Computation of Path Constrained Time Optimal Motions With Dynamic Singularities

An algorithm for computing the time optimal motions of robotic manipulators along specified paths is presented which accounts for singular points and arcs, at which one actuator does not contribute to the acceleration along the path. It is proven that the optimal trajectory is extremal in the acceleration along the path at all times except at singular points and arcs where it maximizes the feasible velocity along the path. This algorithm is robust to path variations unlike the original methods (Bobrow et al., 1985; Shin and McKay, 1984) that fail at singular points. The algorithm is demonstrated for a two-link planar manipulator to produce smooth controls along singular arcs.