Complete Path Planning for Planar Closed Chains Among Point Obstacles

A method to compute an exact cell decomposition and corresponding connectivity graph of the configuration space (C-space) of a planar closed chain manipulator moving among point obstacles is developed. By studying the global properties of the loop closure and collision constraint set, a cylindrical decomposition of the collision-free portion of C-space (C-free) is obtained without translating the constraints into polynomials as required by Collins’ method [1]. Once the graph is constructed, motion planning proceeds in the usual way; graph search followed by path construction. Experimental results demonstrate the effectiveness of the algorithm.