A Formally Verified Checker of the Safe Distance Traffic Rules for Autonomous Vehicles

One barrier in introducing autonomous vehicle technology is the liability issue when these vehicles are involved in an accident. To overcome this, autonomous vehicle manufacturers should ensure that their vehicles always comply with traffic rules. This paper focusses on the safe distance traffic rule from the Vienna Convention on Road Traffic. Ensuring autonomous vehicles to comply with this safe distance rule is problematic because the Vienna Convention does not clearly define how large a safe distance is. We provide a formally proved prescriptive definition of how large this safe distance must be, and correct checkers for the compliance of this traffic rule. The prescriptive definition is obtained by: (1) identifying all possible relative positions of stopping (braking) distances; (2) selecting those positions from which a collision freedom can be deduced; and (3) reformulating these relative positions such that lower bounds of the safe distance can be obtained. These lower bounds are then the prescriptive definition of the safe distance, and we combine them into a checker which we prove to be sound and complete. Not only does our work serve as a specification for autonomous vehicle manufacturers, but it could also be used to determine who is liable in court cases and for online verification of autonomous vehicles' trajectory planner.