Remarks on the application of dynamic programming to the optimal path timing of robot manipulators

Abstract

In this paper, we investigate the use of the dynamic programming approach in the solution of the optimal path timing problem in robotics. This problem is computationally feasible because the path constraint reduces the dimension of the state in the problem to two. The Hamilton–Jacobi–Bellman equation of dynamic programming, a nonlinear first order partial differential equation, is presented and is solved approximately using finite difference methods. Numerical solution of this results in the optimal policy which can then be used to define the optimal path timing by numerical integration. Issues relating to the convergence of the numerical schemes are discussed, and the results are applied to an experimental SCARA manipulator. © 1998 John Wiley & Sons, Ltd.