Planning of Near-Minimum Time Trajectories for Manipulators (The Case of End Effector’s Avoidance of Prohibited Spaces)

There are many papers in which various algorithms of the minimum time trajectory planning problem for manipulators are proposed, but many of them treat the case in which a manipulator moves in a full free task space. In this paper, an efficient algorithm for determining a minimum time trajectory is proposed under the condition that some spaces that the end effector of the manipulator cannot invade exist in the task space. The dynamical equation of the manipulator is expressed by a path parameter ’s’ which does not depend on time and is solved as a two-point boundary value problem. Input torques giving a desired trajectory are composed of two parts. One is for a minimization of the travelling time, and the other is for an avoidance of some spaces where the end effector is prohibited to enter. The avoidance is executed by introducing a potential function in the dynamical equation. Finally, the proposed method is applied to a simple manipulator with two links.