Coordinated patterns of underactuated ships along closed orbits

This paper considers the problem of directing a family of underactuated ships to formation tracking a set of closed orbits and achieve attitude synchronization. It shows that our previous concentric compression design is useful to the coordinated motion of underactuated ships. The condition that the total linear speed of each ship is greater than zero is ensured by introducing a potential function. Asymptotical stabilization is proved when the inter-ship communication topology is bidirectional. The theoretical result is proved by a numerical example.