On time optimal path control of manipulators with bounded joint velocities and torques

In the paper we present a solution to the optimal trajectory planning problem subject to constraints given by joint torques and velocities, and the task. The main result is a trajectory planning algorithm which enables the calculation of the optimal motion due to the given requirements and taking into account the dynamics of the manipulator. First, the dynamic model of the manipulator in the parametric form (as a function of the scalar path parameter) is given. Next, the constraints on torques and velocities are converted to those on the path parameter. Using these, the task and joint trajectories are calculated. In the end, some examples are given to illustrate the capabilities of the given trajectory planning algorithm.