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BP: Fachverband Biologische Physik

BP 32: Posters: Other Topics in Biological Physics

BP 32.9: Poster

Donnerstag, 17. März 2011, 17:15–20:00, P3

A Riemannian geometric approach to human arm dynamics, movement optimization and invariance — •Armin Biess¹, Tamar Flash², and Dario G. Liebermann³ — ¹Max-Planck-Institute for Dynamics and Self-Organization, 37073 Göttingen, Germany — ²Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot 76100, Israel — ³Physical Therapy Department, Sackler Faculty of Medicine, Tel Aviv University, Ramat Aviv 69978, Israel

In modeling human arm movements optimization principles have been used to describe mathematically the kinematics and dynamics of point-to-point arm movements. Most models have assumed an underlying Euclidean structure of space in the formulation of the cost functions that determine the model predictions. We present a generally covariant formulation of human arm dynamics and optimization principles in Riemannian configuration space. We extend the one-parameter familiy of mean squared-derivative (MSD) cost-functionals, previously considered in human motor control, from Euclidean to Riemannian space. Solutions of the one-parameter family of MSD variational problems in Riemannian space are given by (re-parametrized) geodesic paths, which correspond to arm movements with least muscular effort. Finally, movement invariants are derived from symmetries of the Riemannian manifold. We argue that the geometrical structure of the arm's configuration space may provide insights into the emerging properties of the movements generated by the human motor system.