A Model for Perimeter-Defense Problems with Heterogeneous Teams

We develop a model of the multi-agent perimeter-defense game to calculate how an adaptive defense should be organized. This model is inspired by the human immune system and captures settings such as heterogeneous teams, limited resource allocations, partial observability of the attacking side, and decentralization. An optimal defense, that minimizes the harm under constraints of the energy spent to maintain a large and diverse repertoire, must maintain coverage of the perimeter from a diverse attacker population. The model characterizes how a defense might take advantage of its ability to respond strongly to attackers of the same type but weakly to attackers of diverse types to minimize the number of diverse defenders and while reducing harm. We first study the model from a steady-state perimeter-defense perspective and then extend it to mobile defenders and evolving attacker distributions. The optimal defender distribution is supported on a discrete set and similarly a Kalman filter obtaining local information is able to track a discrete, sometimes unknown, attacker distribution. Simulation experiments are performed to study the efficacy of the model under different constraints.Comment: 8 pages, 6 figure

Guarding a Non-Maneuverable Translating Line with an Attached Defender

In this paper we consider a target-guarding differential game where the defender must protect a linearly translating line-segment by intercepting an 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 defenders' maximum speed in inertial frame, which depends on the target's direction of motion. Zero-sum differential game of degree for both the attacker-win and defender-win scenarios are studied, where the payoff is defined to be the distance between the two agents at the time of game termination. 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-win and attacker-win regions. We present simulation results to demonstrate the theoretical results.Comment: 8 pages, 8 figures. arXiv admin note: text overlap with arXiv:2207.0409

The Barrier Surface in the Cooperative Football Differential Game

This paper considers the blocking or football pursuit-evasion differential game. Two pursuers cooperate and try to capture the ball carrying evader as far as possible from the goal line. The evader wishes to be as close as possible to the goal line at the time of capture and, if possible, reach the line. In this paper the solution of the game of kind is provided: The Barrier surface that partitions the state space into two winning sets, one for the pursuer team and one for the evader, is constructed. Under optimal play, the winning team is determined by evaluating the associated Barrier function.Comment: 5 pages, 1 figur