Towards a Complete Safety Framework for Longitudinal Driving

Sidorenko, Galina; Fedorov, Aleksei; Thunberg, Johan; Vinel, Alexey · 2022 · OpenAlex-citations

DOI: 10.1109/tiv.2022.3209910

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Summary

This paper addresses the safety validation of longitudinal automated driving by proposing a formal framework to calculate minimum safe inter-vehicle distances (IVDs). The research is motivated by limitations in the Responsibility-Sensitive Safety (RSS) model, a widely used formal safety standard. Specifically, the authors identify that RSS fails to guarantee safety when the ego vehicle possesses a higher deceleration capacity than the preceding vehicle, and it often yields unnecessarily conservative distances due to improper parameter handling. The goal is to provide a comprehensive theoretical approach that overcomes these conservative results and explicitly defines the conditions under which RSS distances are insufficient. The authors employ a novel three-step methodology to derive safety guarantees. First, they define a "minimum safe braking set," a hypersurface in state space where the follower vehicle must immediately apply maximum deceleration to avoid a collision. Second, they model the trajectories of the leader and follower vehicles during a response time $\tau$, during which the follower is unaware of the emergency braking ahead and follows a specific control law. Third, they calculate the minimum initial distance required such that the trajectories reach the safe braking set exactly at time $\tau$. The framework is applied to two scenarios: the specific RSS assumption where the follower accelerates or moves at constant velocity, and a general case where the follower uses an arbitrary control policy. For the general case, the authors demonstrate that substituting complex, computationally intractable controllers with upper-bounding functions yields safety guarantees equivalent to the original system, albeit with larger IVDs. The results show that RSS-based IVDs are insufficient when the ego vehicle’s maximum deceleration exceeds that of the leader. The authors provide explicit formulas and conditions for this special case, correcting previous literature that missed a critical condition, which led to overly pessimistic distance requirements. Numerical simulations illustrate that the proposed framework calculates tighter, more accurate minimum safe distances compared to both the original RSS model and prior corrections. For arbitrary controllers, the study demonstrates that using tighter bounding functions results in shorter, more efficient IVDs while maintaining safety guarantees. The framework is also shown to be applicable to vehicle-to-vehicle (V2V) enabled cooperative driving, where safety can be guaranteed with a probability corresponding to the likelihood of receiving braking messages. The significance of this work lies in providing a complete, rigorous safety framework for longitudinal driving that enhances the RSS model. By explicitly identifying the parameter intervals where RSS fails and providing comprehensive formulas for arbitrary control policies, the paper enables more efficient road utilization and fuel savings by reducing unnecessary safety margins. The approach allows for the safety validation of complex controllers through tractable bounding functions, facilitating the deployment of autonomous vehicles with short inter-vehicle distances. This contributes to the broader field of automated driving by offering a scalable, formal method for collision avoidance that balances safety guarantees with operational efficiency.

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• following distance