Continuous globally exponential rigid-body angular velocity estimation from attitude measurements

TL;DR

This paper introduces a continuous observer for rigid-body angular velocity estimation from attitude measurements, achieving global exponential convergence with a simple design and straightforward stability proof.

Contribution

The novel observer is designed directly on Euclidean space, simplifying the structure and stability analysis compared to geometry-based approaches.

Findings

The observer guarantees uniform global exponential convergence.

Simulation results demonstrate effective angular velocity estimation.

The design simplifies stability analysis and implementation.

Abstract

A continuous solution is proposed to the problem of uniform global exponential estimation of the angular velocity for rigid bodies by means of direct attitude measurements. The proposed observer is designed on $\mathbb{R}^3\times\mathbb{R}^3\times\mathbb{R}^3$, and not on the inherent geometry $\mathtt{SO}(3)\times\mathbb{R}^3$, which allows for a simple structure of the observer, being a copy of the system plus some correction terms, and a straightforward classical Lyapunov stability proof. The performances of the observer are illustrated by means of a simple simulation scenario.