Safety Driving of the Dubins’ Car

In this paper we consider the problem of safe driving of the Dubins’ car on a straight road where the steering control is in the form (1−h)s+hv where v represents a free control and s is an automatic control preventing the system from undesired behaviors that may result from the action of v. We design the safety control s steering the car to the center of the road in minimum time which fact implies to consider discontinuous feedbacks, hence to face the problem of de£ning a solution to a system with a discontinuous right hand side, and to deal with the de£nition of regular synthesis used in optimal control. We thus consider generalized solutions in Krasowskii and Filippov sense and guarantee that these solutions have a good behavior, i.e., when only s is acting (h = 0) the generalized solutions coincide with the optimal synthesis trajectories. Finally, we illustrate our strategy by simulations.