Robot-world and hand–eye calibration based on quaternion: A new method and an extension of classic methods, with their comparisons

Abstract

As the two main rigid body transformations in robotic vision systems, the problems of robot-world calibration and hand–eye calibration were raised. Classic quaternion as an advantageous representation of rotation exerts its advantage for the separable methods of the hand–eye calibration problems. While the impact of rotation propagation errors on the translation estimate in separable methods was often ignored. In this paper, after a summarization of quaternion-based methods in SO(3) and SE(3), a dual equations model using adjoint transformation was derived which converts the transformation of rigid body motion into a line transformation. Then, a closed-form rotation solution based on quaternion conjugate was proposed, and two translation closed-form solutions with different propagation error paths were given respectively. Based on these, the impact of rotation propagation errors of the four methods on translation estimate was analyzed, and an assessment of when each method works most and least applicable was given. In addition, simulations and experiments were presented to assess all methods and verify the accuracy and efficacy of the proposed method against uncalibrated commercial robot.