Proportional-derivative energy-based control for manipulator using normalized quasi-velocities

Abstract

This paper presents a proportional-derivative (PD) controller for rigid manipulators whose dynamics is expressed in terms of the normalized quasi-velocities (NQV) described by Jain and Rodriguez. It is shown that using the NQV it is possible to shape the kinetic energy reduction of the manipulator and at the same time to realize the PD control in its joint space. The energy-based strategy gives an insight into the position control and allows a different method to be used instead of the classical PD controller in order to change the behaviour of the system. The controller uses quasi-velocities arising from a decomposition of the manipulator mass matrix. Its use yields a globally asymptotically stable closed-loop system. The performance of the controller is illustrated via experiment on a two-degree-of-freedom robot arm and in simulation on a three-degree-of-freedom spatial manipulator.