{"title":"Unveiling $SO(3)$ Parallel Robot Variants: Application of the Optimal Robot to a Humanoid Eye","authors":"Hassen Nigatu;Jihao Li;Gaokun Shi;Jianguo Wang;Guodong Lu;Howard Li;Huixu Dong","doi":"10.1109/LRA.2025.3606380","DOIUrl":null,"url":null,"abstract":"This study presents a systematic motion analysis and classification of <inline-formula><tex-math>$SO(3)$</tex-math></inline-formula>-type parallel robot variants using an analytical Lie algebra approach. These robots are known for their ability to perform arbitrary rotations around a fixed point, making them suitable for various applications. Despite their architectural diversity, existing research has largely treated them on a case-by-case basis, limiting the exploration of all potential variants and the benefits derived from this diversity. By applying a generalized analytical approach through the reciprocal screw method, we systematically examine the kinematic conditions for limbs that generate <inline-formula><tex-math>$SO(3)$</tex-math></inline-formula> motion. As a result, we identify 73 distinct non-redundant limb types capable of producing the desired <inline-formula><tex-math>$SO(3)$</tex-math></inline-formula> motion. Our approach includes an in-depth algebraic motion-constraint analysis, uncovering common characteristics across different variants. This leads us to identify 73 symmetric and 5,256 asymmetric variants, for a total of 5,329, each with unique capabilities. Finally, we selected a computationally optimized, miniaturized robot from this set for use in a humanoid eye system.","PeriodicalId":13241,"journal":{"name":"IEEE Robotics and Automation Letters","volume":"10 11","pages":"11227-11234"},"PeriodicalIF":5.3000,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IEEE Robotics and Automation Letters","FirstCategoryId":"94","ListUrlMain":"https://ieeexplore.ieee.org/document/11151208/","RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ROBOTICS","Score":null,"Total":0}
引用次数: 0
Abstract
This study presents a systematic motion analysis and classification of $SO(3)$-type parallel robot variants using an analytical Lie algebra approach. These robots are known for their ability to perform arbitrary rotations around a fixed point, making them suitable for various applications. Despite their architectural diversity, existing research has largely treated them on a case-by-case basis, limiting the exploration of all potential variants and the benefits derived from this diversity. By applying a generalized analytical approach through the reciprocal screw method, we systematically examine the kinematic conditions for limbs that generate $SO(3)$ motion. As a result, we identify 73 distinct non-redundant limb types capable of producing the desired $SO(3)$ motion. Our approach includes an in-depth algebraic motion-constraint analysis, uncovering common characteristics across different variants. This leads us to identify 73 symmetric and 5,256 asymmetric variants, for a total of 5,329, each with unique capabilities. Finally, we selected a computationally optimized, miniaturized robot from this set for use in a humanoid eye system.
期刊介绍:
The scope of this journal is to publish peer-reviewed articles that provide a timely and concise account of innovative research ideas and application results, reporting significant theoretical findings and application case studies in areas of robotics and automation.