Capturing an Evader Using Multiple Pursuers with Sensing Limitations in Convex Environment

A modified continuous-time pursuit-evasion game with multiple pursuers and a single evader is studied. The game has been played in an obstacle-free convex environment which consists an exit gate through which the evader may escape. The geometry of the convex is unknown to all players except pursuers know the location of the exit gate and they can communicate with each other. All players have equal maximum velocities and identical sensing range. An evader is navigating inside the environment and seeking the exit gate to win the game. A novel sweep-pursuit-capture strategy for the pursuers to search and capture the evader under some necessary and sufficient conditions is presented. We also show that three pursuers are sufficient to finish the operation successfully. Non-holonomic wheeled mobile robots of the same configurations have been used as the pursuers and the evader. Simulation studies demonstrate the performance of the proposed strategy in terms of interception time and the distance traveled by the players.

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