A Note on Three-Dimensional Pursuit–Evasion Game with Bounded Curvature

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Abstract

— The system of kinematic equations which describes Isaacs’ Game of Two Cars has been extended to the case of a three-dimensional pursuit–evasion game between players with bounded curvature. It is shown that in the three-dimensional version of the Homicidal Chauffeur game, both players, when playing optimally, strive to steer the system into a common plane and will remain on this plane until game termination. The situation is somewhat different for the three-dimensional version of the Game of Two Cars, where it is not always advantageous to steer an initially three-dimensional dynamic system into a plane. Nevertheless, if at any instant the velocity vectors and the line of sight between players are coplanar, both players strive to remain on this plane.

Original languageEnglish
Pages (from-to)739-741
Number of pages3
JournalIEEE Transactions on Automatic Control
Volume27
Issue number3
DOIs
StatePublished - Jun 1982

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