NEW EFFICIENT MOTION-PLANNING ALGORITHM FOR A ROD IN TWO-DIMENSIONAL POLYGONAL SPACE.

We present here a new and efficient algorithm for planning collision-free motion of a line segment (a rod or a 'ladder') in two-dimensional space amidst polygonal obstacles. The algorithm calculates the boundary of the (three-dimensional) space of free positions of the ladder, uses this boundary for determining the existence of required motions, and plans such motions whenever possible. The algorithm runs in time O(K log n) equals O(n**2 log n) where n is the number of obstacle corners and where K is the total number of pairs of obstacle walls or corners of distance less than or equal to the length of the ladder. The algorithm also serves as an initial demonstration of the viability of the technique it uses, which we expect to be useful in obtaining efficient motion-planning algorithms for other more complex robot systems.