Obstacle avoidance for kinematically redundant manipulators using polyhedral approximations

Collision avoidance is an essential requirement for a manipulator to complete a task in an environment with obstacles. In this paper, a pseudo-distance function is presented for a pair of convex polyhedra, along with the algorithm for calculating its derivative. On this basis, a potential field-based approach for obstacle avoidance of kinematically redundant manipulators is developed, with the manipulator links and the environmental obstacles being geometrically modelled as a set of convex polyhedra. The potential function is differentiable almost everywhere with respect to the joint configuration variables of the manipulator. It is incorporated in the 'null space projection scheme' in order to achieve obstacle avoidance. Simulation examples are presented to show the effectiveness of the proposed method.