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Abstract-One significant barrier in introducing autonomous driving is the liability issue of a collision; e.g. when two autonomous vehicles collide, it is unclear which vehicle should be held accountable. To solve this issue, we view traffic rules from legal texts as requirements for autonomous vehicles. If we can prove that an autonomous vehicle always satisfies these requirements during its operation, then it cannot be held responsible in a collision. We present our approach by formalising a subset of traffic rules from the Vienna Convention on Road Traffic for highway scenarios in Isabelle/HOL.

Abstract. 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.

Abstract-While a number of efficient methods have been proposed for approximating backward reachable sets, no synthesis method via backward reachable sets has been developed for estimating and enlarging the region of attraction (RA). This paper shows how to use backward reachable sets to enlarge the estimate of the RA of linear discrete-time systems, by using an optimal static feedback controller. Two controller design methods are provided: the first method enlarges the estimate of the RA via invariant sets, whose existence is ensured by zonotope containment; the second method provides the optimal control input by using Lyapunov stability and quadratic stabilization. The backward reachable set is represented by zonotopes which give a good compromise between accuracy and efficiency. The effectiveness of both methods is illustrated by a numerical example.

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Abstract-Future collision avoidance systems, which are capable of fully controlling the vehicle, have to make critical decisions in a very short time. To do this, they need to check constantly if their own vehicle's occupancy collides with the other traffic participants' occupancy. Those collision checks consume a substantial amount of time and consequently, the collision avoidance systems could fail to intervene in complex scenarios. We propose a new approach to reduce the computation time for collision checks significantly. Instead of using geometric methods, we store finitely many possible collision scenarios between two objects in a table and thus collision checks become a matter of lookup table queries. To ensure that the finite number of configurations cover all possible scenarios, we use a novel abstraction technique which guarantees that every collision will be detected. The approach works for arbitrarily many traffic participants by applying the approach pairwise (own vehicle and other object) to each traffic participant. Randomly generated scenarios show that the new approach can be several times faster than geometric intersection techniques thanks to the trade-off between memory consumption and computation time.