Robust Robot Controller Design Using Joint Position and Velocity Dependent Uncertainty Bound

In this paper, we present robust control laws for robot manipulators to track a desired trajectory in the presence of both parametric and unstructured uncertainties. The bound on parametric uncertainty is considered as a constant and the bound on unstructured uncertainty is supposed to include a linear combination of norms the joint position and velocity vectors. These robust control laws include a PD feedback part, a dynamic feedforward compensator with nominal robot parameters and two robust dynamic feedforward compensations for parametric and unstructured uncertainties. The stability of the closed-loop system is established by the Lyapunov function. The system with the first proposed control law is proved to be globally uniformly asymptotically stable (GUAS) and the system with the second control law is proved to have uniformly ultimately bounded (UUB) tracking error. The radius of the ultimate boundedness set is also calculated. The tracking performance of this approach is satisfactory as the simulations carried out on a planar manipulator show