Optimal piecewise linear motion of an object among obstacles

We present an algorithm for determining the shortest restricted path motion of a polygonal object amidst polygonal obstacles. The class of motions which are allowed can be described as follows: a designated vertex,P, of the polygonal object traverses a piecewise linear path, whose breakpoints are restricted to the vertices of the obstacles. The distance measure being minimized is the length of the path traversed byP. Our algorithm runs in timeO(n ⁴kogn). We also discuss a variation of this algorithm which minimizes any positive linear combination of length traversed byP and angular rotation of the ladder aboutP. This variation requiresO(n ₅) time.Research partially supported by a grant from the Hughes Artificial Intelligence Center, part of Hughes Aircraft.