Abstract
Two-target versions of the game of two cars and the homicidal chauffeur game are introduced. This enables us to consider pursuitevasion withouta priori role assignment. A generic example of the two-target homicidal chauffeur game is considered in detail; in particular, a map of the game and its corresponding winning strategies are found using Lyapunov methods of analysis. The effects of altering game parameters, such as the speed and maneuverability ratios, and the weapon system parameters are then presented. It is found that certain winning strategies include a swerve-type maneuver and that, for certain sets of parameters, regions of stagnation and different modes of draw occur.
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References
Isaacs, R.,Differential Games, John Wiley and Sons, New York, New York, 1965.
Merz, A. W.,The Homicidal Chauffeur, AIAA Journal, Vol. 12, pp. 259–260, 1975.
Merz, A. W.,The Game of Two Identical Cars, Journal of Optimization Theory and Applications, Vol. 9, pp. 324–343, 1972.
Blaquière, A., Gérard, F., andLeitmann, G.,Quantitative and Qualitative Differential Games, Academic Press, New York, New York, 1965.
Getz, W. M., andLeitmann, G.,Qualitative Differential Games with Two Targets, Journal of Mathematical Analysis and Applications, Vol. 68, pp. 421–430, 1979.
Stalford, H. L., andLeitmann, G.,Sufficient Conditions for Optimality in Two-Person Zero-Sum Differential Games with State and Strategy Constraints, Journal of Mathematical Analysis and Applications, Vol. 33, pp. 650–654, 1971.
Sticht, D. J., Vincent, T. L., andSchultz, D. G.,Sufficiency Theorems for Target Capture, Journal of Optimization Theory and Applications, Vol. 17, pp. 523–543, 1975.
Leitmann, G., andSkowronski, J.,Avoidance Control, Journal of Optimization Theory and Applications, Vol. 23, pp. 581–591, 1977.
Leitmann, G., andLiu, H. S.,Evasion in the Plane, Proceedings of the 8th IFIP Conference on Optimization Techniques, Würzburg, Germany, 1977; Springer Verlag, Berlin, Germany, 1978.
Leitmann, G.,Guaranteed Avoidance Strategies, Journal of Optimization Theory and Applications, Vol. 32, No. 4, 1980.
Olsder, G. J., andBreakwell, J. V.,Role Determination in Aerial Dogfight, International Journal of Game Theory, Vol. 3, pp. 47–66, 1974.
Merz, A. W., andHague, D. S.,Coplanar Tail-Chase Aerial Combat as a Differential Game, AIAA Journal, Vol. 15, pp. 1419–1423, 1977.
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Communicated by G. Leitmann
This work was partially supported by a grant from Control Data.
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Getz, W.M., Pachter, M. Two-target pursuit-evasion differential games in the plane. J Optim Theory Appl 34, 383–403 (1981). https://doi.org/10.1007/BF00934679
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DOI: https://doi.org/10.1007/BF00934679