Traditional construction methods pose unique challenges, such as lack of skilled workers, long construction time and difficulties in quality control. To solve the limitations of traditional construction methods, modular construction has been widely investigated and applied. With the development of robotic technologies and control algorithms, robotic construction, which can further enhance the advantages of modular construction, has attracted many researchers’ attention. In this study, an automated crane operation framework, which considers the robotic kinematics analysis and a loop shaping control algorithm, is proposed to automate the construction process. The proposed automated crane operation framework was verified through a construction material supply experiment. To test the performance of the loop shaping controller, a constant reference signal and a sine wave signal are used. The constant reference signal is used to assess whether the loop shaping controller can accurately control the crane to transport the construction material to the pre-defined target position. The reference sine signal is used to test the ability of continuous tracking of the loop shaping controller. Through construction supply experiments, the proposed automated crane operation framework can automate the mobile crane operation in a construction material supply task. This research indicates the potential of robotizing traditional mobile cranes by implementing robotic technologies and control algorithms for automated construction projects.