A Central Synergistic Hybrid Approach for Global Exponential Stabilization on SO(3)

TL;DR

This paper introduces a novel hybrid control method for achieving global exponential stabilization of systems on SO(3), utilizing a central family of potential functions with specific quadratic and synergistic properties.

Contribution

It presents a new switching control approach based on non-differentiable potential functions that ensure global exponential stability on SO(3).

Findings

Achieves global exponential stability for attitude control.

Introduces a new class of potential functions with quadratic and synergistic properties.

Demonstrates effectiveness in attitude tracking problems.

Abstract

We propose a new central synergistic hybrid approach for global exponential stabilization on the Special Orthogonal group SO(3). We introduce a new switching concept relying on a central family of (possibly) non-differentiable potential functions that enjoy (as well as their gradients) the following properties: 1) being quadratic with respect to the Euclidean attitude distance, and 2) being synergistic with respect to the gradient's singular and/or critical points. The proposed approach is used to solve the attitude tracking problem, leading to global exponential stability results.