Degenerate Mechanical Systems A Framework for Tracking Control

This paper interprets tracking control as shaping the energy of the error between the system trajectory and the desired trajectory. A notion of "degenerate mechanical systems" is developed by extending the ideas of kinetic energy, potential energy, and dissipative forces to allow for the existence of nonzero velocities with zero kinetic energy. Some familiar stability results of mechanical systems can be extended to these degenerate mechanical systems, and tracking is accomplished by choosing control inputs to force the error to be a degenerate mechanical system. While techniques for tracking control like PD+ often require known bounds on the velocity of the desired trajectory, the emphasis on geometric structures here reveals how certain designs can result in guarantees on the convergence rate and disturbance rejection properties independent of any a priori bounds on the velocity of the desired trajectory.