Constrained coalition games for USV swarm confrontation

Abstract

This paper formulates unmanned surface vehicle (USV) swarm confrontation as a constrained coalition game, capturing cooperation within swarms and competition between swarms. Local task costs are aggregated into coalition objectives to account for tradeoffs among target approach, interception, and formation maintenance, subject to individual geographic constraints and supply line limits shared within each swarm. For prescribed formation sizes and task assignments, explicit linear matrix inequalities in the task weights are derived to establish strong monotonicity of the coalition pseudogradient, thereby guaranteeing the existence of a unique Nash equilibrium (NE) whenever the joint feasible set is nonempty. A distributed robust NE seeking strategy is then developed by integrating gradient tracking and action estimation with projected primal-dual dynamics using local information and neighbor communication. Adaptive compensation addresses unknown hydrodynamic parameters and bounded time-varying disturbances. The disturbance compensation gains are adjusted through local error feedback without requiring disturbance measurements, prior knowledge of disturbance bounds, or a prescribed disturbance generation model. Under the derived weight conditions, the stated dynamics and communication assumptions, and suitable gain conditions, the physical states of all USVs are shown to converge asymptotically to the unique feasible NE. Numerical simulations demonstrate the effectiveness of the proposed algorithm.