  In this paper, we present a dual-layer online optimization strategy for
defender robots operating in multiplayer reach-avoid games within general
convex environments. Our goal is to intercept as many attacker robots as
possible without prior knowledge of their strategies. To balance optimality and
efficiency, our approach alternates between coordinating defender coalitions
against individual attackers and allocating coalitions to attackers based on
predicted single-attack coordination outcomes. We develop an online convex
programming technique for single-attack defense coordination, which not only
allows adaptability to joint states but also identifies the maximal region of
initial joint states that guarantees successful attack interception. Our
defense allocation algorithm utilizes a hierarchical iterative method to
approximate integer linear programs with a monotonicity constraint, reducing
computational burden while ensuring enhanced defense performance over time.
Extensive simulations conducted in 2D and 3D environments validate the efficacy
of our approach in comparison to state-of-the-art approaches, and show its
applicability in wheeled mobile robots and quadcopters.
