Active wave compensation for dual-stage Stewart platforms using VAR-MPC

Ocean-wave-induced multi-degree-of-freedom disturbances degrade the motion-compensation accuracy and stability of shipborne offshore platforms. Although dual-stage Stewart platforms provide enhanced actuation capability, their performance is limited by inter-stage coupling, sensing–actuation phase lag, actuator constraints, and model uncertainty. This study proposes an active wave-compensation framework that integrates a second-order vector autoregression (VAR) model with tube-based model predictive control. The VAR model captures short-horizon coupling among roll, pitch, and heave to provide delay-matched disturbance preview, while the tube-based MPC controller performs constrained receding-horizon optimization and local feedback correction under bounded disturbances and model mismatch. Simulations and physical prototype experiments under irregular Sea State 4 conditions compared the proposed method with representative baseline and advanced MPC-based control strategies. In the physical experiments, VAR-MPC reduced the residual RMSEs to 0.195°, 0.197°, and 0.222 mm in roll, pitch, and heave, respectively. The results demonstrate the effectiveness and superior performance of the proposed framework.