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We present here a new and efficient algorithm for planning collision-free motion of a rod in the plane amidst polygonal obstacles. The algorithm calculates the boundary of the space of free positions of the rod, and then uses this boundary for determining the existence of required motions. The algorithm runs in time &Ogr;(K log n) where n is the number of obstacle corners and where K is the total number of pairs of obstacle walls or corners lying from one another at distance less than or equal to the length of the rod. Since K = &Ogr;(n2), the algorithm has the same worst-case complexity as the best previously developed algorithm of Leven and Sharir [LS1], but if the obstacles are not too cluttered together it will run much more efficiently.

A new efficient motion-planning algorithm for a rod in polygonal space