The application of distance functions to the optimization of robot motion in the presence of obstacles

An approach to robotic path planning, which allows optimization of useful performance indices in the presence of obstacles, is given. The main idea is to express obstacle avoidance in terms of the distances between potentially colliding parts. Mathematical properties of the distance functions are studied and under certain conditions the derivatives of the distance functions are characterized. The results lead to a general formulation of path planning problems and suggest numerical procedures for their solution. A simple numerical example involving a 3-degree of freedom cartesian manipulator is described.