A globally exponentially stable tracking controller for mechanical systems using position feedback

Abstract : A solution to the problem of global exponential tracking of mechanical systems without velocity measurements is given in the technical note. The proposed controller is obtained combining a redesign of the recently reported exponentially stable immersion and invariance velocity observer and a new state-feedback passivity-based controller, which assigns to the closed-loop a port-Hamiltonian structure with a desired energy function. The result is applicable to a large class of mechanical systems including those with unbounded inertia matrix and possible presence of friction forces. Unlike previous results that rely on the presence-exact knowledge and pervasiveness-of these forces, our design treats them as disturbances, which are suitably compensated.