Design of a Discrete Time Observer for the Continuous Time Rotation Kinematics on $\mathbb{S}\mathbb{O}(3)$

TL;DR

This paper introduces a novel discrete-time observer for continuous-time rotation kinematics on SO(3), combining feedback integrators and attitude observer techniques to improve numerical integration on manifolds.

Contribution

It develops a discrete-time observer on SO(3) by modifying Mahony's attitude observer, enabling Euclidean numerical integration on the rotation group.

Findings

Effective discrete-time observer design for SO(3)

Improved numerical integration on manifolds

Combines feedback integrators with attitude observer concepts

Abstract

This report proposes a discrete time observer for the continuous time rigid body kinematics on the rotation group $\mathbb{S}\mathbb{O}(3)$. The work draws on two research schools - one by Chang based on feedback integrators for systems evolving on manifolds,and the other by Mahony, who proposed an observer for attitude dynamics. The discrete time observer is based on the modified dynamics of the Mahony observer for attitude dynamics, where the modification of the vector field enables numerical integration based on Euclidean schemes.