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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Bibliographic Details
Published in:Applied mathematics letters Vol. 163; p. 109466
Main Authors: Liu, Chengdong, Wei, Yimin, Xie, Pengpeng
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.04.2025
Subjects:
Dual matrices
Dual quaternion
Fréchet derivative
Kinematics
Matrix exponential
Dual matrices
Fréchet derivative
Dual quaternion
Kinematics
Matrix exponential
ISSN:0893-9659
Online Access:Get full text
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Summary: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