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file = {/home/dimitri/Nextcloud/Zotero/storage/WBUCWRPK/Fong and Spivak - 2018 - Seven Sketches in Compositionality An Invitation .pdf;/home/dimitri/Nextcloud/Zotero/storage/MT7MPULY/1803.html}
}
@article{sola2018_micro_lie_theor_state_estim_robot,
author = {Sol{\`a}, Joan and Deray, Jeremie and Atchuthan,
Dinesh},
title = {A Micro Lie Theory for State Estimation in Robotics},
journal = {CoRR},
year = {2018},
url = {http://arxiv.org/abs/1812.01537v7},
abstract = {A Lie group is an old mathematical abstract object
dating back to the XIX century, when mathematician
Sophus Lie laid the foundations of the theory of
continuous transformation groups. As it often
happens, its usage has spread over diverse areas of
science and technology many years later. In
robotics, we are recently experiencing an important
trend in its usage, at least in the fields of
estimation, and particularly in motion estimation
for navigation. Yet for a vast majority of
roboticians, Lie groups are highly abstract
constructions and therefore difficult to understand
and to use. This may be due to the fact that most of
the literature on Lie theory is written by and for
mathematicians and physicists, who might be more
used than us to the deep abstractions this theory
deals with. In estimation for robotics it is often
not necessary to exploit the full capacity of the
theory, and therefore an effort of selection of
materials is required. In this paper, we will walk
through the most basic principles of the Lie theory,
with the aim of conveying clear and useful ideas,
and leave a significant corpus of the Lie theory
behind. Even with this mutilation, the material
included here has proven to be extremely useful in
modern estimation algorithms for robotics,
especially in the fields of SLAM, visual odometry,
and the like. Alongside this micro Lie theory, we
provide a chapter with a few application examples,
and a vast reference of formulas for the major Lie
groups used in robotics, including most jacobian
matrices and the way to easily manipulate them. We
also present a new C++ template-only library
implementing all the functionality described here.},
archivePrefix ={arXiv},
eprint = {1812.01537},
primaryClass = {cs.RO},
}
@book{stillwell2008_naive_lie_theor,
author = {John Stillwell},
title = {Naive Lie Theory},
year = 2008,
publisher = {Springer New York},
url = {https://doi.org/10.1007/978-0-387-78214-0},
DATE_ADDED = {Sat Oct 31 17:40:56 2020},
doi = {10.1007/978-0-387-78214-0},
pages = {nil},
series = {Undergraduate Texts in Mathematics},
}