Fully Distributed Formation Control of Autonomous Surface Vessels via Non-Cooperative Game Approach

This paper considers the fully distributed formation control problem of autonomous surface vessels (ASVs) with multiple conflicting tasks using a non-cooperative game approach. In the present problem, each ASV is assigned a global formation task while simultaneously having an individual task to approach a specified target with a local desired displacement. Due to the conflicting relationship between the individual task and the global task, this paper proposes the construction of a local cost function for each ASV. This formulation aims to transform the formation control problem, considering task conflicts, into a non-cooperative game problem. To achieve a balance between the global task and the individual task, a formation control law based on non-cooperative game theory is proposed. The control law aims to enable the ASVs to distributively search for the Nash equilibrium of the non-cooperative game. Specifically, the proposed formation control law is fully distributed, with control gains being designed to be adaptive. Theoretical analysis demonstrates that the designed controllers can drive all ASVs' states to converge to the Nash equilibrium without relying on any global information, even in the context of external disturbances. Finally, numerical simulations are performed to verify the validity of the theoretical results.