Global stabilization of uncertain mechanical systems with bounded controls

This paper considers the problem of globally stabilizing a mechanical system with unknown potential and inertial structure and without the need for velocity measurements or large forces. We first consider two large classes of dynamical controllers and show that in a sense the goals of stabilization without system details and without velocity measurement is incompatible with the requirement of global stabilization without large forces. To solve this problem we turn to a hybrid strategy where we combine an effective stabilization strategy using bounded controls with a semiglobal large force PID-type controller.