Time optimal motions of manipulators with actuator dynamics

This paper presents a method for computing the time optimal motions along specified paths of manipulators with 3rd order dynamics, considering rigid links and actuator dynamics. Using the Pontryagin maximum principle, it is shown that the optimal trajectory is bang-bang in the jerk along the path, except at singular points and along singular arcs. This control structure leads to an efficient algorithm for computing the time optimal trajectory, that, unlike variational methods does not depend on co-states. The algorithm is applicable to general manipulators with 3rd order dynamics between the control input and the position output, with any state inequality constraints. The method is demonstrated for a two link manipulator driven by electric DC motors.