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A Reduced Parallel Transport Equation on Lie Groups with a Left-Invariant Metric

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Geometric Science of Information (GSI 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12829))

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Abstract

This paper presents a derivation of the parallel transport equation expressed in the Lie algebra of a Lie group endowed with a left-invariant metric. The use of this equation is exemplified on the group of rigid body motions SE(3), using basic numerical integration schemes, and compared to the pole ladder algorithm. This results in a stable and efficient implementation of parallel transport. The implementation leverages the python package and is available online.

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Acknowledgments

This work was partially funded by the ERC grant Nr. 786854 G-Statistics from the European Research Council under the European Union’s Horizon 2020 research and innovation program. It was also supported by the French government through the 3IA Côte d’Azur Investments ANR-19-P3IA-0002 managed by the National Research Agency.

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Authors and Affiliations

  1. Université Côte d’Azur and Inria, Epione Project Team, Sophia-Antipolis, France

    Nicolas Guigui & Xavier Pennec

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  1. Nicolas Guigui
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  2. Xavier Pennec
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Correspondence to Nicolas Guigui .

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Editors and Affiliations

  1. Sony Computer Science Laboratories Inc., Tokyo, Japan

    Frank Nielsen

  2. THALES Land & Air Systems, Meudon, France

    Frédéric Barbaresco

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Guigui, N., Pennec, X. (2021). A Reduced Parallel Transport Equation on Lie Groups with a Left-Invariant Metric. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_14

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  • DOI: https://doi.org/10.1007/978-3-030-80209-7_14

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