Avoidance of Convex and Concave Obstacles with Convergence ensured through Contraction

This paper presents a closed-form approach to obstacle avoidance for multiple moving convex and star-shaped concave obstacles. The method takes inspiration in harmonic-potential fields. It inherits the convergence properties of harmonic potentials. We prove impenetrability of the obstacle’s hull and asymptotic stability at a final goal location, using contraction theory. We validate the approach in a simulated co-worker industrial environment, with one KUKA arm engaged in a pick and place grocery task, avoiding in real-time humans moving in its vicinity and in simulation to drive wheel-chair robot in the presence of moving obstacles.