Towards a Complete Safety Framework for Longitudinal Driving

Formal models for the safety validation of autonomous vehicles have become increasingly important. To this end, we present a safety framework for longitudinal automated driving. This framework allows calculating minimum safe inter-vehicular distances for arbitrary ego vehicle control policies. We use this framework to enhance the Responsibility-Sensitive Safety (RSS) model and models based on it, which fail to cover situations where the ego vehicle has a higher decelerating capacity than its preceding vehicle. For arbitrary ego vehicle control policies, we show how our framework can be applied by substituting real (possibly computationally intractable) controllers with upper bounding functions. This comprises a general approach for longitudinal safety, where safety guarantees for the upper-bounded system are equivalent to those for the original system but come at the expense of larger inter-vehicular distances.