ClimbingRobotsinNaturalTerrainTimothyBretl,TeresaMiller,andStephenRockJean-ClaudeLatombeAerospaceRoboticsLabRoboticsLaboratoryDepartmentofAeronauticsandAstronauticsComputerScienceDepartmentStanfordUniversity,Stanford,CA94305StanfordUniversity,Stanford,CA94305tbretl,tgmiller,KeywordsMotionplanning,climbing,robotics,leggedrobots,high-riskaccess,naturalterrain.AbstractThispaperpresentsageneralframeworkforplan-ningthequasi-staticmotionofclimbingrobots.Theframeworkisinstantiatedtocomputeclimbingmotionsofathree-limbedrobotinverticalnaturalterrain.Anexampleresultingpaththroughalargesimulatedenvironmentispresented.Theplanningproblemisoneoffivefundamentalchallengestothedevelopmentofrealroboticsystemsabletoclimbrealnaturalterrain.Eachofthefourotherareashardwaredesign,control,sensing,andgraspingisalsodiscussed.1IntroductionTheworkdescribedinthispaperispartofanefforttodevelopcriticaltechnologiesthatwillenablethedesignandimplementationofanautonomousrobotabletoclimbverticalnaturalterrain.Toourknowl-edge,thiscapabilityhasnotbeendemonstratedpreviouslyforroboticsystems.Priorapproacheshavedealtwithartificialterrain,eitherusingspecial“grasps”(e.g.,pegs,magnets)adaptedtotheterrainssurfaceorexploitingspecificpropertiesorfeaturesoftheterrain(e.g.,ductsandpipes)1-12.Developingthiscapabilitywillfurtherourunder-standingofhowhumansperformsuchcomplextasksasclimbingandscramblinginruggedterrain.Thismayproveusefulinthefuturedevelopmentofsophisticatedroboticsystemsthatwilleitheraidorreplacehumansintheperformanceofaggressivetasksindifficultterrain.Examplesincluderoboticsystemsforsuchmilitaryandcivilianusesassearch-and-rescue,reconnaissance,andplanetaryexploration.Manyissuesneedtobeaddressedbeforerealrobotscanclimbreal,vertical,naturalterrain.Thispaperconsidersfiveofthemostfundamentaloftheseissues:hardwaredesign,control,sensing,planning,andgrasping.Oneoftheseissuesinparticular,themotion-planningproblem,isdescribedinmoredetail.Ageneralframeworkforclimbingrobotsispresentedandthisframeworkisinstantiatedtocomputeclimbingmotionsofthethree-limbedrobotshowninFigure1.Simulationresultsareshownfortherobotinanexampleverticalenvironment.2MotivationTheresultsofresearchinthisareawillbenefitanumberofapplicationsandhaveimplicationsforseveralrelatedresearchareas.2.1ApplicationsThispaperismotivatedbyaneedforroboticsys-temscapableofprovidingremoteaccesstohigh-risknaturalenvironments.Therearemanyterrestrialapplicationsforthesesystems,suchassearch-and-rescue,caveexploration,humanassistanceforrockandmountainclimbing,andtacticalurbanmissions.Eachoftheseapplicationsrequiresclimbing,descending,ortraversingsteepslopesandbrokenterrain,andthusinvolvesconsider-ablehumanrisk.Severalspaceapplicationscouldalsobenefitfromtheseaggressiveroboticsystems.Forexample,sitesonMarswithpotentiallyhighsciencevaluehavebeenidentifiedonclifffaces13.Often,itisneitherpracticalnorfeasibleforflyingrobotstoaccesstheseFig1.Athree-limbedclimbingrobotmovingverticallyonnaturalsurfaces.locations.Therefore,toreachthesesites,robotsmustclimb,descend,ortraversesteepslopes.Futuregoalsforexplorationonotherplanetarybodiesmayrequireaccesstoequallyruggedterrain.2.2ImplicationsInadditiontofurtheringthedevelopmentofaclimbingrobotforverticalnaturalterrain,theresultsofresearchinthisareacouldprovidefundamentalinsightintoseveralrelatedresearchareas.Forexample,thisstudycouldleadtothedevelopmentofbetterstrategiesforroboticwalkingordexterousmanipulation.Humanclimbersoftencommentonanincreaseinbalanceandanexpandedrangeofmovementineverydayactivityastheybecomemoreproficientatthesport.Thisenhancedmobilityisoftenreferredtoas“discoveringnewdegreesoffreedom,”andisrelatedtotheideaofdiscoveringusefulnewmodesofmobilityforex-tremelycomplicatedhumanoidrobotsordigitalactors.Also,thedevelopmentofplanningalgorithmsforclimbingrobotscouldleadtoabettersetofcriteriaforthedesignofthesetypesofrobots.Thesealgorithmscouldbeappliedtocandidatedesignsinsimulationtodeterminethecapabilitiesoftheresultingrobots,andthustoselectadesign.3FundamentalIssuesTherearefivefundamentalissuesinvolvedinclimbingsteepnaturalterrain:hardwaredesign,control,sensing,grasping,andplanning.Asubstantialamountofworkneedstobedoneineachoftheseareasinordertodeveloparealclimbingrobot.Thissectiondescribesthechallengesinvolvedinthefirstfouroftheseareas；theplanningproblemwillbediscussedinmoredetailinSection4.3.1HardwareDesignAgoodhardwaredesigncanincreasetheperform-anceoftherobot,andoftencanmakeeachoftheotherfundamentalissueseasiertodealwith.However,pastuseofhardwaresolutionsinmaintainingequilibriumgenerallyresultedinafundamentallimitationontheterrainthatcouldbetraversed.Wheeledroboticsystemshavebeenusedtoascendandtraversenaturalslopesofupto50degrees,todescendslopesofupto75degrees,andtoclimboversmallobstaclesinroughterrain.Thesesystemseitherusesomeformofactiveorrocker-bogiesuspensionasin12,14-16,oruserappellingasin1.Similarresultshavebeenobtainedusingleggedrappellingrobots3,17andasnake-likerobot4.Theterrainthattheseroverscantraverserobustlyisimpressive,butnoneoftheexistingsystemshasbeenshowntobecapableofclimbingnaturalslopesof90degreesorhigher.Wheeledroversandsnake-likerobotshaveaninherentgraspinglimitationthatpreventstheiruseinascendingsustainednear-verticalordescendingsustainedpast-verticalnaturalslopes.Existingleggedroboticsystemsdonothavethislimitation,butstillhavebypassedtheissueofmain-tainingcontactwiththeslopebyusingrappeltethers.Relianceonthesetethersprohibitsinitialcliffascent,andlimitstheslopegradeoncliffdescenttobelow90degrees.Awidevarietyofrobotscapableofclimbingverticalartificialsurfacesisavailable.Mostoftheserobotsexploitsomepropertyofthesurfaceforeasygrasping.Forexample,someoftheserobotsusesuctioncupsorpermanentmagnetstoavoidslipping5-8.Otherstakeadvantageoffeaturessuchasbalconyhandrails9orpoles10.However,thesurfacepropertiesthatareexploitedbytheserobotsgenerallyarenotavailableinnaturalterrain.Incontrast,thesimplerhardwaredesignsusedby2,11hadnosuchlimitations.Itisexpectedthatsolutionstotheplanningproblemsuchastheonepresentedinthispaperwillallowbasicnaturalverticalterraintobeclimbedbysimilarsystems,inadditiontotheductsandpipesclimbedbyexistingsystems,andwillsuggestdesignmodificationsforbetterperform-ance.Futurestudiescouldaddresstheuseofothertypesoftoolsforgraspingverticalnaturalsurfaces,suchastoolsfordrillingboltsorplacingothertypesofgearinrock.Theuseofthesetoolswouldallowmorechallengingclimbstobeaccomplished,inthesamewaythat“aid”helpshumanclimbers18,19.However,thesetoolsbringanincreaseinweightandcomplexity,slowingmovementandlimitingpotentialapplications.3.2ControlTherearethreeprimarycomponentsofthecontrolproblemforaclimbingrobot:maintenanceofequilib-rium,endpointslipcontrol,andendpointforcecontrol.Thesethreecomponentsaretightlyrelated.Inordertomaintainbalance,boththelocationofthecenterofmassoftherobotandtheforcesfromcontactswithnaturalfeaturesmustbecontrolled.Controlofslipatthesecontactsisdirectlyrelatedtothedirectionandmagnitudeofthecontactforces.Existingcontroltechniquessuchasthosebasedontheoperationalspaceformulation20couldformabaselineapproachtothedesignofacontrolarchitec-tureforaclimbingrobot.However,thesetechniquescouldbeextendedinanumberofdifferentwaystoachievebetterperformance.Forexample,futureresearchmightaddressthedesignofanendpointslipcontrollerthatisstablewithrespecttothecurvatureofacontactsurface,ratherthanwithrespecttoapointcontactonly.3.3SensingForcontrolandgrasping,therobotmustbecapableofsensingtheorientationofitsbodywithrespecttothegravityvector,thelocationofitscenterofmass,therelativelocationofcontactsurfacesfromitslimbendpoints,andtheforcesthatitisexertingatcontactswithnaturalfeatures.Forplanning,therobotmustadditionallybeabletolocatenewholdsandgenerateadescriptionoftheirproperties,possiblyrequiringameasurementoflevelsofslipatcontactpoints.Sensorintegration,inordertoacquireandusethisinformationwithalgorithmsforcontrol,grasping,andplanning,isachallengingproblem.Existingengineeringsolutionsareavailablewhichcanleadtothedevelopmentofabaselineapproachineachcase.Forexample,sensorssuchasthosede-scribedin21,22canprovidebasicendpointforceandslipmeasurements,aninertialunitandmagneticcompasscanprovidepositioninformation,anon-boardvisionsystemcanprovidearoughcharacterizationofholdlocationsandproperties,andencoderscanprovidethelocationofthecenterofmass.However,theimprovementofeachofthesesensorsintermsofperformance,massreduction,orcostreduc-tionpresentsanopenareaforresearch.Althoughtheperformanceoftheplanningframe-workthatwillbepresentedinSection4wouldbeimprovedwithbettersensorinformation,itdoesnotdependonaperfectmodeloftheenvironmentapriori.Sincetheframeworkleadstofast,onlineimplementa-tion,planscanbeupdatedtoincorporatenewsensorinformationasitbecomesavailable.3.4GraspingTheperformanceofaclimbingrobotisdependentonitsabilitytograsp“holds,”orfeaturesonasteepnaturalsurface.Ithasalreadybeennotedthatspecial-izedgraspingschemes,relyingonspecificpropertiesofthesurfacesuchasverysmoothtextures,pegs,orhandles,cannotbeusedforgraspingarbitrarynaturalfeatures.Theproblemsinvolvedingraspingnaturalholdswillbeexaminedfurtherinthissection.Traditionallygraspresearchhasbeeninterestedineitherpickingupanobjectorholdingitimmobile(alsocalled“fixturing.”)Researchinthissubjectdatesasfarbackas1876itwasshownthataplanarobjectcouldbeimmobilizedusingaminimumoffourfrictionlesspointconstraints23.Goodoverviewsofmorerecentworkcanbefoundin24,25.Inthisfieldanimpor-tantconceptis“force-closure,”definedasagraspthat“canresistallobjectmotionsprovidedthattheend-effectorcanapplysufficientlylargeforcesattheunilateralcontacts.”25Nearlyallresearchongraspshasfocusedonselecting,characterizing,andoptimiz-inggraspsthathavethepropertyofforce-closure.However,forthetaskofclimbingagraspneednotachieveforce-closuretobeausefulgrasp.Forexample,arobotmayfindashelf-likeholdveryeffectiveforpullingitselfup,eventhoughthisgraspwouldbecompletelyunabletoresistforcesexertedinotherdirections.Forthisreason,thetechniquesforselecting,characterizing,andoptimizinggraspsmustbeexpandedsignificantlytoapplytoclimbingrobots.Characterizationinvolvesexaminingthedirectionandmagnitudesofforcesandtorques(alsocalledwrenches)thatcanbeexertedbythegrasp.Forexample,forone-fingergraspsonpointholds,anadequaterepresentationofthisinformationisafrictioncone,whichwillbeusedfortheplanningalgorithmdescribedinSection4.Theideaofcharacterizationalsoencompassesa“qualityfactor.”Measuresofgraspqualityhavebeenresearchedextensivelyandarewellreviewedin26.Thisworklistseightdexteritymeasuresthatincludeminimizationofjointangledeviationsandmaximiza-tionofthesmallestsingularvalueofthegraspmatrix.Otherrelevantresearchhasbeendoneusingtheconceptofthewrenchspace.Usingthisconcept,qualityisdefinedasthelargestwrenchspaceballthatcanfitwithintheunitgraspwrenchspace27.Thevolumeofthegraspwrenchspace,orofmorespecializedtaskellipsoids,couldbeusedasaqualitymeasure28.Theseideashavebeenexpandedtoincludelimitingmaximumcontactforceandappliedinagraspsimulatortocomputeoptimalgraspswithvarioushandsin3D29,30.However,theconceptofgraspqualityisilldefinedforgraspsthatdonotprovideforce-closure.Depend-ingonthedirectionthataclimberwishestogo,differentgraspsmaybeofhigherquality.Furthermore,graspqualitygenerallyincludesaconceptofsecurityorstability,andthistooisilldefinedfornon-force-(a)(b)(c)(d)Fig.2.Fourdifferenthumanclimbinggrasps,the(a)opengrip,(b)crimp,(c)finger-lock,and(d)handjam.closuregrasps.Again,dependingonthedirectionofappliedforces,thesecurityofagraspmaychange.Theconceptofholdqualitymustbedefinedbeforeusefuloptimizationispossible.Also,anefficientwayoftransmittingthisinformationtoacontrollerorplannerisnecessarytoaccomplishtheclimbingtask.Aqualitativeclassificationofdifferenttypesofgraspsalreadyexistsintheliteratureforhumanclimbers19,31.Inthisclassification,graspsarefirstbrokenintotwocategories,thosemeantforpockets,edges,andotherimperfectionsonotherwiseunbrokenverticalrockfaces,andthosemeantforsustainedverticalcracks.SeveralexamplesofdifferentfaceandcrackgraspsareshowninFigure2.Theliteraturegivesaroughideaofthequalityanduseofeachtypeofgraspintermsofcriteriasuchasaperceivedlevelofsecurity,theamountoftorquethatcanbeexertedonahold,andtheamountoffrictionatthe“powerpoint.”Notonlyisthisexpertintuitionqualitative,butalsoitisclearthathumanclimbersneedtoperformadditionalgraspplanningforspecificcases.AsputbyLong,“Thereareasmanydifferentkindsofholdsastherearewaystograbthem3