Parameter Estimation and Adaptive Control of Euler-Lagrange Systems Using the Power Balance Equation Parameterization

TL;DR

This paper introduces a simplified parameter estimation and adaptive control method for Euler-Lagrange systems based on the power balance equation, overcoming excitation challenges with a novel regressor generation technique, demonstrated through robot simulations.

Contribution

It presents a new online parameter estimation approach using power balance equation parameterization combined with a regressor excitation method for Euler-Lagrange systems.

Findings

Simpler adaptive control design avoiding Coriolis and centrifugal terms

Successful application to a 2-DOF robot manipulator

Enhanced parameter estimation with practical excitation requirements

Abstract

It is widely recognized that the existing parameter estimators and adaptive controllers for robot manipulators are extremely complicated to be of practical use. This is mainly due to the fact that the existing parameterization includes the complicated signal and parameter relations introduced by the Coriolis and centrifugal forces matrix. In an insightful remark of their seminal paper Slotine and Li suggested to use the parameterization of the power balance equation, which avoids these terms -- yielding significantly simpler designs. To the best of our knowledge, such an approach was never actually pursued in on-line implementations, because the excitation requirements for the consistent estimation of the parameters is ``very high". In this paper we use a recent technique of generation of ``exciting" regressors developed by the authors to overcome this fundamental problem. The result is applied to general Euler-Lagrange systems and the fundamental advantages of the new parameterization are illustrated with comprehensive simulations of a 2 degrees-of-freedom robot manipulator.