On the method of energy shaping via static output feedback for stabilization of mechanical systems

We develop theory of energy shaping via static output feedback to asymptotically stabilize mechanical systems. We first obtain matching conditions for equivalence via static output feedback of two given controlled mechanical systems. We then show that potential shaping is a special case of energy shaping via output feedback. Finally, we discover a class of mechanical systems that can be asymptotically stabilized by the potential shaping method. This class includes underactuated robots with elastic joints.