Objectives  In view of the problem about the control of the swarm system composed of several underactuated Unmanned Surface Vehicles(USVs), the control strategy of virtual structure method is studied.

  Methods  In this paper, the problem about the swarm control was transformed into a problem about the stabilization of the position tracking error between the USVs and the virtual structure. The formation transformation of USV swarm was realized based on the changed geometry of the virtual structure. The design of the swarm controller was divided into two parts, i.e. kinematics and dynamics. With adequate consideration of the uncertainty disturbance, the underactuated USV swarm controller was proposed based on adaptive backstepping techniques combined with the sliding-mode control method. The stability of the closed loop system was demonstrated by the Lyapunov theory. The simulation test of straight and curve course running and swarm formation transformation were carried out.

  Results  The simulation results show that the synergy of the USV swarm is remarkable, the formation transformation is smooth, and the UAV swarm can adapt to various uncertain disturbances.

  Conclusions  The swarm system shows strong robustness and flexibility which lays a theoretical foundation for subsequent USV swarm tests.