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61外文翻譯ONACCESSOntheBiomimeticDesignofAgile-RobotLegsAbstract:Thedevelopmentoffunctionalleggedrobotshasencountereditslimitsinhuman-madeactuationtechnology.Thispaperdescribesresearchonthebiomimeticdesignoflegsforagilequadrupeds.Abiomimeticlegconceptthatextractskeyprinciplesfromhorselegswhichareresponsiblefortheagileandpowerfullocomotionoftheseanimalsispresented.Theproposedbiomimeticlegmodelde?nestheeffectiveleglength,legkinematics,limbmassdistribution,actuatorpower,andelasticenergyrecoveryasdeterminantsofagilelocomotion,andvaluesforthese?vekeyelementsaregiven.Thetransferoftheextractedprinciplestotechnologicalinstantiationsisanalyzedindetail,consideringtheavailabili tyofcurrentmaterials,structuresandactuators.Areallegprototypehasbeendevelopedfollowingthebiomimeticlegconceptproposed.Theactuationsystemisbasedonthehybriduseofserieselasticityandmagneto-rheologicaldamperswhichprovidesvariablecompliancefornaturalmotion.Fromtheexperimentalevaluationofthisprototype,conclusionsonthecurrenttechnologicalbarrierstoachieverealfunctionalleggedrobotstowalkdynamicallyinagilelocomotionarepresented.Keywords:leggedrobots;agilequadrupeds;biomimeticdesign;newactuatorsforrobots621.State-of-the-ArtAgileLeggedLocomotion1.1.MachinesLeggedlocomotionisattractingtheinterestofresearchersofabroadrangeofareas.Engineers,biologistsandneurologistsareallpoolingtheirknowledgeforthesuccessofaleggedlocomotiondevice[1].ThemajorimpetusforthistechnologyiscomingfromthegovernmentoftheUnitedStatesofAmerica,whichhasgivenaboosttothetopicthroughasigni?cantnumberofprogramssponsoredbytheDefenseAdvancedResearchProjectsAgency(DARPA)inthelasttenyears[2].Someoftheseprogramsstartedin2001andendedrecentlywhileothersarestillopen.ThemorerelevantexamplesaretheLearningLocomotionProgram[3];TheBigDogProgram[4];TheExoskeletonsforHumanPerformanceAugmentationProgram[5]andthemorerecentLeggedSquadSupportSystemProgram[6].However,despitethestrongimpulseintheresearchandtheforecasteddemandfortheserobots[7],veryfewadvancesinrealapplicationsexist.Thechallengesofautonomyandthelargepower-to-weightratiodemandedfortheactuatorsmakeconventionalactuationandcontroltechnology,inheritedfromindustrialrobotics,inadequateforthemostpromising?eldandserviceapplicationsofleggedlocomotionwhichexhibitsigni?cantexpectedimpactonthefuturesociety[7].TheHADE(HybridActuatorDevelopment)project[8]developedattheCentreforAutomationandRoboticsattheSpanishNationalResearchCouncil(CSIC)aimsprimarilyatsolvingthisproblembyestablishinganewlineofresearchfocusedonspeci?cactuationandcontroltechnologiesforthenewgenerationofleggedrobots:Agile-locomotionrobots.Quadrupedrobots,emulatingtheirbiologicalcounterparts,arethebestchoicefor?eldmissionsinanaturalenvironment.However,itiswellknownthatcurrentlegged-locomotiondevicesfeaturehighcomplexityandverylowspeedparticularlyifhighpayloadshavetobetransported,andarefarfromreachingtheperformanceofbiologicalquadrupedsinnaturalenvironments.Table1.Performanceofsigni?cantquadrupedrobotsdevelopedinthelast12years.Robot Supports Payload/Weight Max.dimensionless Yeardynamicload speedAibo[9]No00.351999ScoutII[10 Yes0.021.171999SILO4[11]No0.590.062002TITANXI[12 N 0.060.0032002TekkenII[13]Yes00.652003LittleDog[14 No0 a 0.232005Tekken3 b Althoughthe?rstBigDogrobotwasdevelopedin2005,thisdatacorrespondstothe2008BigDogprototype.63Table1listsmostrelevantquadrupedrobotsdevelopedinthelast12years,showingtheirpayload-to-weightratiosandmaximumdimensionlessforwardspeed,whichhasbeencomputedfromrobotdimensionsandspeedpublishedbytherobot’sauthorsasu= ?FR,whereFRistheFroudenumber,obtainedfrom[18]:FR= v2gL (1)beingv,theforwardspeed;g= 9.81ms_ 2;andL,thecharacteristicleglength.Aleggedvehicledesignedtoperforminanaturalterrainshouldbeprovidedwithoptimumperformanceagainstmobili ty,payload,andendurance.Suchspeci?cationswereimposedbyDARPAforanAgileGroundVehicleintheUGCVprogram[19].Asimilardenominationishereusedforaleggedgroundvehicle,whichwecall“Agile”ifitisabletoreachadimensionlessspeedofu= 0.54andfeaturesapayload-to-weightratiolargerthan1,tobecomparablewithbiologicalquadrupeds.Besides,aquadrupedrobottoperformusinghigh-speedgaits(i.e.,trotandgallop)mustmakeathrusttothegroundyieldingdynamicimpactloadsthatcouldexceedthreetimesthestaticloadonthesupportingleg[20].Inatrotorinadynamicwalk,wheretwolegsthrustthegroundsimultaneously,bothlegssharethebodyweightandpayload,sothestaticloadoneachlegisonehalftherobot’sweightandaddedpayload.Therefore,inatrotgaitdynamicloadsoneachlegcanreach1.5timestherobot’sweightandpayload.Foradynamicwalk,dynamicimpactloadsateachlegapproximatelyequaltherobot’sweightandpayload.Therefore,thestructuraldesignofanagilerobotlegshouldmakesurealoadcapacity-to-robot’sweightratioof1–1.5dependingontheenvisagedgait.Figure1.State-of-the-artagilerobots:(a)KOLT,jointprojectbyStanfordUniversityandTheOhioStateUniversity,imagecourtesyofProf.Waldron;(b)HyQ,imagecourtesyoftheItalianInstituteofTechnology;(c)BigDog,imagecourtesyofBostonDynamics.(a)(b)(c)Biologicalquadrupedstransitionfromwalkingtorunninggaitsatadimensionlessspeedbetween0.54to0.7.Concretely,horsestransitionfromwalktotrotatu= 0.59[21].Asexceedingthisdimensionlessspeedrequiresthequadrupedtorun(trotorgallop)andsomecomplexterrainscouldimpedetheuseofthosehigh-speedgaits,wehaveconsideredthedimensionlessspeedof0.54asthelowerspeedlimitforaleggedrobottobeconsideredagile.ByhavingalooktoTable1itisnoticedthatveryfewquadrupedsachieveagilelocomotionperformance,becausethoserobotsfeaturingdimensionlessspeedabove0.54havealmostnegligiblepayload-to-weightratio.Althoughsomeresearchlabsareworking64inthisdirection(StanfordUniversity[22],ItalianInstituteofTechnology[23]),theonlyexistingrobotreachingthosetargetsisBigDog[4],aquadrupedunderdevelopmentatBostonDynamics(USA)(seeFigure1).TheBigDogprojectissponsoredbyDARPA,theUSMarineCorpsandtheUSArmy.ThegoaloftheBigDogProjectistobuildaclassofagileunmannedgroundvehicleswithrough-terrainmobili tysuperiortoexistingwheeledandtrackedvehicles.TheBigDogrobotscurrentlybuilt“havetakenthestepstowardthesegoals,thoughthereremainssigni?cantworktobedone”[4].Unfortunately,theinsandoutsofthetechnologyunderlyingBigDogarenotavailabletotheresearchcommunity.1.2.ActuationSystemsSupplyingpowertoahigh-speedleggedmachineusingcurrentlyavailableactuationtechnologyisachallenge.Thisisparticularlytrueifthemachineisexpectedtobeenergeticallyautonomous.Indynamiclocomotion,theloadexperiencedbyeachlegisatleastthreetimesthestaticloadonthatleg,anditmaybemuchmoreforrunninggaits.Thecostofbuildingastructureandactuationsystemcapableofprovidingtheperformanceneededforthedynamiclocomotionofamid-tolarge-sizedmachineisprohibitive,evenwithoutconsideringpayload.Consideringthemammalianmuscleasareference,directmeasurementsofmusclefunctionhaveyieldedinsightintotheversatilewaymusclesoperate.Ithasbeendiscoveredthatmusclesactasmotors,brakes,springs,dampersandstruts[24].Themultifunctionalityofnaturalmuscledistinguishesitfromanyhuman-madeactuatoranditmayholdthekeytothesuccessofleggedlocomotion.Inmanybiologicaltissuesitishardtodistinguishbetweenmaterialandstructure.Theuseofviscoelasticmaterialscangivetherobotthespring-massenergy-cyclingcapacitiesoflegged-animallocomotion,whichalsoreducesthecomputationalcomplexityofthecontrol.Viscoelasticmaterialsgreatlysimplifythemechanicsoftherobot,servingsimultaneouslyasshockabsorbers,springsandcompletejoints.Thespring-massenergy-cyclingcapabili tiescanplayakeyroleinthedynamiclocomotionofaleggedvehicle.Kineticenergycanonlybeputintothesystemwhenthefootisontheground.Itisnecessarytokeepthemechanicalenergyinthesystembyusinginternalenergystorage,thatis,compliantactuation.Moreover,thelegisamechanicaloscill ator,anditisenergeticallyexpensivetodriveitatafrequencysigni?cantlydifferenttoitsnaturalfrequency[20].Anymeanstomodifythenaturalfrequencyonthelegwouldhelptomakeitoscill ateatdifferentfrequencieswithoptimalenergyexpenditure.Thus,inherentadaptablecomplianceisrequired[25].Therefore,toef?cientlyrunadynamicleggedvehicle,highpower-densityhighforce-densityfastactuatorswithadaptablecompliancearerequired.Addedtothis,energeticautonomyisexpected.Itisevidentthattheserequirementsarenotmettogetherbyconventionaltechnology[26].HADEisalong-termproject[8]aimedatdesigningenergyef?cient,largepower-to-weightratioactuatorsandenergy-ef?cient-locomotioncontrolschemesforthenewgenerationofleggedrobotsfollowingnaturalmusclemultifunctionality.Thismultifunctionalityisapproachedbymeansofmergingdifferenttechnologies(smartmaterialsandconventionaltechnologies)inordertoextractthebestpropertiesofeachone.Someprototypeshavealreadybeentestedandcharacterized[27].Thispaperpresentsthedevelopmentofabiomimeticmodelofalegforagilelocomotionofquadrupedrobots.Thekeyprinciplesunderlyingthesuperiorcapabili tiesofstrength,speed,agili tyandenduranceofcursorialmammals,likehorses,areanalyzedinSection2andtransferredtotechnological65instantiationsinSection3,whereamodelofabiomimeticlegforagilelocomotionispresented.Theproposedconcepthasbeenimplementedonarealprototype.Section4describesthelegdesign,actuationsystemandsensorialsystem.Section5describeshowvariablecomplianceisachievedatthejointsoftheleg.ExperimentalanalysisofthelegperformancetoachieveagilelocomotionisanalyzedinSection6,and?nallySection7presentsadiscussiononthetechnologicalbarriersthathavebeenencounteredinthetechnologicalinstantiationofthebiomimeticlegmodelandconcludeswithsomeproposals.2.BiologicalInspirationforEmpoweringRobotLegsAsstatedabove,aquadrupedisconsideredtoperforminagilelocomotionwhenitisabletoachievedimensionlessspeedsupto0.54whilecarryingapayloadatleastequaltoitsownweight.Inordertodesignalegmechanismabletoprovidetherobotwiththosefeatures,natureisthebestsourceforinspiration.Horselegsareadaptedtoprovidespeed,endurance,agili tyandstrengthsuperiortoanyotheranimalofequalsize[28].Thisadaptationisbasedonlongerlegsthansimilarquadrupedsrelativetothebodysize,whichprovidelongerstridelengths.Thelengthofthehorselegisoptimalforrunning,longerlegswouldprobablybedif?culttooscill ate(giraffesarenotabletotrot).Thecauseforthehorserelativelylonglegsistheevolutionoftheanatomicalfootandtoe.Horsesfeethaveundergoneextensivemodi?cationwhichhaveenabledtheseanimalstobecomepowerfulrunners.Themostconspicuouschangeisthereductionofthenumberofdigits:theyhaveretainedonlyonesinglefunctionaldigit.Thisdigitcorrespondstothethirdtoeinhumans(seeFigure2)anditisabletowithstandforceslargelysuperiortothosesupportedbymulti-digittoes.Besides,themetatarsalhasbeensolengthenedthatitseemsmorepartofthelegthanthefoot;humanmetatarsalsarelocatedinthearchasshowninFigure2.Unliketruelegbones,however,itisnotdirectlypoweredbymuscles.Instead,themetatarsalemploysspring-likeforcesfrommassiveligaments.Figure2.Comparisonofhorsefootandhumanfoot[28].Thigh bone(Femur)KneeShank bone(Tibia)HeelHock jointFetlock jointHeelHUMANHORSEMetatarsals66Sensors2011,1 11310Thehorserearlegsarerelativelylightweight,yetstrongenoughtodeliververylargethrustsandtosustaintremendouslyheavyloads.Again,theleghasevolvedtooptimizetheuseofitsjointsforloadbearing.Thehorsehipjointismainlyahingetoturnthethighforwardandbackward.Theabduction/adductionmovementispracticallynegligible[28,29].Similarly,knee,ankleandfetlockjoints(thejointbetweentoeandmetatarsal)are1DoFjoints.Thus,allthemusclesandtendonsfocustheireffortinsimplejointmotions.Andallthiswithenougheconomyofefforttoprovideendurance,whichisachievedbymeansofelasticenergystorageintendonsduringcertainphasesofthelocomotioncycleandthelaterreturnofthisenergytothemoreexigentphases.Intheprocessofcopyingfromnatureadesiredsystemperformance,onehastobecarefulinwhatissuesmustbeextractedandtranslatedtoatechnologicaldesign.Thejobofthebiomimeticististoidentifythoseelementsresponsibleforproducingthedesiredcharacteristicsonbiologicalsystemsandtoextractthekeyprinciplesunderlyingtheirbiologicalfunctionandthentranslatethemtoatechnologicalinstantiationthatislimitedbyitsownhumanengineering[30].Onecannotsimplycopynature,butrathercarefullyextractconceptsatthelevelofdescriptionthataretechnicallypossibletoimplement.Otherwise,theresultofadirectcopywouldyieldasub-optimalapproximationtothedesiredperformance.Whendesigningpowerfulrobotlegs,theengineercoulddecidetoextractthedesiredcharacteristicsofhorselegswhicharetheirsuperiorspeed,endurance,agili tyandstrength.Inordertotranslatethesecharacteristicstoarti?cialquadrupedlegs,thekeyelementsthatshouldbecopiedhavebeensummarizedinTable2andenumeratedasfollows:(1)Effectiveleglengthdirectlyaffectsspeedandendurance.Longereffectiveleglengthimprovesstridelengthandconsequentlylegspeed,whilelongerlegsreducetheenergeticcostoftransport.Theaverageeffectiveleglengthofhorsesis1.24m[31]anditrepresentsthe60%ofthehorizontalhorselengthfromnosetotail[32].(2)Massdistributionalongthelegdeterminesthenaturalfrequencyoflegmovementandthereforeaffectsspeed.Itwasdemonstratedthathighspeedrunnerbreedsofhorseshavegreatermasslocatednearthehipjointthanotherbreeds.Concretelythe80%–90%oflegmassislocatedinthethighinrunners.Thisfeaturefavorsahighnaturalfrequencyoflegmovementandfacili tatesahigherstridefrequency[33].Addedtothis,thelegmassrelativetobodymassin?uencesagilityofmotion.Thisratioisbetween5%to8%inhorses.(3)Legkinematicsin?uencesgaitenergeticsandendurance.Movementsintheequinelimbsoccurpredominantlyinthesagittalplane,whichisenergeticallyadvantageousincursorialspecies[29].Besides,theuseof1-DOFjointsoptimizetheuseofitsjointsforloadbearing,thusimprovingthestructuralstrengthoftheanimal.(4)Elasticenergystorageintendonsprovidesagilityandelasticenergystorage,reducingthepowerrequirementsatmusclesforthemoreenergeticexigentmotionsandimprovingendurance[34].Theinherentstiffnessoftendonsalsoaffectsthelimbnaturalfrequency,whichdeterminesthedurationofthesupportphase[35]andconsequentlyin?uenceslegspeed.(5)Musclepowercapacitydirectlydeterminesjointspeedandlimbstrength.67Table2.Keyelementsandtheirin?uenceondesiredcharacteristicsofhorselegs.SpeedEnduranceAgilityStrengthEffectivelengthXXMassdistribution XKinematic XXElasticityXXXMusclepower XTakingintoconsiderationthesekeyelementsandtheirroleinagilelocomotion,aconceptualmodelofalegforanagilequadrupedhasbeenoutlinedanditsperformancehasbeensimulated.Thisisdetailedinthenextsection.3.DerivingtheBiomimeticLegConceptTheaboveprinciplesunderlyinghorsepowercapabili tieshavebeenextractedandtranslatedtotechnologicalimplementation.Firstly,alegconceptwhichencompassesthekeyelementshasbeendesignedandafterwards,itsperformancehasbeenanalyzedthroughdynamicsimulation.3.1.EffectiveLegLengthTakingintoconsiderationthatbuildingaquadrupedwiththesizeofahorsewouldbedif?culttohandleinthelaboratory,scalingoftheleglengthmakingsurethattheeffectiveleglengthisthe60%ofthebodysizewouldcomplywiththespeci?cations.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,crusandhoofareproportionaltorealhorseleg’splusascalingfactortoreachthedesiredeffectiveleglength,takingintoconsiderationthattheuseofa3-DoFmodeloflegshortensthetotalleglengthina34%comparedtoahorseleg.The35%reductionineffectiveleglengthplustheincreaseof34%inlimblengthresultsina?nal1%decreaseineachleglinklength.Table3liststhe?nallinklengths.68Table3.Characteristicrobotlengths(inmeters)basedonbiomimetism.BodyEffectivelegThighCrusHoof1.30.80.40.360.19Figure3andTable4showDenavit–Hartenbergparametersforthelegkinematics,whichcorrespondtoaconventionalthree-linkplanarstructure.Followingthisconvention,thedirectkinematicmodelprovideshoofpositionandorientationfromjointanglesasfollows: x0y0f= a1C1 a2C12 a3C123a1S1 a2S12 a3S123q1 q2 q3 (2)where(x0,y0,f)arehoofxandypositionandorientationrespectivelyintheleg’sbasereferenceframe,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.Denavit–Hartenbergparametersofthelegmodel.Jointai di _i _iHip(1)a1 00q1Knee(2)a2 00q2Fetlock(3)a3 00q33.3.MassDistributionPublishedworkontheexperimentaldeterminationofequinelimbinertialpropertiesshowwiderangesofaveragevaluesforlegsegmentmassesfordifferenthorsebreeds.Table5summarizesaverageresultsofanexperimentalworkperformedonsixDutchWarmbloodhorses[36].Consideringthatourlegmodelaccountswiththreelinks,theselectionoflinkmassescannotbedirectlyextractedfromthebiologicalinertialdata,andthereforeitwasperformedinaniterativeoptimizationapproachforalatercomparisonwiththeaveragevalueslistedinTable5.Intheoptimizationapproach,thelinkmasseswhichminimizedmechanicalpowerinalocomotioncycleatanaveragenondimensionallegspeedof0.54weresearchedfor.Thecostfunctionisgivenbythesumofthemechanicalpoweratthelegjoints,givenbytheproductofjointtorqueandjointspeedasfollows:CW =3?i= 1ò T0ti(t)· _qi(t)d (3)wherejointtorqueisanonlinearfunctionofalllimbmassesmi,lengthsai,inertiamomentsIi andjointangles,speedsandaccelerations,givenbytheinversedynamicsmodeloftheleg:t=D(mi,ai,Ii,q, _q, q)(4)Table5.Experimentalaveragevaluesofhorselegsegmentmassesexpressedinkilograms,extractedfromrelatedliterature[36],andcomparedto?nalresultsofaniterativesearchperformedthroughsimulationofa3-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!SimulationConstructionSetsoftware[37].ThisdynamicssimulationpackagewasdevelopedattheMITLegLaboratoryfortheanalysisofcontrolalgorithmsinleggedlocomotion,anditwaslatercommercializedbyYoboticsInc.,spinoffcompanyfromtheMIT.Theprogrammedrobotsimulationprovidesjointposition,speedandtorquebasedonlinkinertialpropertiessuchasmass,centerofmasspositionandinertiatensorbyimplementingtheFeatherstonealgorithmforderivingtheequationsof70motion.Figure4showsresultsoftheiterativeprocessforhipandkneejoints,whosevariationresultedmoresigni?cant,anditsconvergenceforthe?naloptimallegmassdistribution.Afteriteration,theresultinglegmassdistributionwas2.5kg,1.9kgand0.6kgforthigh,crusandhoofrespectively,whichrepresenta50%,38%and12%ofthe?nallegweightwhichresults5kg.FromthisresultsandbycomparisonwithbiologicalmassdistributionshowninTable5itseemsthatthemasscorrespondingtothesuppressedmetatarsushasbeendistributedbetweencrusandhoofinordertoresembletheinertialpropertiesofhorselegs.Theresultingmassdistributionmaintainsmostofthelegmassintheupperlegsegment,asinbiologicalhorselegs.Figure4.Iterativeoptimizationoflegmassdistributionbyminimizingthepowerrequiredatthejoints.Convergenceisshowninbackthickerlinefor2.5kg,1.9kgand0.6kgatthigh(TH),crus(CR)andhoof(HF)respectively:(a)hippowerforvaryinglinkmasses;(b)kneepowerforvaryinglinkmasses.Initialandintermediatevaluesoftheiterationareprovidedinthe?gurelegend.?2?1.5?1?0.500.5?300?200?1000100200300400500Whip(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:0.600.511.522.5?400?300?200?1000100200Wknee(Watt)?knee (rad)(a)(b)3.4.ActuatorPowerRequirementsThetechnologicalcounterpartofthemammalianmuscleisthejointactuationsystem.Inordertodet