Path Planning Using Laplace's Equation

A method for planning smooth robot paths is presented. The method relies on the use of Laplace's Equation to constrain the generation of a potential function over regions of the configuration space of an effector. Once the function is computed, paths may be found very quickly. These functions do not exhibit the local minima which plague the potential field method. Unlike decompositional and algebraic techniques, Laplace's Equation is very well suited to computation on massively parallel architectures. 1 Introduction The use of potential functions was introduced by Khatib [10] for robot path planning. The potential field method of path planning (as proposed by Khatib) envisions every obstacle as exerting a repelling force on an effector, while the goal exerts an attractive force. Other authors [2, 12, 17, 14, 1, Office of Naval Research URI N00014-86-K-0764, DARPA contract DACA 76-85-C0008 y In Proc. 1990 IEEE Conference on Robotics and Automation. Figures were unavailable for th..