This paper gives approximation algorithms of solving the following motion planning problem: Given a set of polyhedral obstacles and points <italic>s</italic> and <italic>t</italic>, find a shortest path from <italic>s</italic> to <italic>t</italic> that avoids the obstacles. The paths found by the algorithms are piecewise linear, and the length of a path is the sum of the lengths of the line segments making up the path. Approximation algorithms will be given for versions of this problem in the… CONTINUE READING