Game-theoretic planning for multiplayer defense task with online objective function parameter estimation

This work investigates a game-theoretic path planning algorithm with online objective function parameter estimation for a multiplayer intrusion-defense game, where the defenders aim to prevent intruders from entering the protected area. At first, an intruder is assigned to each defender to perform a one-to-one interception by solving an integer optimization problem. Then, the intrusion-defense game is formulated in a receding horizon manner by designing the objective function and constraints for the defenders and intruders, respectively. Their objective functions are coupled because they both consider the predicted interactions between the intruders and defenders. Therefore, a distributed proximal iterative best response scheme is designed for the group of defenders to cooperatively compute the Nash equilibrium. Each defender iteratively solves its own and its interception target's optimization problems, and shares information within the defender group. Since the defenders cannot know the parameters of the intruders' objective functions, an unscented Kalman filter-based estimator is constructed to online estimate the opponent's unknown parameters. Extensive simulation experiments verify the effectiveness of the proposed method.