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Performance-Sensitive Potential Functions for Efficient Flow of Connected and Automated Vehicles

Filippos N. Tzortzoglou, Dionysios Theodosis, Aditya Dave, Andreas Malikopoulos

TL;DR

This work tackles lane-based coordination of connected automated vehicles by addressing limitations of traditional repulsive potentials that can cause aggressive accelerations and suboptimal spacing. It introduces a parameterized performance-sensitive potential $V_{new}$, governed by $(\alpha, r, p)$, and formulates an offline optimization to minimize accelerations and inter-vehicle gaps, followed by a neural network surrogate that maps initial conditions to optimal parameters for real-time use. The approach preserves safety under a sampled-data framework by deriving sufficient conditions for collision avoidance and positive speeds, and it demonstrates improved acceleration profiles and traffic flow in simulations compared to the prior $V_{old}$ approach. The combination of Lyapunov-based control, parameter optimization, and data-driven real-time parameterization offers a practical path toward more comfortable, efficient, and scalable CAV coordination on single-lane roads, with future extensions to lane-free scenarios and mixed traffic.

Abstract

Connected and automated vehicles (CAVs) provide the most intriguing opportunity for enabling users to monitor transportation network conditions and make better decisions for improving safety and transportation efficiency. In this paper, we address the problem of effectively coordinating CAVs on lane-based roadways. Our approach utilizes potential functions to generate repulsive forces between CAVs that ensure collision avoidance. However, such potential functions can lead to unrealistic acceleration profiles and large inter-vehicle distances. The primary contribution of this work is the introduction of performance-sensitive potential functions to address these challenges. In our approach, the parameters of a potential function are determined through an optimization problem aiming to reduce both acceleration and inter-vehicle distances. To circumvent the computational implications due to the complexity of the resulting optimization problem that prevents the derivation of a real-time solution, we train a neural network model to learn the mapping of initial conditions to optimal parameters derived offline. Then, we prove sufficient criteria for the sampled-data model to ensure that the neural network output does not activate any of the state and safety constraints. Finally, we provide simulation results to demonstrate the effectiveness of the proposed approach.

Performance-Sensitive Potential Functions for Efficient Flow of Connected and Automated Vehicles

TL;DR

This work tackles lane-based coordination of connected automated vehicles by addressing limitations of traditional repulsive potentials that can cause aggressive accelerations and suboptimal spacing. It introduces a parameterized performance-sensitive potential , governed by , and formulates an offline optimization to minimize accelerations and inter-vehicle gaps, followed by a neural network surrogate that maps initial conditions to optimal parameters for real-time use. The approach preserves safety under a sampled-data framework by deriving sufficient conditions for collision avoidance and positive speeds, and it demonstrates improved acceleration profiles and traffic flow in simulations compared to the prior approach. The combination of Lyapunov-based control, parameter optimization, and data-driven real-time parameterization offers a practical path toward more comfortable, efficient, and scalable CAV coordination on single-lane roads, with future extensions to lane-free scenarios and mixed traffic.

Abstract

Connected and automated vehicles (CAVs) provide the most intriguing opportunity for enabling users to monitor transportation network conditions and make better decisions for improving safety and transportation efficiency. In this paper, we address the problem of effectively coordinating CAVs on lane-based roadways. Our approach utilizes potential functions to generate repulsive forces between CAVs that ensure collision avoidance. However, such potential functions can lead to unrealistic acceleration profiles and large inter-vehicle distances. The primary contribution of this work is the introduction of performance-sensitive potential functions to address these challenges. In our approach, the parameters of a potential function are determined through an optimization problem aiming to reduce both acceleration and inter-vehicle distances. To circumvent the computational implications due to the complexity of the resulting optimization problem that prevents the derivation of a real-time solution, we train a neural network model to learn the mapping of initial conditions to optimal parameters derived offline. Then, we prove sufficient criteria for the sampled-data model to ensure that the neural network output does not activate any of the state and safety constraints. Finally, we provide simulation results to demonstrate the effectiveness of the proposed approach.
Paper Structure (11 sections, 2 theorems, 13 equations, 5 figures)

This paper contains 11 sections, 2 theorems, 13 equations, 5 figures.

Table of Contents

  1. INTRODUCTION
  2. Modeling Framework
  3. Performance-sensitive Potential Function
  4. Influence of the Parameters in $V_{new}$
  5. Optimization Framework
  6. Solution Approach
  7. Challenges in Analytical Solution
  8. Real Time Implementation using Supervised Learning
  9. Exact Discrete Model
  10. Simulations
  11. Concluding remarks and discussion

Key Result

Theorem 1

For every initial condition $(s_2(t_0),\ldots,s_n(t_0),v_1(t_0),\ldots,v_n(t_0))\in\Omega$, the solution $(s_2(t),\ldots,s_n(t),v_1(t),\ldots,v_n(t))\in\Omega$ is defined for all $t\ge t_0$ and satisfies $\lim_{t\to+\infty}(v_i(t))=v^*$ for all $i=1,\ldots,n$ and $\lim_{t\to +\infty}(V'(s_i(t))=0$ f

Figures (5)

  • Figure 1: Single lane road with four vehicles.
  • Figure 2: The potential $V_{new}$ under different combinations of parameters $\alpha$, $r$ and $p$.
  • Figure 3: The derivative $V'_{new}$ of the potential $V_{new}$ under different combinations of parameters $\alpha$, $r$ and $p$.
  • Figure 4: Results using the potential function $V_{old}$ defined in karafyllis2022stability.
  • Figure 5: Results using the proposed parameterized potential function $V_{new}$.

Theorems & Definitions (10)

  • Theorem 1: karafyllis2022stability
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Remark 6
  • Remark 7
  • Lemma 1
  • proof