Desingularization of resolved motion rate control of mechanisms

Resolved motion rate control is an algorithm for solving the path-tracking problem in robotic control which can fail at singular points of the kinematic function. In this paper we find a new second-order condition which, when satisfied, ensures the existence of a solution path with continuous, bounded joint rates. The condition is related to the curvature of the path at the singular value. As an application, we give a sufficient condition for the existence of self-motion for redundant manipulators at singular points. We derive a simple formula for the rate of recovery of the manipulability measure along the path at the singularity, and prove that the usual resolved motion rate control algorithm can be modified to compute these solution paths. Several realistic simulations are presented