Robust globally exponentially stable control for mechanical systems in free/constrained-motion tasks

In this paper, we address the global exponential stability problem of perturbed mechanical systems in free-motion and interacting with passive environments. Particularly, we are interested in incorporating an exponentially stable response to a robust passivity-based control design. We formulate and analyse the stability of the proposed controllers based on the port-Hamiltonian framework. One of the novelties of the presented control design, is that exponential stability is achieved without removing the natural non-linearity of the mechanical system. To the best of our knowledge, this is the first time an exponentially stable controller is reported with this passivity-based method.