Stability analysis of an adaptive controller for robotic manipulators

Abstract

The stability analysis of an adaptive control scheme for robotic manipulators, originally introduced by Horowitz and Tomizuka (1980). is presented in this paper. In the previous stability proof it was assumed that the manipulator parameter variation is negligible compared with the speed of adaptation. I t isshown that this key assumption can be removed by introducing two modifications in the adaptive control scheme: 1. Reparametrizing the nonlinear terms in dynamic equations as linear functions of unknown but constant terms. 2. Defining the Coriolis compensation term in the control law as a bilinear function of the manipulator and model reference jointvelocities, instead o f a quadratic function of the manipulator joint velocities. The modified adaptive control scheme is shown to be globally asymptotically stable.

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Passivity-based tracking control of multiconstraint complementarity Lagrangian systems

“…In the sequel U nc coincides with the fixed-parameter controller proposed in [20,21] and the closed-loop stability analysis of the system is based on Proposition 1. First, let us introduce some notations:…”

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