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Safe and Efficient Coexistence of Autonomous Vehicles with Human-Driven Traffic at Signalized Intersections

Filippos N. Tzortzoglou, Logan E. Beaver, Andreas A. Malikopoulos

TL;DR

This work addresses the challenge of safely and efficiently coordinating autonomous and human-driven vehicles at signalized intersections by presenting an integrated optimal-control framework that jointly optimizes CAV trajectories and adaptive signal timings while accounting for HDV behavior. The method employs a two-layer optimization: an upper-level time-optimal decision determines CAV exit times, and a lower-level energy-optimal control yields smooth, safe trajectories; unconstrained solutions are preferred and solved analytically, with fallback to constrained trajectories or standby modes when needed. The framework incorporates rear-end and state constraints, traffic-light timing, IDM-based HDV predictions, and an event-triggered replanning mechanism to adapt to evolving intersection states, all validated through MATLAB simulations. Results demonstrate that adaptive signal timings coupled with CAV trajectory optimization can substantially improve throughput and energy efficiency, especially at higher CAV penetration, with cycle duration playing a critical role in system performance.

Abstract

The proliferation of connected and automated vehicles (CAVs) has positioned mixed traffic environments, which encompass both CAVs and human driven vehicles (HDVs), as critical components of emerging mobility systems. Signalized intersections are paramount for optimizing transportation efficiency and enhancing energy economy, as they inherently induce stop and go traffic dynamics. In this paper, we present an integrated framework that concurrently optimizes signal timing and CAV trajectories at signalized intersections, with the dual objectives of maximizing traffic throughput and minimizing energy consumption for CAVs. We first formulate an optimal control strategy for CAVs that prioritizes trajectory planning to circumvent state constraints, while incorporating the impact of signal timing and HDV behavior. Furthermore, we introduce a traffic signal control methodology that dynamically adjusts signal phases based on vehicular density per lane, while mitigating disruption for CAVs scheduled to traverse the intersection. Acknowledging the system's inherent dynamism, we also explore event triggered replanning mechanisms that enable CAVs to iteratively refine their planned trajectories in response to the emergence of more efficient routing options. The efficacy of our proposed framework is evaluated through comprehensive simulations in MATLAB.

Safe and Efficient Coexistence of Autonomous Vehicles with Human-Driven Traffic at Signalized Intersections

TL;DR

This work addresses the challenge of safely and efficiently coordinating autonomous and human-driven vehicles at signalized intersections by presenting an integrated optimal-control framework that jointly optimizes CAV trajectories and adaptive signal timings while accounting for HDV behavior. The method employs a two-layer optimization: an upper-level time-optimal decision determines CAV exit times, and a lower-level energy-optimal control yields smooth, safe trajectories; unconstrained solutions are preferred and solved analytically, with fallback to constrained trajectories or standby modes when needed. The framework incorporates rear-end and state constraints, traffic-light timing, IDM-based HDV predictions, and an event-triggered replanning mechanism to adapt to evolving intersection states, all validated through MATLAB simulations. Results demonstrate that adaptive signal timings coupled with CAV trajectory optimization can substantially improve throughput and energy efficiency, especially at higher CAV penetration, with cycle duration playing a critical role in system performance.

Abstract

The proliferation of connected and automated vehicles (CAVs) has positioned mixed traffic environments, which encompass both CAVs and human driven vehicles (HDVs), as critical components of emerging mobility systems. Signalized intersections are paramount for optimizing transportation efficiency and enhancing energy economy, as they inherently induce stop and go traffic dynamics. In this paper, we present an integrated framework that concurrently optimizes signal timing and CAV trajectories at signalized intersections, with the dual objectives of maximizing traffic throughput and minimizing energy consumption for CAVs. We first formulate an optimal control strategy for CAVs that prioritizes trajectory planning to circumvent state constraints, while incorporating the impact of signal timing and HDV behavior. Furthermore, we introduce a traffic signal control methodology that dynamically adjusts signal phases based on vehicular density per lane, while mitigating disruption for CAVs scheduled to traverse the intersection. Acknowledging the system's inherent dynamism, we also explore event triggered replanning mechanisms that enable CAVs to iteratively refine their planned trajectories in response to the emergence of more efficient routing options. The efficacy of our proposed framework is evaluated through comprehensive simulations in MATLAB.

Paper Structure

This paper contains 20 sections, 1 theorem, 20 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Literature Review
  3. Control of traffic signals
  4. Control of CAVs
  5. Joint control of traffic signals and CAVs
  6. Contributions of this paper
  7. Modeling Framework
  8. Control of Connected and Automoated Vehicles
  9. Rear-end constraints
  10. State constraints
  11. Traffic light constraint
  12. Finding an unconstrained trajectory
  13. Case where no feasible solution exists due to traffic light constraints
  14. Finding a constrained trajectory
  15. Standby mode
  16. ...and 5 more sections

Key Result

Theorem 1

For CAV $i$, the latest stopping time $t_i^s$ to stop at $p_i^{tr}$ under an unconstrained trajectory, is defined as: where $t_b=\frac{-v_i^0+\sqrt{(v_i^0)^2-6u_{\min}p_i^{tr}}}{-u_{\min}}$ and $u_i^c=-\frac{2(v_i^0)^2}{3p_i^{tr}}$ .

Figures (4)

  • Figure 1: Illustration of intersection set-up and traffic signal phases.
  • Figure 2: Illustration of different instants with varying crossing intervals and times $\mathcal{T}_i^{\min}$, $t_i^{c_1}$, and $t_i^{c_2}.$
  • Figure 3: CAVs and HDVs crossing the traffic light under different traffic cycles.
  • Figure 4: Snapshots from different scenarios.

Theorems & Definitions (6)

  • Remark 1
  • Remark 2
  • Theorem 1
  • proof
  • Remark 3
  • Remark 4