In this paper we consider the problem of safe driving of the Dubins car on a straight road where the steering control is the sum of a free control v and of an automatic control s 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 defining a solution to a system with a discontinuous right hand side, and to deal with the definition of regular synthesis used in optimal control. We thus consider generalized solutions in Krasovskii and Filippov sense and guarantee that these solutions have a “good behavior”, i.e., when only s is acting the generalized solutions coincide with the optimal synthesis trajectories. Finally, we illustrate our strategy by simulations.