Tube-based nonlinear model predictive control for lateral maneuvering of trans-media vehicle considering planing avoidance

The trans-media vehicle can reduce frictional drag and increase speed by traveling inside a cavity. However, the planing force generated by the contact between the vehicle and the cavity wall can induce oscillations and instability. This paper presents a novel tube-based nonlinear model predictive control (NMPC) method incorporating both an optimal nominal control law and a state feedback law to solve the planing avoidance problem during lateral maneuvering under the external disturbances. First, the planing avoidance problem is reformulated as a state constraint problem by analyzing the geometric relationship of the cavity and vehicle. Then, a finite-horizon optimal control problem for the nominal system is solved to obtain the nominal control law. Subsequently, the state feedback law is designed based on the deviations of the actual and nominal states to obtain robust control invariant sets for tracking errors and improve control accuracy. Furthermore, the sets of state and control constraints in the optimal control problem are tightened based on the robust control invariant sets, which guarantees that the actual system satisfies all constraints strictly. According to the stability analyses, the closed-loop system is input-to-state stable. Finally, simulations show that the proposed control law enables the vehicle to follow the reference signal without generating the planing force. Moreover, the controller satisfies both the state and control constraints in the presence of external disturbances, and surpasses the conventional control method in achieving higher control accuracy.