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Optimal Statistical Operators for 3-Dimensional Rotational Data: Geometric Interpretations and Application to Prosthesis Kinematics

机译：三维旋转数据的最优统计算子：几何解释及其在修复运动学中的应用

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Rotational data in the form of measured three-dimensional rotations or orientations arise naturally in many fields of science, including biomechanics, orthopaedics and robotics. The cyclic topology of rotation spaces calls for special care and considerations when performing statistical analysis of rotational data. Relevant theory has been developed during the last three decades, and has become a standard tool in some areas. In relation to the study of human kinematics and motion however, these concepts have hardly been put to use. This paper gives an introduction to the intricacies of three-dimensional rotations, and provides a thorough geometric interpretation of several approaches to averaging rotational data. A set of novel, simple operators is presented. Simulations and a prosthetics-related real-world example involving wrist kinematics illuminate important aspects of the results. Finally generalizations and related subjects for further research are suggested.
机译：以测量的三维旋转或方向形式出现的旋转数据在许多科学领域自然而然地出现，包括生物力学，骨科学和机器人技术。旋转空间的循环拓扑在进行旋转数据的统计分析时需要特别注意和考虑。相关理论在过去的三十年中得到了发展，并已成为某些领域的标准工具。然而，关于人体运动学和运动的研究，这些概念几乎没有被使用。本文介绍了三维旋转的复杂性，并对几种平均旋转数据的方法进行了详尽的几何解释。提出了一组新颖，简单的运算符。模拟和与假肢相关的真实世界实例（涉及手腕运动学）阐明了结果的重要方面。最后提出了概括和相关主题，以供进一步研究。

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