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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 it is seen that various types of derivatives of the distance functions are easily characterized. The results lead to the formulation of path planning problems as problems in optimal control and suggest numerical procedures for their solution. A simple numerical example involving a three-degree-of-freedom Cartesian manipulator is described.
Gilbert et al. (Tue,) studied this question.