Optimal Control of a Dubins Car with a Capture Set and the Homicidal Chauffeur Differential Game

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The optimal control of a Dubins car endowed with a circular or a line segment capture set is considered and the connection to their Homicidal Chauffeur differential game (HCDG) analogues is discussed. The capture set endowed Dubins cars are tasked to reach a stationary target point in minimum time. The solutions to the Dubins car optimal control problems (DCOCP) are similar to the solutions of the HCDG where the Evader, which is slower than the pursuing car, has simple motion. The similarities can be attributed to the fact that both the DCOCPs and the HCDG dynamics have two states and the Pursuer in the HCDG is modeled as a Dubins car. Because of these similarities, the solutions to the DCOCPs yield insights into the solutions of the attendant HCDGs where the Pursuer is endowed with a circular, or a line segment, capture set. This paper develops the solution to the optimal control problem of a Dubins car with a line segment capture set, presents the solution when the car is endowed with a circular capture set, and then draws comparisons to the respective HCDGs.


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