Collocated Adaptive Control of Underactuated Mechanical Systems

TL;DR

This paper extends adaptive control methods to underactuated mechanical systems by introducing a fictitious control input, enabling stability and convergence analysis, validated through simulations and experiments.

Contribution

It introduces a novel approach using a fictitious control input to handle the nonlinear collocated dynamics in underactuated systems, extending existing adaptive control results.

Findings

Proves local stability and convergence for the proposed control scheme.

Validates the approach with simulations and experiments on a two-link manipulator.

Abstract

Collocated adaptive control of underactuated systems is still a main concern for the control community, all the more so because the collocated dynamics is no longer linear with respect to the constant base parameters. This work extends and encompasses the well known adaptive control result for fully actuated mechanical systems to the underactuated case. The key point is the introduction of a fictitious control input that allows us to consider the complete system dynamics, which is assumed to be linear with respect to the base parameters. Local stability and convergence of time varying reference trajectories for the collocated dynamics are demonstrated by using Lyapunov and Barbalat arguments. Simulation and experimental results on a two-link manipulator verify the soundness of the proposed approach.