A globally exponentially convergent immersion and invariance speed observer for mechanical systems with non-holonomic constraints

The problem of velocity estimation for general, n degrees-of-freedom, mechanical systems, is of great practical and theoretical interest. For unconstrained systems many partial solutions have been reported in the literature. However, even in this case, the basic question of whether it is possible to design a globally convergent speed observer remains open. In this paper, an affirmative answer to the question is given for general mechanical systems with k non-holonomic constraints, by proving the existence of a 3 n − 2 k + 1 -dimensional globally exponentially convergent speed observer. An observer for unconstrained mechanical systems is obtained as a particular case of this general result. Instrumental for the construction of the speed observer is the use of the Immersion and Invariance technique, in which the observer design problem is recast as a problem of rendering attractive and invariant a manifold defined in the extended state-space of the plant and the observer.