Velocity observer based controller design for second order systems, with application to constrained robotic systems

In this note two related problems for stabilization of a class of Lipschitz nonlinear systems are considered. (1) observer design for the estimation of system states (2) observer based controller design which consists of two parts: observer part that estimates system states from the measured ones and a linear feedback part that utilizes these estimated states. A Lyapunov-based stability analysis is developed to show that this computationally efficient controller results in global asymptotic stability of the estimation and tracking error. An interesting feature of the developed method is that it can be used for a wide class of mechanical systems including serial and parallel robotic systems with kinematic constraints. Numerical validations of the proposed method on a slider crank as a sample of constrained robotic systems is presented.