用一个附加的后卫来守卫一条翻译线
Guarding a Translating Line with an Attached Defender
摘要：
本文考虑了一个目标保护微分对策，在这个对策中，防守者必须通过拦截试图到达直线运动的攻击者来保护直线运动的线段.与一般的目标保护问题不同，我们假设防守者附着在目标上并与目标一起运动.这个假设影响防守者的最大速度取决于它的前进方向.研究了攻击者获胜情形下的零和度微分对策，其中收益定义为两个智能体到达目标时的距离。我们通过利用无限长目标场景的解来推导均衡策略和价值函数。该Value函数的零级集提供了将状态空间划分为防守方获胜区域和进攻方获胜区域的屏障表面。最后给出了仿真结果来验证理论结果。
英文摘要：
In this paper we consider a Target-guarding differential game where the Defender must protect a linearly moving line segment by intercepting the Attacker who tries to reach it. In contrast to common Target-guarding problems, we assume that the Defender is attached to the Target and moves along with it. This assumption affects the Defender's maximum speed depending on its heading direction. A zero-sum differential game of degree for the Attacker-winning scenario is studied, where the payoff is defined to be the distance between the two agents at the time of reaching the Target. We derive the equilibrium strategies and the Value function by leveraging the solution for the infinite-length Target scenario. The zero-level set of this Value function provides the barrier surface that divides the state space into Defender-winning and Attacker-winning regions. We present simulation results at the end to demonstrate the theoretical results.
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