Mathematical Definitions of Scene and Scenario for Analysis of Automated Driving Systems in Mixed-Traffic Simulations

This paper introduces a unified mathematical definition for describing commonly used terms encountered in systematical analysis of automated driving systems in mixed-traffic simulations. The most significant contribution of this work is in translating the terms that are clarified previously in literature into a mathematical set and function based format. Our work can be seen as an incremental step towards further formalisation of Domain-Specific-Language (DSL) for scenario representation. We also extended the previous work in the literature to allow more complex scenarios by expanding the model-incompliant information using set-theory to represent the perception capacity of the road-user agents. With this dynamic perception definition, we also support interactive scenarios and are not limited to reactive and pre-defined agent behavior. Our main focus is to give a framework to represent realistic road-user behavior to be used in simulation or computational tool to examine interaction patterns in mixed-traffic conditions. We believe that, by formalising the verbose definitions and extending theprevious work in DSL, we can support automatic scenario generation and dynamic/evolving agent behavior models for simulating mixed traffic situations and scenarios. In addition, we can obtain scenarios that are realistic but also can represent rare-conditions that are difficult to extract from field-tests and real driving data repositories.