In this letter, a resilient path planning scheme is proposed to navigate a UAV to the planned (nominal) destination with minimum energy-consumption in the presence of a smart attacker. The UAV is equipped with two sensors, a GPS sensor, which is vulnerable to the spoofing attacker, and a well-functioning Ultra-Wideband (UWB) sensor, which is possible to be fooled. We show that a covert attacker can significantly deviate the UAV's path by simultaneously corrupting the GPS signals and forging control inputs without being detected by the UWB sensor. The prerequisite for the attack occurrence is first discussed. Based on this prerequisite, the optimal attack scheme is proposed, which maximizes the deviation between the nominal destination and the real one. Correspondingly, an energy-efficient and resilient navigation scheme based on Pontryagin's maximum principle \cite{gelfand2000calculus} is formulated, which depresses the above covert attacker effectively. To sum up, this problem can be seen as a Stackelberg game \cite{bacsar1998dynamic} between a secure path planner (defender) and a covert attacker. The effectiveness and practicality of our theoretical results are illustrated via two series of simulation examples and a UAV experiment.

中文翻译：

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无人机对UWB传感器进行隐式攻击的弹性路径规划

在这封信中，提出了一种弹性路径规划方案，可以在智能攻击者在场的情况下以最小的能耗将无人机导航到计划的（名义）目的地。无人机配备有两个传感器，一个是容易受到欺骗攻击者攻击的GPS传感器，另一个是功能强大的超宽带（UWB）传感器，该传感器可能会被欺骗。我们表明，秘密攻击者可以通过同时破坏GPS信号和伪造控制输入而不会被UWB传感器检测到，从而大大偏离无人机的路径。首先讨论了发生攻击的前提。在此前提下，提出了一种最优的攻击方案，该方案使标称目的地与真实目的地之间的偏差最大。相应地，基于Pontryagin'的高能效和弹性导航方案 制定了最大原则\ cite {gelfand2000calculus}，有效地压制了上述秘密攻击者。综上所述，该问题可以看作是安全路径规划器（防御者）和秘密攻击者之间的Stackelberg游戏\ cite {bacsar1998dynamic}。我们的理论结果的有效性和实用性通过两个系列的仿真示例和一个无人机实验进行了说明。