Distributed TMPC formation trajectory tracking of multiple underwater unmanned vehicles with uncertainties and external perturbations

The tracking task of a multiple underwater unmanned vehicle (UUV) formation system with model uncertainty and external perturbation in three-dimensional space is studied, and a distributed tube model predictive controller (DTMPC) based on a double closed-loop is proposed. First, the position controller and velocity controller are designed separately according to the idea of cascade control to decrease the complexity of the optimal control problem. The position controller utilizes the kinematic incremental model to ensure the smooth variation of the target velocity, and the velocity controller combines the TMPC with the finite-time extended state observer to improve the stability and robustness of the velocity controller. Even with model uncertainties and external perturbations, the formation system can quickly create a formation and converge the tracking error to near zero. In addition, the feasibility and closed-loop stability of the formation controller are demonstrated. Eventually, the effectiveness of the theory is proven by numerical experimentation, and the UUV formation can be used to accurately track the target trajectory.