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Tendon topology inference : Update meeting Manish Kurse March 29,

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Overview Use of Eureqa in inference of analytical expressions for tendon movements of a robotic finger: First draft ready : Fco currently reviewing. Validation of existing models of the finger’s tendon networks. Inference of tendon network topology and parameters - updates 2

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Following up on a point raised in my qualifying exam : – Why do the complex inference? How bad are existing models? 3 TE=RB+UB RB=0.133 RI EDC LU UB=0.313 UI EDC ES=0.133 RI UI EDC LU TETE LU and RI EDC UIUI RBRB UBUB ESES Chao et al. 1978,79 Valero Cuevas et al An et al. 1983

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Evaluation of existing models of the extensor mechanism 4 (Submitted to ASB 2011) P1 P2 P3

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These models don’t match, but does that justify inference of topology and parameters? Optimization of normative model 5 TE=RB+UB RB=0.133 RI EDC LU UB=0.313 UI EDC ES=0.133 RI UI EDC LU TE LU and RI EDC UI RBRB UBUB ESES Chao et al. 1978,1979

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6 Hill climber optimization : 8 parameters TE=RB+UB RB=0.133 RI EDC LU UB=0.313 UI EDC ES=0.133 RI UI EDC LU TE LU and RI EDC UI RB UB ES Chao et al. 1978,1979

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7 P1 P2 P3

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Qualms : – How good is good enough? – Is this convincing enough to the committee that we need simultaneous inference of topology and parameters? – I could go on with this optimization of biomechanical models. But the goal of my PhD is not just to model the finger tendon networks, instead – Introduction of the concept of automatic inference of complex biomechanical models from sparse data. – The fingers’ tendon networks happens to be an example 8

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Tendon network inference To begin optimization : FEM solver should be fast and robust. 9 FEM solver : several updates.

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Optimization of network on solid Simple problem. Topology fixed, parameter optimization. Start with very simple problem 10

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Cross On Hemisphere 11 α

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12 Converged to optimum solution : alpha = 0.5 α Hill climber optimization Cost fun : Normalized error in Reaction forces at the fixed nodes

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13 Multi – parameter optimization 5 Parameters : alpha (fraction defining location of node) AND 4 cross sectional areas of the 4 elements : A1, A2, A3, A4 α A1 A2 A3 A4

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14 α A1 A2 A3 A4 Non uniqueness and problem of observability : Soln : More data points? Hill climber optimization Cost fun : Normalized error in Reaction forces at the fixed nodes

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Conclusions: – For the first time optimization of an elastic tendon network on an arbitrary solid. – Simple network : Parameter optimization successful. Next steps : – Fixed topology parameter estimation. Extensor mechanism on hemisphere, finger 15

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