{"title":"On the Computation of the Average of Planar Displacements.","authors":"Q Jeffrey Ge, Zihan Yu, Mona Arbab, Mark P Langer","doi":"10.1007/978-3-030-99826-4_20","DOIUrl":null,"url":null,"abstract":"<p><p>In this paper, we present four parametric representations of a planar displacements and studied the problem of how to compute the average displacement from a set of given planar displacements using these representations. It has been shown that the optimal average displacement is obtained by using planar quaternions and the concept of relative displacements. Examples are provided to show the comparisons of these methods.</p>","PeriodicalId":520225,"journal":{"name":"Proceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics. USCToMM Symposium on Mechanical Systems and Robotics (2nd : 2022 : Rapid City, S.D.)","volume":"118 ","pages":"232-242"},"PeriodicalIF":0.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11412073/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2022 USCToMM Symposium on Mechanical Systems and Robotics. USCToMM Symposium on Mechanical Systems and Robotics (2nd : 2022 : Rapid City, S.D.)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/978-3-030-99826-4_20","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2022/4/1 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this paper, we present four parametric representations of a planar displacements and studied the problem of how to compute the average displacement from a set of given planar displacements using these representations. It has been shown that the optimal average displacement is obtained by using planar quaternions and the concept of relative displacements. Examples are provided to show the comparisons of these methods.
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