A bilevel optimization approach to obtain optimal cost functions for human arm movements

Sebastian Albrecht; Marion  Leibold; Michael Ulbrich

doi:10.3934/naco.2012.2.105

Article Contents

2012, Volume 2, Issue 1: 105-127. Doi: 10.3934/naco.2012.2.105

This issue Previous Article Solvability of a class of thermal dynamical contact problems with subdifferential conditions Next Article An efficient algorithm for convex quadratic semi-definite optimization

A bilevel optimization approach to obtain optimal cost functions for human arm movements

1.
Chair for Mathematical Optimization, Department of Mathematics, Technische Universität München (TUM), Boltzmannstr. 3, 85747 Garching b. München
2.
Institute of Automatic Control Engineering, Technische Universität München (TUM), Arcisstr. 21, 80290 München
3.
Chair for Mathematical Optimization, Department of Mathematics, Technische Universität München (TUM), Boltzmannstr. 3, 85747 Garching b. München

Received: April 2011

Revised: August 2011

Published: February 2012

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Abstract

Using a bilevel optimization approach, we investigate the question how humans plan and execute their arm motions. It is known that human motions are (approximately) optimal for suitable and unknown cost functions subject to the dynamics. We investigate the following inverse problem: Which cost function out of a parameterized family (e.g., convex combinations of functions suggested in the literature) reproduces recorded human arm movements best? The lower level problem is an optimal control problem governed by a nonlinear model of the human arm dynamics. The approach is analyzed for a dynamical 3D model of the human arm. Furthermore, results for a two-dimensional experiment with human probands are presented.

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Mathematics Subject Classification: 90C90, 49N45, 49M25.

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