L1 robustness of computed torque method for robot manipulators

Abstract

This paper revisits computed torque method for robot manipulators and aims at developing its new framework based on the L1 robustness, in which the L∞ norm together with its induced norm is employed to characterize model uncertainties and a performance measure. More precisely, we consider the L1 robust stability and performance for a given robot manipulator with a computed torque controller. We first show that the modelling errors in the computed torque method can be divided into an exogenous disturbance and a multiplicative model uncertainty, which are bounded in terms of the L∞ norm and its induced norm, respectively. It is next shown that the robot manipulator with the computed torque controller can be equivalently represented by an interconnection of a continuous-time linear time-invariant (LTI) nominal plant and a stabilizing controller together with the L∞-induced norm bounded model uncertainty. Based on the interconnected representation, the L1 robust stability condition and an upper bound of the L1 performance against the exogenous disturbance with respect to all model uncertainties in a class of a bounded L∞-induced norm are dealt with by using the small-gain theorem. Finally, the effectiveness of the theoretical results is demonstrated through some experiment results. ？ 2018 IEEE.