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Rare Collision Risk Estimation of Autonomous Vehicles with Multi-Agent Situation Awareness

Mahdieh Zaker, Henk A. P. Blom, Sadegh Soudjani, Abolfazl Lavaei

TL;DR

The paper tackles rare collision risk estimation for autonomous vehicles operating in multi-agent environments with multi-agent situation awareness (MA-SA). It models AV dynamics as General Stochastic Hybrid Systems (GSHS) and uses an interacting particle system with fixed assignment splitting (IPS-FAS) to efficiently estimate rare-event probabilities, aided by transforming GSHS to a tractable SHS formulation. It introduces a MA-SA framework to capture information sharing between vehicles and employs a time-to-collision (TTC) measure to inform decisions in lane-change scenarios. Through a lane-change case study, the authors demonstrate that IPS-FAS can reliably estimate collision probabilities on the order of $10^{-7}$, while traditional Monte Carlo can fail to detect such rare events, and that SA significantly reduces risk, underscoring the method's safety-validation value for safety-critical AV systems.

Abstract

This paper offers a formal framework for the rare collision risk estimation of autonomous vehicles (AVs) with multi-agent situation awareness, affected by different sources of noise in a complex dynamic environment. In our proposed setting, the situation awareness is considered for one of the ego vehicles by aggregating a range of diverse information gathered from other vehicles into a vector. We model AVs equipped with the situation awareness as general stochastic hybrid systems (GSHS) and assess the probability of collision in a lane-change scenario where two self-driving vehicles simultaneously intend to switch lanes into a shared one, while utilizing the time-to-collision measure for decision-making as required. Due to the substantial data requirements of simulation-based methods for the rare collision risk estimation, we leverage a multi-level importance splitting technique, known as interacting particle system-based estimation with fixed assignment splitting (IPS-FAS). This approach allows us to estimate the probability of a rare event by employing a group of interacting particles. Specifically, each particle embodies a system trajectory and engages with others through resampling and branching, focusing computational resources on trajectories with the highest probability of encountering the rare event. The effectiveness of our proposed approach is demonstrated through an extensive simulation of a lane-change scenario.

Rare Collision Risk Estimation of Autonomous Vehicles with Multi-Agent Situation Awareness

TL;DR

The paper tackles rare collision risk estimation for autonomous vehicles operating in multi-agent environments with multi-agent situation awareness (MA-SA). It models AV dynamics as General Stochastic Hybrid Systems (GSHS) and uses an interacting particle system with fixed assignment splitting (IPS-FAS) to efficiently estimate rare-event probabilities, aided by transforming GSHS to a tractable SHS formulation. It introduces a MA-SA framework to capture information sharing between vehicles and employs a time-to-collision (TTC) measure to inform decisions in lane-change scenarios. Through a lane-change case study, the authors demonstrate that IPS-FAS can reliably estimate collision probabilities on the order of , while traditional Monte Carlo can fail to detect such rare events, and that SA significantly reduces risk, underscoring the method's safety-validation value for safety-critical AV systems.

Abstract

This paper offers a formal framework for the rare collision risk estimation of autonomous vehicles (AVs) with multi-agent situation awareness, affected by different sources of noise in a complex dynamic environment. In our proposed setting, the situation awareness is considered for one of the ego vehicles by aggregating a range of diverse information gathered from other vehicles into a vector. We model AVs equipped with the situation awareness as general stochastic hybrid systems (GSHS) and assess the probability of collision in a lane-change scenario where two self-driving vehicles simultaneously intend to switch lanes into a shared one, while utilizing the time-to-collision measure for decision-making as required. Due to the substantial data requirements of simulation-based methods for the rare collision risk estimation, we leverage a multi-level importance splitting technique, known as interacting particle system-based estimation with fixed assignment splitting (IPS-FAS). This approach allows us to estimate the probability of a rare event by employing a group of interacting particles. Specifically, each particle embodies a system trajectory and engages with others through resampling and branching, focusing computational resources on trajectories with the highest probability of encountering the rare event. The effectiveness of our proposed approach is demonstrated through an extensive simulation of a lane-change scenario.
Paper Structure (8 sections, 1 theorem, 39 equations, 3 figures, 2 tables, 4 algorithms)

This paper contains 8 sections, 1 theorem, 39 equations, 3 figures, 2 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. General Stochastic Hybrid Systems
  3. Preliminaries and Notation
  4. General Stochastic Hybrid Systems
  5. Multi-Agent Situation Awareness
  6. IPS-based Rare-event Estimation
  7. Time-to-collision Measure
  8. Results and Discussions

Key Result

Proposition 4.1

The factorization is satisfied by the reach probability where $\gamma_k \triangleq \mathbb{E} \{\chi_k \!=\! 1 \,| \,\chi_{k-1}\!=\!1\}=\mathds{P}(\tau_k \!<\! T \,| \, \tau_{k-1}\!<\!T)$.

Figures (3)

  • Figure 1: Lane-change scenario: Two AVs are recognized as $e \in \mathcal{E} = \{ EL, ER \}$, with the first letter indicating their status as ego vehicles and the second letter specifying their lane (right or left).
  • Figure 2: Ellipsoidal level sets $\mathcal{O}_{k, i}$ as in \ref{['eq:ellipse level sets']} around each AV.
  • Figure 3: GSHS model transition graphs for AVs $i=ER$ (a), and $j = EL$ (b), where, $w_L$ represents lane width, and $T_{{lc}_i}$, $T_{{lc}_j}$ signify moments when vehicles $i$ and $j$ decide to change lanes, respectively. The intent $\hat{\upsilon}_{t,i}^j$ is obtained from $\hat{\theta}_{t,i}^j$.

Theorems & Definitions (3)

  • Definition 2.1: GSHS
  • Proposition 4.1
  • Remark 4.2