Neural Robust Control on Lie Groups Using Contraction Methods (Extended Version)

TL;DR

This paper introduces a framework combining neural networks and contraction metrics to design robust controllers for systems on Lie groups, demonstrated on quadrotor control.

Contribution

It presents a novel joint training method for neural controllers and contraction metrics respecting Lie group geometry, with theoretical guarantees.

Findings

Successfully designed a neural feedback controller for a quadrotor.

The controller enforces contraction conditions on the Lie group manifold.

Numerical simulations show improved robustness compared to geometric controllers.

Abstract

In this paper, we propose a learning framework for synthesizing a robust controller for dynamical systems evolving on a Lie group. A robust control contraction metric (RCCM) and a neural feedback controller are jointly trained to enforce contraction conditions on the Lie group manifold. Sufficient conditions are derived for the existence of such an RCCM and neural controller, ensuring that the geometric constraints imposed by the manifold structure are respected while establishing a disturbance-dependent tube that bounds the output trajectories. As a case study, a feedback controller for a quadrotor is designed using the proposed framework. Its performance is evaluated using numerical simulations and compared with a geometric controller.