Avoidance of many pursuers in the simple motion case

Borówko, Piotr; Rzymowski, Witold

doi:10.1016/0022-247x(85)90233-1

Cited by 10 publications

(4 citation statements)

References 2 publications

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“…It is used when capture of an evader within a bounded domain is considered, [62], [63]. In [64] sufficient conditions are presented for the existence of an evasion strategy where simple motion kinemtics for the players is considered. The paper [65] considered a more general case of N-pursuers engaged against one evader.…”

Section: B N Pursuers 1 Evader (Nv1)mentioning

confidence: 99%

An Introduction to Pursuit-evasion Differential Games

Weintraub¹,

Pachter²,

García³

2020

Preprint

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Pursuit and evasion conflicts represent challenging problems with important applications in aerospace and robotics. In pursuit-evasion problems, synthesis of intelligent actions must consider the adversary's potential strategies. Differential game theory provides an adequate framework to analyze possible outcomes of the conflict without assuming particular behaviors by the opponent. This article presents an organized introduction of pursuit-evasion differential games with an overview of recent advances in the area. First, a summary of the seminal work is outlined, highlighting important contributions. Next, more recent results are described by employing a classification based on the number of players: one-pursuer-one-evader, N-pursuers-one-evader, one-pursuer-M-evaders, and N-pursuer-M-evader games. In each scenario, a brief summary of the literature is presented. Finally, two representative pursuit-evasion differential games are studied in detail: the two-cutters and fugitive ship differential game and the active target defense differential game. These problems provide two important applications and, more importantly, they give great insight into the realization of cooperation between friendly agents in order to form a team and defeat the adversary.

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Section: B N Pursuers 1 Evader (Nv1)mentioning

confidence: 99%

An Introduction to Pursuit-evasion Differential Games

Weintraub¹,

Pachter²,

García³

2020

Preprint

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“…Later on, this result was extended by Zak [10]. The work [11] presented a sufficient condition of existence of evasion strategy in the game of many pursuers in the plane.…”

Section: Introductionmentioning

confidence: 96%

Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean Metric

Kuchkarov

Ibragimov

Феррара

2016

Discrete Dynamics in Nature and Society

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We consider pursuit and evasion differential games of a group of pursuers and one evader on manifolds with Euclidean metric. The motions of all players are simple, and maximal speeds of all players are equal. If the state of a pursuer coincides with that of the evader at some time, we say that pursuit is completed. We establish that each of the differential games (pursuit or evasion) is equivalent to a differential game of groups of countably many pursuers and one group of countably many evaders in Euclidean space. All the players in any of these groups are controlled by one controlled parameter. We find a condition under which pursuit can be completed, and if this condition is not satisfied, then evasion is possible. We construct strategies for the pursuers in pursuit game which ensure completion the game for a finite time and give a formula for this time. In the case of evasion game, we construct a strategy for the evader. Hindawi Publishing Corporation

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“…On the other hand, there are some applications of these games to the problems of motion vehicles, collisions of avoidance for ships and others. Among a large number of papers, devoted to the pursuitevasion games with a group of pursuers, mention the works [16]- [33]. Works [24], [26]- [31] is devoted to model problems, where all players have a simple motion.…”

Section: Introductionmentioning

confidence: 99%

“…In [32], [33] proved the possibility of evasion evader from group of pursuers in linear differential game with a simple matrix if the number of pursuers less then dimension of space and evader does not leave the confines of a convex cone. Problem of evasion group of evaders from a group of pursuers in various productions considered in [14], [16], [30]. This work is devoted to two non-stationary problems of evasion of one the evader from a group of pursuers.…”

Section: Introductionmentioning

confidence: 99%

About the Problem of Group Persecution in Linear Differential Games With a Simple Matrix and State Constraints

Петров¹,

Shchelchkov²

2014

Int. J. of Pure and Appl. Math.

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Consider two dependent problems of evasion one evader from many pursuers. In the first problem assumed, that the all players have a simple motion, among the pursuers are both participants the maximum speed of which coincide with the maximum speed of evader and parties who maximum speeds strictly less than the maximum speed of evader while evader is not leaves the convex compact set with non-empty interior. In the second problem consider linear dipendent problem of persecution one evader by group pursuers, provided that the matrix of the system is the product of a function and identity matrix, among the pursuers are both participants, which the set of admissible controls, is a sphere with center at the origin, coincides with the set of admissible controls the evader, and the pursuers with fewer opportunities and evader does not leave the confines of a convex cone with vertex at the origin. We prove that if the number of pursuers, opportunities coincide with opportunities the evader, less than the dimension space, then the pursuers with fewer features do not affect the solvability evasion problem.

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Avoidance of many pursuers in the simple motion case

Cited by 10 publications

References 2 publications

An Introduction to Pursuit-evasion Differential Games

An Introduction to Pursuit-evasion Differential Games

Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean Metric

About the Problem of Group Persecution in Linear Differential Games With a Simple Matrix and State Constraints

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