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1、2012IEEE/RSJInternationalConferenceonIntelligentRobotsandSystemsOctober7-12,2012.Vilamoura,Algarve,PortugalTheCubli:ACubethatcanJumpUpandBalanceMohanarajahGajamohan,MichaelMerz,IgorThommenandRaffaelloD’AndreaAbstract—ThispaperintroducestheCubli,a151515cmOn
2、cetheCubliisbalancingonitsedge,thenexttwowheelscubethatcanjumpupandbalanceonacorner.Momentumareinstantaneouslystoppedtomakeitstandonitscorner.wheelsmountedonthreefacesofthecube(Fig.1)rotateathighFinally,aninertialmeasurementunit(IMU)basedstateangularvelociti
3、esandthenbrakesuddenly,causingtheCublitoestimationisperformedandthemotortorquesarepreciselyjumpup.OncetheCublihasalmostreachedthecornerstand-upposition,controlledmotortorquesareappliedtomakeitcontrolledtomaketheCublicontinuestanding.balanceonitscorner.Thispa
4、pertracksthedevelopmentoftheWhereasarelativelylargeportionofresearchtriestoavoidCubli’sonedimensionalprototypeatETHZurichandpresentsimpactorovercometheeffectsofit[10]–[12],onlyasmallpreliminaryresults.portion[13],includingtheCubli,takesadvantageofit.Whileano
5、n-impulsiveforceislimitedbytheactuatortorquelimits,I.INTRODUCTIONanimpactgivesforcesthatarewellbeyondtheactuatorInvertedpendulumsystemshaveaveryrichhistory[1]andlimitations.havebeenwidelyusedtotest,demonstrateandbenchmarknewcontrolconceptsandtheories[2].Furt
6、hermore,devel-opmentofnewcontrolalgorithmsforthependulumsystemitselfisstillanactiveareaofresearch[3]–[5].Comparedtoother3Dinvertedpendulumtest-beds[8],[9]theCublihastwouniquefeatures.Oneisitsrelativelysmallfootprint,(hencethenameCubli,whichisderivedfromtheSw
7、issGermandiminutivefor”cube”).Theotherfeature4535:3isitsabilitytojumpupfromarestingpositionwithoutanyexternalsupport,notonlyaninterestingconceptforthecontrolengineerbutalsoalsoanappealingdemonstrationfor(a)(b)thegeneralpublic.Fig.2.TheCublijump-upstrategy:
8、(a)FlattoEdge:Initiallylyingflatonitsface,theCublijumpsuptostandonitsedge.(b)EdgetoCorner:TheCubligoesfrombalancingaboutanedgetobalancingonacorner.Oncecomplete,theCubliwillprovideaninexpensive,op
