On the game of two cars

Borówko, Piotr; Rzymowski, Witold

doi:10.1007/bf00935458

Cited by 19 publications

(2 citation statements)

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“…Rublein in [3]. Necessary and sufficient conditions for the existence of an evasion strategy are presented in [4]. The publications [2,3,4] suppose that interception is a coincide of the pursuer and evader planar coordinates.…”

Section: Introductionmentioning

confidence: 99%

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The Game of Two Identical Cars: an Analytical Description of the Barrier

Buzikov¹,

Galyaev²

2022

Preprint

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In this paper, a pursuit-evasion game of two players known as the game of two identical cars is examined. It is assumed that the game proceeds on a twodimensional plane. Both players have constant speeds and limited turn radii. The goal of the first player (pursuer) is to ensure that the second player (evader) is guaranteed to be within a capture circle as quickly as possible. The goal of the evader is to avoid the capture or delay it as long as possible. The kinematics of both players are described by the same equations. Thus, the game has only one free parameter, the capture radius. This work aims at a fully analytical description of the barrier surface for all values of the capture radius. Previously, A.W. Merz analytically investigated the barrier of the game of two identical cars. In this work, it is found that there is a certain critical value of the capture radius, above which the barrier occurs qualitatively differently from Merz's example. Also, we obtained an analytical description of the optimal feedback controls on the barrier.

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Section: Introductionmentioning

confidence: 99%

“…∈ ( J , +∞). 4 The root can be found by Newton's method with an initial guess w 0 = ϑ J , for example. 5 The root can be found by Newton's method with an initial guess m 0 = π, for example.…”

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confidence: 99%