Exponentially Stable Projector-based Control of Lagrangian Systems with Gaussian Processes

TL;DR

This paper introduces a novel projector-based control method for uncertain Lagrangian systems using Gaussian Processes, providing probabilistic stability guarantees and demonstrating effectiveness through simulations on robotic manipulators.

Contribution

The paper develops a structure-preserving control law for Lagrangian systems that incorporates Gaussian Process uncertainty quantification with explicit stability guarantees.

Findings

Proven exponential stability with probabilistic guarantees.

Validated control performance on robotic manipulators.

Explicit convergence rate and radius expressions.

Abstract

Designing accurate yet robust tracking controllers with tight performance guarantees for Lagrangian systems is challenging due to nonlinear modeling uncertainties and conservative stability criteria. This article proposes a structure-preserving projector-based tracking control law for uncertain Euler-Lagrange (EL) systems using physically consistent Lagrangian-Gaussian Processes (L-GPs). We leverage the uncertainty quantification of the L-GP for adaptive feedforward-feedback balancing. In particular, an accurate probabilistic guarantee for exponential stability is derived by leveraging matrix analysis results and contraction theory, where the benefit of the proposed controller is proven and shown in the closed-form expressions for convergence rate and radius. Extensive numerical simulations not only demonstrate the controller's efficacy based on a two-link and a soft robotic manipulator but also all theoretical results are explicitly analyzed and validated.