Time-Discretized Simulation of Vehicle Platoons for Safety Analysis with Guaranteed Error Bounds

TL;DR

Addresses safety of vehicle platoons under concurrent sudden braking and wireless packet losses by extending a continuous-time linear platoon model with explicit braking dynamics and stochastic losses, and evaluating the minimum inter-vehicle distance with guaranteed error bounds. Introduces time-discretized simulation methods with two strategies for selecting time steps to bound distance error and develops a lifted-state approach to improve efficiency. Demonstrates that some string-stable parameter settings provide better safety under outages and braking, supported by numerical experiments for both ℓ-consecutive and random losses and shows substantial speedups over classical methods. The work enables reliable safety analysis for platoon controllers and supports integration with realistic traffic simulation environments.

Abstract

Wireless communication is essential to achieve coordinated control in vehicle platoons. However, packet losses in wireless communication can cause critical safety issues when they occur in conjunction with sudden brakes. In this paper, we propose simulation-based methods that allow the study of such safety issues by determining the absolute minimum distance between vehicles over time for various control parameters that guarantee string stability. For our proposed time-discretized simulations, we provide two methods for selecting different time-step intervals to ensure that the error in distance approximation remains within specified bounds at all times. Through numerical examples we demonstrate that among control parameters that guarantee string stability some perform better than others under simultaneously occurring packet losses and sudden brakes.

Figures (5)

• Figure 1: Illustration of a vehicle platoon with $n$ vehicles.
• Figure 2: Minimum of minimum inter-vehicle distances ($d^{\prime}_{\min}$) of Theorem \ref{['Theorem-7']} with respect to control parameters ($k_{{\mathrm{p}}}$ and $k_{{\mathrm{d}}}$).
• Figure 3: Difference of $d^{\prime}_{\min}$ obtained by using the simulation approaches in Theorem \ref{['Theorem-Main']} and in Theorem \ref{['Theorem-7']} with respect to control parameters ($k_{{\mathrm{p}}}$ and $k_{{\mathrm{d}}}$).
• Figure 4: Plots of total simulation steps $k'_{\mathrm{end}}$ with respect to control parameters $k_{{\mathrm{p}}}$ and $k_{{\mathrm{d}}}$ for Theorem \ref{['Theorem-Main']} (top) and Theorem \ref{['Theorem-7']} (bottom).
• Figure 5: Histograms of the minimum of minimum inter-vehicle distances ($d'_{\min}$) over 10000 simulations for Theorem \ref{['Theorem-7']} under random packet losses with respect to control parameters $k_\mathrm{p}$ and $k_\mathrm{d}$. (Top: $k_{\mathrm{p}}=0.2,k_{\mathrm{d}}=1.2$, Bottom: $k_{\mathrm{p}}=0.25,k_{\mathrm{d}}=1.2$)

Theorems & Definitions (12)

• Remark 1
• Lemma 1
• proof
• Proposition 1
• proof
• Lemma 2
• proof
• Theorem 1
• Theorem 2
• proof