This study introduces a comprehensive model addressing the dynamic interaction between a crane and platform in the presence of realistic surge-roll-heave movements induced by ocean waves. While the motion of the payload is ascertainable, the surge-roll-heave motions of the floating platform are considered unknown. Consequently, we proposed a control design strategy integrating a backstepping controller and a high-gain observer. The primary objectives of this design are to accurately track the desired (linear) trajectories of the cart position and mitigate its swing (angular) motion. Moreover, the proposed controller is designed to handle challenges such as unknown dynamic friction, dynamic coupling, and external disturbances, all while ensuring dynamic. The extended high-gain observer is crucial in estimating dynamic states and external disturbances. Through simulation, we validate the effectiveness of our model-based control approach, demonstrating its robust performance in the face of unknown nonlinearities and disturbances caused by wave motion.