Hand-Eye Parameter Estimation Based on 3D Observation of A Single Marker

Hand-eye calibration (HEC) aims to determine the geometrical transformation between camera and robot, which is essential for vision-guided robotic (VGR) systems. On the one hand, the classic pose-based and the recent pixel-based HEC methods mainly focus on multi-pixel research for initializing or solving. However, in these multi-marker cases, additional connector assembly and wide coverage area are not user-friendly in practical data collection operations. Furthermore, both accuracy and efficiency are not ideal due to the transition calculation of multi-marker poses. On the other hand, with the development of 3D sensing technology, 3D position data can be obtained in increasing scenes. However, HEC research on 3D observation is relatively insufficient, and previous position-based formulations ignore the relationship among parameters. Motivated by the above shortcomings, this paper thoroughly investigates the hand-eye parameter estimation based on 3D observation of a single marker. First, a uniform single-marker formulation is proposed. This formulation is unique in the optimization sense without factor-extraction variants and covers both the eye-in-hand and eye-to-hand configurations. Then, an analytical solution and an iterative solution are derived through different rotation treatments. It is worth noting that these solutions are in a consistent and compact form due to the precalculated variables and the equivalent transformation. Meanwhile, the solvability, estimation accuracy, and computational efficiency are discussed. Finally, comprehensive simulations and real-world experiments are provided to demonstrate the advantages of the proposed method over previous methods in terms of accuracy, computational efficiency, and operational efficiency. The codes and datasets are open-source at http://github.com/MatthewJin001/Single3D and http://github.com/MatthewJin001/3Ddata, respectively.