Trace inequalities and kinematic metrics
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Robotica
Abstract
Kinematics remains one of the cornerstones of robotics, and over the decade, Robotica has been one of the venues in which groundbreaking work in kinematics has always been welcome. A number of works in the kinematics community have addressed metrics for rigid-body motions in multiple different venues. An essential feature of any distance metric is the triangle inequality. Here, relationships between the triangle inequality for kinematic metrics and so-called trace inequalities are established. In particular, we show that the Golden-Thompson inequality (a particular trace inequality from the field of statistical mechanics) which holds for Hermitian matrices remarkably also holds for restricted classes of real skew-symmetric matrices. We then show that this is related to the triangle inequality for SO(3) and SO(4) metrics.
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This article was originally published in Robotica. The version of record is available at: https://doi.org/10.1017/S0263574724000778.
© The Author(s), 2024. Published by Cambridge University Press.
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided that no alterations are made and the original article is properly cited. The written permission of Cambridge University Press must be obtained prior to any commercial use and/or adaptation of the article.
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Y. Wu and G. S. Chirikjian, “Trace inequalities and kinematic metrics”, Robotica. https://doi.org/10.1017/S0263574724000778
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Except where otherwised noted, this item's license is described as Attribution-NonCommercial-NoDerivatives 4.0 International