Trajectory tracking control of mechanical systems with obstacle avoidance

This paper addresses a trajectory tracking problem of obstacle avoidance in mechanical systems. Our strategy for obstacle avoidance is based on a field potential method using an existing navigation function. However, direct application of this function to trajectory tracking can hinder obstacle avoidance. To overcome this problem, we newly introduce a parameterized function representing a reference trajectory, and propose a feedback law to control this parameter, thereby ensuring effective obstacle avoidance. Successful trajectory tracking is achieved by the convergence of the coordinates of the systems to the parameterized function. Because our method adopts a bounded navigation function, the proposed controller produces a bounded input signal even when the coordinates approach obstacles. Finally, a simulation of a two-link manipulator illustrates the effectiveness of the proposed method.