Robust formation tracking of multiple autonomous surface vessels with individual objectives: A noncooperative game-based approach

Distributed robust formation tracking of multiple autonomous surface vessels (ASVs) with uncertain dynamics and individual objectives is investigated in this paper by developing a noncooperative game-based approach. Compared with the multiple ASVs model commonly studied in existing literature, two distinct features of the present multiple ASVs model are: (i) the ASVs are allowed to have individual objectives, and (ii) the evolution of each ASV is subjected to unmodeled dynamics and time-varying external disturbances. Specifically, the ASVs are required to cooperatively achieve the group objective of tracking a time-varying reference trajectory in a specific formation pattern, while each ASV also needs to complete its own individual objective of maintaining desired displacement with respect to the reference trajectory during the formation tracking process according to its own benefit. A noncooperative game-based approach is developed for the ASVs to achieve the goal of formation tracking in the presence of individual objectives where the formation tracking problem is cast into the Nash equilibrium seeking problem of a noncooperative game among ASVs subject to unmodeled dynamics and external disturbances. To make each ASV seek the Nash equilibrium efficiently, adaptive neural network (NN) is adopted to approximate the unmodeled dynamics and nonsmooth feedback is utilized to deal with the effect of bounded external disturbances. It is theoretically shown that the states of ASVs including the position and heading angle states could asymptotically converge to the Nash equilibrium if the underlying communication graph is strongly connected and the control parameters of the Nash equilibrium seeking algorithms are suitably selected. Finally, an experimental study is performed to verify the validity of the theoretical results.