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

被引：64
|
作者：
Wang, Xiangke [1 ,2 ]
Han, Dapeng [3 ]
Yu, Changbin [2 ]
Zheng, Zhiqiang [1 ]
机构：
[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
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 389卷 / 02期
关键词：
Lie-group structure; Unit dual quaternion; Logarithmic mapping; Kinematic control; ATTITUDE-CONTROL PROBLEM; MOTIONS; DESIGN;
D O I：
10.1016/j.jmaa.2012.01.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
引用
收藏
页码：1352 / 1364
页数：13
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