Path planning and the topology of configuration space

This work considers the path planning problem for planar revolute manipulators operating in a workspace of polygonal obstacles. This problem is solved by determining the topological characteristics of obstacles in configuration space, thereby determining where feasible paths can be found. A collision-free path is then calculated by using the mathematical description of the boundaries of only those configuration space obstacles with which collisions are possible. The key to this technique is a simple test for determining whether two disjoint obstacles are connected in configuration space. This test allows the path planner to restrict its calculations to regions in which collision-free paths are guaranteed a priori, thus avoiding unnecessary computations and resulting in an efficient implementation. Typical timing results for environments consisting of four polyhedral obstacles comprising a total of 27 vertices are of the order of 22 ms on a SPARC-IPC workstation