On the relation between the exponential of real matrices and that of dual matrices - Liu, Chengdong; Wei, Yimin; Xie, Pengpeng (Applied mathematics letters, 2025)
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.