Tube MPC-Based Tracking Control of AUVs Using Contraction Metric

This paper investigates trajectory tracking of autonomous underwater vehicles (AUV) subject to thruster saturation and environmental disturbances. We propose a tube model predictive control (MPC) framework to robustly stabilize the AUV tracking error defined in the local frame. The essence of our design centers on leveraging a robust control contraction metric (RCCM) to construct a disturbance invariant set, ensuring bounded deviation between the actual and nominal system states under the RCCM-based feedback control law. Subsequently, an outer approximation of this RCCM-based invariant set is developed to design the tube cross-section and tighten the input constraint. The resulting RCCM-based tube MPC (RCCM-MPC) scheme is independent of the spatially varying metric, enhancing the computational efficiency of the proposed scheme. Then we establish sufficient conditions for ensuring the recursive feasibility of the proposed RCCM-MPC scheme and stability of the closed-loop tracking error dynamics. Simulation results demonstrate the effectiveness of the proposed RCCM-MPC approach.