Simulating Discrete and Rhythmic Multi-joint Human Arm Movements by Optimization of Nonlinear Performance Indices

Abstract

An optimization approach applied to mechanical linkage models is used to simulate human arm movements. Predicted arm trajectories are the result of minimizing a nonlinear performance index that depends on kinematic or dynamic variables of the movement. A robust optimization algorithm is presented that computes trajectories which satisfy the necessary conditions with high accuracy. It is especially adapted to the analysis of discrete and rhythmic movements. The optimization problem is solved by parameterizing each generalized coordinate (e.g., joint angular displacement) in terms of Jacobi polynomials and Fourier series, depending on whether discrete or rhythmic movements are considered, combined with a multiple shooting algorithm. The parameterization of coordinates has two advantages. First, it provides an initial guess for the multiple shooting algorithm which solves the optimization problem with high accuracy. Second, it leads to a low dimensional representation of discrete and rhythmic movements in terms of expansion coefficients. The selection of a suitable feature space is an important prerequisite for comparison, recognition and classification of movements. In addition, the separate computational analysis of discrete and rhythmic movements is motivated by their distinct neurophysiological realizations in the cortex. By investigating different performance indices subject to different boundary conditions, the approach can be used to examine possible strategies that humans adopt in selecting specific arm motions for the performance of different tasks in a plane and in three-dimensional space.