Accession Number : AD0885270

Title :   The Homicidal Chauffeur - A Differential Game

Corporate Author : STANFORD UNIV CA DEPT OF AERONAUTICS AND ASTRONAUTICS

Personal Author(s) : Merz, Antony W

PDF Url : AD0885270

Report Date : Mar 1971

Pagination or Media Count : 117

Abstract : 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 chauffeur's control is his turn rate, bounded in magnitude, and the pedestrian's 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 pursuer's 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.

Descriptors :   *GAME THEORY, CURVE FITTING, EQUATIONS OF MOTION, EVASION, MINIMAX TECHNIQUE, NUMERICAL ANALYSIS, NUMERICAL INTEGRATION, OPTIMIZATION, PARTIAL DIFFERENTIAL EQUATIONS, TRAJECTORIES

Subject Categories : Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE