We study a novel principle for safe and efficient collision avoidance that adopts a mathematically elegant and general framework abstracting as much as possible from the controlled vehicles dynamics and of its environment. Vehicle dynamics is characterized by pre-computed functions for accelerating and braking to a given speed. Environment is modeled by a function of time giving the free distance ahead of the controlled vehicle under the assumption that the obstacles are either fixed or are moving in the same direction. The main result is a control policy enforcing the vehicles speed so as to avoid collision and efficiently use the free distance ahead, provided some initial safety condition holds. The studied principle is applied to the design of two discrete controllers, one synchronous and another asynchronous. We show that both controllers are safe by construction. Furthermore, we show that their efficiency strictly increases for decreasing granularity of discretization. We present implementations of the two controllers, their experimental evaluation in the Carla autonomous driving simulator and investigate various performance issues.
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