Attitude Observation for Second Order Attitude Kinematics

TL;DR

This paper introduces a novel observer for estimating attitude and angular velocity of a rigid object using accelerometers and magnetometers, extending equivariant observer design to second order kinematics with proven stability.

Contribution

It proposes a new observer design leveraging second order kinematic models and multiple sensors, extending equivariant observer theory with stability proofs.

Findings

Observer achieves almost global asymptotic stability.

Simulation results demonstrate effective attitude estimation.

Method is useful when angular velocity data is unavailable.

Abstract

This paper addresses the problem of estimating the attitude and angular velocity of a rigid object by exploiting its second order kinematic model. The approach is particularly useful in cases where angular velocity measurements are not available and the attitude and angular velocity of an object need to be estimated from accelerometers and magnetometers. We propose a novel sensor modality that uses multiple accelerometers to measure the angular acceleration of an object as well as using magnetometers to measure partial attitude. We extend the approach of equivariant observer design to second order attitude kinematics by demonstrating that the special Euclidean group acts as a symmetry group on the system considered. The observer design is based on the lifted kinematics and we prove almost global asymptotic stability and local uniform exponential stability of the estimation error. The performance of the observer is demonstrated in simulation.