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.

翻译：本文提出一种针对在一般凸环境中进行多人避碰博弈的防御机器人的双层在线优化策略。我们的目标是在不预先知晓攻击者策略的情况下，尽可能多地拦截攻击机器人。为平衡最优性与效率，我们的方法交替进行以下步骤：协调防御者联盟以对抗单个攻击者，以及基于预测的单次攻击协调结果将联盟分配给攻击者。我们开发了一种用于单次攻击防御协调的在线凸规划技术，该技术不仅能适应联合状态，还能识别出确保成功拦截攻击的初始联合状态的最大区域。我们的防御分配算法采用一种分层迭代方法来近似具有单调性约束的整数线性规划，降低了计算负担，同时确保了随时间推移的防御性能提升。在二维和三维环境中进行的大量仿真验证了我们方法相较于现有先进方法的有效性，并展示了其在轮式移动机器人和四旋翼飞行器中的适用性。