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MCE-2.6

Identification of Stochastic Hybrid System Models

Shankar SastrySam BurdenUC Berkeley

MCE-2.6 #1MCE-2.6 OverviewSam BurdenPhD Candidate, UC BerkeleyAdvised by Prof. Shankar SastryCollaborators:Prof. Ronald Fearing (MCE, UC Berkeley)Prof. Robert Full (MCE, UC Berkeley)Prof. Daniel Goldman (MCE, GATech)Goal: model reduction and system identification tools for hybrid models of terrestrial MAST platformsTheorem: reduction of N-DOF polypeds to common 3-DOF modelAlgorithm: scalable identification of detailed & reduced modelsIdentification of Stochastic Hybrid System ModelsMCE-2.6 #Technical Relevance:Dynamics of Terrestrial LocomotionOctoRoACH designed by Andrew Pullin, Prof. Ronald Fearing

MCE-2.6 #3physical systemrobot, animal

polyped models10100 DOFreduced model< 10 DOFsystem identificationmodel reductionTechnical Relevance:Reduction and Identification of Polyped DynamicsMCE-2.6 #physical systemrobot, animal

polyped models10100 DOFreduced model< 10 DOFsystem identificationmodel reductionReduction of Polyped DynamicsMCE-2.6 #Reduction of Polyped DynamicsDetailed morphologyMultiple limbsMultiple joints per limbMass in every limb segmentPrecedence in literatureMultiple massless limbs (Kukillaya et al. 2009)Realistic disturbancesFractured terrain (Sponberg and Full 2008)Granular media (Goldman et al. 2009)

: body mass: moment of inertia: leg mass: leg lengthMIml: leg stiffness: leg dampingkmM, Il, k, MCE-2.6 #6

Reduction of Polyped DynamicsTheorem: polyped model reduces to 3-DOF modelLet H = (D, F, G, R) be hybrid system with periodic orbit gThen there exists reduced system (M, G) and embeddingDynamics of H are approximated by (M, G) (Burden, Revzen, Sastry 2013 (in preparation) )

MCE-2.6 #7physical systemrobot, animal

polyped models10100 DOFreduced model< 10 DOFsystem identificationmodel reductionIdentification of Polyped DynamicsMCE-2.6 #Identification of Polyped Dynamics

circulating limbs introduce nonlinearities in dynamics & transitionsimpact of limb with substrate introduces discontinuities in stateMathematical models are necessarily approximationsModel parameters must be identified & validated using empirical dataIdentification problem for hybrid system H = (D, F, G, R):

Challenging to solve for terrestrial locomotion:

MCE-2.6 #9

Lateral perturbation experimentreal-timeMCE-2.6 #Lateral perturbation experimentPlatform accelerates laterally at 0.6 0.1 g in a 0.1 sec interval providing a 50 3 cm/sec specific impulse, then maintains velocity.Cockroach running speed: 36 8 cm/sec Stride frequency: 12.6 2.9 Hz(~80ms per stride)

trackwaycameradiffusermirrormagnetic lockanimal motioncartcart motionrailpulleymasscableelasticgroundRevzen, Burden, Moore, Mongeau, & Full, Biol. Cyber. (to appear) 2013MCE-2.6 #Lateral perturbation experiment

Measured:Heading, body orientationLinear, rotational velocityDistal tarsal (foot) positionCart acceleration induces equal & opposite animal accelerationMCE-2.6 #

3 legs act as oneMechanical self-stabilizationCart acceleration induces equal & opposite animal accelerationAnimalLateral Leg Spring (LLS)Apply measured acceleration directly to modelQuantitative predictions for purely mechanical feedbackSchmitt & Holmes 2000

MCE-2.6 #Lateral Leg Spring (LLS)Apply measured acceleration directly to modelInertial Disc

Cart acceleration induces equal & opposite animal accelerationAnimalSchmitt & Holmes 2000Mechanical self-stabilizationMCE-2.6 #

Result: LLS Fits Recovery for >100msAnimalInertial Disc

Lateral Leg Spring (LLS)MCE-2.6 #physical systemrobot, animal

polyped models10100 DOFreduced model< 10 DOFsystem identificationmodel reductionTechnical Accomplishments:Reduction and Identification of Polyped DynamicsMCE-2.6 #