One-Step Solving the Robot-World and Hand–Eye Calibration Based on the Principle of Transference

Principle of transference is very important in the kinematic analysis of spatial mechanisms, which enables the extension of point transformations to line transformations inbuilt with the dual mapping. An ideal conceptualization for applying kinematic calibration is to extend the solution of the rotational equations to the kinematic equations via dual mapping. However, this necessitates an analytic representation of the rotational solution, a task that is typically unachievable. Duffy and his coauthors used the principle of transference to generate the spatial equations from the spherical equations. Therefore, the application of the principle of transference to kinematic calibration allows one to start with the process of deriving and solving the equations of kinematics. In this article, the kinematic calibration problem is used as an application to discuss the implementation process of principle of transference in detail. First, the process of transforming the rotational equations into a linear null-space computational system based on quaternion matrix operators is reviewed. Then, fusing the dual matrix operators converts the kinematic equations into the dual linear system of equations, which reflects the forward process of principle of transference. Finally, eliminating the dual operations in the dual linear system of equations turns it into a high-dimensional linear null-space computational system, which embodies the inverse process of principle of transference. This article provides a new closed-form solution for the $AX=YB$ problem.