Collision-Free Trajectory Planning for Manipulator Using Potential Function

This paper proposes a method for planning the collision-free trajectory for a manipulator. In this method, geometrical constraints to avoid obstacles are represented by constraint potential functions. 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 shortening of the travelling time, and the other is for an avoidance of the collision by a potential function. Finally, the proposed method is applied to a manipulator with three links.