Hybrid Attitude Observer on SO(3) with Global Asymptotic Stability

TL;DR

This paper introduces a hybrid attitude observer for rigid body dynamics on SO(3) that guarantees global asymptotic stability and improves convergence rates over traditional smooth observers.

Contribution

A novel hybrid attitude observer is proposed that overcomes topological limitations, ensuring global stability and faster convergence.

Findings

Demonstrates improved convergence rates in simulations

Guarantees global asymptotic stability

Outperforms smooth observers in initial convergence speed

Abstract

This paper presents a deterministic hybrid observer for the attitude dynamics of a rigid body that guarantees global asymptotical stability. Any smooth attitude observer suffers from the inherent topological restriction that it is impossible to achieve global attractivity, and as such, attitude observers have been developed with almost global asymptotic stability. We demonstrate that such attitude observer may yields very slow initial convergence rates, and motivated by this, we propose a hybrid attitude observer that guarantees global asymptotic stability on the special orthogonal group. We illustrate that the proposed observer exhibits substantially improved convergence rate uniformly via numerical examples and experiments.