An error energy shaping interpretation of tracking controllers for mechanical systems

This paper interprets tracking control as shaping the energy of the error between the system trajectory and the reference trajectory. First, a notion of degenerate mechanical systems is introduced extending the ideas of kinetic energy, potential energy, and dissipation. These systems are based on Riemannian vector bundles to allow for degenerate kinetic energies. The familiar asymptotic stability results of mechanical systems are then extended to these degenerate mechanical systems. Asymptotic tracking is accomplished by choosing the control inputs to force the error to be a degenerate mechanical system.