Monitoring of Traffic Manoeuvres with Imprecise Information

Abstract

In monitoring, we algorithmically check if a single behavior satisfies a property. Here, we consider monitoring for Multi-Lane Spatial Logic (MLSL). The behavior is given as a finite transition sequence of MLSL and the property is that a spatial MLSL formula should hold at every point in time within the sequence. In our procedure we transform the transition sequence and the formula to the first-order theory of real-closed fields, which is decidable, such that the resulting formula is valid iff the MLSL formula holds throughout the transition sequence. We then assume that temporal data may have an error of up to $\varepsilon$, and that spatial data may have an error of up to $\delta$. We extend our procedure to check if the MLSL formula $\varepsilon$-$\delta$-robustly holds throughout the transition sequence.Comment: In Proceedings FVAV 2017, arXiv:1709.0212

Formal methods to comply with rules of the road in autonomous driving: State of the art and grand challenges

“…Others propose new logics, specifically tailored for formalizing ROTRs [124][125][126]. With few exceptions (e.g., [81,112,124,134]), which use high-order temporal logic (i.e., logics that allow for universal and existential quantifiers), all the reviewed works focus on propositional and predicate temporal logics.…”

“…Safety specifications Monitoring for compliance with safety specifications is presented in [17,63,64,134]. The authors of [17] use backward reachability analysis to construct the monitor.…”

“…The authors of [17] use backward reachability analysis to construct the monitor. Monitoring for Multi-Lane Spatial Logic is considered in [134], where the authors show that formula satisfaction can be mapped to feasibility of formulas in the first-order theory of real-closed fields. Runtime monitoring techniques based on predictions of future behaviors of traffic participants are developed for safety specifications in [63,64].…”

Enforcing Timing Properties in Motorway Traffic

“…Over the set of actions, which are the transitions without the one where only time passes, we define timed words of actions ω = ⟨(α 0 ,t 0 ),...,(α n ,t n )⟩, with α i an action and ⟨t 0 ,...,t n ⟩ a real-time sequence. For a formal account, we refer to [14].…”

Imperfect Knowledge in Autonomous Urban Traffic Manoeuvres

“…Our approach differs from the work of Ody [20] on monitoring of traffic situations, where the author also uses the abstract model and MLSL from [11]. There for single sequences of traffic snapshots it is automatically checked if a MLSL formula holds globally throughout the sequence.…”