On the globally exponentially convergent immersion and invariance speed observer for mechanical systems

In this article we present a reformulation of the invariance and immersion speed observer of Astolfi et al. as applied to mechanical systems with bounded inertia matrices. This is done to explore the possibility of its practical implementation e.g. for 6 degrees-of-freedom industrial robots. The reformulation allows us find an explicit expression for one of the bounds used in the observer, and a constructive method for the second. We show that the observer requires either analytically or numerically solving at most 2n2 integrals, where n is the number of generalized coordinates in the mechanical system.