Design of Robust PD-Type Control Laws for Robotic Manipulators with Parametric Uncertainties

In this paper, design of a simple robust control law that achieves desired positions and orientations for robotic manipulators with parametric uncertainties is studied. A discontinuous control law is proposed, which consists of a high gain linear proportional plus derivative (PD) term and additional terms that compensate for the effect of gravitation. The stability of the robotic system under the proposed control law is proved by LaSalle´s stability theorem. Furthermore, by the theory of singularly perturbed systems, it is shown that if the proportional and derivative gain matrices are diagonal with large positive elements, then the system is decoupled into a set of first-order linear systems.