymartixofunderacutatedmanipulatorin ufllactuatedmode cna bewrittenas c：Jk一、J (17) TheGFE ofrtheunderacutatedmanipulatorcna alsobede finedaccordingasEq(71Eq(17)indicatesthesatticfeatureof the system afterthemechanism reconfiguredOneemore，we showitbyhteplnara3Rmanipulator(Fig4、Foranonredundant manipulatorifwegiveapointinthetaskspacethereisonlyone flexibility ellipsoid corresponding to itBy contrary，thereare manyonescorrespondingtoapointintaskspaceofraredun dant Fig4 Planar3Rmanipulator mechanismSupposingthelinkslengthofthe3Rmanipulatorrae L，=L，=05m na d L ：10m ，the initialconfiguration is Byreasonthattheunderacutatedmanipulatorhavedifferent = 60。， =一60。， =一30。，someoftheGFEscorresponding kinematicsmodes，onecna selectan optimalconfiguration and reconfigurethemanipulatorofradaptingtoadifferenttaskAn totheinitialpositionofhteendeffectorraegiveninFig5 essentialproblem ishow topredicttheperfomr anceofthema Itisobviouslythereraealotofconfigurationsiniointspace nipulatorofrfu11一actuatedmodelbasedontheunderacutatedmode correspondingtoonestateoftheatskspaceTheseconfigurations ofitUnlikeafu11actuatedredundnatmanipulator,theunderacut rae corresponding to differentgeneralized flexibility ellipsoids atedredundna tmanipulatorcannotimprovetheperofmr anceby respectivelyThusna underacutatedredundantmnaipulatorhas itselfand implementama nipulationtask simultaneously tothe thecapabilityofreconfigurationGenerally，weexpectthegener reasonoffewerdimensionsininputspacethanthetaskspaceA alizedflexibility ellipsoidhasasimilra perfomr na ceindifferent feasibleapproachistodecomposethesetaskstoindifferenttime direction oftheprincipleaxesIn otherwords，the ellipsoid foractualizingForexamplewhenthemanipulatorisworkingin ismore similra to abal1So hte firstconfiguration hasthe theun deracutatedmode，onecanreconfigurethemechanism ofr bestperfomr anceamongthethreeconfigurationsthatisgivenin an appropriateconfigurationWhereaswhen htemanipulatoris Fig5 维普资讯 CHINESEJOURNALOFMECHANICALENGINEERING 95 Oa=Aosinrot (21) 0 =一Aco cosot (22) b j一日 J(= 日一； 昌_力 g cIP】0o0 where A AInplitLldeoftheharmonicfunction 09 Angularrfequencyoftheharmonicfunction Singularityvalue (a) 0 10 Timets (a) Coordinatezm (b) 。 10【Joao互o Fig5 Generalizedflexibilityellipsoids 。 ao一一日 o勺 of3Runderactuatedmanipulator 一 5 0 1 809。， =4819。， 一9O32。 20r2485。， 1789。，03_8115。 Positionofpassivejoint0(。) 3 6O。， 舡_6O。， 一3O。 ) Fig6 HeliconmotionoftwoDOFs 3 NoNLINEAR CoNTRoL planarunderactuatedmna ipulator Forfindingan approachthatcan controltheunderactuated IfweapproximateEq(22)byhtefirstitemofitsexponential manipulatorefficaciously,weanalyzethedynamicsystemThe progression，nadsubstituteittoEq(19)，weobtain dny amicequationsfortheunderactuatedmanipulatorcanbewrit tenas J(c口一AIf(o) (23) I a+I p+ca= M (18) Generally，thenagularrfequency 09 isalragenumber, +Jp p+cp：口 (19) htereforetheperiod 2nofhteham 。ni cufnction isasmall one，andtheitemssuchas Jp-p1c口，and cna berteatedas where J= consatntinthetimeofaperiod TheintergalofEq(23)canbe 乏Japdenotesmemassineniama仃ix， approximatelywrittenas c=Icac口IisthevectorofCoriolis，centriufgal，rgavitational LI-l(Cp-AI ) (24) nadfrictionaltorque，M istorquevectorofhteactuatedioints， isthegeneralizedCO0rdinatesvectorcorrespondingtotheactuated Eq(24)indicatesanapproximatedeviationafteraperiodic joints， whereascorrespondingtothepassivejointsEq(19)is time Itisobviouslyhtatthevalueoftheintergaldependsonhte secondordernonholonomicconsrtaintsgenerallythathavebeen ma plitudenadangulra rfequencyoftheharmonicinputsThisis provedbyJainetalt Anunderactuatedredundantmanipulator htereasonofthathtehamronicinputsinactuatedjointscancon- hasthecapabilityofimprovingtheperofrmna ceofhtemechanism rtolthemotionofthepassiveone ofragivenpositionintaskspacebyreconfigurationFortherea sonoflessdimensionofinputspacethna thatoftheiointspace， 4 SELFRECoNFIGURATIoN CoNTRoL htepositionconrtolofthepassiveiointcanonlyberealizedbythe dynma iccouplingBasedontheBrockett stheoryt”J Th eself-reconfiguration needsasatbleconrtoltechnology htereisno smoothsatticstatefeedbacklaw thatasymptoticallysatbilizesthe Basedontheharmonicinputnonlinearconrtolmehtodthatgiven system toagivenconfigurationThereofre，theresultsthathave insection3briefly,nextwewilldesignanew conrtolschemeto been proposedofrconrtolling ofthenonholonomicsystem rae implementtheself-reconfigurationmotionThismethodwillbe nonlinera,timevaryinganddiscreteinnatureA nonlinera con usedto optimizethegeneralizedflexibility ellipsoidforagiven rtolmethodthathas amannerofhamr onicufnctionofracutated positioninthetaskspace jointisproposedinRef17Thebasisofthismethodisthatthe Given denotesan expectedconfiugration thatisderived passivejointsiswilldeviatehteirequilibriumpositionwhenthe rfom someoptimizingmethod，0istheactualpositionofhtema actuatedjointismovinginaperiodicmanner(Fig6) nipulator Theharmonicmotionisinputtotheactuatedjoint，suchas Iet e= d一0 (25) 0=Acosot (20) 维普资讯 HeGuangping，etal：Self-reconfigurationofunderactuatedredundantmanipulators 96 withoptimizinghteflexibilityellipsoid whereeVectorofjointpositionerrors 5 SlMULATIoN STUDY decomposingEq(24)tofollowingform Inthissectiontheplanra 3R manipulatorisselectedasa jld。一0 (26) simulationmode1which isshown inFig4，Supposingthathte da 一 j secondiointofthemanipulatorispassive，nadtheohteriointsrae acutatedIftheinitialconfigurationis =60。， =一60。， =一 aslidingmodelisgivenby 30。，ofrimprovingtheperfomr anceofhtefiexibilityellipsoid。a sa= a+klea (27) betterconfiguration iS 2485。，81l789。 一8115。 whichisgiveninsection3Weregradhtelateroneas hteexpected andtheconvergencelaw isselectedas configurationInaccordancewiht htemethodthatissuggested in = 一 k2sgn(S,)一k3 (28) section4htesimulationresultisshowninFig7Fig7aindicates where，kl0，七20，如0，andsgn()indicatesasigmoidfunction， whichhashtefomr of f1 s0 。gn()1一l0 Ifvector hasamnanerof ： ，fol lowingequationmaybeobtained j O，砰一4kp0，sohtatfollowingrelationscanbe dbtained 。v 墨口趸 s】o暑 口。鼍o 。v 暑口量 0口。互s0 +kddp+kpep=0 (30) Substiutting htetwice time derivation ofhte second row of Eq(26)intoEq(30)，aresultcnabegivenby ： + P (31) p Lethteinputsofhteactuatedjointsbe = 一 Aco cost (32) substiuttingEqs(31)nad(32)intoEq(19)，htefollowingrelations hold (一Aco2cOSO)t)+Ipp( +l|)+c=0 (33) nadhteampliutdeofhteharmoniccna begivenby g 4：(Io2cosn，f)+，(rd+kep)+c (34) 口 0 Thusifthepassivejointisnotintheexpectedposition，the o controlinputoftheacutatedjointisdefinedbyEqs(32)and(34) U Onhteohterhnad，ifhtepassivejointisinhteexpectedposition， hteconrtolinputwillchnagetohtefollowingequationFrom Eq(27)，htetimederivationis Coordinatezm ： + =一 +kte, (35) (c) CombiningEqs(28)nad(35)，theconrtollawisgivenby = kid+k2sgn(S)+k3S。 (36) Itisobviouslyhtathtemethodsuggestedhereisnonlinera and timevarying，whichobeyshteBrockeRstheoryRearrangingthe algorithmabove，theconrtollaw cna bewrittenas = +klea (37) When ep=0 issatisfied 6：k、I+k2sgn(S)+k3SI (38) Wh en ep0 issatisfied Positionerrorsofthejoints (。) = c。s小1op(+kpep)+Cp_O(2COSO(39) (d) Fig7 Self-reconfigurationofhte3Runderactuatedmanipulator M = I +I +cl (40) 1Joint1 2Joint2 3Joint3 维普资讯 CHINESEJOURNALOFMECHANICALENGINEERING 97 theiointspositionerrorswithrespecttotime；Fig7bistheioints 7 ColbaughR，BaranyEGlassKAdaptivestabilizationofuncertaninon holonomicmechnaica1systemsRobotica，l998，16f21：181192 trajectoryrespecttotime；Fig7cshowsthetransofrmationofthe 8 RobertTM Joe1W BPeriodicmotionsofahoppingrobotwiht vertical manipulators configuration in the self-reconfiguring conrtol； nadforwardmotion1nternationa1Journa1ofRoboticsResearch1993 Fig7dshowshtephaserelationsbetweenhtespeedandpositionof 12(31：197218 hteiointsObviously,themanipulatorisreconfiguredtohteex 9 PapadopoulosEDubowskySOnhtenatureofcontro1ofalgorihtmsfor pectde configurationbyitself free-floating space manipulatorsIEEETransactionson Roboticsna d Automa tion，1991，7(6)：75O758 6 CoNCLUSIoNS 10 BlochA MWilsonCHConrto1nadsatbilizationofnonholonomicdv- namicsystemsIEEETransactionsonAutomaticConrtol，1992，37(111：1 746l757 Theunderactua【ted technologyisacrucialproblem notonly ll AraiHSenvi1LTimescalingcontro1ofna underactuatedmanipulatonJ forfaulttolernaceofspacerobotsystemsbutalsoofrcooperation ofRoboticSystems，1998，15(9)：525-536 robotnadmetamorphicmechanismsTheunderactuatedredundant 12 LeeKVictoriaC CConrto1algorithmsofrstabiliznigunderactuated manipulatorhas thecapabilityofrealizingthemechna ism recon robotsJofRoboticSystem，1998，15(12)：681-697 figuration by itsel Thenew generalized flexibility ellipsoid 13 BrockerR AsymptoticsatbilitynadfeedbacksatbilizationinDeferen tialGeometricConrtolTheoryIn：BrockerR W MillmanR SSussmna measureoftheunderactuatedredundantmanipulatorwiht passive H Jedsin：Birkgauser,1983：181-208 iointsbrakedmodeissuggested，nadhtemeasurecanbeusedto 14 Rivhterk Pfei雎 rFA flexible1inkmnaipulatoras aoficemeasuringnad optimizethestaticperformanceofhtesystemA novelnonlinear eontmllnigunitIn：Proceedingsofhte199