Obstacle representation by Bump-surfaces for optimal motion-planning

This paper introduces a new method for global, near optimal, motion-planning of a robot (either mobile or redundant manipulator) moving in an environment cluttered with a priori known prohibited areas which have arbitrary shape, size and location. The proposed method is based on the novel notion of Bump-surfaces (or B-surfaces) which represent the entire robot environment through a single mathematical entity. The motion-planning solution is searched on a higher-dimension B-surface in such a way that its inverse image into the robot environment satisfies the given objectives and constraints. The computed solution for a mobile robot consists of a smooth curve without self-loops which connects the starting and destination points with the shortest possible path. The same approach is also used for nth degree-of-freedom manipulators where the end-effector reaches the destination position following a smooth short path avoiding the prohibited areas. For clarity reasons the proposed method is introduced in this paper for the case of a two-dimensional (2D) planar terrain with static obstacles, while a generalization to motion-planning problems on curved terrains is also discussed. Extensive experiments are presented and discussed to illustrate the efficiency and effectiveness of the proposed motion-planning method in a variety of complex environments.