The on-site assembly process in modular construction (MC) requires precise placement of bulky modules, which involves dangerous and labor-intensive manual work in the current practice. This study aims to automate the process by designing a hybrid pose adjustment (HyPA) robot to achieve complete pose control of the module. To this end, this paper presents the mechanism design and working principle of the HyPA system, demonstrating that module position control, leveling control, steering control, and sway damping can be achieved. The modeling of the HyPA robot is also presented, including the essential parameters to define the model and the construction of the relevant mathematical expressions. Furthermore, a model-based motion generation scheme is proposed to validate the working principle, which combines feedforward motion planning and feedback error correction. Lastly, functionality verification is conducted through both simulation and hardware tests, showcasing the capability of the HyPA robot to perform desired translation and steering angle change while maintaining horizontal leveling.