A Globally Exponentially Convergent Immersion and Invariance Speed Observer for n Degrees of Freedom Mechanical Systems

The problem of velocity estimation for mechanical systems is of great practical interest. Although many partial solutions have been reported in the literature the basic question of whether it is possible to design a globally convergent speed observer for general n degrees of freedom mechanical systems remains open. In this paper an affirmative answer to the question is given by proving the existence of a 3n + 1-dimensional globally exponentially convergent speed observer. 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. Finally, the observer design scheme is illustrated on a 2-link planar robotic manipulator and is shown to be robust in the presence of uncertainties in the sensor measurements.