Position–feedback Stabilization of Mechanical Systems with Underactuation Degree One

We consider in this paper the problem of (asymptotic) stabilization, via position feedback, of mechanical systems with underactuation degree one. A full state–feedback design is first derived applying Interconnection and Damping Assignment PassivityBased Control to which an Immersion and Invariance speed estimator is then added. The technique is applied to obtain an (almost) globally stabilizing scheme for the vertical takeoff and landing aircraft with strong input coupling, and a controller for the chariot with the pendulum that can swing–up the pendulum from any position in the upper half plane and stop the chariot at any desired location. In both cases we obtain very simple and intuitive position–feedback solutions that do not rely on, rather unnatural and technique– driven, linearization or decoupling procedures but instead endows the closed–loop system with a Hamiltonian structure with desired potential and kinetic energy functions.