Composite Adaptive Disturbance Rejection in Robotics via Instrumental Variables based DREM

Abstract

In this paper we consider trajectory tracking problem for robotic systems affected by unknown external perturbations. Considering possible solutions, we restrict our attention to composite adaptation, which, particularly, ensures parametric error convergence being desirable to enhance overall stability and robustness of a closed-loop system. At the same time, existing composite approaches cannot simultaneously relax stringent persistence of excitation requirement and guarantee convergence of parametric error to zero for a perturbed scenario. So, a new composite adaptation scheme is proposed, which successfully overcomes mentioned problems of known counterparts and has several salient features. First, it includes a novel adaptive disturbance rejection control law for a general n-DoF dynamical model in the Euler-Lagrange form, which, without achievement of the parameter estimation goal, ensures global stability via application of a high-gain external torque observer augmented with some adaptation law. Secondly, such law is extended with a composite summand derived via the recently proposed Instrumental Variables based Dynamic Regressor Extension and Mixing procedure, which relaxes excitation conditions and ensures asymptotic parameter estimation and reference tracking in the presence of external torque under some non-restrictive assumptions. An illustrative example shows the effectiveness and superiority of the proposed approach in comparison with existing solutions.