Saturated coordinated control of multiple underactuated unmanned surface vehicles over a closed curve

This paper presents a design method for saturated coordinated control of multiple underactuated unmanned surface vehicles (USVs) on a closed curve, holding a symmetric formation pattern. Each vehicle is subject to unknown sideslip, uncertain vehicle kinetics, and limited control torques. First, the course angle and surge velocity are considered as immediate signals to stabilize the along-track and cross-track path following errors. In the vehicle kinematics, a reduced-order extended state observer is utilized to compensate for the effect of the unknown sideslip. Next, a bounded neural network control law is constructed at the kinetic level with the aid of the a saturated function, a projection operator, and a dynamic surface design method. Finally, a parameter cyclic pursuit approach is presented to guarantee that the vehicles are evenly spaced over the closed curve for achieving a symmetric formation pattern. The input-to-state stability of the closed-loop system is analyzed via cascade theory. Comparative studies are given to show the effectiveness of the proposed method.