Adaptive Control for Nonlinearly Parameterized Uncertainties in Robot Manipulators

In this brief, a new adaptive control framework to compensate for uncertain nonlinear parameters in robot manipulators is developed. The designed adaptive controllers possess a linear parameter structure, guarantee global boundedness of the closed-loop system as well as tracking of a given trajectory within any prescribed accuracy. Our design approach takes advantage of a Lipschitzian property with respect to the plant nonlinear parameters. The outcome is that a very broad class of nonlinearly parameterized adaptive control problems for robot manipulators can be solved using this technique. Another feature of the proposed method is the design of low-dimensional estimator, even 1-D if desired, independently of the unknown parameter vector dimension. Simulations and experiments in friction compensation task for low-velocity tracking of a 2 degree-of-freedom planar robot demonstrate the viability of the technique and emphasize its advantages relatively to more classical approaches.

I. Introduction

The ORIGINAL and popular adaptive control theory usually deals with linear parameterizations (LP) of uncertainties, that is, it is assumed that uncertain quantities in dynamic systems are expressed linearly with respect to unknown parameters. Actually, most developed approaches such as gradient-based ones or recursive least squares [2], [11] rely heavily on this assumption. In the literature of robot control, most adaptive control techniques exploit the linear structure of manipulator dynamics [3] and effective techniques have been proposed in this context [11].