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ClimbingRobotsinNaturalTerrainTimothyBretl,TeresaMiller,andStephenRockJeanClaudeLatombeAerospaceRoboticsLabRoboticsLaboratoryDepartmentofAeronauticsandAstronauticsComputerScienceDepartmentStanfordUniversity,Stanford,CA94305StanfordUniversity,Stanford,CA94305{tbretl,tgmiller,rock}sunvalley.stanford.edulatombecs.stanford.eduKeywordsMotionplanning,climbing,robotics,leggedrobots,highriskaccess,naturalterrain.AbstractThispaperpresentsageneralframeworkforplanningthequasistaticmotionofclimbingrobots.Theframeworkisinstantiatedtocomputeclimbingmotionsofathreelimbedrobotinverticalnaturalterrain.Anexampleresultingpaththroughalargesimulatedenvironmentispresented.Theplanningproblemisoneoffivefundamentalchallengestothedevelopmentofrealroboticsystemsabletoclimbrealnaturalterrain.Eachofthefourotherareashardwaredesign,control,sensing,andgraspingisalsodiscussed.1IntroductionTheworkdescribedinthispaperispartofanefforttodevelopcriticaltechnologiesthatwillenablethedesignandimplementationofanautonomousrobotabletoclimbverticalnaturalterrain.Toourknowledge,thiscapabilityhasnotbeendemonstratedpreviouslyforroboticsystems.Priorapproacheshavedealtwithartificialterrain,eitherusingspecialgraspse.g.,pegs,magnetsadaptedtotheterrainssurfaceorexploitingspecificpropertiesorfeaturesoftheterraine.g.,ductsandpipes112.Developingthiscapabilitywillfurtherourunderstandingofhowhumansperformsuchcomplextasksasclimbingandscramblinginruggedterrain.Thismayproveusefulinthefuturedevelopmentofsophisticatedroboticsystemsthatwilleitheraidorreplacehumansintheperformanceofaggressivetasksindifficultterrain.Examplesincluderoboticsystemsforsuchmilitaryandcivilianusesassearchandrescue,reconnaissance,andplanetaryexploration.Manyissuesneedtobeaddressedbeforerealrobotscanclimbreal,vertical,naturalterrain.Thispaperconsidersfiveofthemostfundamentaloftheseissueshardwaredesign,control,sensing,planning,andgrasping.Oneoftheseissuesinparticular,themotionplanningproblem,isdescribedinmoredetail.AgeneralframeworkforclimbingrobotsispresentedandthisframeworkisinstantiatedtocomputeclimbingmotionsofthethreelimbedrobotshowninFigure1.Simulationresultsareshownfortherobotinanexampleverticalenvironment.2MotivationTheresultsofresearchinthisareawillbenefitanumberofapplicationsandhaveimplicationsforseveralrelatedresearchareas.2.1ApplicationsThispaperismotivatedbyaneedforroboticsystemscapableofprovidingremoteaccesstohighrisknaturalenvironments.Therearemanyterrestrialapplicationsforthesesystems,suchassearchandrescue,caveexploration,humanassistanceforrockandmountainclimbing,andtacticalurbanmissions.Eachoftheseapplicationsrequiresclimbing,descending,ortraversingsteepslopesandbrokenterrain,andthusinvolvesconsiderablehumanrisk.Severalspaceapplicationscouldalsobenefitfromtheseaggressiveroboticsystems.Forexample,sitesonMarswithpotentiallyhighsciencevaluehavebeenidentifiedonclifffaces13.Often,itisneitherpracticalnorfeasibleforflyingrobotstoaccesstheseFig1.Athreelimbedclimbingrobotmovingverticallyonnaturalsurfaces.locations.Therefore,toreachthesesites,robotsmustclimb,descend,ortraversesteepslopes.Futuregoalsforexplorationonotherplanetarybodiesmayrequireaccesstoequallyruggedterrain.2.2ImplicationsInadditiontofurtheringthedevelopmentofaclimbingrobotforverticalnaturalterrain,theresultsofresearchinthisareacouldprovidefundamentalinsightintoseveralrelatedresearchareas.Forexample,thisstudycouldleadtothedevelopmentofbetterstrategiesforroboticwalkingordexterousmanipulation.Humanclimbersoftencommentonanincreaseinbalanceandanexpandedrangeofmovementineverydayactivityastheybecomemoreproficientatthesport.Thisenhancedmobilityisoftenreferredtoasdiscoveringnewdegreesoffreedom,andisrelatedtotheideaofdiscoveringusefulnewmodesofmobilityforextremelycomplicatedhumanoidrobotsordigitalactors.Also,thedevelopmentofplanningalgorithmsforclimbingrobotscouldleadtoabettersetofcriteriaforthedesignofthesetypesofrobots.Thesealgorithmscouldbeappliedtocandidatedesignsinsimulationtodeterminethecapabilitiesoftheresultingrobots,andthustoselectadesign.3FundamentalIssuesTherearefivefundamentalissuesinvolvedinclimbingsteepnaturalterrainhardwaredesign,control,sensing,grasping,andplanning.Asubstantialamountofworkneedstobedoneineachoftheseareasinordertodeveloparealclimbingrobot.ThissectiondescribesthechallengesinvolvedinthefirstfouroftheseareastheplanningproblemwillbediscussedinmoredetailinSection4.3.1HardwareDesignAgoodhardwaredesigncanincreasetheperformanceoftherobot,andoftencanmakeeachoftheotherfundamentalissueseasiertodealwith.However,pastuseofhardwaresolutionsinmaintainingequilibriumgenerallyresultedinafundamentallimitationontheterrainthatcouldbetraversed.Wheeledroboticsystemshavebeenusedtoascendandtraversenaturalslopesofupto50degrees,todescendslopesofupto75degrees,andtoclimboversmallobstaclesinroughterrain.Thesesystemseitherusesomeformofactiveorrockerbogiesuspensionasin12,1416,oruserappellingasin1.Similarresultshavebeenobtainedusingleggedrappellingrobots3,17andasnakelikerobot4.Theterrainthattheseroverscantraverserobustlyisimpressive,butnoneoftheexistingsystemshasbeenshowntobecapableofclimbingnaturalslopesof90degreesorhigher.Wheeledroversandsnakelikerobotshaveaninherentgraspinglimitationthatpreventstheiruseinascendingsustainednearverticalordescendingsustainedpastverticalnaturalslopes.Existingleggedroboticsystemsdonothavethislimitation,butstillhavebypassedtheissueofmaintainingcontactwiththeslopebyusingrappeltethers.Relianceonthesetethersprohibitsinitialcliffascent,andlimitstheslopegradeoncliffdescenttobelow90degrees.Awidevarietyofrobotscapableofclimbingverticalartificialsurfacesisavailable.Mostoftheserobotsexploitsomepropertyofthesurfaceforeasygrasping.Forexample,someoftheserobotsusesuctioncupsorpermanentmagnetstoavoidslipping58.Otherstakeadvantageoffeaturessuchasbalconyhandrails9orpoles10.However,thesurfacepropertiesthatareexploitedbytheserobotsgenerallyarenotavailableinnaturalterrain.Incontrast,thesimplerhardwaredesignsusedby2,11hadnosuchlimitations.Itisexpectedthatsolutionstotheplanningproblemsuchastheonepresentedinthispaperwillallowbasicnaturalverticalterraintobeclimbedbysimilarsystems,inadditiontotheductsandpipesclimbedbyexistingsystems,andwillsuggestdesignmodificationsforbetterperformance.Futurestudiescouldaddresstheuseofothertypesoftoolsforgraspingverticalnaturalsurfaces,suchastoolsfordrillingboltsorplacingothertypesofgearinrock.Theuseofthesetoolswouldallowmorechallengingclimbstobeaccomplished,inthesamewaythataidhelpshumanclimbers18,19.However,thesetoolsbringanincreaseinweightandcomplexity,slowingmovementandlimitingpotentialapplications.3.2ControlTherearethreeprimarycomponentsofthecontrolproblemforaclimbingrobotmaintenanceofequilibrium,endpointslipcontrol,andendpointforcecontrol.Thesethreecomponentsaretightlyrelated.Inordertomaintainbalance,boththelocationofthecenterofmassoftherobotandtheforcesfromcontactswithnaturalfeaturesmustbecontrolled.Controlofslipatthesecontactsisdirectlyrelatedtothedirectionandmagnitudeofthecontactforces.Existingcontroltechniquessuchasthosebasedontheoperationalspaceformulation20couldformabaselineapproachtothedesignofacontrolarchitectureforaclimbingrobot.However,thesetechniquescouldbeextendedinanumberofdifferentwaystoachievebetterperformance.Forexample,futureresearchmightaddressthedesignofanendpointslipcontrollerthatisstablewithrespecttothecurvatureofacontactsurface,ratherthanwithrespecttoapointcontactonly.3.3SensingForcontrolandgrasping,therobotmustbecapableofsensingtheorientationofitsbodywithrespecttothegravityvector,thelocationofitscenterofmass,therelativelocationofcontactsurfacesfromitslimbendpoints,andtheforcesthatitisexertingatcontactswithnaturalfeatures.Forplanning,therobotmustadditionallybeabletolocatenewholdsandgenerateadescriptionoftheirproperties,possiblyrequiringameasurementoflevelsofslipatcontactpoints.Sensorintegration,inordertoacquireandusethisinformationwithalgorithmsforcontrol,grasping,andplanning,isachallengingproblem.Existingengineeringsolutionsareavailablewhichcanleadtothedevelopmentofabaselineapproachineachcase.Forexample,sensorssuchasthosedescribedin21,22canprovidebasicendpointforceandslipmeasurements,aninertialunitandmagneticcompasscanprovidepositioninformation,anonboardvisionsystemcanprovidearoughcharacterizationofholdlocationsandproperties,andencoderscanprovidethelocationofthecenterofmass.However,theimprovementofeachofthesesensorsintermsofperformance,massreduction,orcostreductionpresentsanopenareaforresearch.AlthoughtheperformanceoftheplanningframeworkthatwillbepresentedinSection4wouldbeimprovedwithbettersensorinformation,itdoesnotdependonaperfectmodeloftheenvironmentapriori.Sincetheframeworkleadstofast,onlineimplementation,planscanbeupdatedtoincorporatenewsensorinformationasitbecomesavailable.3.4GraspingTheperformanceofaclimbingrobotisdependentonitsabilitytograspholds,orfeaturesonasteepnaturalsurface.Ithasalreadybeennotedthatspecializedgraspingschemes,relyingonspecificpropertiesofthesurfacesuchasverysmoothtextures,pegs,orhandles,cannotbeusedforgraspingarbitrarynaturalfeatures.Theproblemsinvolvedingraspingnaturalholdswillbeexaminedfurtherinthissection.Traditionallygraspresearchhasbeeninterestedineitherpickingupanobjectorholdingitimmobilealsocalledfixturing.Researchinthissubjectdatesasfarbackas1876itwasshownthataplanarobjectcouldbeimmobilizedusingaminimumoffourfrictionlesspointconstraints23.Goodoverviewsofmorerecentworkcanbefoundin24,25.Inthisfieldanimportantconceptisforceclosure,definedasagraspthatcanresistallobjectmotionsprovidedthattheendeffectorcanapplysufficientlylargeforcesattheunilateralcontacts.25Nearlyallresearchongraspshasfocusedonselecting,characterizing,andoptimizinggraspsthathavethepropertyofforceclosure.However,forthetaskofclimbingagraspneednotachieveforceclosuretobeausefulgrasp.Forexample,arobotmayfindashelflikeholdveryeffectiveforpullingitselfup,eventhoughthisgraspwouldbecompletelyunabletoresistforcesexertedinotherdirections.Forthisreason,thetechniquesforselecting,characterizing,andoptimizinggraspsmustbeexpandedsignificantlytoapplytoclimbingrobots.Characterizationinvolvesexaminingthedirectionandmagnitudesofforcesandtorquesalsocalledwrenchesthatcanbeexertedbythegrasp.Forexample,foronefingergraspsonpointholds,anadequaterepresentationofthisinformationisafrictioncone,whichwillbeusedfortheplanningalgorithmdescribedinSection4.Theideaofcharacterizationalsoencompassesaqualityfactor.Measuresofgraspqualityhavebeenresearchedextensivelyandarewellreviewedin26.Thisworklistseightdexteritymeasuresthatincludeminimizationofjointangledeviationsandmaximizationofthesmallestsingularvalueofthegraspmatrix.Otherrelevantresearchhasbeendoneusingtheconceptofthewrenchspace.Usingthisconcept,qualityisdefinedasthelargestwrenchspaceballthatcanfitwithintheunitgraspwrenchspace27.Thevolumeofthegraspwrenchspace,orofmorespecializedtaskellipsoids,couldbeusedasaqualitymeasure28.Theseideashavebeenexpandedtoincludelimitingmaximumcontactforceandappliedinagraspsimulatortocomputeoptimalgraspswithvarioushandsin3D29,30.However,theconceptofgraspqualityisilldefinedforgraspsthatdonotprovideforceclosure.Dependingonthedirectionthataclimberwishestogo,differentgraspsmaybeofhigherquality.Furthermore,graspqualitygenerallyincludesaconceptofsecurityorstability,andthistooisilldefinedfornonforceabcdFig.2.Fourdifferenthumanclimbinggrasps,theaopengrip,bcrimp,cfingerlock,anddhandjam.closuregrasps.Again,dependingonthedirectionofappliedforces,thesecurityofagraspmaychange.Theconceptofholdqualitymustbedefinedbeforeusefuloptimizationispossible.Also,anefficientwayoftransmittingthisinformationtoacontrollerorplannerisnecessarytoaccomplishtheclimbingtask.Aqualitativeclassificationofdifferenttypesofgraspsalreadyexistsintheliteratureforhumanclimbers19,31.Inthisclassification,graspsarefirstbrokenintotwocategories,thosemeantforpockets,edges,andotherimperfectionsonotherwiseunbrokenverticalrockfaces,andthosemeantforsustainedverticalcracks.SeveralexamplesofdifferentfaceandcrackgraspsareshowninFigure2.Theliteraturegivesaroughideaofthequalityanduseofeachtypeofgraspintermsofcriteriasuchasaperceivedlevelofsecurity,theamountoftorquethatcanbeexertedonahold,andtheamountoffrictionatthepowerpoint.Notonlyisthisexpertintuitionqualitative,butalsoitisclearthathumanclimbersneedtoperformadditionalgraspplanningforspecificcases.AsputbyLong,Thereareasmanydifferentkindsofholdsastherearewaystograbthem31.However,thisintuitioncanbeusedasastartingpointfordeterminingmeaningfulquantitativecriteriaforgraspselectionandoptimization.Acomparisonoftheclimbingliteraturewithpastworkonroboticgraspplanningrevealsseveralotherfundamentaldifferencesbetweenthetwoapplicationsthatmaybecomeimportantinfutureresearch.Forexample,manyclimbingholdsareverysmall,sothefingersusedinaclimbinggraspoftenhavelargediametersrelativetotheobjecttobegrasped.Literatureonroboticgraspingprimarilyconsidersthecasewherethefingershavesmalldiametersrelativetotheobject.Inaddition,someclimbinggrasps,asmentionedaboveandshowninFigure2,arebasedonjammingfingersinacrack.Thistechniqueisverydifferentfromonearobotmightusetopickupanobject,andrequiresahighdegreeofflexibilityandsmalldegreesoffreedominordertounjamthefingers.Clearly,continuedworkonclimbingrobotseventuallywillleadtotheconsiderationofawealthofnewissuesingrasping.4PlanningTheplanningproblemisthefifthfundamentalchallengeforclimbingrobotsinnaturalterrain.Detailsofthemotionplanningframeworkpresentedinthissectionaregivenin32.4.1ChallengesTheplanningproblemforaclimbingrobotconsistsofgeneratingatrajectorythatmovestherobotthroughaverticalenvironmentwhilemaintainingequilibrium.ThisproblemischallengingevenforhumanclimbersClimbingisdescribedbyLongasasingularabcFig.3.Threedifferenthumanclimbingmoves,theabackstep,bstem,andchighstep.
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