Construction of Barrier in a Fishing Game With Point Capture

This paper addresses a particular pursuit-evasion game, called as “fishing game” where a faster evader attempts to pass the gap between two pursuers. We are concerned with the conditions under which the evader or pursuers can win the game. This is a game of kind in which an essential aspect, barrier, separates the state space into disjoint parts associated with each player's winning region. We present a method of explicit policy to construct the barrier. This method divides the fishing game into two subgames related to the included angle and the relative distances between the evader and the pursuers, respectively, and then analyzes the possibility of capture or escape for each subgame to ascertain the analytical forms of the barrier. Furthermore, we fuse the games of kind and degree by solving the optimal control strategies in the minimum time for each player when the initial state lies in their winning regions. Along with the optimal strategies, the trajectories of the players are delineated and the upper bounds of their winning times are also derived

Usable boundary for visibility-based surveillance-evasion games

We consider a surveillance-evasion game in an environment with obstacles. In such an environment, a mobile pursuer seeks to maintain the visibility with a mobile evader, who tries to get occluded from the pursuer in the shortest time possible. In this two-player zero-sum game setting, we study the discontinuities of the value of the game near the boundary of the target set (the non-visibility region). In particular, we describe the transition between the usable part of the boundary of the target (where the value vanishes) and the non-usable part (where the value is positive). We show that the value enjoys a different behaviour depending on the regularity of the obstacles involved in the game. Namely, we prove that the boundary profile is continuous for the case of smooth obstacles, and that it exhibits a jump discontinuity when the obstacle contains corners. Moreover, we prove that, in the latter case, there is a semi-permeable barrier emanating from the interface between the usable and the non-usable part of the boundary of the target set.Comment: 33 pages, 8 figure

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-player pursuit–evasion games with one superior evader

Inspired by the hunting and foraging behaviors of group predators, this paper addresses a class of multi-player pursuit–evasion games with one superior evader, who moves faster than the pursuers. We are concerned with the conditions under which the pursuers can capture the evader, involving the minimum number and initial spatial distribution required as well as the cooperative strategies of the pursuers. We present some necessary or sufficient conditions to regularize the encirclement formed by the pursuers to the evader. Then we provide a cooperative scheme for the pursuers to maintain and shrink the encirclement until the evader is captured. Finally, we give some examples to illustrate the theoretical results

Variations on Cops and Robbers

We consider several variants of the classical Cops and Robbers game. We treat the version where the robber can move R > 1 edges at a time, establishing a general upper bound of N / \alpha ^{(1-o(1))\sqrt{log_\alpha N}}, where \alpha = 1 + 1/R, thus generalizing the best known upper bound for the classical case R = 1 due to Lu and Peng. We also show that in this case, the cop number of an N-vertex graph can be as large as N^{1 - 1/(R-2)} for finite R, but linear in N if R is infinite. For R = 1, we study the directed graph version of the problem, and show that the cop number of any strongly connected digraph on N vertices is at most O(N(log log N)^2/log N). Our approach is based on expansion.Comment: 18 page

Roadmap-Based Techniques for Modeling Group Behaviors in Multi-Agent Systems

Simulating large numbers of agents, performing complex behaviors in realistic environments is a difficult problem with applications in robotics, computer graphics and animation. A multi-agent system can be a useful tool for studying a range of situations in simulation in order to plan and train for actual events. Systems supporting such simulations can be used to study and train for emergency or disaster scenarios including search and rescue, civilian crowd control, evacuation of a building, and many other training situations. This work describes our approach to multi-agent systems which integrates a roadmap-based approach with agent-based systems for groups of agents performing a wide range of behaviors. The system that we have developed is highly customizable and allows us to study a variety of behaviors and scenarios. The system is tunable in the kinds of agents that can exist and parameters that describe the agents. The agents can have any number of behaviors which dictate how they react throughout a simulation. Aspects that are unique to our approach to multi-agent group behavior are the environmental encoding that the agents use when navigating and the extensive usage of the roadmap in our behavioral framework. Our roadmap-based approach can be utilized to encode both basic and very complex environments which include multi- level buildings, terrains and stadiums. In this work, we develop techniques to improve the simulation of multi-agent systems. The movement strategies we have developed can be used to validate agent movement in a simulated environment and evaluate building designs by varying portions of the environment to see the effect on pedestrian flow. The strategies we develop for searching and tracking improve the ability of agents within our roadmap-based framework to clear areas and track agents in realistic environments. The application focus of this work is on pursuit-evasion and evacuation planning. In pursuit-evasion, one group of agents, the pursuers, attempts to find and capture another set of agents, the evaders. The evaders have a goal of avoiding the pursuers. In evacuation planning, the evacuating agents attempt to find valid paths through potentially complex environments to a safe goal location determined by their environmental knowledge. Another group of agents, the directors may attempt to guide the evacuating agents. These applications require the behaviors created to be tunable to a range of scenarios so they can reflect real-world reactions by agents. They also potentially require interaction and coordination between agents in order to improve the realism of the scenario being studied. These applications illustrate the scalability of our system in terms of the number of agents that can be supported, the kinds of realistic environments that can be handled, and behaviors that can be simulated

Synchronous intercept strategies for a robotic defense-intrusion game with two defenders

We study the defense-intrusion game, in which a single attacker robot tries to reach a stationary target that is protected by two defender robots. We focus on the "synchronous intercept problem", where both robots have to reach the attacker robot synchronously to intercept it. Assume that the attacker robot has the control policy which is based on attraction to the target and repulsion from the defenders, two kinds of synchronous intercept strategies are proposed for the defense-intrusion game, introduced here as Attacker-oriented and Neutral-position-oriented. Theoretical analysis and simulation results show that: (1) the two strategies are able to generate different synchronous intercept patterns: contact intercept pattern and stable non-contact intercept pattern, respectively. (2) The contact intercept pattern allows the defender robots to intercept the attacker robot in finite time, while the stable non-contact intercept pattern generates a periodic attractor that prevents the attack robot from reaching the target for infinite time. There is potential to apply the insights obtained into defense-intrusion in real systems, including aircraft escort and the defense of military targets or territorial boundaries

Dagstuhl Reports : Volume 1, Issue 2, February 2011

Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn