A distance function and its gradient for manipulator online obstacle detection and avoidance

A novel concept of a smooth distance function for online collision detection and avoidance is presented. The concept is well suited for real-time obstacle avoidance path planning. Computation efficiency is achieved by three properties: 1) the `collision´ surfaces of obstacles need to be approximated by local grid point sets only; 2) a manipulator is approximated by a finite set of ellipsoids (or balls); and 3) its gradient exists and can be calculated efficiently due to the smoothness of the distance function. The concept exploits the recursive forward kinematic structure and is not based on a configuration space representation. Hence it is also applicable for kinematically redundant (multi-) manipulator systems