An efficient algorithm that finds collision-free paths for a manipulator with five or six revolute joints is described. It solves the problem for four-degree-of-freedom pick-and-place operations. Examples are given of paths found by the algorithm in tightly cluttered workspaces. The algorithm first describes free space in two ways: as freeways for the hand and payload ensemble and as freeways for the upper arm. Freeways match volumes swept out by manipulator motions and can be "inverted" to find a class of topologically equivalent path segments. The two freeway spaces are searched concurrently under projection of constraints deter mined by motion of the forearm.
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