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Abstract We present an algorithm that solves a two‐dimensional case of the following problem which arises in robotics: Given a body B , and a region bounded by a collection of “walls”, either find a continuous motion connecting two given positions and orientations of B during which B avoids collision with the walls, or else establish that no such motion exists. The algorithm is polynomial in the number of walls ( O ( n 5 ) if n is the number of walls), but for typical wall configurations can run more efficiently. It is somewhat related to a technique outlined by Reif.
Schwartz et al. (Sun,) studied this question.