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

页码：1352 / 1364

页数：13

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