Gyroscopic Forces and Collision Avoidance with Convex Obstacles

This paper introduces gyroscopic forces as an tool that can be used in addition to the use of potential forces in the study of collision and convex obstacle avoidance. It makes use of the concepts of a detection shell and a safety shell and shows, in an appropriate context, that collisions are avoided, while at the same time guaranteeing that control objectives determined by a potential function are met. In related publications, we refine and extend the method to include flocking and swarming behavior.