We consider a path guarding problem in dynamic Defender-Attacker Blotto games (dDAB), where a team of robots must defend a path in a graph against adversarial agents. Multi-robot systems are particularly well suited to this application, as recent work has shown the effectiveness of these systems in related areas such as perimeter defense and surveillance. When designing a defender policy that guarantees the defense of a path, information about the adversary and the environment can be helpful and may reduce the number of resources required by the defender to achieve a sufficient level of security. In this work, we characterize the necessary and sufficient number of assets needed to guarantee the defense of a shortest path between two nodes in dDAB games when the defender can only detect assets within $k$-hops of a shortest path. By characterizing the relationship between sensing horizon and required resources, we show that increasing the sensing capability of the defender greatly reduces the number of defender assets needed to defend the path.

翻译：我们研究了动态防御者-攻击者布洛托博弈（dDAB）中的路径保护问题，其中一组机器人必须防御图中一条路径免受对抗性代理的攻击。多机器人系统尤其适用于此类应用，因为近期研究已表明这些系统在周边防御和监控等相关领域的有效性。在设计保证路径安全的防御策略时，关于对手和环境的信息可能具有帮助作用，并可能减少防御者实现充分安全水平所需的资源。本文中，我们刻画了在dDAB博弈中，当防御者仅能检测到距离最短路径$k$跳范围内的资产时，保证两个节点之间最短路径安全所需资产数量的充分必要条件。通过阐明感知范围与所需资源之间的关系，我们证明增加防御者的感知能力能够大幅降低防御路径所需的防御者资产数量。