A robot planning algorithm that constructs a global skeleton of free-space by incremental local methods is described. The curves of the skeleton are the loci of maxima of an artificial potential field that is directly proportional to the distance of the robot from obstacles. The method has the advantage of fast convergence of local methods in uncluttered environments, but it also has a deterministic and efficient method of escaping local extremal points of the potential function. The authors present a general algorithm, for configuration spaces of any dimension, and describe instantiations of the algorithm for robots with two and three degrees of freedom.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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