61外文翻譯ONACCESSOntheBiomimeticDesignofAgile-RobotLegsAbstract:Thedevelopmentoffunctionalleggedrobotshasencountereditslimitsinhuman-madeactuationtechnology.Thispaperdescribesresearchonthebiomimeticdesignoflegsforagilequadrupeds.Abiomimeticlegconceptthatextractskeyprinciplesfromhorselegswhichareresponsiblefortheagileandpowerfullocomotionoftheseanimalsispresented.Theproposedbiomimeticlegmodeldenestheeffectiveleglength,legkinematics,limbmassdistribution,actuatorpower,andelasticenergyrecoveryasdeterminantsofagilelocomotion,andvaluesforthesevekeyelementsaregiven.Thetransferoftheextractedprinciplestotechnologicalinstantiationsisanalyzedindetail,consideringtheavailabili tyofcurrentmaterials,structuresandactuators.Areallegprototypehasbeendevelopedfollowingthebiomimeticlegconceptproposed.Theactuationsystemisbasedonthehybriduseofserieselasticityandmagneto-rheologicaldamperswhichprovidesvariablecompliancefornaturalmotion.Fromtheexperimentalevaluationofthisprototype,conclusionsonthecurrenttechnologicalbarrierstoachieverealfunctionalleggedrobotstowalkdynamicallyinagilelocomotionarepresented.Keywords:leggedrobots;agilequadrupeds;biomimeticdesign;newactuatorsforrobots621.State-of-the-ArtAgileLeggedLocomotion1.1.MachinesLeggedlocomotionisattractingtheinterestofresearchersofabroadrangeofareas.Engineers,biologistsandneurologistsareallpoolingtheirknowledgeforthesuccessofaleggedlocomotiondevice1.ThemajorimpetusforthistechnologyiscomingfromthegovernmentoftheUnitedStatesofAmerica,whichhasgivenaboosttothetopicthroughasignicantnumberofprogramssponsoredbytheDefenseAdvancedResearchProjectsAgency(DARPA)inthelasttenyears2.Someoftheseprogramsstartedin2001andendedrecentlywhileothersarestillopen.ThemorerelevantexamplesaretheLearningLocomotionProgram3;TheBigDogProgram4;TheExoskeletonsforHumanPerformanceAugmentationProgram5andthemorerecentLeggedSquadSupportSystemProgram6.However,despitethestrongimpulseintheresearchandtheforecasteddemandfortheserobots7,veryfewadvancesinrealapplicationsexist.Thechallengesofautonomyandthelargepower-to-weightratiodemandedfortheactuatorsmakeconventionalactuationandcontroltechnology,inheritedfromindustrialrobotics,inadequateforthemostpromisingeldandserviceapplicationsofleggedlocomotionwhichexhibitsignicantexpectedimpactonthefuturesociety7.TheHADE(HybridActuatorDevelopment)project8developedattheCentreforAutomationandRoboticsattheSpanishNationalResearchCouncil(CSIC)aimsprimarilyatsolvingthisproblembyestablishinganewlineofresearchfocusedonspecicactuationandcontroltechnologiesforthenewgenerationofleggedrobots:Agile-locomotionrobots.Quadrupedrobots,emulatingtheirbiologicalcounterparts,arethebestchoiceforeldmissionsinanaturalenvironment.However,itiswellknownthatcurrentlegged-locomotiondevicesfeaturehighcomplexityandverylowspeedparticularlyifhighpayloadshavetobetransported,andarefarfromreachingtheperformanceofbiologicalquadrupedsinnaturalenvironments.Table1.Performanceofsignicantquadrupedrobotsdevelopedinthelast12years.Robot Supports Payload/Weight Max.dimensionless Yeardynamicload speedAibo9No00.351999ScoutII10 Yes0.021.171999SILO411No0.590.062002TITANXI12 N 0.060.0032002TekkenII13Yes00.652003LittleDog14 No0 a 0.232005Tekken3 b AlthoughtherstBigDogrobotwasdevelopedin2005,thisdatacorrespondstothe2008BigDogprototype.63Table1listsmostrelevantquadrupedrobotsdevelopedinthelast12years,showingtheirpayload-to-weightratiosandmaximumdimensionlessforwardspeed,whichhasbeencomputedfromrobotdimensionsandspeedpublishedbytherobotsauthorsasu= ÖFR,whereFRistheFroudenumber,obtainedfrom18:FR= v2gL (1)beingv,theforwardspeed;g= 9.81ms_ 2;andL,thecharacteristicleglength.Aleggedvehicledesignedtoperforminanaturalterrainshouldbeprovidedwithoptimumperformanceagainstmobili ty,payload,andendurance.SuchspecicationswereimposedbyDARPAforanAgileGroundVehicleintheUGCVprogram19.Asimilardenominationishereusedforaleggedgroundvehicle,whichwecall“Agile”ifitisabletoreachadimensionlessspeedofu= 0.54andfeaturesapayload-to-weightratiolargerthan1,tobecomparablewithbiologicalquadrupeds.Besides,aquadrupedrobottoperformusinghigh-speedgaits(i.e.,trotandgallop)mustmakeathrusttothegroundyieldingdynamicimpactloadsthatcouldexceedthreetimesthestaticloadonthesupportingleg20.Inatrotorinadynamicwalk,wheretwolegsthrustthegroundsimultaneously,bothlegssharethebodyweightandpayload,sothestaticloadoneachlegisonehalftherobotsweightandaddedpayload.Therefore,inatrotgaitdynamicloadsoneachlegcanreach1.5timestherobotsweightandpayload.Foradynamicwalk,dynamicimpactloadsateachlegapproximatelyequaltherobotsweightandpayload.Therefore,thestructuraldesignofanagilerobotlegshouldmakesurealoadcapacity-to-robotsweightratioof11.5dependingontheenvisagedgait.Figure1.State-of-the-artagilerobots:(a)KOLT,jointprojectbyStanfordUniversityandTheOhioStateUniversity,imagecourtesyofProf.Waldron;(b)HyQ,imagecourtesyoftheItalianInstituteofTechnology;(c)BigDog,imagecourtesyofBostonDynamics.(a)(b)(c)Biologicalquadrupedstransitionfromwalkingtorunninggaitsatadimensionlessspeedbetween0.54to0.7.Concretely,horsestransitionfromwalktotrotatu= 0.5921.Asexceedingthisdimensionlessspeedrequiresthequadrupedtorun(trotorgallop)andsomecomplexterrainscouldimpedetheuseofthosehigh-speedgaits,wehaveconsideredthedimensionlessspeedof0.54asthelowerspeedlimitforaleggedrobottobeconsideredagile.ByhavingalooktoTable1itisnoticedthatveryfewquadrupedsachieveagilelocomotionperformance,becausethoserobotsfeaturingdimensionlessspeedabove0.54havealmostnegligiblepayload-to-weightratio.Althoughsomeresearchlabsareworking64inthisdirection(StanfordUniversity22,ItalianInstituteofTechnology23),theonlyexistingrobotreachingthosetargetsisBigDog4,aquadrupedunderdevelopmentatBostonDynamics(USA)(seeFigure1).TheBigDogprojectissponsoredbyDARPA,theUSMarineCorpsandtheUSArmy.ThegoaloftheBigDogProjectistobuildaclassofagileunmannedgroundvehicleswithrough-terrainmobili tysuperiortoexistingwheeledandtrackedvehicles.TheBigDogrobotscurrentlybuilt“havetakenthestepstowardthesegoals,thoughthereremainssignicantworktobedone”4.Unfortunately,theinsandoutsofthetechnologyunderlyingBigDogarenotavailabletotheresearchcommunity.1.2.ActuationSystemsSupplyingpowertoahigh-speedleggedmachineusingcurrentlyavailableactuationtechnologyisachallenge.Thisisparticularlytrueifthemachineisexpectedtobeenergeticallyautonomous.Indynamiclocomotion,theloadexperiencedbyeachlegisatleastthreetimesthestaticloadonthatleg,anditmaybemuchmoreforrunninggaits.Thecostofbuildingastructureandactuationsystemcapableofprovidingtheperformanceneededforthedynamiclocomotionofamid-tolarge-sizedmachineisprohibitive,evenwithoutconsideringpayload.Consideringthemammalianmuscleasareference,directmeasurementsofmusclefunctionhaveyieldedinsightintotheversatilewaymusclesoperate.Ithasbeendiscoveredthatmusclesactasmotors,brakes,springs,dampersandstruts24.Themultifunctionalityofnaturalmuscledistinguishesitfromanyhuman-madeactuatoranditmayholdthekeytothesuccessofleggedlocomotion.Inmanybiologicaltissuesitishardtodistinguishbetweenmaterialandstructure.Theuseofviscoelasticmaterialscangivetherobotthespring-massenergy-cyclingcapacitiesoflegged-animallocomotion,whichalsoreducesthecomputationalcomplexityofthecontrol.Viscoelasticmaterialsgreatlysimplifythemechanicsoftherobot,servingsimultaneouslyasshockabsorbers,springsandcompletejoints.Thespring-massenergy-cyclingcapabili tiescanplayakeyroleinthedynamiclocomotionofaleggedvehicle.Kineticenergycanonlybeputintothesystemwhenthefootisontheground.Itisnecessarytokeepthemechanicalenergyinthesystembyusinginternalenergystorage,thatis,compliantactuation.Moreover,thelegisamechanicaloscill ator,anditisenergeticallyexpensivetodriveitatafrequencysignicantlydifferenttoitsnaturalfrequency20.Anymeanstomodifythenaturalfrequencyonthelegwouldhelptomakeitoscill ateatdifferentfrequencieswithoptimalenergyexpenditure.Thus,inherentadaptablecomplianceisrequired25.Therefore,toefcientlyrunadynamicleggedvehicle,highpower-densityhighforce-densityfastactuatorswithadaptablecompliancearerequired.Addedtothis,energeticautonomyisexpected.Itisevidentthattheserequirementsarenotmettogetherbyconventionaltechnology26.HADEisalong-termproject8aimedatdesigningenergyefcient,largepower-to-weightratioactuatorsandenergy-efcient-locomotioncontrolschemesforthenewgenerationofleggedrobotsfollowingnaturalmusclemultifunctionality.Thismultifunctionalityisapproachedbymeansofmergingdifferenttechnologies(smartmaterialsandconventionaltechnologies)inordertoextractthebestpropertiesofeachone.Someprototypeshavealreadybeentestedandcharacterized27.Thispaperpresentsthedevelopmentofabiomimeticmodelofalegforagilelocomotionofquadrupedrobots.Thekeyprinciplesunderlyingthesuperiorcapabili tiesofstrength,speed,agili tyandenduranceofcursorialmammals,likehorses,areanalyzedinSection2andtransferredtotechnological65instantiationsinSection3,whereamodelofabiomimeticlegforagilelocomotionispresented.Theproposedconcepthasbeenimplementedonarealprototype.Section4describesthelegdesign,actuationsystemandsensorialsystem.Section5describeshowvariablecomplianceisachievedatthejointsoftheleg.ExperimentalanalysisofthelegperformancetoachieveagilelocomotionisanalyzedinSection6,andnallySection7presentsadiscussiononthetechnologicalbarriersthathavebeenencounteredinthetechnologicalinstantiationofthebiomimeticlegmodelandconcludeswithsomeproposals.2.BiologicalInspirationforEmpoweringRobotLegsAsstatedabove,aquadrupedisconsideredtoperforminagilelocomotionwhenitisabletoachievedimensionlessspeedsupto0.54whilecarryingapayloadatleastequaltoitsownweight.Inordertodesignalegmechanismabletoprovidetherobotwiththosefeatures,natureisthebestsourceforinspiration.Horselegsareadaptedtoprovidespeed,endurance,agili tyandstrengthsuperiortoanyotheranimalofequalsize28.Thisadaptationisbasedonlongerlegsthansimilarquadrupedsrelativetothebodysize,whichprovidelongerstridelengths.Thelengthofthehorselegisoptimalforrunning,longerlegswouldprobablybedifculttooscill ate(giraffesarenotabletotrot).Thecauseforthehorserelativelylonglegsistheevolutionoftheanatomicalfootandtoe.Horsesfeethaveundergoneextensivemodicationwhichhaveenabledtheseanimalstobecomepowerfulrunners.Themostconspicuouschangeisthereductionofthenumberofdigits:theyhaveretainedonlyonesinglefunctionaldigit.Thisdigitcorrespondstothethirdtoeinhumans(seeFigure2)anditisabletowithstandforceslargelysuperiortothosesupportedbymulti-digittoes.Besides,themetatarsalhasbeensolengthenedthatitseemsmorepartofthelegthanthefoot;humanmetatarsalsarelocatedinthearchasshowninFigure2.Unliketruelegbones,however,itisnotdirectlypoweredbymuscles.Instead,themetatarsalemploysspring-likeforcesfrommassiveligaments.Figure2.Comparisonofhorsefootandhumanfoot28.Thigh bone(Femur)KneeShank bone(Tibia)HeelHock jointFetlock jointHeelHUMANHORSEMetatarsals66Sensors2011,1 11310Thehorserearlegsarerelativelylightweight,yetstrongenoughtodeliververylargethrustsandtosustaintremendouslyheavyloads.Again,theleghasevolvedtooptimizetheuseofitsjointsforloadbearing.Thehorsehipjointismainlyahingetoturnthethighforwardandbackward.Theabduction/adductionmovementispracticallynegligible28,29.Similarly,knee,ankleandfetlockjoints(thejointbetweentoeandmetatarsal)are1DoFjoints.Thus,allthemusclesandtendonsfocustheireffortinsimplejointmotions.Andallthiswithenougheconomyofefforttoprovideendurance,whichisachievedbymeansofelasticenergystorageintendonsduringcertainphasesofthelocomotioncycleandthelaterreturnofthisenergytothemoreexigentphases.Intheprocessofcopyingfromnatureadesiredsystemperformance,onehastobecarefulinwhatissuesmustbeextractedandtranslatedtoatechnologicaldesign.Thejobofthebiomimeticististoidentifythoseelementsresponsibleforproducingthedesiredcharacteristicsonbiologicalsystemsandtoextractthekeyprinciplesunderlyingtheirbiologicalfunctionandthentranslatethemtoatechnologicalinstantiationthatislimitedbyitsownhumanengineering30.Onecannotsimplycopynature,butrathercarefullyextractconceptsatthelevelofdescriptionthataretechnicallypossibletoimplement.Otherwise,theresultofadirectcopywouldyieldasub-optimalapproximationtothedesiredperformance.Whendesigningpowerfulrobotlegs,theengineercoulddecidetoextractthedesiredcharacteristicsofhorselegswhicharetheirsuperiorspeed,endurance,agili tyandstrength.Inordertotranslatethesecharacteristicstoarticialquadrupedlegs,thekeyelementsthatshouldbecopiedhavebeensummarizedinTable2andenumeratedasfollows:(1)Effectiveleglengthdirectlyaffectsspeedandendurance.Longereffectiveleglengthimprovesstridelengthandconsequentlylegspeed,whilelongerlegsreducetheenergeticcostoftransport.Theaverageeffectiveleglengthofhorsesis1.24m31anditrepresentsthe60%ofthehorizontalhorselengthfromnosetotail32.(2)Massdistributionalongthelegdeterminesthenaturalfrequencyoflegmovementandthereforeaffectsspeed.Itwasdemonstratedthathighspeedrunnerbreedsofhorseshavegreatermasslocatednearthehipjointthanotherbreeds.Concretelythe80%90%oflegmassislocatedinthethighinrunners.Thisfeaturefavorsahighnaturalfrequencyoflegmovementandfacili tatesahigherstridefrequency33.Addedtothis,thelegmassrelativetobodymassinuencesagilityofmotion.Thisratioisbetween5%to8%inhorses.(3)Legkinematicsinuencesgaitenergeticsandendurance.Movementsintheequinelimbsoccurpredominantlyinthesagittalplane,whichisenergeticallyadvantageousincursorialspecies29.Besides,theuseof1-DOFjointsoptimizetheuseofitsjointsforloadbearing,thusimprovingthestructuralstrengthoftheanimal.(4)Elasticenergystorageintendonsprovidesagilityandelasticenergystorage,reducingthepowerrequirementsatmusclesforthemoreenergeticexigentmotionsandimprovingendurance34.Theinherentstiffnessoftendonsalsoaffectsthelimbnaturalfrequency,whichdeterminesthedurationofthesupportphase35andconsequentlyinuenceslegspeed.(5)Musclepowercapacitydirectlydeterminesjointspeedandlimbstrength.67Table2.Keyelementsandtheirinuenceondesiredcharacteristicsofhorselegs.SpeedEnduranceAgilityStrengthEffectivelengthXXMassdistribution XKinematic XXElasticityXXXMusclepower XTakingintoconsiderationthesekeyelementsandtheirroleinagilelocomotion,aconceptualmodelofalegforanagilequadrupedhasbeenoutlinedanditsperformancehasbeensimulated.Thisisdetailedinthenextsection.3.DerivingtheBiomimeticLegConceptTheaboveprinciplesunderlyinghorsepowercapabili tieshavebeenextractedandtranslatedtotechnologicalimplementation.Firstly,alegconceptwhichencompassesthekeyelementshasbeendesignedandafterwards,itsperformancehasbeenanalyzedthroughdynamicsimulation.3.1.EffectiveLegLengthTakingintoconsiderationthatbuildingaquadrupedwiththesizeofahorsewouldbedifculttohandleinthelaboratory,scalingoftheleglengthmakingsurethattheeffectiveleglengthisthe60%ofthebodysizewouldcomplywiththespecications.Foratrade-offbetweenreproducinghorsesdimensionsandhavingareliableprototype,ascalingfactorof65%hasbeenappliedtothedesign,thereforearobotlengthof1.2mwasconsidered,havinganeffectiveleglengthof0.8m.3.2.LegKinematicsThecomplexityofcontrolli ngaplanar4-DoFredundantkinematicchainaddedtothecostofelectronicsandactuatorsandthedirectconsequenceofincreasinglegmassasthenumberofdegreesoffreedomincreasesmakeunfeasiblethedevelopmentofanexacthorse-likeleg.However,theelectionofredundantkinematicsfavorsreducingjointtorquesandthusactuatorrequirementsandpowerconsumption.Apossiblesolutionistousepassiveelasticelementstodriveoneormorejoints,however,theanalysisofjointpowerrequirementsforaslowtrot(seeSection3.4)advisesagainstpurelypassiveactuation.Asatrade-off,aplanar3-DoFleghasbeenoutlinedcomposedofthreelinks:thigh,crusandhoof,connectedthrough1-DoFjoints:thehip,kneeandfetlockjoints.Thelengthsofthigh,crusandhoofareproportionaltorealhorselegsplusascalingfactortoreachthedesiredeffectiveleglength,takingintoconsiderationthattheuseofa3-DoFmodeloflegshortensthetotalleglengthina34%comparedtoahorseleg.The35%reductionineffectiveleglengthplustheincreaseof34%inlimblengthresultsinanal1%decreaseineachleglinklength.Table3liststhenallinklengths.68Table3.Characteristicrobotlengths(inmeters)basedonbiomimetism.BodyEffectivelegThighCrusHoof1.30.80.40.360.19Figure3andTable4showDenavitHartenbergparametersforthelegkinematics,whichcorrespondtoaconventionalthree-linkplanarstructure.Followingthisconvention,thedirectkinematicmodelprovideshoofpositionandorientationfromjointanglesasfollows: x0y0f= a1C1 a2C12 a3C123a1S1 a2S12 a3S123q1 q2 q3 (2)where(x0,y0,f)arehoofxandypositionandorientationrespectivelyinthelegsbasereferenceframe,andqi withi= 13arejointanglesnumberedfromhiptofetlockjoint.Parametersai aretherespectivelinklengthsmeasuredasthedistancebetweenadjacentjointaxes,andcorrespondtothevalueslistedinTable3.InEquation(2)Ci andSi meancos(qi)andsin(qi)respectively,whileexpressionCijk meanscos(qi +qj +qk)andSijk meanssin(qi +qj +qk).Figure3.Kinematicmodelofrobotleg.69Table4.DenavitHartenbergparametersofthelegmodel.Jointai di _i _iHip(1)a1 00q1Knee(2)a2 00q2Fetlock(3)a3 00q33.3.MassDistributionPublishedworkontheexperimentaldeterminationofequinelimbinertialpropertiesshowwiderangesofaveragevaluesforlegsegmentmassesfordifferenthorsebreeds.Table5summarizesaverageresultsofanexperimentalworkperformedonsixDutchWarmbloodhorses36.Consideringthatourlegmodelaccountswiththreelinks,theselectionoflinkmassescannotbedirectlyextractedfromthebiologicalinertialdata,andthereforeitwasperformedinaniterativeoptimizationapproachforalatercomparisonwiththeaveragevalueslistedinTable5.Intheoptimizationapproach,thelinkmasseswhichminimizedmechanicalpowerinalocomotioncycleatanaveragenondimensionallegspeedof0.54weresearchedfor.Thecostfunctionisgivenbythesumofthemechanicalpoweratthelegjoints,givenbytheproductofjointtorqueandjointspeedasfollows:CW =3åi= 1ò T0ti(t)· _qi(t)d (3)wherejointtorqueisanonlinearfunctionofalllimbmassesmi,lengthsai,inertiamomentsIi andjointangles,speedsandaccelerations,givenbytheinversedynamicsmodeloftheleg:t=D(mi,ai,Ii,q, _q, q)(4)Table5.Experimentalaveragevaluesofhorselegsegmentmassesexpressedinkilograms,extractedfromrelatedliterature36,andcomparedtonalresultsofaniterativesearchperformedthroughsimulationofa3-DoFleg;percentagesofsegmentmassrelativetolegmassaregiveninsidebrackets.ThighCrusMetatarsusHoofDutchWarmbloodhorses2.1(59.6)0.96(26.5)0.39(10.8)0.1(2.9)Resultsfor3-DoFleg2.5(50)1.9(38)0.6(12)Numericallysolvingtheaboveoptimizationproblemiscomputationallyunavoidable.Therefore,ithasbeensolvedbymeansofaniterativeprocessthroughdynamicsimulationofthelegmodelusingYobotics!SimulationConstructionSetsoftware37.ThisdynamicssimulationpackagewasdevelopedattheMITLegLaboratoryfortheanalysisofcontrolalgorithmsinleggedlocomotion,anditwaslatercommercializedbyYoboticsInc.,spinoffcompanyfromtheMIT.Theprogrammedrobotsimulationprovidesjointposition,speedandtorquebasedonlinkinertialpropertiessuchasmass,centerofmasspositionandinertiatensorbyimplementingtheFeatherstonealgorithmforderivingtheequationsof70motion.Figure4showsresultsoftheiterativeprocessforhipandkneejoints,whosevariationresultedmoresignicant,anditsconvergenceforthenaloptimallegmassdistribution.Afteriteration,theresultinglegmassdistributionwas2.5kg,1.9kgand0.6kgforthigh,crusandhoofrespectively,whichrepresenta50%,38%and12%ofthenallegweightwhichresults5kg.FromthisresultsandbycomparisonwithbiologicalmassdistributionshowninTable5itseemsthatthemasscorrespondingtothesuppressedmetatarsushasbeendistributedbetweencrusandhoofinordertoresembletheinertialpropertiesofhorselegs.Theresultingmassdistributionmaintainsmostofthelegmassintheupperlegsegment,asinbiologicalhorselegs.Figure4.Iterativeoptimizationoflegmassdistributionbyminimizingthepowerrequiredatthejoints.Convergenceisshowninbackthickerlinefor2.5kg,1.9kgand0.6kgatthigh(TH),crus(CR)andhoof(HF)respectively:(a)hippowerforvaryinglinkmasses;(b)kneepowerforvaryinglinkmasses.Initialandintermediatevaluesoftheiterationareprovidedinthegurelegend.21.510.500.53002001000100200300400500Whip(Watt)hip (rad)TH:2.5 CR:1.9 HF:0.8TH:2.4 CR:2.0 HF:1.1TH:2.1 CR:2.1 HF:2.1TH:2.5 CR:1.9 HF:0.600.511.522.54003002001000100200Wknee(Watt)knee (rad)(a)(b)3.4.ActuatorPowerRequirementsThetechnologicalcounterpartofthemammalianmuscleisthejointactuationsystem.Inordertodet