Repetitive control of nonlinear systems via feedback linearization: An application to robotics

In this paper, a novel Repetitive Control (RC) scheme for a class of nonlinear systems is presented and discussed. This work generalizes the approach proposed in Biagiotti et al. (2015) where a RC scheme based on the modification of a B-spline reference trajectory has been presented. Also in this case, the generation of the B-splines based on dynamic filters plays a crucial role in the control scheme since it allows to implement a feedforward action that, coupled with an exact feedback linearization and a stabilizing state feedback, makes the RC robustly asymptotically stable. In this manner, the tracking error at the via-points defining the reference trajectory is nullified even if parametric uncertainties on the system model or exogenous (cyclic) disturbances are present. The application to a two-dof robot manipulator shows the effectiveness of the proposed method and its inherent robustness.