Control of underactuated mechanical systems: Observer design and position feedback stabilization

We identify a class of mechanical systems for which a globally exponentially stable reduced order observer can be designed. The class is characterized by (the solvability of) a set of partial differential equations and contains all systems that can be rendered linear in (the unmeasurable) momenta via a (partial) change of coordinates. It is shown that this class is larger than the one reported in the literature of observer design and linearization. We also prove that, under very weak assumptions, the observer can be used in conjunction with an asymptotically stabilizing full state-feedback interconnection and damping assignment passivity-based controller, preserving stability. Caveat Emptor: This paper is a shortened version of the technical note [1] which can be obtained upon request from the authors.