On Angular Speed Estimation of Rigid Bodies

TL;DR

This paper introduces a novel observer for estimating the angular speed of rigid bodies from attitude measurements, simplifying analysis and ensuring stability without manifold constraints, with adaptations for systems on the unit circle.

Contribution

It presents a new observer design that simplifies angular speed estimation analysis and extends to systems on the unit circle, with proven stability guarantees.

Findings

Observer ensures global asymptotic stability.

Method is adaptable to systems on the unit circle.

Numerical simulations validate the approach.

Abstract

The problem of estimating the angular speed of a solid body from attitude measurements is addressed. To solve this problem, we propose an observer whose dynamics are not constrained to evolve on any specific manifold. This drastically simplifies the analysis of the proposed observer. Using Lyapunov analysis, sufficient conditions for global asymptotic stability of a set wherein the estimation error is equal to zero are established. In addition, the proposed methodology is adapted to deal with angular speed estimation for systems evolving on the unit circle. The approach is illustrated through several numerical simulations.