On Deterministic Attitude Observers on the Special Orthogonal Group SO(3)

TL;DR

This paper analyzes and compares smooth and non-smooth gradient-based attitude observers on SO(3), providing explicit error dynamics solutions and demonstrating the superior stability and convergence of non-smooth filters.

Contribution

It offers explicit solutions for attitude estimation error dynamics and compares stability and performance of smooth versus non-smooth observers on SO(3).

Findings

Non-smooth observers are Input-to-State-Stable (ISS) under disturbances.

Non-smooth filters show faster convergence rates.

Smooth filters lack ISS with bounded disturbances.

Abstract

We revisit the gradient based nonlinear attitude complementary filters (observers) on the Special Orthogonal group SO(3) and provide explicit solutions of the norm of the attitude estimation error dynamics. One smooth and two non-smooth attitude observers are considered. The stability and performance properties of theses attitude observers can be easily deduced from the obtained explicit solutions. We show that the smooth complementary attitude filter, previously proposed in the literature, is not Input-to-State-Stable (ISS) with respect to bounded measurement disturbances while the non-smooth versions are. We also show that the non-smooth versions of the attitude complementary filter exhibit better convergence rates. Some simulations are provided to illustrate our results.