Attack-Resilient Path Planning Using Dynamic Games With Stopping States

In this article, we consider a path planning problem on a graph, wherein a vehicle (defender) seeks to find an optimal path from a source to a destination vertex in the presence of an attacker. The defender is equipped with a countermeasure that can detect and permanently disable the attack if it occurs concurrently. We model the problem over an edge as a zero-sum multistage game played between the defender and the attacker with a stopping state, termed as the edge game. We analyze this game under full information, in which each player has complete knowledge of the past actions taken by the opponent at every stage. We also analyze the game under a partial information structure, wherein the defender obtains complete knowledge of the attacker's actions only when the defender uses the countermeasure. We characterize the Nash equilibria of the edge game in both information structures with two actions per player and analyze its sensitivity to the game parameters. We then construct a meta-game using the edge game solutions to determine an attack-resilient path and compare it with an efficient novel heuristic with a constraint on the number of edges attacked. We illustrate our methodology through simulations in a Robot Operating System/Gazebo environment and with experiments on a ground robot.