Singularity-robust trajectory generation

A singularity-robust trajectory generator is presented that, given a prescr ibed manipulator path and corresponding kinematic solution, computes a feas ible trajectory in the presence of kinematic singularities. The resulting t rajectory is close to minimum time, subject to individual bounds on joint v elocities and accelerations, and follows the path with precision. The algor ithm 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 singularit ies is controlled using the fastest changing joint coordinate. This allows the handling of singular situations, including linear self-motions (e.g., w rist singularities), where the speed along the path is zero bur some joint velocities are nonzero. To compute the trajectory knot points are inserted along the path, dividing it into intervals, with the knot density increasin g near singularities. An appropriate path velocity is then computed at each knot paint and the resulting knot velocity sequence is integrated to yield the path timing. Examples involving the PUMA manipulator are shown.