Formalizing Vocabulary for Scenario-Based Testing of Automated Driving Systems: From Semantics to Mathematics

Safety assurance of Automated Driving System equipped Vehicles (ADS-Vs) is currently a topic of significant research interest in the intelligent vehicles community. Scenario-Based Testing (SBT) is the most widely used method for safety verification and validation of ADS- Vs. To comply with ISO 21448, a key standard for ADS-V safety assurance, SBT can be formulated as an optimization problem to identify unknown hazardous scenarios within the ADS-V's Operational Design Domain (ODD). For an unambiguous, standardized formulation of this optimization problem, a precise mathematical definition for scenarios and related concepts is necessary. Numerous definitions for standardizing the description of scenarios exist in the literature. However, there is no widely accepted mathematical definition for scenarios and no related terminology that is consistent and rigorous. In this work, we present consistent, self-contained mathematical definitions for the vocabulary of SBT in ADS-Vs. Notably, we define concrete, logical, and abstract scenarios. To formulate these definitions, we propose a mathematical framework to model traffic constellations using the Behavioral Modeling (BM) approach and showcase it using an example. The presented approach can be used as a framework to formulate the SBT optimization problem for the safety assurance of ADS- Vs.