The Homicidal Chauffeur - A Differential Game
STANFORD UNIV CA DEPT OF AERONAUTICS AND ASTRONAUTICS
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The homicidal chauffeur is the name of a pursuit-evasion differential game originated by Isaacs in his book, Differential Games. In this game, the chauffeur chases a slower pedestrian in an unbounded parking lot. The chauffeurs control is his turn rate, bounded in magnitude, and the pedestrians control is his velocity direction, which can be changed at will. The pursuer and evader seek respectively to minimize and maximize the capture time, when the radial separation becomes less than a known capture radius. The two equations of relative motion and the terminal conditions can then be written in terms of the two constant parameters of the game the speed ratio, the ratio of capture radius to pursuers minimum turn radius. The solution to the problem consists in finding the optimizing strategies of both players as functions of the position relative to the pursuer. These min-max strategies are specified in terms of the local position variables and the local components of the gradient in the optimal time-to-go, values of which are known at the termination of the game.
- Operations Research