Hand–eye calibration problem

In robotics and mathematics, the hand–eye calibration problem (also called the robot–sensor or robot–world calibration problem) is the problem of determining the transformation between a robot end-effector and a sensor or sensors (camera or laser scanner) or between a robot base and the world coordinate system. It is conceptually analogous to biological hand–eye coordination (hence the name). It takes the form of $AX=ZB$ , where A and B are two systems, usually a robot base and a camera, and $X$ and $Z$ are unknown transformation matrices. A highly studied special case of the problem occurs where $X=Z$ , taking the form of the problem $AX=XB$ . Solutions to the problem take the forms of several types of methods, including separable closed-form solutions, simultaneous closed-form solutions, and iterative solutions. The covariance of $X$ in the equation can be calculated for any randomly perturbed matrices $A$ and $B$ .

The problem is an important part of robot calibration, with efficiency and accuracy of the solutions determining the speed accuracy of the calibrations of robots.

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