Potential and kinetic shaping for control of underactuated mechanical systems

This paper combines techniques of potential shaping with those of kinetic shaping to produce some new methods for stabilization of mechanical control systems. As with each of the techniques themselves, our method employs the energy methods and LaSalle's invariance principle. We give explicit criteria for asymptotic stabilization of equilibria of mechanical systems which, in the absence of controls, have a kinetic energy function that is invariant under an Abelian group.