双四元数上的广义手眼标定矩阵方程 $AX-YB=C$
The generalized hand-eye calibration matrix equation $AX-YB=C$ over dual quaternions
AI总结：
本文研究双四元数矩阵方程 $AX-YB=C$，给出其可解性条件与通解，并将其用于彩色图像加解密，实验验证了方案的高可行性。
摘要：
在机器人研究领域，一个重要的应用问题是手眼标定问题，它涉及求解矩阵方程 $AX=YB$。然而，该矩阵方程只是更一般的双四元数矩阵方程 $AX-YB=C$ 的一个特例，后者在系统与控制理论中也具有重要应用。因此，本文建立了这一广义手眼标定双四元数矩阵方程的可解性条件，并在其可解时给出解的一般表达式。作为应用实例，我们基于该双四元数矩阵方程设计了一种彩色图像加密与解密方案。从实验中可以观察到，解密图像与原始图像几乎完全相同。因此，利用该双四元数矩阵方程设计的加密和解密方案具有很高的可行性。
英文摘要：
In the field of robotics research, a crucial applied problem is the hand-eye calibration issue, which involves solving the matrix equation $AX = YB$. However, this matrix equation is merely a specific case of the more general dual quaternion matrix equation $AX-YB=C$, which also holds significant applications in system and control theory. Therefore, we in this paper establish the solvability conditions of this generalized hand-eye calibration dual quaternion matrix equation and provide a general expression for its solutions when it is solvable. As an example of applications, we design a scheme for color image encryption and decryption based on this dual quaternion matrix equation. From the experiment, it can be observed that the decrypted images are almost identical to the original images. Therefore, the encryption and decryption scheme designed using this dual quaternion matrix equation is highly feasible.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
