Singularity-Robust Trajectory Generation

Abstract

A singularity-robust trajectory generator is presented that, given a prescribed manipulator path and corresponding kinematic solution, computes a feasible trajectory in the presence of kinematic singularities. The resulting trajectory is close to minimum time, subject to individual bounds on joint velocities and accelerations, and follows the path with precision. The algorithm has complexity O(M log M), where M is the number of robot joints, and works using “coordinate pivoting,” in which the path timing near singularities is controlled using the fastest changing joint coordinate. This allows the handling of singular situations, including linear self-motions (e.g., wrist singularities), where the speed along the path is zero but some joint velocities are nonzero. To compute the trajectory, knot points are inserted along the path, dividing it into intervals, with the knot density increasing near singularities. An appropriate path velocity is then computed at each knot point, and the resulting knot velocity sequence is integrated to yield the path timing. Examples involving the PUMA manipulator are shown.