Parameterizations for Reducing Camera Reprojection Error for Robot-World Hand-Eye Calibration

Accurate robot-world, hand-eye calibration is crucial to automation tasks. In this paper, we discuss the robot-world, hand-eye calibration problem which has been modeled as the linear relationship AX = ZB, where X and Z are the unknown calibration matrices composed of rotation and translation components. While there are many different approaches to determining X and Z, including linear and iterative methods, we parameterize the rotation components using Euler angles and find a solution using Levenberg-Marquadt iterative approach. We also offer a method to determine A, X, and Z, by formulating the robot-world, hand-eye calibration problem in terms of camera reprojection error. We compare both of these approaches to the state-of-the-art and conclude that our approaches yield lower values of camera reprojection error. In addition, we demonstrate the improved reconstruction accuracy when using the robot-world, hand-eye calibrations produced from our methods.