GUARANTEED RATES OF CONVERGENCE OF A CLASS OF PD CONTROLLERS FOR TRAJECTORY TRACKING PROBLEMS OF ROBOTIC MANIPULATORS WITH DYNAMIC UNCERTAINTIES

The paper provides a better understanding of the behaviour of a class of simple proportional plus derivative (PD) controllers applied to rob otic manipulators and to highlight some useful design criteria. stabil ity and robustness of PD controllers for trajectory tracking problems of robotic manipulators with dynamic uncertainties is investigated. Ba sed on LyaDunov's second method it is shown that the composite velocit y and position tracking error vector is guaranteed to exponentially co nverge from any initial condition to a closed ball, defined by its L(2 ) norm being less than a certain threshold provided that the PD contro ller gains are chosen greater than a specific bound depending on the d ynamic parameters, desired trajectories and levels of external disturb ances. Moreover, the size of the ball can be made arbitrarily small by increasing the controller gains wherever appropriate and possible. As a result, both transient and steady-state performance of the simple P D controllers for trajectory tracking is assured.