Diffusion-Based Spatial Generalization of Optimal Motor Control

摘要

Biological studies on human arm movements show that, the point to point (PTP) arm movement tends to optimize some performance index such as to minimize the torqur change. The computational problem then arises that how can human brain act to solve this optimal problem? Generally, optimal control requires to solve a two point boundary value problem with respect to increase and decrease of time, it is very difficult to be solved analytically because of the nonlinear arm dynamics. This paper presents a diffusion-based learning approach to generalize optimal control over a bounded work space. This approach first assumes that, for some sets of initial and desired terminal conditions of the arm's positions, the numerical optimal solutions are exactly known (for example, using some complex numerical computation techniques). By using radial basis function (RBF) network, these control inputs are parameterized by a set of constant weight matrixes. Finally, our diffusion-based algorithm is applied to generalize these weight matrixes for different terminal position conditions. Computer simulations of a 2 D.O.F. planner arm show the effectiveness of our approach.