Robust point stabilization of underactuated mechanical systems via the extended chained form

This paper addresses point stabilization for the extended chained form (ECF), a control system that may be used to model a number of mechanical underactuated systems. A control law is proposed, based on well-known hybrid open-loop/feedback techniques, which exponentially stabilizes the origin of a dynamic extension of the ECF and ensures a degree of robustness to additive disturbance terms that may represent, for instance, model uncertainties. Numerical simulations are included to illustrate the performance of the presented stabilizers.