A New Repetitive Control Framework for Robot Manipulators: Optimal Controller Design and Stability Analysis

Abstract

This paper provides a new repetitive control framework for robot manipulators with periodic reference and disturbance signals. We first take the inverse dynamics (ID) approach to a robot manipulator to transform its nonlinear input/output behavior into an equivalent linear time-invariant (LTI) system, for which the conventional repetitive control strategy is employed. To facilitate an optimal controller synthesis and an associated stability analysis, we next derive the so-called delay-feedback system. We then provide two linear matrix inequality (LMI)-based optimal controller synthesis procedures for minimizing the H_infty and the generalized H_2 norms from the disturbance to the tracking error, respectively. We next established operator-theoretic stability assertions in terms of the monodromy operator. In particular, a necessary and sufficient condition for the exponential stability of the delay-feedback system is derived for the case without external disturbances and we show that the delay-feedback system is input-to-state stable if it is exponentially stable. Finally, experiment comparisons are given to demonstrate the overall developed arguments.