Global stability of trajectory tracking of robot underPD control

It is shown for the first time that, even if there exist nonlinear unknown dynamics, aPD feedback control without higher-order nonlinear compensation can guarantee global stability for the trajectory following problem of a robot manipulator. ThePD control under investigation is a position and velocity feedback control with a time-varying gain, and does not contain any higher-order nonlinearity. The proposed control is in general continuous and does not require any knowledge of robotic systems except size bounding function on nonlinear dynamics. Asymptotic stability of velocity tracking error and arbitrarily small position tracking error are guaranteed. Another novel and interesting result shown in this paper is that a measure on protection against saturation of actuators has been incorporated into consideration of control design and robustness analysis.This work is supported in part by U.S. National Science Foundation under grant MSS-9110034.