论为不确定的空间位移构建运动学置信椭圆体

Zihan Yu, Qiaode Jeffrey Ge, Mark P Langer, Mona Arbab
{"title":"论为不确定的空间位移构建运动学置信椭圆体","authors":"Zihan Yu, Qiaode Jeffrey Ge, Mark P Langer, Mona Arbab","doi":"10.1007/978-3-031-45705-0_75","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":520223,"journal":{"name":"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","volume":"147 ","pages":"777-785"},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11392034/pdf/","citationCount":"0","resultStr":"{\"title\":\"On the Construction of Kinematic Confidence Ellipsoids for Uncertain Spatial Displacements.\",\"authors\":\"Zihan Yu, Qiaode Jeffrey Ge, Mark P Langer, Mona Arbab\",\"doi\":\"10.1007/978-3-031-45705-0_75\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>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.</p>\",\"PeriodicalId\":520223,\"journal\":{\"name\":\"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\",\"volume\":\"147 \",\"pages\":\"777-785\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11392034/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"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\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/978-3-031-45705-0_75\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2023/11/5 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"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","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/978-3-031-45705-0_75","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2023/11/5 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

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

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.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信