Right in Time: Reactive Reasoning in Regulated Traffic Spaces

TL;DR

This work proposes a reactive mission design framework that jointly considers uncertain environmental data and declarative, logical traffic regulations and leverages the Frequency of Change inherent in heterogeneous data streams to subdivide inference formulas into memoized, isolated tasks, ensuring that only the specific components affected by new sensor data are re-evaluated.

Abstract

Exact inference in probabilistic First-Order Logic offers a promising yet computationally costly approach for regulating the behavior of autonomous agents in shared traffic spaces. While prior methods have combined logical and probabilistic data into decision-making frameworks, their application is often limited to pre-flight checks due to the complexity of reasoning across vast numbers of possible universes. In this work, we propose a reactive mission design framework that jointly considers uncertain environmental data and declarative, logical traffic regulations. By synthesizing Probabilistic Mission Design (ProMis) with reactive reasoning facilitated by Reactive Circuits (RC), we enable online, exact probabilistic inference over hybrid domains. Our approach leverages the Frequency of Change inherent in heterogeneous data streams to subdivide inference formulas into memoized, isolated tasks, ensuring that only the specific components affected by new sensor data are re-evaluated. In experiments involving both real-world vessel data and simulated drone traffic in dense urban scenarios, we demonstrate that our approach provides orders of magnitude in speedup over ProMis without reactive paradigms. This allows intelligent transportation systems, such as Unmanned Aircraft Systems (UAS), to actively assert safety and legal compliance during operations rather than relying solely on preparation procedures.

Figures (7)

• Figure 1: Reasoning in Regulated Traffic Spaces via Reactive Circuits for Reactive Mission Landscapes: By compiling a First-Order Logic representation into an initial Weighted Model Counting formula and then optimizing the formula's structure based on the update frequency of incoming signals, methods such as Probabilistic Mission Design can move from expensive preparation procedures to real-time applications.
• Figure 2: Quasi-static statistical spatial relations in complex urban environments: We precompute high-resolution statistical spatial relations from crowd-sourced map data in order to provide a precise basis for mission design reasoning. In contrast to relations that depend on dynamic signals (see \ref{['fig:dynamic_relations']}), these parameters do not need to be updated frequently and can incorporate more sophisticated statistical evaluation and refinements. Hence, in an RC, they will gather at the formula nodes furthest away from the root node (e.g., $f_2$ in \ref{['fig:motivation']}).
• Figure 3: Dynamic statistical spatial relations in multi-modal traffic environments: While statistical spatial relations based on, e.g., OpenStreetMap data, are quasi-static and can be prepared at high resolution beforehand, we sample the parameters of dynamic relations, such as agent distances around the reported expected locations, and apply both linear and nearest-neighbour interpolation.
• Figure 4: Large-scale and real-time mission design in dense, urban cores: We show the resulting mission landscape as a scalar field of probabilities of satisfying all mission requirements (listed in \ref{['listing:resin']}) across an approximately $64km\squared$ area spanning across New York City, including parts of the East and Hudson rivers.
• Figure 5: Reactive and Probabilistic Mission Design: This Resin program illustrates how statistical spatial relations are integrated to reason over admissible airspaces for an autonomous UAS in a dense urban environment with multiple modes of mobility.