Tendon topology inference : Update meeting

Manish KurseMarch 29, 2011

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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

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• Following up on a point raised in my qualifying exam : – Why do the complex inference? How bad are existing

models?

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TE=RB+UBRB=0.133 RI+0.167 EDC+0.667 LUUB=0.313 UI+0.167 EDCES=0.133 RI+0.313 UI+0.167 EDC+0.333 LU

TE

LU and RI

EDC

UI

RB

UB E

S

Chao et al.

1978,79Valero Cuevas et al. 1998

An et al. 1983

Evaluation of existing models of

the extensor mechanism

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(Submitted to ASB 2011)

P1 P2

P3

These models don’t match, but does that justify inference of topology and parameters?

• Optimization of normative model

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TE=RB+UBRB=0.133 RI+0.167 EDC+0.667 LUUB=0.313 UI+0.167 EDCES=0.133 RI+0.313 UI+0.167 EDC+0.333 LU

TE

LU and RI

EDC

UI

RB

UB ES

Chao et al. 1978,1979

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Hill climber optimization : 8 parameters

TE=RB+UBRB=0.133 RI+0.167 EDC+0.667 LUUB=0.313 UI+0.167 EDCES=0.133 RI+0.313 UI+0.167 EDC+0.333 LU

TE

LU and RI

EDC

UI

RB

UB

ES

Chao et al. 1978,1979

7P1

P2

P3

• 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

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Tendon network inference• To begin optimization : FEM solver should be fast and robust.

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FEM solver : several updates.

Optimization of network on solid

• Simple problem.• Topology fixed, parameter

optimization.• Start with very simple problem

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Cross On Hemisphere

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α

12Converged to optimum solution : alpha = 0.5

α

Hill climber optimizationCost fun : Normalized error in Reaction forces at the fixed nodes

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Multi – parameter optimization

5 Parameters : alpha (fraction defining location of node)

AND4 cross sectional areas of the 4 elements : A1, A2, A3, A4

α A1

A2

A3

A4

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α A1

A2

A3

A4

Non uniqueness and problem of observability :Soln : More data points?

Hill climber optimizationCost fun : Normalized error in Reaction forces at the fixed nodes

• 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

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