Robustness, convergence and stability considerations for the optimal-control-based inverse dynamics solution for flexible robot arms

Abstract

Discusses the inverse dynamics problem for flexible open-chain robot arms. In earlier work the authors (1990) derived an approximate solution to this inverse dynamics problem, using optimal control theory. The solution found with this method is noncausal, and results in excellent open-loop tracking. The method is applicable to multi-link arms by linearization about a nominal trajectory. In the present paper, they discuss issues related to the robustness of the method under parameter variation. They show simulation results for nominal and off-nominal one-link systems. They also consider the convergence of the method with the number of modes used to represent the deformation of the links. They show that sufficiently accurate results are obtained with only two or three modes for each link. Finally they discuss the stability of the system under the solution using Lyapounov theory. >