The geometric structure of unit dual quaternion with application in kinematic control

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:389

Article

Wang, Xiangke^1,2  Han, Dapeng³  Yu, Changbin²  Zheng, Zhiqiang¹ 

[1] Natl Univ Def Technol, Coll Mechatron & Automat, Changsha 410073, Hunan, Peoples R China

[2] Australian Natl Univ, Res Sch Engn, Canberra, ACT 0200, Australia

[3] Natl Univ Def Technol, Coll Aerosp & Mat Engn, Changsha 410073, Hunan, Peoples R China

关键词: Lie-group structure;    Unit dual quaternion;    Logarithmic mapping;    Kinematic control;   

DOI  :  10.1016/j.jmaa.2012.01.016

来源: Elsevier

【 摘 要 】

In this paper, the geometric structure, especially the Lie-group related properties, of unit dual quaternion is investigated. The exponential form of unit dual quaternion and its approximate logarithmic mapping are derived. Correspondingly, Lie-group and Lie-algebra on unit dual quaternions and the approximate logarithms are explored, respectively. Afterwards, error and metric based on unit dual quaternion are given, which naturally result in a new kinematic control model with unit dual quaternion descriptors. Finally, as a case study, a generalized proportional control law using unit dual quaternion is developed. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free