Exponentially Stable Regulation of Mechanical Systems to a Path

In this paper we consider the problem of path following control for fully-actuated mechanical systems using the technique of total energy shaping. To this end, a closed-loop potential function is designed which is minimised along the desired path. In addition, the kinetic energy is shaped to ensure that the trajectories of the system converge exponentially to the desired path. The design method is applied to a 2-DOF robotic manipulator and simulations are presented to demonstrate the closed-loop performance.