Correct by Design Coordination of Autonomous Driving Systems

Abstract: The paper proposes a method for the correct by design coordination of autonomous driving systems (ADS). It builds on previous results on collision avoidance policies and the modeling of ADS by combining descriptions of their static environment in the form of maps, and the dynamic behavior of their vehicles. An ADS is modeled as a dynamic system involving a set of vehicles coordinated by a Runtime that based on vehicle positions on a map and their kinetic attributes, computes free spaces for each vehicle. Vehicles are bounded to move within the corresponding allocated free spaces. We provide a correct by design safe control policy for an ADS if its vehicles and the Runtime respect corresponding assume-guarantee contracts. The result is established by showing that the composition of assume-guarantee contracts is an inductive invariant that entails ADS safety. We show that it is practically possible to define speed control policies for vehicles that comply with their contracts. Furthermore, we show that traffic rules can be specified in a linear-time temporal logic, as a class of formulas that constrain vehicle speeds. The main result is that, given a set of traffic rules, it is possible to derive free space policies of the Runtime such that the resulting system behavior is safe by design with respect to the rules.