TY - JOUR
T1 - The geometric structure of unit dual quaternion with application in kinematic control
AU - Wang, Xiangke
AU - Han, Dapeng
AU - Yu, Changbin
AU - Zheng, Zhiqiang
PY - 2012/5/15
Y1 - 2012/5/15
N2 - 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.
AB - 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.
KW - Kinematic control
KW - Lie-group structure
KW - Logarithmic mapping
KW - Unit dual quaternion
UR - http://www.scopus.com/inward/record.url?scp=84862786385&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2012.01.016
DO - 10.1016/j.jmaa.2012.01.016
M3 - Article
SN - 0022-247X
VL - 389
SP - 1352
EP - 1364
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -