Model Predictive Tracking Control for Invariant Systems on Matrix Lie Groups via Stable Embedding into Euclidean Spaces

TL;DR

This paper develops a model predictive tracking control method for systems on manifolds by embedding them into Euclidean spaces, simplifying controller design and demonstrated on rigid body attitude control.

Contribution

It introduces a stable embedding approach into Euclidean spaces for model predictive control of manifold systems, enabling global coordinate-based design.

Findings

Effective control design on manifolds via Euclidean embedding

Successful application to rigid body attitude control

Simplifies controller synthesis for systems on complex geometries

Abstract

For controller design for systems on manifolds embedded in Euclidean space, it is convenient to utilize a theory that requires a single global coordinate system on the ambient Euclidean space rather than multiple local charts on the manifold or coordinate-free tools from differential geometry. In this article, we apply such a theory to design model predictive tracking controllers for systems whose dynamics evolve on manifolds and illustrate its efficacy with the fully actuated rigid body attitude control system.