# 2009 Research Summary

## Composition of Dynamical Systems for Identification of Human Body Dynamics

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Sumitra Ganesh, Aaron Ames^{1} and Ruzena Bajcsy

This work addresses the problem of identification of human body dynamics from 3D visual data of human motion. Though the structure of the underlying non-autonomous nonlinear dynamical system is well-known [1], physically measuring the system parameters and state requires elaborate setups. Our goal is to estimate the state of the system (joint angle trajectories and velocities) and the control required to produce a given motion from indirect noisy measurements of the joint angle trajectories. However, the estimation scales as O(n^{3}) [2] where *n* is the dimension of the state.

We show how independent lower dimensional dynamical systems can be composed to create an equivalent higher dimensional system which is physically meaningful. Therefore, the estimation problem can be solved in parallel for low dimensional systems and the composition result can be used to arrive at estimates for the higher dimensional system. We focus on two classes of models for an N-link chain in the human body: the first model consists of a set of N independent spherical pendulums, the other consists of a chain of N connected spherical pendulums. We derive the results for a two-link chain in the human body and demonstrate our methods on human arm motion data.

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*Journal of the American Statistical Association,*Vol. 94, No. 446, 1999, pp. 590-599.

^{1}California Institute of Technology