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GJOURNALOFMECHANICALSCIENCEANDTECHNOLOGY21200710181027JOURNALOFMECHANICALSCIENCEANDTECHNOLOGYCONTROLOFTWOAXISPNEUMATICARTIFICIALMUSCLEMANIPULATORWITHANEWPHASEPLANESWITCHINGCONTROLMETHODTUDIEPCONGTHANHB,KYOUNGKWANAHNA,ASCHOOLOFMECHANICALANDAUTOMOTIVEENGINEERING,UNIVERSITYOFULSAN,KOREABMECHATRONICSDEPARTMENT,HOCHIMINHCITYUNIVERSITYOFTECHNOLOGY,VIETNAMMANUSCRIPTRECEIVEDSEPTEMBER25,2006REVISEDAPRIL24,2007ACCEPTEDAPRIL242007ABSTRACTTHEUSEOFROBOTSINREHABILITATIONHASBECOMEANISSUEOFINCREASINGIMPORTANCEBECAUSEOFTHEREQUIREMENTOFFUNCTIONALRECOVERYTHERAPYFORLIMBSANOVELPNEUMATICARTIFICIALMUSCLEPAMACTUATORWHICHHASACHIEVEDINCREASEDPOPULARITYFORPROVIDINGSAFETYANDMOBILITYASSISTANCETOHUMANSPERFORMINGTASKS,ASWELLASPROVIDINGANOTHERADVANTAGESSUCHASHIGHSTRENGTHANDPOWER/WEIGHTRATIO,LOWCOST,COMPACTNESS,EASEOFMAINTENANCE,CLEANLINESS,READILYAVAILABLE,CHEAPPOWERSOURCE,ANDSOONHASBEENCONSIDEREDDURINGTHERECENTDECADESFORUSEINATHERAPYROBOT,WHICHINPARTICULARREQUIRESAHIGHLEVELOFSAFETYHOWEVER,SOMELIMITATIONSSTILLEXIST,SUCHASAIRCOMPRESSIBILITYANDTHELACKOFDAMPINGABILITYOFTHEACTUATORTOBRINGTHEDYNAMICDELAYOFTHEPRESSURERESPONSEANDCAUSETHEOSCILLATORYMOTIONINADDITION,TOAIDREHABILITATIONMOREEFFICIENTLY,THEROBOTSHOULDADJUSTITSIMPEDANCEPARAMETERSACCORDINGTOTHEPHYSICALCONDITIONOFTHEPATIENTFORTHISPURPOSE,THEMANIPULATORJOINISEQUIPPEDWITHAMAGNETORHEOLOGICALBRAKEMRBANEWPHASEPLANESWITCHINGCONTROLMETHODUSINGMRBISPROPOSEDFORTRACKINGSINUSOIDALWAVEFORMSTHEEFFECTIVENESSOFTHEPROPOSEDALGORITHMISDEMONSTRATEDTHROUGHANEXPERIMENTUSINGAFABRICATEDTWOAXISPAMMANIPULATORTHEEXPERIMENTPROVESTHATTHESTABILITYOFTHEMANIPULATORCOULDBEGREATLYIMPROVEDUSINGAHIGHGAINCONTROLWITHOUTREGARDTOTHECHANGEOFTHEFREQUENCIESOFTHEREFERENCEINPUTANDTHEEXTERNALLOADCONDITION,ANDWITHOUTDECREASINGTHERESPONSESPEEDORLOWERINGTHESTIFFNESSOFPAMMANIPULATORGKEYWORDSPNEUMATICARTIFICIALMUSCLEPHASEPLANESWITCHINGCONTROLMANIPULATORMAGNETORHEOLOGICALBRAKE1INTRODUCTIONTHENUMBEROFPEOPLEREQUIRINGREHABILITATIONDUETOBONEFRACTUREORJOINTDISEASECAUSEDBYTRAFFICACCIDENTSANDCEREBRALAPOPLEXY,ANDFORFUNCTIONALMOTORPROBLEMSDUETOADVANCEDAGE,NUMBERSSEVERALHUNDREDSOFTHOUSANDSWORLDWIDETHEAPPLICATIONOFROBOTICSTOREHABILITATIONISTHUSOFGREATCONCERNFUNCTIONALRECOVERYTHERAPYISNORMALLYCARRIEDOUTBYMEDICALTHERAPISTSONAPERSONTOPERSONBASIS,BUTAUTOMATICEQUIPMENTHASBEENPUTTOPRACTICALUSEINPHYSICALTHERAPYPROGRAMSTHATREPEATRELATIVELYSIMPLEOPERATIONS,SUCHASACONTINUOUSPASSIVEMOTIONMACHINE,AWALKINGTRAININGDEVICE,ANDATORQUEMACHINEUSEDFORASINGLEAXISDOI,1993FUJIEETAL,1994FUJIEETAL,1995THISRESEARCHDEALSWITHFUNCTIONALRECOVERYTHERAPY,ONEIMPORTANTASPECTOFPHYSICALREHABILITATIONSINGLEJOINTTHERAPYMACHINESHAVEALREADYBEENCREATEDAHNANDTHANH,20042005A2005BHOWEVER,MULTIJOINTROBOTSARENECESSARYTOACHIEVEMOREREALISTICMOTIONPATTERNS,ANDHENCEARENECESSARYFORMOREEFFICIENTTHERAPYTHISKINDOFROBOTMUSTHAVEAHIGHLEVELOFSAFETYFORHUMANUSETHEPAMMANIPULATORHASBEENUSEDTOCONSTRUCTATHERAPYROBOTWITHTWODEGREESOFFREEDOMDOFA2DOFROBOTFORFUNCTIONALRECOVERYTHERAPYDRIVENBYPNEUMATICCORRESPONDINGAUTHORTEL82522592282,FAX82522591680EMAILADDRESSKKAHNULSANACKRTUDIEPCONGTHANHANDKYOUNGKWANAHN/JOURNALOFMECHANICALSCIENCEANDTECHNOLOGY212007101810271019MUSCLEWASDEVELOPEDBYZOBELZOBELETAL,1999ANDRAPARELLIRAPARELLIETAL,20012003ARTIFICIALMUSCLEACTUATORSFORBIOROBOTICSYSTEMSBYKLUTEKLUTEETAL,1999200020022003APNEUMATICMUSCLEHANDTHERAPYDEVICEBYKOENEMANKOENEMANETAL,2004ANDAHUMANFRIENDLYTHERAPYROBOTTHANHANDAHN,2006AHOWEVER,SOMELIMITATIONSSTILLEXIST,SUCHASTHEAIRCOMPRESSIBILITYANDTHELACKOFDAMPINGABILITYOFTHEACTUATORTOBRINGTHEDYNAMICDELAYOFTHEPRESSURERESPONSE,CAUSINGOSCILLATORYMOTIONINADDITION,TOEXECUTEREHABILITATIONMOREEFFICIENTLY,THEROBOTMUSTADJUSTITSIMPEDANCEPARAMETERSACCORDINGTOTHEPHYSICALCONDITIONOFTHEPATIENTFORTHISPURPOSE,ANEWTECHNOLOGY,ANELECTRORHEOLOGICALFLUIDDAMPERERDAMPER,HASBEENAPPLIEDTOTHEPAMMANIPULATORNORITSUGUANDHISTEAMUSEDANERDAMPERTOIMPROVETHECONTROLPERFORMANCEOFTHEPAMMANIPULATORWITHAPICONTROLLERANDPULSECODEMODULATEDONOFFVALVESNORITSUGUETAL,1994BYSEPARATINGTHEREGIONWHERETHEDAMPERPRODUCESADAMPINGTORQUETORECONCILEBOTHDAMPINGANDRESPONSESPEEDUNDERHIGHGAINCONTROL,THERESULTSSHOWTHATTHEERDAMPERISANEFFECTIVEMETHODFORUSEINAPRACTICALLYAVAILABLE,HUMANFRIENDLYROBOTUSINGTHEPAMMANIPULATORMOREOVER,POSITIONCONTROLISIMPROVEDWITHOUTADECREASEINRESPONSESPEEDHOWEVER,SOMELIMITATIONSHAMPERTHETECHNOLOGY,SINCEERFLUIDERFREQUIRESEXTREMELYHIGHCONTROLVOLTAGEKV,WHICHISPROBLEMATIC,ANDINPARTICULAR,POTENTIALLYDANGEROUS,ONLYOPERATESINANARROWTEMPERATURERANGEANDONEUNSUITABLEFORPAMMANIPULATORS,ANDEXHIBITSNONLINEARCHARACTERISTICSBECAUSEERFHASMANYUNACCEPTABLEDISADVANTAGES,MAGNETORHEOLOGICALFLUIDMRFHASBEENCONSIDEREDANATTRACTIVEALTERNATIVEFORTHEADVANTAGESLISTEDINTABLE1,ANDHASBEENRECENTLYUSEDINHUMANFRIENDLYTHERAPYROBOTSTHANHANDAHN,2006BTHOUGHTHESESYSTEMSWERESUCCESSFULINADDRESSINGSMOOTHACTUATORMOTIONRESPONSETOSTEPINPUTS,ASSUMINGTHATTWOAXESPAMMANIPULATORISUTILIZEDINTHERAPYROBOTINTHEFUTURE,WHICHISTHEFINALGOALOFOURRESEARCH,ITISNECESSARYTOREALIZEFASTRESPONSE,EVENIFTHEEXTERNALINERTIALOADCHANGESSEVERELYWITHSINUSOIDALRESPONSEWITHOUTREGARDTOTHEVARIOUSFREQU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EQ6BELOWINDICATESTHATTHEDAMPERPRODUCESADAMPINGTORQUETBBEDCTKTSIGNG5G56THESTRUCTUREOFTHEPROPOSEDPHASEPLANESWITCHINGCONTROLMETHODISSHOWNINFIG632CONVENTIONALPHASEPLANESWITCHINGCONTROLMETHODFIGURE7SHOWSTHECONVENTIONALPHASEPLANESWITCHINGCONTROLMETHODINTHEREGIONINWHICHTHEJOINTANGLEOFTHEARMAPPROACHESTOTHEDESIREDANGLE,AB,CD,INFIG7A,THECURRENTISNOTAPPLIED,WHEREASINTHEREGIONTHEDIAGONALLYSHADEDAREASBC,DE,THECURRENTISAPPLIEDTOIMPROVETHEDAMPINGPERFORMANCEFORFASTERCONVERGENCETOTHEDESIREDANGLETHOUGHTHESYSTEMSUCCESSFULLYRESPONDSSMOOTHLYTOSTEPINPUTS,ITSQUALITYDEGRADESANDRESPONSELENGTHENSDUETOSINUSOIDALWAVEFORMREFERENCEINPUTOFUNCONTROLLABLEPOINTSC,EANDSOONINADDITION,ASSUMINGTHATTWOAXISPAMMANIPULATORSAREUTILIZEDINFUTURETHERAPYROBOTSTHEFINALGOALOFOURRESEARCH,ITISNECESSARYTOREALIZEAFASTRESPONSE,EVENIFTHEEXTERNALINERTIALOADCHANGESSEVERELYWITHSINUSOIDALRESPONSE,ANDONETHATISINDEPENDENTOFFREQUENCYOVERTHEOCCURRINGFREQUENCYRANGE33PROPOSITIONOFNEWCONCEPTOFPHASEPLANESWITCHINGCONTROLALGORITHMTHEDAMPINGTORQUEBT,WHICHISSHOWNINEQ1,IMPROVESTHEDAMPINGPERFORMANCEOFTHEMANIPULATORSINCETHEDAMPINGTORQUEACTSINTHEDIRECTIONOPPOSITETHEROTATIONALMOTIONOFTHEMANIPULATOR,ITSACCELERATIONPERFORMANCEISDEGRADEDINTHEREGIONWHERETHEJOINTANGLEOFTHEARMAPPROACHESTOTHEDESIREDANGLE,OABCDEFG,INFIG8A,THECURRENTISNOTAPPLIEDSINCEAHIGHRESPONSESPEEDISREQUIREDINTHEREGIONWHERETHEARMPASSESTHROUGHTHEDESIREDANGLE,IETHEDIAGONALLYSHADEDAREASOF,ABCDEFGHINFIG8A,ACURRENTISAPPLIEDTOIMPROVETHEDAMPINGPERFORMANCE,SOTHATTHEARMCONVERGESTOTHEDESIREDANGLEMOREQUICKLYTODETERMINEWHETHERTHEMAGNETICFIELDSHOULDBEAPPLIED,THEPHASEPLANEFIG6BLOCKDIAGRAMOFNEWCONCEPTOFPHASEPLANESWITCHINGCONTROLABFIG7ACONVENTIONALPHASEPLANESWITCHINGCONTROLMETHODSHOWNINFIG8BISUSEDTHEHORIZONTALAXISINTHEPHASEPLANECORRESPONDSTOJOINTANGLEDEVIATIONEBETWEENTHEDESIREDANGLERANDTHEJOINTANGLE,ANDTHEVERTICALAXISCORRESPONDSTOTHETIMEDERIVATIVEOFTHEDEVIATION,DEEDTG5G5EACHPOINTAHONTHEPHASEPLANECORRESPONDSTOTHELIKEWISELETTEREDPOINTINFIG8AHERE,THEREGIONWITHTHEAPPLICATIONOFCURRENTARECONTROLLEDBY1112,HSHS,THEGRADIENTOFTHETUDIEPCONGTHANHANDKYOUNGKWANAHN/JOURNALOFMECHANICALSCIENCEANDTECHNOLOGY212007101810271023ABFIG8ANEWCONCEPTOFPHASEPLANESWITCHINGCONTROLMETHODLINESHOWNINFIG8BTHEREGIONUNDERTHEAPPLICATIONOFTHEDAMPINGTORQUEISCONTROLLEDAS1HAND2HTHEADVANTAGEOFCONTROLLINGTHEREGIONINWHICHMRBISAPPLIEDISNEEDEDTOWITHOUTDECREASINGRESPONSESPEEDTHEEFFECTIVENESSOFPROPOSEDCONTROLLERWILLBEEXPERIMENTALLYINVESTIGATED4EXPERIMENTALRESULTSINTHISSTUDY,ACONTROLLERFORATWOAXISPAMMANIPULATORUSINGTHENEWCONCEPTOFAPHASEPLANESWITCHINGCONTROLLERISFABRICATED,ANDEXPERIMENTSARECARRIEDOUTUSINGASINUSOIDALWAVEFORMASAREFERENCEINPUTATTWODIFFERENTFREQUENCIESF03HZAND05HZTWOEXTERNALINERTIALLOADCONDITIONSLOAD120KGFCM2LOAD240KGFCM2AREALSOTESTEDTHELOADSAREATTACHEDTOTHEENDOFARM2INADDITION,THECONVENTIONALPIDCONTROLLERANDTHEPROPOSEDCONTROLLERARECOMPAREDFIRSTLY,THEEXPERIMENTSARECARRIEDOUTTOVERIFYTHEEFFECTIVENESSOFTHEPROPOSEDCONTROLLERATVARIOUSREFERENCEINPUTFREQUENCIESOFJOINT1FIGURE9SHOWSTHECOMPARISONBETWEENTHECONVENTIONALPIDCONTROLLERANDTHEPROPOSEDCONTROLLEROFEXPERIMENTALRESULTOFJOINT1ANDTHEEFFECTIVENESSOFPROPOSEDCONTROLLEDISSHOWNINDETAILINFIG10WITHRESPECTTOAF03HZBF05HZFIG9COMPARISONBETWEENCONVENTIONALPIDCONTROLLERANDPROPOSEDCONTROLLERJOINT1F03HZANDF05HZINTHEEXPERIMENT,THEINITIALVALUESOFTHEPROPOSEDCONTROLLERARESETTO619010PK,61010IK,615010DK,0015EDK,1208,1,2CTHHTHESEPARAMETERSWEREOBTAINEDBYTRIALANDERRORTHESEEXPERIMENTALRESULTSSHOWTHATTHEREISALARGETRACKINGERRORANDTIMEDELAYWITHRESPECTTOTHEINCREASEOFTHEFREQUENCYOFTHEREFERENCEINPUTWHENUSINGPIDCONTROLLERTHERESPONSEBECOMESWORSEWITHFREQUENCYUPTO05HZ,WHEREASTHESETTLINGTIMEDECREASESANDTHETRACKINGPERFORMANCEISGUARANTEEDBYUSINGTHEPROPOSEDCONTROLLERTHEDAMPINGTORQUEISNOTAPPLIEDFORFASTRESPONSEWHENTHEMANIPULATORSTARTSTOMOVE,ANDTHEDAMPINGTORQUEISAPPLIEDBYTHEMRBTOTHEROTATIONALAXISOFTHEPAMMANI1024TUDIEPCONGTHANHANDKYOUNGKWANAHN/JOURNALOFMECHANICALSCIENCEANDTECHNOLOGY21200710181027AF03HZBF05HZFIG10EXPERIMENTALRESULTSOFTHEPROPOSEDCONTROLLERJOINT1PULATORTOREDUCETHEOVERSHOOTANDOSCILLATIONWHENTHEMANIPULATORREACHESTHEDESIREDANGLENEXT,EXPERIMENTSWERECARRIEDOUTTOINVESTIGATETHECONTROLPERFORMANCEWITHRESPECTTOTHEVARIOUSREFERENCEINPUTFREQUENCIESOFJOINT2INADDITION,THEEXTERNALINERTIALLOADSLOAD120KGFCM2LOAD240KGFCM2AREATTACHEDTOTHEENDOFARMAF03HZBF05HZFIG11COMPARISONBETWEENCONVENTIONALPIDCONTROLLERANDPROPOSEDCONTROLLERJOINT2,LOAD12,ANDTHECONTROLPARAMETERSARESETTOBETHESAMEASJOINT1FIGURES11AND12SHOWTHECOMPARISONBETWEENTHEPIDCONTROLLERANDTHEPROPOSEDCONTROLLERFORTESTEDREFERENCEINPUTFREQUENCIESANDEXTERNALINITIALLOADCONDITIONSTHESEFIGURESSHOWTHATTHEREISALARGEERRORANDTIMEDELAYANDTHATMOREOSCILLATIONOCCURSWITHRESPECTTOINCREASINGREFERENCEINPUTFREQUENCY,ASWELLASTOINCREASINGEXTERNALINITIALLOADSINTHEEXPERIMENTS,THEPAMMANIPULATORJOINTANGLEAGREESWELLWITHTHEREFERENCEWHENUSINGTHENEWPHASEPLANESWITCHINGCONTROLLERTHEEFFECTIVENESSOFTHENEWLYPROPOSEDPHASEPLANESWITCHINGCONTROLALGORITHMISALSOSHOWNINDETAILINFIGS13AND14THEEXPERIMENTALRESULTSSHOWTHATAGOODCONTROLPERFORMANCEANDSTRONGROBUSTNESSARETUDIEPCONGTHANHANDKYOUNGKWANAHN/JOURNALOFMECHANICALSCIENCEANDTECHNOLOGY212007101810271025AF03HZBF05HZFIG12COMPARISONBETWEENCONVENTIONALPIDCONTROLLERANDPROPOSEDCONTROLLERJOINT2,LOAD2OBTAINEDANDDONOTDEPENDONEXTERNALINITIALLOADWHENUSINGTHEPROPOSEDCONTROLMETHODTHESEEXPERIMENTALRESULTSSHOWTHATTHEDAMPINGTORQUEISAPPLIEDANDRELEASEDVERYFREQUENTLYACCORDINGTOTHEAPPROACHTOTHEDESIREDANGLEITISDEMONSTRATEDTHATTHEPROPOSEDALGORITHMISEFFECTIVEINTHECASEOFVARIOUSEXTERNALLOADSANDDOESNOTDEPENDONREFERENCEINPUTFREQUENCYINADDITION,ITISUNDERSTOODTHATTHEROTATIONALANGLEOFTHEPAMMANIPULATORSMOOTHLYCONVERGESTOTHEDESIREDANGLEWITHLITTLEOSCILLATIONITISCONCLUDEDTHATTHENEWLYPROPOSEDPHASEPLANESWITCHINGCONTROLALGORITHMEFFECTIVELYTRACKSCONTROLOFASINUSOIDALWAVEFORMWITHHIGHGAINCONTROL,ANDHASGOODCONTROLPERFORMANCE,AFASTAF03HZBF05HZFIG13EXPERIMENTALRESULTSOFTHEPROPOSEDCONTROLLERJOINT2,LOAD1RESPONSE,ANDSTRONGROBUSTSTABILITYUNDERVARYINGEXTERNALINERTIALLOADSANDREFERENCEINPUTFREQUENCY5CONCLUSIONSINTHISSTUDY,ANEWCONCEPTOFPHASEPLANESWITCHINGCONTROLUSINGAMAGNETORHEOLOGICALBRAKEISPROPOSEDANDAPPLIEDTOATWOAXISPNEUMATICARTIFICIALMUSCLEMANIPULATORTOIMPROVETHECONTROLPERFORMANCEUNDERVARIOUSEXTERNALLOADSANDINDEPENDENTLYOFREFERENCEINPUTFREQUENCY1026TUDIEPCONGTHANHANDKYOUNGKWANAHN/JOURNALOFMECHANICALSCIENCEANDTECHNOLOGY21200710181027AF03HZBF05HZFIG14EXPERIMENTALRESULTSOFTHEPROPOSEDCONTROLLERJOINT2,LOAD2THEEXPERIMENTSSHOWEDTHATTHEPROPOSEDCONTROLALGORITHMWASHIGHLYEFFECTIVEINTHETRACKINGCONTROLOFASINUSOIDALTRAJECTORYANDHADHIGHGAINCONTROL,GOODCONTROLPERFORMANCE,FASTRESPONSEANDSTRONG,ROBUSTSTABILITYWITHRESPECTTOVARIATIONOFBOTHEXTERNALLOADSANDREFERENCEINPUTFREQUENCYTHERESULTSALSOSUGGESTTHATTHEPROPOSEDPHASEPLANESWITCHINGCONTROLUSINGMRBISONEOFTHEMOSTEFFECTIVEMETHODSFORDEVELOPINGAPRACTICALLYAVAILABLE,HUMANFRIENDLYROBOTBYUSINGAPAMMANIPULATORACKNOWLEDGEMENTTHISWORKWASSUPPORTEDBYUNIVERSITYOFULSAN,KOREAREFERENCESAHN,KKANDTHANH,TDC,2004,“IMPROVEMENTOFTHECONTROLPERFORMANCEOFPNEUMATICARTIFICIALMUSCLEMANIPULATORSUSINGANINTELLIGENTSWITCHINGCONTROLMETHOD,”INKSME,INT,JOUR,VOL8,NO8,PP13881400AHN,KKANDTHANH,TDC,2005A,“NONLIEARPIDCONTROLTOIMPROVETHECONTROLPERFORMANCEOFPAMMANIPULATORSUSINGNEURALNETWORK,”INKSME,INT,JOUR,VOL19,NO1,PP106115AHN,KK,THANH,TDCANDAHN,YK,2005B,“PERFORMANCEIMPROVEMENTOFPAMMANIPULATORSUSINGMAGNETORHEOLOGICALBRAKE,”INKSME,INT,JOUR,VOL19,NO3,PP777790DOI,Y,1993,“EXERCISEAPPARATUSFORRESTORATIONOFFUNCTION,”JSOCBIOMECH,VOL17,NO2,PP99105FUJIE,MG,TANIT,HIRANO,K,YOSHIDA,TANDWADA,N,1994,“WALKINGREHABILITATIONSYSTEMFORTHEELDERLY,”INPROC,IEEEINT,CONF,ADVANCEDROBOTICSYSTEMS,VOL3,PP16551662FUJIE,MG,TANIT,HIRANO,K,YOSHIDA,TANDWADA,N,1995,“IMPROVEME