Spatial generalization of optimal control for robot manipulators

This paper presents a diffusion-based learning approach to generalize optimal control of a robot manipulator over a bounded work space. Generally, optimal control requires to solve a two point boundary value problem with respect to increase and decrease of time and is very difficult to be solved analytically. In our approach, we first assume that, for some sets of initial and desired terminal conditions of the robots positions we already have the numerical optimal solutions (for example, using some complex numerical computation techniques). Then by using radial basis function network we parameterize these control inputs by a set of weight matrixes. Finally, we apply our diffusion-based algorithm to generalize these weight matrixes for different terminal position conditions. This approach greatly reduced computation cost for the robot to find its optimal control. In addition, since diffusion-based algorithm is a parallel distributed learning approach which only requires local interaction between the nodes of a learning network (a lattice), it can be realized by resent IC hardware technology easily. Computer simulations of a 2-DOF robot arm show the effectiveness of our approach