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