Hybrid multibody dynamics-based model predictive control of suspended blocks for floating cranes in waves

Block erection using floating cranes requires accurate control of heavy suspended loads under environmental disturbances. This study proposes a hybrid modeling and control framework that integrates a reduced multibody dynamics formulation with disturbance-aware model predictive control (MPC). The crane subsystem is represented using an embedding technique with minimal coordinates, while the block and wire rope subsystem is modeled using a discrete Euler-Lagrange formulation to enforce wire rope length constraints and compute physically consistent constraint forces. Based on this hybrid model, a modified MPC estimates disturbances from prediction errors and incorporates them into the predictive model to enhance robustness in an underactuated setting. The proposed approach enables six-degrees-of-freedom position and orientation control while explicitly handling operational constraints. Numerical case studies demonstrate stable tracking performance and effective constraint enforcement under wave-induced disturbances, indicating the practicality of the framework for block erection operations.