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

Multi-Agent Pursuit of a Faster Evader with Application to Unmanned Aerial Vehicles

Robotic applications like search and rescue missions, surveillance, police missions, patrolling, and warfare can all be modeled as a Pursuit-Evasion Game (PEG). Most of these tasks are multi-agent problems, often including a cooperation between team members and a conflict between adversarial teams. In order to realize such a situation with robots, two major problems have to be solved. Initially, a decomposition of the PEG has to be performed for getting results in reasonable time. Present embedded computers lack the computational power enabling them to process the highly complex solution algorithm of the non-decomposed game fast enough. Secondly, a framework has to be defined, enabling the computation of optimal actions for both the pursuers and the evaders when a cooperation within the teams is possible. It is intended to develop strategies, that allow the team of pursuers to capture a faster evader in a visibility-based PEG setup due to cooperation. For tackling the first problem a game structure is sought, aiming to considerably reduce the time complexity of the solution process. The first step is the decomposition of the action space, and the second is the change of the game structure itself. The latter is reached by defining a two-pursuer one-evader PEG with three different game structures, which are the Non-Decomposed Game, the Multiple Two-Player Game Decomposition (MTPGD) game, and the Team-Subsumption Two-Player Game (TSTPG). Several simulation results demonstrate, that both methods yield close results in respect to the full game. With increasing cardinality of each player’s strategy space, the MTPGD yields a relevant decrease of the run-time. Otherwise, the TSTPG does not minimize the time complexity, but enables the use of more sophisticated algorithms for two-player games, resulting in a decreased runtime. The cooperation within a team is enabled by introducing a hierarchical decomposition of the game. On a superordinate collaboration level, the pursuers choose their optimal behavioral strategy (e.g. pursuit and battue) resulting in the case of a two-pursuer one-evader PEG in a three-player noncooperative dynamic game, which is solved in a subordinate level of the overall game. This structure enables an intelligent behavior change for the pursuers based on game-theoretical solution methods. Depending on the state of the game, which behavioral strategy yields the best results for the pursuers within a predefined time horizon has to be evaluated. It is shown that the pursuer’s outcome can be improved by using a superordinate cooperation. Moreover, conditions are presented under which a capture of a faster evader by a group of two pursuers is possible in a visibility-based PEG with imperfect information. Since Unmanned Aerial Vehicles (UAVs) are increasingly a common platform used in the aforementioned applications, this work focuses only on PEGs with multi-rotor UAVs. Furthermore, the realization of the concepts in this thesis are applied on a real hex rotor. The feasibility of the approach is proven in experiments, while all implementations on the UAV are running in real-time. This framework provides a solution concept for all types of dynamic games with an 1-M or N-1 setup, that have a non-cooperative and cooperative nature. At this stage a N-M dynamic game is not applicable. Nevertheless, an approach to extend this framework to the N-M case is proposed in the last chapter of this work

University catalog, 2018-19

Welcome to the University of Missouri 2018-2019 catalog! We are pleased to provide an interactive and searchable catalog online. The catalog is a comprehensive reference for your academic studies. It includes a list of all degree programs offered at MU, including bachelors, masters, specialists, doctorates, minors, certificates, and emphasis areas. It details the university wide requirements, the curricular requirements for each program, and in some cases provides a sample plan of study. The catalog includes a complete listing and description of approved courses. It also provides information on academic policies, contact information for supporting offices, and a complete listing of faculty members. Information in the catalog is current as of May 2018.--Page 17