论文标题
空中辩护人与地面入侵者之间的外围防守游戏
Perimeter-defense Game between Aerial Defender and Ground Intruder
论文作者
论文摘要
我们在外围防守的背景下研究追求逃避游戏的变体。在这个问题中，入侵者旨在到达半球的基本平面而不会被防御者捕获，而后卫试图捕获入侵者。以前是在防守者绕圈移动的假设下研究的外围防守游戏。我们将问题扩展到后卫在半球上移动的情况。为了解决这个问题，我们根据违规点分析了入侵者试图达到目标并预测目标位置的策略，该策略被定义为最佳突破点，这是通过对两个参与者的最佳策略来实现的。我们提供了将国家空间分为赢得捍卫者和入侵者获奖区域的障碍，并证明这两个参与者的最佳策略是朝着最佳的违规点发展。给出了仿真结果，以证明游戏的最优性作为NASH平衡。
We study a variant of pursuit-evasion game in the context of perimeter defense. In this problem, the intruder aims to reach the base plane of a hemisphere without being captured by the defender, while the defender tries to capture the intruder. The perimeter-defense game was previously studied under the assumption that the defender moves on a circle. We extend the problem to the case where the defender moves on a hemisphere. To solve this problem, we analyze the strategies based on the breaching point at which the intruder tries to reach the target and predict the goal position, defined as optimal breaching point, that is achieved by the optimal strategies on both players. We provide the barrier that divides the state space into defender-winning and intruder-winning regions and prove that the optimal strategies for both players are to move towards the optimal breaching point. Simulation results are presented to demonstrate that the optimality of the game is given as a Nash equilibrium.
