Capture Pursuit Games on Unbounded Domains
نویسندگان
چکیده
We introduce simple tools from geometric convexity to analyze capturetype (or “Lion and Man”) pursuit problems in unbounded domains. The main result is a necessary and sufficient condition for eventual capture in equal-speed discrete-time multi-pursuer capture games on convex Euclidean domains of arbitrary dimension and shape. This condition is presented in terms of recession sets in unit tangent spheres. The chief difficulties lie in utilizing the boundary of the domain as a constraint on the evader’s escape route. We also show that these convex-geometric techniques provide sufficient criteria for pursuit problems in non-convex domains with a convex decomposition.
منابع مشابه
Pursuit and Evasion in Non-convex Domains of Arbitrary Dimensions
Most results in pursuit-evasion games apply only to planar domains or perhaps to higher-dimensional domains which must be convex. We introduce a very general set of techniques to generalize and extend certain results on simple pursuit to non-convex domains of arbitrary dimension which satisfy a coarse curvature condition (the CAT(0) condition). I. PURSUIT / EVASION There is a significant litera...
متن کاملTotal Curvature and Simple Pursuit on Domains of Curvature Bounded Above
We show how circumradius and asymptotic behavior of curves in CAT(0) and CAT(K) spaces (K > 0) are controlled by growth rates of total curvature. We apply our results to pursuit and evasion games of capture type with simple pursuit motion, generalizing results that are known for convex Euclidean domains, and obtaining results that are new for convex Euclidean domains and hold on playing fields ...
متن کاملFormation Control in Multi-player Pursuit Evasion Game with Superior Evaders
In this paper, we consider a multi-pursuer multi-evader pursuit evasion game where some evaders’ maximal speeds are higher than those of all pursuers. In multi-player pursuit evasion game, hierarchical framework is applied widely in order to decompose the original complicated multi-player game into multiple small scale games, i.e. one-pursuer one-evader games and multi-pursuer single-evader gam...
متن کاملGame Theory Models for Pursuit Evasion Games
In a pursuit evasion game, the pursuer tries to capture the evader while the evader tries to prevent this capture. A classical approach is to model this game as an infinite differential game. In this report, we model a pursuit-evasion game as a finite extensive form game, and show that the differential game is a generalization of this game. We prove that a pure-strategy Nash equilibrium always ...
متن کاملGuaranteed Strategies for nonlinear Multi-Player Pursuit-Evasion Games
In this paper, we provide a methodology to design strategies for either guaranteed capture or guaranteed evasion in the case of pursuit-evasion games with multiple players which are represented by nonlinear dynamic models. This methodology is based on the continuously differentiable upper and lower approximations of the minimum and maximum function of an arbitrary number of arguments, compariso...
متن کامل