Dynamical System Approach to Navigation Around Obstacles

In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the idea that an ideal vector field which avoids the obstacle traverses its boundary up to when a clear path to the goal is available. We show the existence of this clear path through a set connecting the boundary of the obstacle and the goal. The traversing vector field is determined for an arbitrary obstacle (de-scribed by a set of points) by separating it into cluster of stars. We propose an algorithm which is linear in number of points inside the obstacle. We verify the theoretical results presented with various hand drawn obstacle sets. Our methodology is also extended to obstacles which are not star-shaped, and, those which exist in high dimensions.