Stabilization of position or uniform motion of mechanical systems via bounded control and without velocity measurements

Abstract

This paper contains two theoretical contributions. Firstly, it is shown that the constant program position of nonlinear Lagrangian system may be globally asymptotically stabilized by dynamic feedback admitting the saturation and not using the velocity measurements. Secondly, it is proved that the uniform motion of Lagrangian system may be stabilized by very computationally simple dynamic feedback not using the velocity measurements. Barbashin theorem on asymptotic stability has been used as tool for demonstration of asymptotic stability. The results may be applied to the stabilization of robots with absolutely rigid links and overhead cranes.