Simultaneous robot–world and hand–eye calibration based on a pair of dual equations

Abstract

Two kinematic loops of hand–eye system have different geometric interpretations, which raises problems in hand–eye calibration and robot–world–hand–eye calibration. While robot–world–hand–eye calibration involves more unknowns for estimation, hand–eye calibration only deals with hand–eye transformation. This study proposed a novel model based on a pair of dual equations that can determine both robot–world and hand–eye transformations. Simultaneous and separable solutions for the dual equations are given under the circumstances of whether the homogeneous matrices are decoupled. Simulations and experiments verified the feasibility and superiority of the proposed methods versus two reference ones in the aspects of accuracy and robustness. Meanwhile, the separable solution is proved to possess better performance as the negative effect caused by the translation scaling and the robot size is removed from rotation. The results show that the prediction errors of rotation and translation based on the new model be reduced to 0.07∘ and 1.3 mm, respectively.