迹不等式和运动学度量

IF 1.9 4区 计算机科学 Q3 ROBOTICS Robotica Pub Date : 2024-09-12 DOI:10.1017/s0263574724000778
Yuwei Wu, Gregory S. Chirikjian
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引用次数: 0

摘要

运动学仍然是机器人学的基石之一,十年来,Robotica 一直是运动学领域开创性工作受到欢迎的场所之一。运动学领域的许多工作都在多个不同的场合探讨了刚体运动的度量问题。任何距离度量的一个基本特征都是三角形不等式。在这里,我们建立了运动学度量的三角形不等式与所谓的迹不等式之间的关系。特别是,我们证明了对赫米特矩阵成立的 Golden-Thompson 不等式(统计力学领域的一种特殊迹不等式)也明显地对受限制的实倾斜对称矩阵类成立。然后,我们证明这与 $SO(3)$ 和 $SO(4)$ 度量的三角形不等式有关。
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Trace inequalities and kinematic metrics

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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来源期刊
Robotica
Robotica 工程技术-机器人学
CiteScore
4.50
自引率
22.20%
发文量
181
审稿时长
9.9 months
期刊介绍: Robotica is a forum for the multidisciplinary subject of robotics and encourages developments, applications and research in this important field of automation and robotics with regard to industry, health, education and economic and social aspects of relevance. Coverage includes activities in hostile environments, applications in the service and manufacturing industries, biological robotics, dynamics and kinematics involved in robot design and uses, on-line robots, robot task planning, rehabilitation robotics, sensory perception, software in the widest sense, particularly in respect of programming languages and links with CAD/CAM systems, telerobotics and various other areas. In addition, interest is focused on various Artificial Intelligence topics of theoretical and practical interest.
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