Ultrasound (US) calibration is an important step in robotic 3D US reconstruction. It determines the spatial transformation from the tracking sensor frame to the US image frame. Up to now, many free-hand calibration methods have been developed. Some of them were applied in robotic systems. However, there is no comparative analysis for those employed methods in the robotic US system. Moreover, the required robotic scanning trajectory was normally unclear in previous work. Therefore, in this paper, we provided a comparative analysis of three popular US image calibration methods, namely cross-wire phantom, sphere phantom and Z phantom. Meanwhile, we attempted to provide concrete examples of using three phantoms to establish automatic robotic calibration frameworks. Demonstrated on a KUKA lightweight robot attached with a 2D US probe, different aspects were assessed to show the calibration performance and 3D US reconstruction accuracy. With the proposed robotic calibration frameworks, the total time of entire calibration procedure was shortened within 3 minutes for all three phantoms. The reconstruction results showed that the RMSE were less than 1.6 mm. The proposed automatic robotic US image calibration frameworks together with their quantitative analyses provide a foundation for further development and optimization. It could potentially facilitate the development of robotic US system.