Time-optimal PTP motion including dynamics for robotic manipulators

Singular controls in the time-optimal point to point (PTP) motion are considered. An analytic approach based on the specific structure of n-link rigid manipulators is presented. The keys to the characterization are Lie brackets of vector fields, cyclic generalized coordinates, the maximum principle, and high-order optimality conditions. How such an approach leads to significant complexity reduction in numerical dynamic programming methods by eliminating those cases which cannot exist is shown. Two-degree-of-freedom manipulators are studied in depth