An algorithm for generating convex obstacle-free regions based on stereographic projection

Many of the existing motion planning algorithms require the free space to be decomposed into convex obstacle-free regions. This paper presents an algorithm for generating such regions. The algorithm is based on stereographic projection. The algorithm requires relatively simple computations, compared with some of the known methods. Three applications of the algorithm were demonstrated: motion planning for a walking robot, trajectory generation for an unmanned aerial vehicle and a motion planning for an in-pipe robot.