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Safe and Stable Connected Cruise Control for Connected Automated Vehicles with Response Lag

Yuchen Chen, Gabor Orosz, Tamas G. Molnar

TL;DR

The paper tackles safety guarantees for connected cruise control (CCC) in connected automated vehicles by leveraging control barrier functions (CBFs). It models the CAV response with a first-order lag and V2X connectivity to vehicles ahead, deriving safety charts and identifying a critical lag $\xi_{cr}$ beyond which safe CCC gains do not exist. To preserve performance while ensuring safety, it proposes safety-critical CCC that minimally modifies nominal CCC via a CBF-based safety filter, with proofs and simulations demonstrating safety across lag and connectivity patterns. The approach integrates stability analysis (plant and head-to-tail string stability) with safety guarantees, and demonstrates practical improvement in safety using real traffic data. Overall, the work provides a rigorous, implementable framework for safe and stable CCC in the presence of communication delays and multi-vehicle connectivity.

Abstract

Controlling connected automated vehicles (CAVs) via vehicle-to-everything (V2X) connectivity holds significant promise for improving fuel economy and traffic efficiency. However, to deploy CAVs and reap their benefits, their controllers must guarantee their safety. In this paper, we apply control barrier function (CBF) theory to investigate the safety of CAVs implementing connected cruise control (CCC). Specifically, we study how stability, connection architecture, and the CAV's response time impact the safety of CCC. Through safety and stability analyses, we derive stable and safe choices of control gains, and show that safe CAV operation requires plant and head-to-tail string stability in most cases. Furthermore, the reaction time of vehicles, which is represented as a first-order lag, has a detrimental effect on safety. We determine the critical value of this lag, above which safe CCC gains do not exist. To guarantee safety even with lag while preserving the benefits of CCC, we synthesize safety-critical CCC using CBFs. With the proposed safety-critical CCC, the CAV can leverage information from connected vehicles farther ahead to improve its safety. We evaluate this controller by numerical simulation using real traffic data.

Safe and Stable Connected Cruise Control for Connected Automated Vehicles with Response Lag

TL;DR

The paper tackles safety guarantees for connected cruise control (CCC) in connected automated vehicles by leveraging control barrier functions (CBFs). It models the CAV response with a first-order lag and V2X connectivity to vehicles ahead, deriving safety charts and identifying a critical lag beyond which safe CCC gains do not exist. To preserve performance while ensuring safety, it proposes safety-critical CCC that minimally modifies nominal CCC via a CBF-based safety filter, with proofs and simulations demonstrating safety across lag and connectivity patterns. The approach integrates stability analysis (plant and head-to-tail string stability) with safety guarantees, and demonstrates practical improvement in safety using real traffic data. Overall, the work provides a rigorous, implementable framework for safe and stable CCC in the presence of communication delays and multi-vehicle connectivity.

Abstract

Controlling connected automated vehicles (CAVs) via vehicle-to-everything (V2X) connectivity holds significant promise for improving fuel economy and traffic efficiency. However, to deploy CAVs and reap their benefits, their controllers must guarantee their safety. In this paper, we apply control barrier function (CBF) theory to investigate the safety of CAVs implementing connected cruise control (CCC). Specifically, we study how stability, connection architecture, and the CAV's response time impact the safety of CCC. Through safety and stability analyses, we derive stable and safe choices of control gains, and show that safe CAV operation requires plant and head-to-tail string stability in most cases. Furthermore, the reaction time of vehicles, which is represented as a first-order lag, has a detrimental effect on safety. We determine the critical value of this lag, above which safe CCC gains do not exist. To guarantee safety even with lag while preserving the benefits of CCC, we synthesize safety-critical CCC using CBFs. With the proposed safety-critical CCC, the CAV can leverage information from connected vehicles farther ahead to improve its safety. We evaluate this controller by numerical simulation using real traffic data.
Paper Structure (12 sections, 85 equations, 9 figures, 1 table)

This paper contains 12 sections, 85 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Connected Cruise Control
  3. Stability Analysis
  4. Background on Control Barrier Functions
  5. Safe Connected Cruise Control
  6. Safe Nominal CCC Design
  7. Safety-critical CCC
  8. Conclusions
  9. Expressions of Stability Boundaries
  10. Proof of Theorem \ref{['theo:Saf Region A-B1-BN']}
  11. Proof of Corollary \ref{['cor:critical lag']}
  12. Proof of Theorem 4

Figures (9)

  • Figure 1: (a) A connected automated vehicle (CAV) responds to the preceding human-driven vehicles (HVs) and to the head connected human-driven vehicle (CHV) using vehicle-to-everything (V2X) connectivity and connected cruise control (CCC). (b-c) Behavior of the CCC with unsafe control parameter choice (blue), and the proposed safety-critical CCC that minimally modifies the above CCC to ensure safety using the safety filter (orange).
  • Figure 2: Simulations of system (\ref{['eq:CAV system w/ lag']}) for $\xi=0\, \mathrm{s}$ (green) and $\xi=0.6\, \mathrm{s}$ (orange) using CCC (\ref{['eq:CCC general']}) with $n=1$, where a CAV performs an emergency brake to avoid crashing with the stopped CHV.
  • Figure 3: Stability charts of the CCC (\ref{['eq:CAV system w/ lag']},\ref{['eq:CCC 3veh']}) for ${\xi=0.2\, \rm{s}}$ and ${n=1}$ in (b) ${(A,B_1)}$ plane, (c) ${(B_1,B_2)}$ plane. (d-e) Simplified string stable domains, along with plant stable regions.
  • Figure 4: Safety charts of the nominal CCC (\ref{['eq:CCC general']}) when the CAV responds to the vehicle immediately ahead of it; see panel (a). The time headway criterion (\ref{['eq:TH']}) is considered for (b) different CAV lags $\xi$ in system (\ref{['eq:CAV system w/ lag']}) and (c) different bounds $\bar{v}$ on the speed difference in (\ref{['eq:Saf Region']}) with ${\xi=0.15\, \rm{s}}$.
  • Figure 5: Safety charts of the nominal CCC (\ref{['eq:CCC 3veh']}) when the CAV responds to the CHV two vehicles ahead ${(n=1)}$, see panel (a). The time headway criterion (\ref{['eq:TH']}) is considered for the lag (b-c) ${\xi = 0\, \rm{s}}$; (d-e) ${\xi = 0.15\, \rm{s}}$; (f-g) ${\xi = 0.2\, \rm{s}}$ in CAV system (\ref{['eq:CAV system w/ lag']}).
  • ...and 4 more figures

Theorems & Definitions (3)

  • proof : Proof of Theorem \ref{['theo:Saf Region A-B1-BN']}
  • proof : Proof of Corollary \ref{['cor:critical lag']}
  • proof : Proof of Theorem \ref{['theo:Saf Region general CCC']}