Generating robust trajectories in the presence of ordinary and linear-self-motion singularities

An algorithm is presented which computes feasible manipulator trajectories along fixed paths in the presence of kinematic singularities. The resulting trajectories are close to minimum time, given an inverse kinematic solution for the path and bounds on joint velocities and accelerations. The algorithm has complexity O(M log M), with respect to the number of joint coordinates M, and works using “coordinate pivoting”, in which the path timing is generated locally with respect to whichever joint coordinate is changing the fastest. This allows the handling of singularities, including linear self-motions (e.g., wrist singularities), where the path speed is zero but other joint velocities are non-zero. Examples involving the PUMA manipulator are shown