Objective  Aiming at the obstacle avoidance of unmanned ship swarm, this paper proposes an elastic formation control method based on a virtual navigator and improved Hooke's law.

  Methods  First, the external ellipse is obtained according to the length and width of the obstacle, and the virtual obstacle avoidance area, obstacle avoidance response area and free navigation area are then extended outward according to the aspect ratio in order to simplify obstacle avoidance on the surface of the water. Second, based on the virtual navigator and improved Hooke's law, the constraints on relative distance and speed between each members of the formation as well as those between each members of the formation and the virtual navigator are given, and the formation configuration of the multiple unmanned ships is set in the form of coordinates so as to construct an elastic formation model. Further, based on the obstacle annular repulsive field, the obstacle avoidance of a single unmanned ship is realized. The obstacle avoidance of the multiple unmanned ships can then be realized under the organization of the elastic formation. Moreover, the sailing process of unmanned ship is optimized to eliminate the phenomena of "wandering" and "shaking" in the process of formation and obstacle avoidance, and increase the smoothness of the movement of the unmanned ship. Finally, four unmanned ships are used to form a formation, and a simulation experiment based on Matlab is carried out.

  Result  The results show that all obstacles are successfully bypassed, verifying the effectiveness and feasibility of the proposed method.

  Conclusions  This method can achieve the avoidance of surface obstacles for unmanned ship swarms, giving them a certain ability to pass through complex environments, thereby providing references for the application and research of unmanned ship swarm obstacle avoidance.