On the Construction of Kinematic Confidence Ellipsoids for Uncertain Spatial Displacements.

Advances in mechanism and machine science : proceedings of the 16th IFToMM World Congress 2023. Volume 1. International Federation for the Promotion of Mechanism and Machine Science. World Congress Pub Date : 2023-01-01 Epub Date: 2023-11-05 DOI:10.1007/978-3-031-45705-0_75

Zihan Yu, Qiaode Jeffrey Ge, Mark P Langer, Mona Arbab

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Abstract

This paper deals with the problem of estimating confidence regions of a set of uncertain spatial displacements for a given level of confidence or probabilities. While a direct application of the commonly used statistic methods to the coordinates of the moving frame is straight-forward, it is also the least effective in that it grossly overestimate the confidence region. Based on the dual-quaternion representation, this paper introduces the notion of the kinematic confidence ellipsoids as an alternative to the existing method called rotation and translation confidence limit (RTCL). An example is provided to demonstrate how the kinematic confidence ellipsoids can be computed.

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论为不确定的空间位移构建运动学置信椭圆体

本文讨论的问题是在给定置信度或概率水平下，估计一组不确定空间位移的置信区域。虽然将常用的统计方法直接应用于运动帧坐标是简单易行的，但它也是最无效的，因为它会严重高估置信区域。本文以双四元数表示法为基础，引入了运动学置信椭球的概念，以替代现有的旋转和平移置信极限（RTCL）方法。本文举例说明了如何计算运动学置信椭圆。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Advances in mechanism and machine science : proceedings of the 16th IFToMM World Congress 2023. Volume 1. International Federation for the Promotion of Mechanism and Machine Science. World Congress

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On the Construction of Kinematic Confidence Ellipsoids for Uncertain Spatial Displacements.