The pursuit-evasion game on the 1-skeleton graph of a regular polyhedron. I

We consider a game between a group of n pursuers and one evader moving with the same maximum velocity along the 1-skeleton graph of a regular polyhedron. The goal of the paper is finding, for each regular polyhedron M , a number N ( M ) with the following properties: if n ≥ N ( M ), the group of pur...

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Bibliographic Details
Published in:Automation and remote control 2017-04, Vol.78 (4), p.754-761
Main Authors: Azamov, A. A., Kuchkarov, A. Sh, Holboyev, A. G.
Format: Article
Language:English
Subjects:
CAE) and Design
Calculus of Variations and Optimal Control
Optimization
Computer-Aided Engineering (CAD
Control
Mathematical Game Theory and Applications
Mathematics
Mathematics and Statistics
Mechanical Engineering
Mechatronics
Polyhedra
Pursuit-evasion games
Robotics
Systems Theory
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Summary:We consider a game between a group of n pursuers and one evader moving with the same maximum velocity along the 1-skeleton graph of a regular polyhedron. The goal of the paper is finding, for each regular polyhedron M , a number N ( M ) with the following properties: if n ≥ N ( M ), the group of pursuers wins, while if n < N ( M ), the evader wins. Part I of the paper is devoted to the case of polyhedra in ℝ 3 ; Part II will be devoted to the case of ℝ d , d ≥ 5; and Part III, to the case of ℝ 4 .
ISSN:0005-1179
1608-3032
DOI:10.1134/S0005117917040166