On the relation between the exponential of real matrices and that of dual matrices

Dual number matrices play a significant role in engineering applications such as kinematics and dynamics. The matrix exponential is ubiquitous in screw-based kinematics. In this paper, we develop an explicit formula for the dual matrix exponential. The result is closely related to the Fréchet deriva...

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Vydáno v:Applied mathematics letters Ročník 163; s. 109466
Hlavní autoři: Liu, Chengdong, Wei, Yimin, Xie, Pengpeng
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.04.2025
Témata:
Dual matrices
Dual quaternion
Fréchet derivative
Kinematics
Matrix exponential
Dual matrices
Fréchet derivative
Dual quaternion
Kinematics
Matrix exponential
ISSN:0893-9659
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Shrnutí:Dual number matrices play a significant role in engineering applications such as kinematics and dynamics. The matrix exponential is ubiquitous in screw-based kinematics. In this paper, we develop an explicit formula for the dual matrix exponential. The result is closely related to the Fréchet derivative, which can be formed by the standard part and dual part of the original matrix. We only need to compute the exponential of a real matrix. Then, we give a formula of computing the dual quaternion matrix exponential. Our results are illustrated through a practical example from robotic kinematics.
ISSN:0893-9659
DOI:10.1016/j.aml.2025.109466