Distributed Optimal Formation Control of Multiple Unmanned Surface Vehicles With Stackelberg Differential Graphical Game

In this work, a cooperative formation control methodology is proposed for multiple six-degree-of-freedom (six-DoF) unmanned surface vehicles (USVs) subject to input saturation. Our method includes several key steps. To begin, we formulate the optimal formation control problem for USVs as Stackelberg differential graphical games. According to this design principle, each USV is partitioned into a primary follower and a secondary follower. The primary followers coalesce into one team, while the secondary followers constitute another team independently. Second, a new type of barrier Lyapunov function (BLF) with a hyperbolic tangent function is introduced to indirectly constrain velocity vector. Third, an auxiliary system is established to compensate for the input saturation. Then, the Lyapunov stability theory is employed to prove that all closed-loop signals of multiple USVs are semiglobal uniform ultimate boundedness (SGUUB). Finally, we present the simulation results of our proposed control scheme. These results demonstrate the effectiveness and feasibility of our proposed methodology for cooperative formation control of multiple USVs.