Stability of Robotic Obstacle Avoidance and Force Interaction*

Stability problems associated with robot control with obstacle avoidance are analysed. Obstacle avoidance algorithms based on potential function are revised to accomplish stable re-design. A stability proof using Lyapunov theory and passivity theory is provided for the re-designed obstacle avoidance algorithm. The paper presents a modification of potential functions for obstacle avoidance aiming towards stable obstacle avoidance and force interaction. The input is modified to permit block decomposition into a strict positive real (SPR) block and a passive high-gain block. This modification suggested involves a velocity-dependent potential-like repulsive force action from the obstacle. Stability proofs using Lyapunov theory and passivity theory as well as simulations demonstrate asymptotic stability, eliminating oscillatory or divergent behaviors.