A Dynamical System Approach to Real-time Three-Dimensional Concave Obstacle Avoidance

Abstract

In this paper, we propose an approach based on Dynamical System (DS) to avoid three-dimensional concave obstacles in real-time. Most three-dimensional concave obstacles can be divided into multiple parts, each of which can be approximated by a convex ellipsoid, and the ellipsoids intersect in pairs. The key of this method is that when the trajectory computed according to the deformed DS reaches a point on the intersection line between two of the convex ellipsoids, the trajectory evolves along the intersection line. We prove that the proposed approach can ensure the impenetrability of the concave obstacles. We validate the effectiveness of the method in the simulations on several different concave objects and experiments on the arm of the UBTECH humanoid robot.