On the stability of the hybrid-damped resolved-acceleration control

This paper points out that the stability analysis of the hybrid-damped resolved-acceleration control in our earlier work is incomplete, since the stability was concluded directly from the fact that the joint velocities come to rest as time approaches infinity. A similar incomplete technique was also used in the work of Wampler and Leifer to prove the stability of a damped least-squares resolved-acceleration control scheme. In this paper, we use LaSalle’s invariance principle rigorously to show that the solution trajectory of the hybrid-damped resolved-acceleration control will eventually come to the target without steady-state error or will stay at a kinematic singular point with some steady-state error. Discussions on the case of staying at a singular point are also given. Q 1998 John Wiley & Sons, Inc.