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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.>
Connolly et al. (2002) studied this question.