On the Design of Hybrid Pose and Velocity-bias Observers on Lie Group SE(3)

TL;DR

This paper introduces a hybrid observer design on SE(3) that ensures global exponential stability for pose and velocity-bias estimation, with a decoupled rotational-translational error dynamic beneficial for noisy data.

Contribution

It presents a generic hybrid observer scheme on SE(3) based on a potential function, explicitly formulated with inertial vectors and landmarks, and featuring decoupled rotational and translational error dynamics.

Findings

Observer achieves global exponential stability.

Decoupled rotational and translational error dynamics.

Applicable to noisy measurements and disturbances.

Abstract

This paper deals with the design of globally exponentially stable invariant observers on the Special Euclidian group SE(3). First, we propose a generic hybrid observer scheme (depending on a generic potential function) evolving on $SE(3)\times \mathbb{R}^6$ for pose (orientation and position) and velocity-bias estimation. Thereafter, the proposed observer is formulated explicitly in terms of inertial vectors and landmark measurements. Interestingly, the proposed observer leads to a decoupled rotational error dynamics from the translational dynamics, which is an interesting feature in practical applications with noisy measurements and disturbances.