Proceedings of MSR-RoManSy 2024 : combined IFToMM Symposium of RoManSy and USCToMM Symposium on Mechanical Systems and Robotics. MSR-RoManSy (Symposium) (2024 : Saint Petersburg, Fla.)最新文献
Q Jeffrey Ge, Zihan Yu, Anurag Purwar, Mark P Langer
{"title":"Constructing Kinematic Confidence Regions With Double Quaternions.","authors":"Q Jeffrey Ge, Zihan Yu, Anurag Purwar, Mark P Langer","doi":"10.1007/978-3-031-60618-2_18","DOIUrl":"10.1007/978-3-031-60618-2_18","url":null,"abstract":"<p><p>A spatial displacement as an element of <math><mrow><mi>SE</mi> <mo>(</mo> <mn>3</mn> <mo>)</mo></mrow> </math> can be approximated by a 4D rotation, which is an element of <math><mrow><mi>SO</mi> <mo>(</mo> <mn>4</mn> <mo>)</mo></mrow> </math> . In this way, the problem of constructing confidence regions of uncertain spatial displacements may be studied as that of constructing confidence ellipsoids in <math><mrow><mi>SO</mi> <mo>(</mo> <mn>4</mn> <mo>)</mo></mrow> </math> . In this light, a double-quaternion formulation of kinematic confidence regions is presented that approximately preserve the geometry of <math><mrow><mi>SE</mi> <mo>(</mo> <mn>3</mn> <mo>)</mo></mrow> </math> . Examples are provided to demonstrate the efficacy of this approach in comparison with the dual-quaternion formulation.</p>","PeriodicalId":520092,"journal":{"name":"Proceedings of MSR-RoManSy 2024 : combined IFToMM Symposium of RoManSy and USCToMM Symposium on Mechanical Systems and Robotics. MSR-RoManSy (Symposium) (2024 : Saint Petersburg, Fla.)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11380430/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142157156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}