Robot manipulators output regulation: Position measurements approach

Abstract

In order to demonstrate exponential convergence for Mechanical Lagrangian Systems (when not all states are available to be measured), in this paper we present a controller based on nonlinear state estimation. The present methodology is based only in the joint velocities estimation of the robot manipulators. Its well known that in the case of robot manipulators, the optical incremental encoders are widely used to monitor joint position information. However, joint velocities can be measured only by processing of position data (by filtering or by state estimation). In this paper, we present a new method for velocity estimation of robotic joint by using only the position and the knowledge of the robot dynamics. The knowledge of system dynamics for the design of non linear observers (Luemberger-type for linear systems) is fundamental to define global stability. One of the main results is the Global Asymptotic Convergence of the system state estimates to their true values. Finally, in order to define exponential stability we used a particular Lyapunov function.