Time-scale separation of a class of robust PD-type tracking controllers for robot manipulators

In this paper, the trajectory tracking control of robot manipulators is studied from the theoretical and practical point of view. By using the theory of singularly perturbed systems, a class of PD-type robust controllers is introduced. Our analysis departs from parameterizing the proportional and derivative gains with a perturbing parameter. We prove that the smaller the value of perturbing parameter, the smaller the ultimate bound of the joint position tracking error. Derived from the introduced analysis, two forms of extending the proposed class of controllers are discussed. In one, error-varying PD gains are considered while in the another one, a dynamic extension to avoid joint velocity measurements is incorporated. An experimental study in a planar two degrees-of-freedom direct-drive robot is also presented. Under similar implementation conditions, four controllers are tested. The best performance is obtained for a nonlinear PD controller derived from the proposed class of controllers.