A geometric approach to clearance based path optimization

For path planning, an optimal path is defined both by its length and by its clearance from obstacles. Many motion planning techniques such as the roadmap method, the cell decomposition method, and the potential field method generate low quality paths with redundant motions which are post-processed to generate high quality approximations of the optimal path. In this paper, we present a O(h2 (log n + k)) algorithm to optimize a path between a source and a destination in a plane based on a preset clearance from obstacles and overall length, where h is a multiple of the number of vertices on the given path, n is a multiple of the number of obstacle vertices, and k is the average number of obstacle edges against which the clearance check is done for each of the O(h2) queries to determine whether a potential edge of the path is collision-free. This improves the running time of the geometric algorithm presented by Bhattacharya and Gavrilova (2007) which already generates a high quality approximation of the optimal path.