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

Dynamic network analysis of a target defense differential game with limited observations

In this paper, we study a Target-Attacker-Defender (TAD) differential game involving one attacker, one target and multiple defenders. We consider two variations where (a) the attacker and the target have unlimited observation range and the defenders are visibility constrained (b) only the attacker has unlimited observation range and the remaining players are visibility constrained. We model the players' interactions as a dynamic game with asymmetric information. Here, the visibility constraints of the players induce a visibility network which encapsulates the visibility information during the evolution of the game. Based on this observation, we introduce network adapted feedback or implementable strategies for visibility constrained players. Using inverse game theory approach we obtain network adapted feedback Nash equilibrium strategies. We introduce a consistency criterion for selecting a subset (or refinement) of network adapted feedback Nash strategies, and provide an optimization based approach for computing them. Finally, we illustrate our results with numerical experiments.Comment: 8 figure

Monte Carlo Tree Search Applied to a Modified Pursuit/Evasion Scotland Yard Game with Rendezvous Spaceflight Operation Applications

This thesis takes the Scotland Yard board game and modifies its rules to mimic important aspects of space in order to facilitate the creation of artificial intelligence for space asset pursuit/evasion scenarios. Space has become a physical warfighting domain. To combat threats, an understanding of the tactics, techniques, and procedures must be captured and studied. Games and simulations are effective tools to capture data lacking historical context. Artificial intelligence and machine learning models can use simulations to develop proper defensive and offensive tactics, techniques, and procedures capable of protecting systems against potential threats. Monte Carlo Tree Search is a bandit-based reinforcement learning model known for using limited domain knowledge to push favorable results. Monte Carlo agents have been used in a multitude of imperfect domain knowledge games. One such game was in which Monte Carlo agents were produced and studied in an imperfect domain game for pursuit-evasion tactics is Scotland Yard. This thesis continues the Monte Carlo agents previously produced by Mark Winands and Pim Nijssen and applied to Scotland Yard. In the research presented here, the rules for Scotland Yard are analyzed and presented in an expansion that partially accounts for spaceflight dynamics in order to study the agents within a simplified model, while having some foundation for use within space environments. Results show promise for the use of Monte- Carlo agents in pursuit/evasion autonomous space scenarios while also illuminating some major challenges for future work in more realistic three-dimensional space environments

Search and Pursuit-Evasion in Mobile Robotics, A survey

This paper surveys recent results in pursuitevasion and autonomous search relevant to applications in mobile robotics. We provide a taxonomy of search problems that highlights the differences resulting from varying assumptions on the searchers, targets, and the environment. We then list a number of fundamental results in the areas of pursuit-evasion and probabilistic search, and we discuss field implementations on mobile robotic systems. In addition, we highlight current open problems in the area and explore avenues for future work

Contributions To Pursuit-Evasion Game Theory.

This dissertation studies adversarial conflicts among a group of agents moving in the plane, possibly among obstacles, where some agents are pursuers and others are evaders. The goal of the pursuers is to capture the evaders, where capture requires a pursuer to be either co-located with an evader, or in close proximity. The goal of the evaders is to avoid capture. These scenarios, where different groups compete to accomplish conflicting goals, are referred to as pursuit-evasion games, and the agents are called players. Games featuring one pursuer and one evader are analyzed using dominance, where a point in the plane is said to be dominated by a player if that player is able to reach the point before the opposing players, regardless of the opposing players' actions. Two generalizations of the Apollonius circle are provided. One solves games with environments containing obstacles, and the other provides an alternative solution method for the Homicidal Chauffeur game. Optimal pursuit and evasion strategies based on dominance are provided. One benefit of dominance analysis is that it extends to games with many players. Two foundational games are studied; one features multiple pursuers against a single evader, and the other features a single pursuer against multiple evaders. Both are solved using dominance through a reduction to single pursuer, single evader games. Another game featuring competing teams of pursuers is introduced, where an evader cooperates with friendly pursuers to rendezvous before being captured by adversaries. Next, the assumption of complete and perfect information is relaxed, and uncertainties in player speeds, player positions, obstacle locations, and cost functions are studied. The sensitivity of the dominance boundary to perturbations in parameters is provided, and probabilistic dominance is introduced. The effect of information is studied by comparing solutions of games with perfect information to games with uncertainty. Finally, a pursuit law is developed that requires minimal information and highlights a limitation of dominance regions. These contributions extend pursuit-evasion game theory to a number of games that have not previously been solved, and in some cases, the solutions presented are more amenable to implementation than previous methods.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120650/1/dwoyler_1.pd

Optimal Intermittent Sensing for Pursuit-Evasion Games

We consider a class of pursuit-evasion differential games in which the evader has continuous access to the pursuer's location, but not vice-versa. There is a remote sensor (e.g., a radar station) that can sense the evader's location upon a request from the pursuer and communicate that sensed location to the pursuer. The pursuer has a budget on the total number of sensing requests. The outcome of the game is determined by the sensing and motion strategies of the players. We obtain an equilibrium sensing strategy for the pursuer and an equilibrium motion strategy for the evader. We quantify the degradation in the pursuer's pay-off due to its sensing limitations