Robust Control for the Tracking of Robot Motion

In this paper, we examine the stability of a Proportional Derivative (PD) controller for the trajectory following problem of a robot manipulator. We use Lyapunov's second method to derive a uniform boundness result for the PD controller. We show that if the PD controller gains are chosen greater than a specific bound and if the Initial tracking error is zero, the velocity and position tracking errors are uniformly bounded. We then develop two additional controllers that use auxiliary control inputs along with the PD controller. Both of these controllers are shown to yield a uniform ultimate boundness property for the tracking error.