1. The geometric structure of unit dual quaternion with application in kinematic control
- Author
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Wang, Xiangke, Han, Dapeng, Yu, Changbin, and Zheng, Zhiqiang
- Subjects
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GEOMETRIC analysis , *DUALITY theory (Mathematics) , *QUATERNIONS , *KINEMATICS , *APPROXIMATION theory , *EXPONENTIAL functions , *LIE groups , *LOGARITHMIC functions , *MATHEMATICAL mappings , *ERROR analysis in mathematics - Abstract
Abstract: 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. [Copyright &y& Elsevier]
- Published
- 2012
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