Abstract
This paper describes a third-order pursuit—evasion game in which both players have the same speed and minimum turn radius. The game of kind is first solved for thebarrier or envelope of capturable states. When capture is possible, the game of degree is then solved for the optimal controls of the two players as functions of the relative position. The solution is found to include a universal surface for the pursuer and a dispersal surface for the evader.
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References
Isaacs, R.,Differential Games, John Wiley and Sons, New York, 1965.
Merz, A.,The Homicidal Chauffeur—A Differential Game, Stanford University, Department of Aeronautics and Astronautics, Ph.D. Thesis, 1971.
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Communicated by Y. C. Ho
The author is grateful to Professor J. V. Breakwell, Stanford University, for constructive criticism of the manuscript. Financial support for the research was provided at Stanford University under Air Force Contract No. F33615-70-C-1637.
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Merz, A.W. The game of two identical cars. J Optim Theory Appl 9, 324–343 (1972). https://doi.org/10.1007/BF00932932
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DOI: https://doi.org/10.1007/BF00932932