PD Control with Desired Gravity Compensation of Robotic Manipulators

Abstract

One of the simplest position controllers for robot manipula tors is the PD control with desired gravity compensation. The objective of this article is to review important aspects of this control scheme that are reported in the literature. We begin by showing the boundedness of solutions for the closed-loop system, and conditions for equilibrium uniqueness. The global asymptotic stability analysis provided by Takegaki and Arimoto (1981) is discussed in detail, as well as an alternative method that uses a strict Lyapunov function. The stability robustness of the control system against parametric uncertainties is also ad dressed. We show that interesting phenomena such as equilibria bifurcation can appear if the design procedure is violated. To overcome parametric uncertainties, we review an adaptive ver sion of the PD control with desired gravity compensation, and finally, we revise an extension of the controller to handle robots with elastic joints.