外文資料:RobotsIntroductionNowadays,theapplicationsofmachinesandrobotstoassisthumaninperformingtheirtaskshasbecomeincreasinglyextensive.Inindustrialapplications,theuseofroboticssystemhasreachedthelevelwhichsurpasseshumanabilityintermsofspeedandaccuracy.Ontheotherhand,inthefieldofdomesticrobotsorservicerobots,thedevelopmentsarestillfarfromperfection.Themainfactorthatdistinguishesindustrialrobotsfromservicerobotsistheirworkingenvironment.Foraservicerobottoperfectlyperformitstasks,itneedstobeabletoadaptandcopewiththenormalhumanlivingenvironment.Fromthepracticalpointofview,bipedalrobotisthemostsuitablerobotstructureduetoitssimilarityofphysicalconfigurationwithhumanespeciallyintermsoflocomotionmethod.Howevei,therealizationofbipedalrobotismorechallengingcomparedtoothertypesofmobilerobotduetheunstablenatureofbipedalwalking.Therefore,manystudieshavebeencarriedoutespeciallyconcerningthestabilitysensingandcontrolstrategiesofbipedalrobot.Thecommonapproachindefiningthestabilityofbipedalrobotisbyusingthe''ZeroMomentPoint”(ZMP)criterion[1].ThesimplestimplementationofZMPistogeneratethejointtrajectoriesbasedonthepre-plannedwalkinggaitwhilemaintainingtheZMPatthegivenreferences,butthisapproachhasalimitationinmaintainingthebalanceifthereisanyunknownexternaldisturbance[2-5].Manystudiesspecificallyfocusonthetechniquestomonitorthereal-timeZMPpositionfromthephysicalsystemanduseditasthefeedbackcomponent[6-9].TakanishiandKato[7]proposedamethodtomonitortheZMPpositionbymeasuringtheforceandmomentactingontherobot'sshankbyusinguniversalforcemomentsensor.Anothermethodutilizesanarrayofforcesensitiveresistorplacedonthesoleoftherobot'sfoottoobtainthegroundreactionforceatdifferentlocationsofthefoot.ThereactionforcesmeasuredfromthesensorarrayisthenusedtocomputethepositionofthecenterofpressurewhichreflectsthepositionoftheZMP[9].Theinvertedpendulumtechniqueisanotheralternativeforanalyzingtherobotstability[10].Thismethodmonitortheinstabilitybyconstantlyreadingthebodyaccelerationandtiltanglebymeansofaccelerometerandgyroscope.However,thereadingsfrombothsensorsaresubjecttonoiseanddriftduringtheoperationandtheefforttoapplyfiltersincorrectingthemeasurementsoftenrequiresconsiderableamountofcomputingpower[11].Thispaperproposedanovelmethodforsensingandstabilitycontrolofbipedalrobot.Theuseofspeciallydesignedflexibleanklejointallowsfastdetectionandpredictionofrobotsidewayinstability.Placinganadditionalonedegree-offreedomrotaryjointwithbuilt-inangledetectionsensorattherobotankleallowstherobot'sbodytotiltfreelyinanysidewaydirectionanddetectthetendencyofimbalancethatmaypotentiallyoccur.Basedonthisessentialsensor'sinformation,thecontrollerwillquicklyadjustpositionofthecounterbalancemasslocatedattherobotwaistinordertorestorethesidewaybalanceoftherobot.Theadvantageofusingcounterbalancemassandrotaryjointattheankleistoallowthewalkingsubsystemandsidewaybalancingsubsystemoftherobottobedecoupledfromeachotherandworkin

independentlycontrolledmodes.Itisdifferentfromthetraditionalapproachwhentherobot'spostureiscorrectedtosatisfybothconditionsatonce,smoothforwardwalkingandcontinuoussideway(sagittal)stability.Detailsoftheproposedmethodarepresentedasfollows.Insection2thelocomotionmechanism,anklestructure,sensingtechniqueandbalancingstrategyareintroduced.Section3discussesthemathematicalmodelofthesystem.Insection4experimentmethodisdiscussedandtheviabilityoftheproposedsystemisprovenbytheexperimentalresult.Finally,theconclusionsaredescribedinsection5.MechanicalStructureofBipedRobotRobotlocomotionmechanismThebipedrobotisdesignedtorealizetwodimensionalwalkingwithminimumnumberofactuations.Thelocomotionsystemoftherobotconsistsoffouractuators,twoforthehipjointsandtwoforthekneejoints.Theanklejointisnotactuatedbyanyactuatorsbutinsteaditutilizesaseriesofparallelogrammechanismtopassivelycontroltheanklejointinordertomaintainthepositionofthefoot.Theusageofparallelogrammechanismprovidesbenefitsbyreducingthenumberofactuatorsneededwhichresultsinthesimplificationofthemechanismdesignandreductionoftheoverallrobot'sweight.Fig1(a)showsthestickdiagramofthelegindifferentconfiguration.Theorientationoflinkaisalwaysparalleltothehipduetotheconstraintappliedbylink1andlink2.Theorientationoflinkbwhichrepresentsthefootisalwaysparalleltolinkaduetotheconstraintappliedbylink3andlink4.Therefore,thefootisalwayskeptparallelbytheparallelogrammechanismregardlessofanyconfigurationoftheleg.Fig1(b),(c)showthephysicalimplementationoftheparallellegindifferentpostures.Theprototypeofthebipedrobotismainlyconstructedusinghollowsectionsofextrudedaluminiumduetoitslightnessandstrength.Theoverallheightofthebipedrobotis0.9mwiththetotalweightof7kg.Thelengthforboththighandshankare0.3mandthespacingbetweentwolegsis0.15m.Fortheactuation,eachjointisequippedwithRobotisDynamixelRX-64SmartActuator,whichcombinesgeartransmission,controller,driverandnetworkfunctioninasinglepackage.Theoutputofthehipmotorisconnecteddirectlytothehipjointandtheoutputofthekneemotoristransmittedtothekneejointviaafourbarlinkage.Thepurposeofplacingtheactuatorsonthehipistoreducetheweightofthelegwhichwillminimizethedynamicsforcescreatedbythelegmovement.Theotheradvantageofthisstructuralarrangementisthattheangularcountateachjointisalwaysreferencedtothefixedverticalaxisofthestationaryworldcoordinateframeregardlessofthelegpostures.(a)(b)

(a)(b)Fig.1.(a)Stickdiagramofparallelogramleg;(b),(c)RobotstandingwithdifferentlegconfigurationsFlexibleanklejointtoutilizestabilitymeasurementInordertoachieveastablewalkonabipedrobot,theabilitytoaccuratelydetectanypossibleinstabilityisquitecrucial.Thispaperintroducesanewapproachofsensingtheinstabilitybyintroducinganadditionaldegreeoffreedominsidewaydirectionnexttotheanklejoint.Fig2(a)showsthestructureofthatdegreeoffreedomwherethefreerotaryjointonthefrontalplaneisplacedattheanklebetweenthefootandanklejoint.Itwilllettheunconstrainedrobotbodystandingononelegtotilt(angle□)freelyinsideway(sagittal)directionforanypossibledisturbanceinthatdirection.Byinstallingarotarysensoronthefreejointthecontrollerwillbeabletodetectinstantlyanyinstabilityandimmediatelyreacttorestorethebalance.(a)Fig.2(a)Schematic(a)Fig.2(a)Schematicpictureoftheflexibleanklestructure;(b)Physicalimplementationofflexibleankle(b)SplitbalancingmassforfastersystemresponseThewalkingcycleofbipedalrobotconsistsofsinglesupportphaseanddoublesupportphasewhichareexecutedsequentiallyandrepeatedly.Insinglesupportphase,therobotisstandingononelegwhileanotherlegistransferredforward.Duringthisphase,therobotbodywillbetiltedsidewaysduetotheunbalancedtorquecreatedbytheweightoftheliftedlegandthedynamicforcesgeneratedduetothelegmovement.Inordertomaintainstabilityoftherobot,asetofcounterbalancemassesarelocatedataspecificpositiontocompensatetheunbalancedmassoftheliftedlegandotherpossibledisturbance.Fig3showsthesimplified3-massesmodelofbipedalrobot:mLrepresentsthelumpedmassofthehangingleg,mB1representsthemajorbalancingmassandmB2representstheminorbalancingmass.Majorbalancingmassismainlyusedtocompensatetheweightoftheliftedleg.ThismassispositionedataprecalculatedlocationinordertobalancethetorquecreatedbythemassoftheliftedlegmL.TheminorbalancingmassmB2iscontinuouslyrepositionedbasedontheinformationgatheredfromthesensorlocatedattheadditionalanklejoint.Thismassworksasacounterbalancetomaintaintherobottobealwaysverticalregardlessofanyexternalsidewaydisturbance.Theuseoftwoseparatecounterbalancemassesprovidesseveraladvantagessuchas:

?Fasterresponsetimecanbeachievedbyonlymovingsmallinertiacounterbalancingmassinsteadofmovingalargerone,?Energyefficiencycanbeimprovedbyreducingloadofthemotorthatdrivesasmallerinertiacounterbalancingmass.Fig.3Fig.3Simplifiedmodelofthebipedalrobot—5(2)(3)3.Systemmodelingandcontrol—5(2)(3)FromthediagramonFig3,thedynamicequationusingNewton’ssecondlawaboutpointOgives:ZTo=i0Tdis1+mLg(dcos9+rsin9)—mB2g(acos9+rsin9)—mB1g(dscos0+sin0)+mB2ar—c。一網(wǎng)=0(mL(r2+d2)+mfi2(r2+羽)+mfii(d52+r2))(1)Sincethemajorbalancingmassmfiiismainlyusetocompensateforthetorquecreatedbytheweightofthehanginglegm^,themajorbalancingmasscanbepositionedatthepre-calculatedlocationontheoppositesideofthehangingleg.Therequiredpositionofthemajorbalancingmass電canbecalculatedbasedontheequilibriumoftorqueatpointOasfollows:立。=°

m^d—mfiid5=0

m^d=mfiid5

m

電=—d

meiSubstituting電fromEq.(2)intoL.H.SofEq.(1)gives:Tdis1+m*(dcos9+rsin。)一mfi2g(acos6+rsin。)dcos。+rsin0)mfi2ar—c。一k。=0(m^(r2+d2)+mfi2(r2+羽)+^B1(^s2+"))Tdis1+gcos0(m^d—m^d—mfi2a)+grsin0+mfi2ar—mfi2a206(m^(r2+d2)+mfi2r2+mfii(d52+r2))+c。+網(wǎng)RearrangingthedifferentialequationfromEq.(3)gives:Tdis1—mfi2g?acos6+(m^+mfi2+mfii)g?rsin9+mB2ar—mB2a20=6(m^(r2+d2)+mB2r2+mBi(ds2+r2))+cO+kO(4)ThedifferentialequationinEq.(4)hastwodistinctparts.Therighthandsideonlypresentspartsoftheordinarydifferentialequationwithconstanttimeinvariantcoefficientsandthelefthandsidepresentsallremainingpartsoftheequation.Therefore,thelefthandsideincludes:?Non-linearfunctionsofthemaindependentarguments,namelysin。，cos。?Additionalbutindependentfromthemainargument0parametera?TheparametersthatcomprisesbothaandQarguments,namely^罪羽。Fig4showsthesimplifiedcontrolblockdiagramofthebalancingsystem.ThePIDcontrollerconstantlymonitorsthetiltangle(。)fromthesensoroftheadditionalanklejointandcomparesthereadingwiththatofthedesiredangle.Ifanytiltisdetected,thecontrollerwillactuatethebalancingmasstotheoppositedirectioninordertoregainthebalance.Fig.4SimplifiedblockdiagramofthestabilitycontrolsystemExperimentalresultsTheexperimentiscarriedouttoverifytheeffectivenessoftheproposedmechanicalstructureandcontrolstrategiesinmaintainingtherobot'sbalanceinsinglesupporlphase.Duringtheexperiment,therobotisstandingononelegwithanotherlegliftedupandfloating.Theexternaldisturbanceisappliedbymakingapushontheedgeoftherobot'shipwhichwillcausetherobottotiltsideways(Fig5(a)).Theintensityofthepushingforceismeasuredbyaforcesensormountedonthehip(Fig5(b)).Fig6showsthemeasurementofthetiltangle0fromtheadditionalanklejoint,balancingmasspositionaandthedisturbanceforcewhentheexternaldisturbanceisapplied.Itisapparentfromthefigurethatoncethedisturbanceisappliedthesensordetectschangeintiltangleandthecontrollerimmediatelyreactsbymovingthemasstotheoppositedirectionofthetiltinordertoregainthebalance.Fig7showsthemeasurementwhenanexcessivedisturbanceforceisappliedapproximatelyatthe37thseconds,thetiltanglechangesabruptlyandthebalancingmassisnotabletorecoverthebalance.Thesaturatedanglemeasurementattheendoftheplotsindicatesthattherobotisfalling.ItisduetothefactthatthevalueofminormassmB2andtheallowablerangeof

itsmotionaarelimitedinthisdesign.TheoverallresistancetotheexternallygeneratedforcecanbeincreasedbyeitherincreasingmB2ora.(a)Fig.5(a)Hipplaneoftherobot;(b)Forcesensorattachmentto(a)Fig.5(a)Hipplaneoftherobot;(b)Forcesensorattachmenttomeasureapplieddisturbanceforce(b)eo4090Tine(s)20Fig.6.Systemresponsetodisturbance(balancemaintained)Fig.7.Systemresponsetodisturbance(excessiveFig.7.Systemresponsetodisturbance(excessiveforceapplied)L1111L1:riiiiriii05101520259095404650Time悟)Thispaperpresentsstabilitycontrolmethodforbipedalwalkingrobotwhichincludesthelegdesignwithadditional(redundant)degreeoffreedomattheanklejointandsplitbalancingmass.Theproposedmethodenablesthesensing,controlandbalancingofbipedalrobottobeimplementedinasimpleyetcosteffectivemanner.Theeffectivenessofthedesignmethodisprovenbytheexperimentalresults.Theimplementationofthismethodalsoallowsthewalkcontrollingalgorithmstobedecoupledfromthestabilitycontrolalgorithmstoincreasethesystemresponsetime.ReferencesVukobratovicM.,JuricicD.,1969.Contributiontothesynthesisofbipedgait,IEEETransactiononBiomedicalEngineering16,p.1-6.ErbaturK.,KurtO.,2006.“HumanoidWalkingRobotControlwithNaturalZMPReferences,”IEEEIndustrialElectronics-Proceedingsofthe32ndAnnualConference,p.4100-4106.LimH.-ok,SetiawanS.A.,TakanishiA.,2001.“Balanceandimpedancecontrolforbipedhumanoidrobotlocomotion,”IntelligentRobotsandSystems-Proceedingsofthe2001IEEE/RSJInternationalConference,p.494-499.LiuL.,ZhaoM.,LinD.,WangJ.,ChenK.,2003.“Gaitdesigningofbipedrobotaccordingtohumanwalkingbasedonsix-axisforcesensors,”ComputationalIntelligenceinRoboticsandAutomation-Proceedingsofthe2003IEEEInternationalSymposium,p.360-365.SardainP.,BessonnetG.,2004.Zeromomentpoint-measurementsfromahumanwalkerwearingrobotfeetasshoes,IEEETransactionsonSystems,ManandCybernetics,PartA:SystemsandHumans34,p.638-648.LofflerK.,GiengerM.,PfeifferF.,UlbrichH.,2004.Sensorsandcontrolconceptofabipedrobot,IEEETransactionsonIndustrialElectronics51,p.972-980.TakanishiA.,KatoI.,1991.“AbipedwalkingrobothavingaZMPmeasurementsystemusinguniversalforce-momentsensors,”IntelligentRobotsandSystems-Proceedingsofthe1991IEEE/RSJInternationalWorkshop,p.1568-1573.KagamiS.,TakahashiY.,NishiwakiK.,MochimaruM.,MizoguchiH.,“High-speedmatrixpressuresensorforhumanoidrobotbyusingthinforcesensingresistancerubbersheet,”Sensors-Proceedingsofthe2004IEEEConference,p.1534-1537.KalamdaniA.,MessomC.,SiegelM.,2007.Robotswithsensitivefeet,IEEEInstrumentationandMeasurementMagazine10,p.46-53.CauxS.,MateoE.,ZapataR.,1998.“Balanceofbipedrobots:specialdoubleinvertedpendulum”Systems,ManandCybernetics-IEEEInternationalConference,p.3961-3969.BraunlT.,2006.EmbeddedRobotics,Springer,Germany.譯文資料:機(jī)器人1、介紹現(xiàn)在，機(jī)械和機(jī)器人的應(yīng)用幫助人類執(zhí)行他們的任務(wù)已經(jīng)變得越來越廣泛。在工業(yè)應(yīng)用中，使用機(jī)器人系統(tǒng)已經(jīng)達(dá)到了在速度和準(zhǔn)確度上超過人類能力的水平。另一方面，在家用或服務(wù)機(jī)器人的領(lǐng)域，發(fā)展的還很不完善。區(qū)別工業(yè)機(jī)器人和服務(wù)機(jī)器人的主要因素在于它們的工作環(huán)境。對于服務(wù)機(jī)器人，去完美的執(zhí)行它的任務(wù)，需要適應(yīng)和應(yīng)對正常人的生活環(huán)境。來自實(shí)踐的觀點(diǎn)，雙足機(jī)器人是最合適的機(jī)器人結(jié)構(gòu)，這歸因于它的身體形態(tài)與人類相似，特別在運(yùn)動方法方面（intermsof）。然而，由于雙足行走不穩(wěn)定的天性，對比其它類型的移動機(jī)器人，雙足機(jī)器人的實(shí)現(xiàn)（realization）更具挑戰(zhàn)。因此，很多研究一直在繼續(xù)，尤其關(guān)心雙足機(jī)器人的穩(wěn)定感和控制策略。通常定義雙足機(jī)器人穩(wěn)定性的途徑是使用“零力矩點(diǎn)”（ZMP）標(biāo)準(zhǔn)。ZMP最簡單的實(shí)施辦法是設(shè)法產(chǎn)生一個(gè)基于預(yù)先計(jì)劃行走步法的節(jié)點(diǎn)軌跡，同時(shí)保持ZMP有一個(gè)給定參考但是這個(gè)途徑在存在不明外部干擾的情況下有一個(gè)限制。許多技術(shù)研究尤其關(guān)注從物理系統(tǒng)中監(jiān)視ZMP的實(shí)時(shí)位置，并且把它當(dāng)作反饋元件。Takanishi和Kato提出了一個(gè)監(jiān)視ZMP位置的方法，就是通過使用普通的力學(xué)傳感器測量作用于機(jī)器人小腿的力和力矩。另一種方法是利用大量的布置在機(jī)器人腳底的力敏傳感器，去獲得腳底上不同位置的地面反作用力。隨后用這些傳感器陣列測得的數(shù)據(jù)計(jì)算出能反映ZMP中心位置的受力中心。倒立擺技術(shù)是另一個(gè)可供選擇的分析機(jī)器人穩(wěn)定性的方法。這個(gè)方法通過加速度計(jì)和陀螺儀不斷讀取身體加速度和傾角信息，來監(jiān)測不穩(wěn)定性。然而，從這兩個(gè)傳感器讀到的數(shù)據(jù)受制于（besubjectto）操作過程中的噪聲和漂移，并且修正測量數(shù)據(jù)的努力需要強(qiáng)大的計(jì)算能力。本文提供了雙足機(jī)器人的感知和穩(wěn)定控制的新方法。使用特制的靈活踝關(guān)節(jié)，快速探測和預(yù)報(bào)機(jī)器人的側(cè)面失穩(wěn)。在機(jī)器人的踝關(guān)節(jié)上放置一個(gè)額外的單自由度角位移傳感器，允許機(jī)器人向任何方向自由傾斜，探測潛在發(fā)生的不穩(wěn)趨勢?；谶@個(gè)必要的傳感器的信息，控制器將會快速調(diào)整平衡塊的位置，為了恢復(fù)機(jī)器人的側(cè)面平衡，抵消聚集在機(jī)器人腰部的不平衡力。使用平衡塊和回轉(zhuǎn)頭的優(yōu)勢在于讓行走子系統(tǒng)和平衡子系統(tǒng)彼此不掛鉤，并運(yùn)行在獨(dú)立的兩個(gè)控制模塊里。這與傳統(tǒng)方法不同，當(dāng)機(jī)器人的姿態(tài)同時(shí)滿足兩個(gè)條件，順利的向前行走和不斷地穩(wěn)定調(diào)整。該方法提出了如下（asfollows）的細(xì)節(jié)。第二節(jié)介紹了運(yùn)動裝置、關(guān)節(jié)結(jié)構(gòu)、測知技術(shù)和平衡策略。第三節(jié)討論了系統(tǒng)的數(shù)學(xué)模型。第四節(jié)，用實(shí)驗(yàn)結(jié)果證實(shí)了所討論的實(shí)驗(yàn)方法和所提出系統(tǒng)的可行性。最終，第五章描述了結(jié)論。2、雙足機(jī)器人的機(jī)械結(jié)構(gòu)2.1機(jī)器人行走機(jī)構(gòu)設(shè)計(jì)雙足機(jī)器人的目的是驅(qū)動最小量實(shí)現(xiàn)二維面的行走。機(jī)器人的運(yùn)動系統(tǒng)包含了四個(gè)驅(qū)動器，兩個(gè)用在髖關(guān)節(jié)，兩個(gè)用于膝關(guān)節(jié)。踝關(guān)節(jié)不由驅(qū)動器驅(qū)動，但是代替它的是一系列的平行四邊形機(jī)構(gòu)，來被動控制踝關(guān)節(jié)，為維持腳的位置。使用平行四邊形機(jī)構(gòu)能提供利益通過減少所需驅(qū)動器的數(shù)量，還能簡化機(jī)械設(shè)計(jì)，減輕機(jī)器人質(zhì)量。圖1（a）展示了機(jī)械腿在不同位置下的符號圖。由于1桿和2桿的約束作用，A桿的連接方向總是跟臀部平行。由于3桿和4桿的約束作用，B桿（腳）的連接方向始終跟A桿平行。這樣，腳總是通過平行四邊形機(jī)構(gòu)保持平行，不管腿怎樣配置。圖1（b）（c）展

示了平行的腿在不同姿態(tài)下的物理實(shí)現(xiàn)。出于輕盈和強(qiáng)度的需要，雙足機(jī)器人的模型主要使用擠制鋁材的空心管構(gòu)造。機(jī)器人全高0.9m，總質(zhì)量7kg。每條大腿和小腿的長度為0.3m，兩腿間距0.15m。為了驅(qū)動，每個(gè)關(guān)節(jié)配備有RobotisDynamixelRX-64SmartActuator,它結(jié)合了齒輪傳動裝置、控制器、驅(qū)動程序和網(wǎng)絡(luò)功能在單一封裝里。臀部的輸出馬達(dá)直接連接臀部關(guān)節(jié)，膝蓋的輸出馬達(dá)通過四桿機(jī)構(gòu)給膝蓋傳遞動力。把驅(qū)動器放在臀部的目的是減輕腿部的重量，這樣可以讓使腿部運(yùn)動的驅(qū)動力最小化。這種結(jié)構(gòu)布局的其它優(yōu)勢在于不管腿的姿勢，每個(gè)關(guān)節(jié)的角度計(jì)算都能參照固定坐標(biāo)系的縱軸。(a)(b)(a)(b)圖1(a)平行四邊形腿的符號圖；(b)，(c)機(jī)器人腿在不同配置下的站立圖2.2靈活的踝關(guān)節(jié)利用穩(wěn)定的測量為了在雙足機(jī)器人上實(shí)現(xiàn)穩(wěn)定行走，精確探測任何可能不穩(wěn)的能力十分重要。本文介紹了一種新的測知不穩(wěn)的途徑，通過在側(cè)面引進(jìn)一個(gè)額外的自由度放在踝關(guān)節(jié)之后。圖(2)展示了前面板上自由旋轉(zhuǎn)節(jié)的結(jié)構(gòu)，它被放在腳和踝關(guān)節(jié)的連接之間。這將會讓無約束的機(jī)器人在身體站立的同時(shí)，一只腳能在側(cè)面(矢狀面)方向自由傾斜(角度。)任意可能的距離。通過在自由關(guān)節(jié)處安裝角位移傳感器，控制器將能夠立刻(instantly)探測到任何不穩(wěn)并立即(immediately)反應(yīng)恢復(fù)平衡。(a)(b)圖2(a)靈活踝關(guān)節(jié)的結(jié)構(gòu)圖片；(b)靈活踝關(guān)節(jié)的物理實(shí)現(xiàn)(a)(b)2.3分割平衡塊為更快的系統(tǒng)響應(yīng)雙足機(jī)器人的行走周期包含被順序(sequentially)和循環(huán)(repeatedly)執(zhí)行的單足支

撐階段和雙足支撐階段。在單足支撐階段，當(dāng)機(jī)器人另一條腿移動時(shí)，一條腿站立。在這個(gè)階段，由于抬腿重量產(chǎn)生（created）的不平衡扭矩以及腿部運(yùn)動產(chǎn)生（generated）的動態(tài)力，機(jī)器人的身體會向側(cè)面傾斜。為了保持機(jī)器人的穩(wěn)定，一套抵消平衡質(zhì)量塊被放置在特別的位置去補(bǔ)償抬腿的不平衡質(zhì)量。圖（3）展示了已簡化的雙足機(jī)器人3質(zhì)量塊模型：m乙代表腿在掛立時(shí)的集中質(zhì)量，mB1代表主要質(zhì)量平衡塊，m^代表次要質(zhì)量平衡塊。主要質(zhì)量平衡塊主要用于抬腿時(shí)的重量補(bǔ)償。為了平衡抬腿質(zhì)量^乙產(chǎn)生的扭矩，這個(gè)質(zhì)量塊被安放在預(yù)先計(jì)算好的位置。次要質(zhì)量平衡塊mB2基于放置在踝關(guān)節(jié)的額外傳感器收集到的信息，不斷改變位置。這個(gè)質(zhì)量塊作為一個(gè)平衡力維持機(jī)器人垂直，無論側(cè)面怎么受干擾。使用兩個(gè)分離的平衡質(zhì)量塊能提供不少優(yōu)勢，例如：獲得更快的響應(yīng)時(shí)間，能使平衡質(zhì)量塊移動很小的距離，而不是很大距離，能源效率能提高，通過驅(qū)動小的平衡質(zhì)量塊，減少電機(jī)的負(fù)載。圖3雙足機(jī)器人的簡化模型系統(tǒng)模型和控制圖3中，動力方程使用牛頓第二定律關(guān)于坐標(biāo)系原點(diǎn)O給出：￡T°=I。Td，s1+mLg(dcos9+rsin9)—mfi2g(acos9+rsin9)—mBig(dscos0+sin0)+

mB2ar—c。一網(wǎng)=0(m^(r2+d2)+mfi2(r2+羽)+^B1(^s2+r2))(1)由于主要的平衡質(zhì)量塊m^主要用于補(bǔ)償懸掛著的腿的重量rnf所產(chǎn)生的扭矩，主要平O1L衡質(zhì)量塊能放置在預(yù)先計(jì)算好的位置，在懸掛腿的相反方向。主要平衡質(zhì)量塊所需的位置電能基于在坐標(biāo)系原點(diǎn)計(jì)算出的平衡扭矩，建立方程如下：(2)立。=0

m^d—皿時(shí)電=0

m^d=m^1^5

m

電=—」d

mB1(2)把方程（2）中的代入方程（1）得:

Tdis1+mLg(dcos9+rsin。)一mB2g(acos6+rsin。)—^B19dcosO+rsinO)mB2ar—cd—kd=0(mL(r2+d2)+mB2(r2+a2)+mBi(ds2+r2))Tdis1+gcos0(mLd—mLd—mfi2a)+grsin0+mB2ar—mB2a20=(3)6(