A bundle framework for observer design on smooth manifolds with symmetry
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Abstract
The article presents a bundle framework for nonlinear observer design on a manifold having a Lie group action. The group action on the manifold decomposes the manifold to a quotient structure and an orbit space, and the problem of observer design for the entire system gets decomposed to a design over the orbit (the group space) and a design over the quotient space. The emphasis throughout the article is on presenting an overarching geometric structure; the special case when the group action is free is given special emphasis. Gradient based observer design on a Lie group is given explicit attention. The concepts developed are illustrated by applying them on well known examples, which include the action of \(\mathbb{SO}(3)\) on \(\mathbb{R}^3 \setminus \{0\}\) and the simultaneous localisation and mapping (SLAM) problem.
Citation
@article{1941-4889_2021_2_247,
title = {A bundle framework for observer design on smooth manifolds with symmetry},
journal = {Journal of Geometric Mechanics},
volume = {13},
number = {2},
pages = {247-271},
year = {2021},
author = {Anant A. Joshi, D. H. S. Maithripala, Ravi N. Banavar},
}