资源预览需要最新版本的Flash Player支持。
您尚未安装或版本过低,建议您
ZEROMOMENTPOINTTRAJECTORYMODELINGOFABIPEDWALKINGROBOTUSINGANADAPTIVENEUROFUZZYSYSTEMDKIM,SJSEOANDGTPARKABSTRACTABIPEDALARCHITECTUREISHIGHLYSUITABLEFORAROBOTBUILTTOWORKINHUMANENVIRONMENTSSINCESUCHAROBOTWILLFINDAVOIDINGOBSTACLESARELATIVELYEASYTASKHOWEVER,THECOMPLEXDYNAMICSINVOLVEDINTHEWALKINGMECHANISMMAKETHECONTROLOFSUCHAROBOTACHALLENGINGTASKTHEZEROMOMENTPOINTZMPTRAJECTORYINTHEROBOT’SFOOTISASIGNIfiCANTCRITERIONFORTHEROBOT’SSTABILITYDURINGWALKINGIFTHEZMPCOULDBEMEASUREDONLINETHENITBECOMESPOSSIBLETOCREATESTABLEWALKINGCONDITIONSFORTHEROBOTANDHEREALSOSTABLYCONTROLTHEROBOTBYUSINGTHEMEASUREDZMP,VALUESZMPDATAISMEASUREDINREALTIMESITUATIONSUSINGABIPEDWALKINGROBOTANDTHISZMPDATAISTHENMODELLEDUSINGANADAPTIVENEUROFUZZYSYSTEMANFSNATURALWALKINGMOTIONSONflATLEVELSURFACESANDUPANDDOWNA10SLOPEAREMEASUREDTHEMODELLINGPERFORMANCEOFTHEANFSISOPTIMIZEDBYCHANGINGTHEMEMBERSHIPFUNCTIONSANDTHECONSEQUENTPARTOFTHEFUZZYRULESTHEEXCELLENTPERFORMANCEDEMONSTRATEDBYTHEANFSMEANSTHATITCANNOTONLYBEUSEDTOMODELROBOTMOVEMENTSBUTALSOTOCONTROLACTUALROBOTS1INTRODUCTIONTHEBIPEDALSTRUCTUREISONEOFTHEMOSTVERSATILESETUPSFORAWALKINGROBOTABIPED,ROBOTHASALMOSTTHESAMEMOVEMENTMECHANISMSASAHUMANANDITABLETOOPERATEINENVIRONMENTSCONTAININGSTAIRS,OBSTACLESETCHOWEVER,THEDYNAMICSINVOLVEDAREHIGHLYNONLINEAR,COMPLEXANDUNSTABLETHUS,ITISDIFfiCULTTOGENERATEAHUMANLIKEWALKINGMOTIONTHEREALISATIONOFHUMANLIKEWALKINGROBOTSISANAREAOFCONSIDERABLEACTIVITY1–4INCONTRASTTOINDUSTRIALROBOTMANIPULATORS,THEINTERACTIONBETWEENAWALKINGROBOTANDTHEGROUNDISCOMPLEXTHECONCEPTOFAZEROMOMENTPOINTZMP2HASBEENSHOWNTOBEUSEFULINTHECONTROLOFTHISINTERACTIONTHETRAJECTORYOFTHEZMPBENEATHTHEROBOTFOOTDURINGAWALKISAFTERTAKENTOBEANINDICATIONOFTHESTABILITYOFTHEWALK1–6USINGTHEZMPWECANSYNTHESISETHEWALKINGPATTERNSOFBIPEDROBOTSANDDEMONSTRATEAWALKINGMOTIONWITHACTUALROBOTSTHUS,THEZMPCRITERIONDICTATESTHEDYNAMICSTABILITYOFABIPEDROBOTTHEZMPREPRESENTSTHEPOINTATWHICHTHEGROUNDREACTIONFORCEISTAKENTOOCCURTHELOCATIONOFTHEZMPCANBECALCULATEDUSINGAMODELOFTHEROBOTHOWEVER,ITISPOSSIBLETHATTHERECANBEALARGEERRORBETWEENTHEACTUALZMPVALUEANDTHECALCULATEDVALUE,DUETODEVIATIONSINTHEPHYSICALPARAMETERSBETWEENTHEMATHEMATICALMODELANDTHEREALMACHINETHUS,THEACTUALZMPSHOULDBEMEASUREDESPECIALLYIFITISTOBEUSEDINATOPARAMETERSACONTROLMETHODFORSTABLEWALKINGINTHISWORKACTUALZMPDATATAKENTHROUGHOUTTHEWHOLEWALKINGCYCLEAREOBTAINEDFROMAPRACTICALBIPEDWALINGROBOTTHEROBOTWILLBETESTEDBOTHONAflATflOORANDALSOON10SLOPESANADAPTIVENEUROFUZZYSYSTEMANFSWILLBEUSEDTOMODELTHEZMPTRAJECTORYDATATHEREBYALLOWINGITSUSETOCONTROLACOMPLEXREALBIPEDWALKINGROBOT2BIPEDWALKINGROBOT21DESIGNOFTHEBIPEDWALKINGROBOTWEHAVEDESIGNEDANDIMPLEMENTEDTHEBIPEDWALKINGROBOTSHOWNINFIG1THEROBOTHAS19JOINTSTHEKEYDIMENSIONSOFTHEROBOTAREALSOSHOWNINFIG1THEHEIGHTANDTHETOTALWEIGHTAREABOUT380MMAND1700GINCLUDINGBATTERIES,RESPECTIVELYTHEWEIGHTOFTHEROBOTISMINIMISEDBYUSINGALUMINIUMINITSCONSTRUCTIONEACHJOINTISDRIVENBYARCSERVOMOTORTHATCONSISTSOFADCMOTOR,GEARSANDASIMPLECONTROLLEREACHOFTHERCSERVOMOTORSISMOUNTEDINALINKEDSTRUCTURETHISSTRUCTUREENSURESTHATTHEROBOTISSTABLEIEWILLNOTFALLDOWNEASILYANDGIVESTHEROBOTAHUMANLIKEAPPEARANCEABLOCKDIAGRAMOFOURROBOTSYSTEMISSHOWNINFIG2OUTROBOTISABLETOWALKATARATEOFONESTEP48MMEVERY14SONAflATflOORORANSHALLOWSLOPESTHESPECIfiCATIONSOFTHEROBOTARELISTEDINTABLE1THEWALKINGMOTIONSOFTHEROBOTARESHOWNINFIGS3–6FIGURES3AND4ARESHOWFRONTANDSIDEVIEWSOFTHEROBOT,RESPECTIVELYWHENTHEROBOTISONAflATSURFACEFIGURE5ISASNAPSHOTOFTHEROBOTWALKINGDOWNASLOPEWHEREASFIG6ISASNAPSHOTOFTHEROBOTWALKINGUPASLOPETHELOCATIONSOFTHEJOINTSDURINGMOTIONARESHOWNINFIG7THEMEASUREDZMPTRAJECTORYISOBTAINEDFROMTENDEGREEOFFREEDOMDOFDATAASSHOWNINFIG7TWODEGREESOFFREEDOMAREASSIGNEDTOTHEHIPSANDANKLESANDONEDOFTOEACHKNEEUSINGTHESEJOINTANGLES,ACYCLICWALKINGPATTERNHASBEENREALISEDOURROBOTISABLETOWALKCONTINUOUSLYWITHOUTFALLINGDOWNTHEJOINTANGLESINTHEFOURSTEPMOTIONOFOURROBOTARESUMMARISEDINTHEAPPENDIX22ZMPMEASUREMENTSYSTEMTHEZMPTRAJECTORYINAROBOTFOOTISASIGNIfiCANTCRITERIONFORTHESTABILITYOFTHEWALKINMANYSTUDIES,ZMPCOORDINATESARECOMPUTEDUSINGAMODELOFTHEROBOTANDINFORMATIONFROMTHEENCODERSONTHEJOINTSHOWEVER,WEEMPLOYEDAMOREDIRECTAPPROACHWHICHISTOUSEDATAMEASUREDUSINGSENSORSMOUNTEDONTHEROBOT’SFEETTHEDISTRIBUTIONOFTHEGROUNDISREACTIONFORCEBENEATHTHEROBOT’SFOOTISCOMPLICATEDHOWEVER,ATANYPOINTPONTHESOLEOFTHEFOOTTOTHEREACTIONCANBEREPRESENTEDBYAFORCENANDMOMENTM,ASSHOWNINFIG8THEZMPISSIMPLYTHECENTREOFTHEPRESSUREOFTHEFOOTONTHEGROUND,ANDTHEMOMENTAPPLIEDBYTHEGROUNDABOUTTHISPOINTISZEROINOTHERWORDS,THEPOINTPONTHEGROUNDISTHEPOINTATWHICHTHENETMOMENTOFTHEINERTIALANDGRAVITYFORCESHASNOCOMPONENTALONGTHEAXESPARALLELTOTHEGROUND1,7FIGURE9ILLUSTRATESTHEUSEDSENSORSANDTHEIRPLACEMENTONTHESOLEOFTHEROBOT’SFOOTTHETYPEOFFORCESENSORUSEDINOUREXPERIMENTSISAFLEXIFORCEA201SENSOR8THEYAREATTACHEDTOTHEFOURCORNERSOFTHEPLATETHATCONSTITUTESTHESOLEOFTHEFOOTSENSORSIGNALSAREDIGITISEDBYANADCBOARD,WITHASAMPLINGTIMEOF10MSMEASUREMENTSARECARRIEDOUTINREALTIMETHEFOOTPRESSUREISOBTAINEDBYSUMMINGTHEFORCESIGNALSUSINGTHESENSORDATAITISEASYTOCALCULATETHEACTUALZMPVALUESTHEZMPSINTHELOCALFOOTCOORDINATEFRAMEARECOMPUTEDUSING1WHEREEACHFIISTHEFORCEATASENSORRIISTHESENSORPOSITIONWHICHISAVECTORTHESEAREDEfiNEDINFIG10INTHEfiGURE,‘O’ISTHEORIGINOFTHEFOOTCOORDINATEFRAMEWHICHISLOCATEDATTHELOWERLEFTHANDCORNERTHELEFTFOOTEXPERIMENTALRESULTSARESHOWNINFIGS11–16FIGURES11,13AND15SHOWTHEXCOORDINATEANDYCOORDINATEOFTHEACTUALZMPPOSITIONSFORTHEFOURSTEPMOTIONOFTHEROBOTWALKINGONAflATflOORANDALSODOWNANDUPASLOPEOF10,RESPECTIVELYFIGURES12,14AND16SHOWNTHEZMPTRAJECTORYOFTHEONESTEPMOTIONOFTHEROBOTUSINGTHEACTUALZMPPOSITIONSSHOWNINFIGS11,13AND15ASSHOWNINTHETRAJECTORIES,THEZMPSEXISTINARECTANGULARDOMAINSHOWNBYASOLIDLINETHUS,THEPOSITIONSOFTHEZMPSAREWITHINTHEROBOT’SFOOTANDHENCETHEROBOTISSTABLE3ZMPTRAJECTORYMODELLINGINMANYSCIENTIfiCPROBLEMSANESSENTIALSTEPTOWARDSTHEIRSOLUTIONISTOACCOMPLISHTHEMODELLINGOFTHESYSTEMUNDERINVESTIGATIONTHEIMPORTANTROLEOFMODELLINGISTOESTABLISHEMPIRICALRELATIONSHIPSBETWEENOBSERVEDVARIABLESTHECOMPLEXDYNAMICSINVOLVEDINMAKINGAROBOTWALKMAKETHECONTROLOFTHEROBOTCONTROLACHALLENGINGTASKHOWEVER,IFTHEHIGHLYNONLINEARANDCOMPLEXDYNAMICSCANBECLOSELYPRODUCEDTHENTHISMODELLINGCANBEUSEDINTHECONTROLOFTHEROBOTINADDITION,MODELLING,CANEVENBEUSEDINROBUSTINTELLIGENTCONTROLTOMINIMISEDISTURBANCESANDNOISE31ANFSFUZZYMODELLINGTECHNIQUESHAVEBECOMEANACTIVERESEARCHAREAINRECENTYEARSBECAUSEOFTHEIRSUCCESSFULAPPLICATIONTOCOMPLEX,ILLDEfiNEDANDUNCERTAINSYSTEMSINWHICHCONVENTIONALMATHEMATICALMODELSFAILTOGIVESATISFACTORYRESULTS9INTHISLIGHTWEINTENDTOUSEASYSTEMTOMODELTHEZMPTRAJECTORYTHEFUZZYINFERENCESYSTEMISAPOPULARCOMPUTINGFRAMEWORKTHATISBASEDONTHECONCEPTSOFFUZZYSETTHEORY,FUZZYIFTHENRULES,ANDFUZZYREASONINGWEWILLUSETHESUGENOFUZZYMODELINWHICHSINCEEACHRULEHASACRISPOUTPUT,THEOVERALLOUTPUTISOBTAINEDVIAAWEIGHTEDAVERAGE,THUSAVOIDINGTHETIMECONSUMINGPROCESSOFDEFUZZIfiCATIONWHENWECONSIDERFUZZYRULESINTHEFUZZYMODEL,THECONSEQUENTPARTCANBEEXPRESSEDBYEITHERACONSTANTORALINEARPOLYNOMIALTHEDIFFERENTFORMSOFPOLYNOMIALSTHATCANBEUSEDINTHEFUZZYSYSTEMARESUMMARISEDINTABLE2THEMODELLINGPERFORMANCEDEPENDSONTHETYPEOFCONSEQUENTPOLYNOMIALUSEDINTHEMODELLINGMOREOVER,WECANEXPLOITVARIOUSFORMSOFMEMBERSHIPFUNCTIONSMFS,SUCHASTRIANGULARANDGAUSSIAN,FORTHEFUZZYSETINTHEPREMISEPARTOFTHEFUZZYRULESTHESEAREANOTHERFACTORTHATCONTRIBUTESTOTHEflEXIBILITYOFTHEPROPOSEDAPPROACHTHETYPESOFTHEPOLYNOMIALAREASFOLLOWSABLOCKDIAGRAMOFTHEMODELLINGSYSTEMISSHOWNINFIG17THEPROPOSEDMETHODISfiRSTUSEDTOMODELANDTHENCONTROLAPRACTICALBIPEDWALKINGROBOTTOOBTAINTHEFUZZYRULESFORTHEFUZZYMODELLINGSYSTEMWEMUSTNOTESTHATTHENONLINEARSYSTEMTOBEIDENTIfiEDISABIPEDWALKINGROBOTWITHTENINPUTVARIABLESANDEACHINPUTVARIABLESHASTWOFUZZYSETS,RESPECTIVELYFORTHEFUZZYMODEL,THEIFTHENRULESAREASFOLLOWSWHEREAI，BI，,,,JIINTHEPREMISEPARTOFTHERULESHAVELINGUISTICVALUESSUCHAS‘SMALL’OR‘BIG’ASSOCIATEDWITHTHEINPUTVARIABLE,X1,X2,,X10；RESPECTIVELYFJX1,X2,,X10；ISTHECONSTANT,ORfiRSTORDERCONSEQUENTPOLYNOMIALFUNCTIONFORTHEJTHRULEASDEPICTEDINFIG18,TWOTYPESOFMFSWEREEXAMINEDONEISTHETRIANGULARANDTHEOTHERISGAUSSIANFIGURE19ISANADAPTIVENEUROFUZZYINFERENCESYSTEM10ARCHITECTURETHATISEQUIVALENTTOTHETENINPUTFUZZYMODELCONSIDEREDHERE,INWHICHEACHINPUTISASSUMEDTOHAVEONEOFTHETWOMFSSHOWNINFIG18NODESLABELLEDPGIVETHEPRODUCTOFALLTHEINCOMINGSIGNALSANDTHESELABELLEDNCALCULATETHERATIOOFACERTAINRULE’SfiRINGSTRENGTHTOTHESUMOFALLTHERULE’SfiRINGSTRENGTHSPARAMETERVARIATIONINANFISISOCCUREDUSINGEITHERAGRADIENTDESCENTALGORITHMORARECURSIVELEASTSQUARESESTIMATIONALGORITHMTOADJUSTBOTHTHEPREMISEANDCONSEQUENTPARAMETERSITERATIVELYHOWEVER,WEDONOTUSETHECOMPLEXHYBRIDLEARNINGALGORITHMBUTINSTEADUSETHEGENERALLEASTSQUARESESTIMATIONALGORITHMANDONLYDETERMINETHECOEFfiCIENTSINTHECONSEQUENTPOLYNOMIALFUNCTION32SIMULATIONRESULTSAPPROXIMATELYMODELSWERECONSTRUCTEDUSINGTHEANFSTHENACCURACYWASQUANTIfiEDINTERMSOFTHEREMEANSQUAREDERRORMSE,VALUESTHEANFSWASAPPLIEDTOMODELTHEZMPTRAJECTORYOFABIPEDWALKINGROBOTUSINGDATAMEASUREDFROMOUTROBOTTHEPERFORMANCEOFTHEANFSWASOPTIMISEDBYWARYINGTHEMFANDCONSEQUENTTYPEINTHEFUZZYRULETHEMEASUREDZMPTRAJECTORYDATAFROMOURROBOTSHOWNINFIGS32–41AINTHEAPPENDIXAREUSEDASTHEPROCESSPARAMETERSWHENTRIANGULARANDGAUSSIANMFSAREUSEDINTHEPREMISEPARTANDACONSTANTINTHECONSEQUENTPARTTHEN,THECORRESPONDINGMSEVALUESARELISTEDINTABLE3WEHAVEPLATTEDOURRESULTSINFIGS20–25THEGENERATEDZMPPOSITIONSFROMTHEANFSARESHOWNINFIGS20,22AND24FORAflATLEVELflOOR,WALKINGDOWNA10SLOPEANDWALKINGUPA10SLOPE,RESPECTIVELYINFIGS21,23AND25,WECANSEETHECORRESPONDINGZMPTRAJECTORIESWHICHAREGENERATEDFROMTHEANFSFORSIMPLICITY,THEPROCESSPARAMETEROFBOTHKNEESCANBEIGNOREDASARESULT,WECANREDUCETHEDIMENSIONOFTHEFUZZYRULESANDTHEREBYLOWERTHECOMPUTATIONALBURDENINTHISCASETHESIMULATIONCONDITIONSOFTHEANFSANDITSCORRESPONDINGMSEVALUESAREGIVENINTABLE4FROMTHEFIGURESANDTABLESTHATPRESENTTHESIMULATIONRESULTS,WECANSEETHATTHEGENERATEDZMPTRAJECTORYFROMTHEFUZZYSYSTEMISVERYSIMILARTOACTUALZMPTRAJECTORYOFMEASUREDFOROURWALKINGROBOTSHOWNINFIGS11–16THEDEMONSTRATEDHIGHPERFORMANCEABILITYOFTHEANFS,MEANSTHATANFSCANBEEFFECTIVELYUSEDTOMODELANDCONTROLAPRACTICALBIPEDWALKINGROBOT33COMPARISONSWENOWCOMPARETHEPERFORMANCEOFANFSWITHNUMERICALMETHODSINCLUDINGTHREETYPESOFSTATISTICALREGRESSIONMODELSFOREACHSTATISTICALREGRESSIONMODEL,FOURDIFFERENTCASETYPESWERECONSTRUCTEDTHEIRGE
