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A Feasibility Analysis at Signal-Free Intersections

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

TL;DR

The paper tackles feasibility limitations in a decentralized coordination framework for connected and automated vehicles at signal-free intersections as traffic increases. It extends the traditional $3^{\text{rd}}$-order trajectory solution by employing Vandermonde-based numerical interpolation to construct higher-order polynomials, enabling online, real-time trajectory generation. A two-level optimization approach is used: an upper-level time-optimal problem to select exit times and a lower-level energy-optimal problem that minimizes jerk, all while enforcing rear-end and lateral safety constraints. Theoretical results guarantee the existence of interpolating polynomials under increasing time-node sequences, and numerical simulations demonstrate real-time performance and the practical benefits of the interpolation strategy in expanding the feasible domain and improving energy efficiency.

Abstract

In this letter, we address the problem of improving the feasible domain of the solution of a decentralized control framework for coordinating connected and automated vehicles (CAVs) at signal-free intersections as the traffic volume increases. The framework provides the optimal trajectories of CAVs to cross the intersection safely without stop-and-go driving. However, as the traffic volume increases, the domain of the feasible trajectories decreases. We use concepts of numerical interpolation to identify appropriate polynomials that can serve as alternative trajectories of the CAVs, expanding the domain of the feasible CAV trajectories. We provide the conditions under which such polynomials exist. Finally, we demonstrate the efficacy of our approach through numerical simulations.

A Feasibility Analysis at Signal-Free Intersections

TL;DR

The paper tackles feasibility limitations in a decentralized coordination framework for connected and automated vehicles at signal-free intersections as traffic increases. It extends the traditional -order trajectory solution by employing Vandermonde-based numerical interpolation to construct higher-order polynomials, enabling online, real-time trajectory generation. A two-level optimization approach is used: an upper-level time-optimal problem to select exit times and a lower-level energy-optimal problem that minimizes jerk, all while enforcing rear-end and lateral safety constraints. Theoretical results guarantee the existence of interpolating polynomials under increasing time-node sequences, and numerical simulations demonstrate real-time performance and the practical benefits of the interpolation strategy in expanding the feasible domain and improving energy efficiency.

Abstract

In this letter, we address the problem of improving the feasible domain of the solution of a decentralized control framework for coordinating connected and automated vehicles (CAVs) at signal-free intersections as the traffic volume increases. The framework provides the optimal trajectories of CAVs to cross the intersection safely without stop-and-go driving. However, as the traffic volume increases, the domain of the feasible trajectories decreases. We use concepts of numerical interpolation to identify appropriate polynomials that can serve as alternative trajectories of the CAVs, expanding the domain of the feasible CAV trajectories. We provide the conditions under which such polynomials exist. Finally, we demonstrate the efficacy of our approach through numerical simulations.
Paper Structure (13 sections, 5 theorems, 12 equations, 5 figures, 1 algorithm)

This paper contains 13 sections, 5 theorems, 12 equations, 5 figures, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Problem Formulation
  3. Safety Constraints
  4. Low-Level Optimization
  5. Upper-level optimization problem
  6. Enhancing the Domain of Feasible Solutions
  7. Theoretical Results
  8. Implementation in CAVs
  9. Lateral constraints
  10. Rear-End Constraints
  11. Solution
  12. Numerical Simulations
  13. Concluding Remarks

Key Result

Theorem 1

Given $n+1$ distinct nodes, $\{x_0, \ldots, x_{n}\}$ and $n+1$ corresponding values $\{y_0, \ldots, y_{n}\}$, there exists a unique polynomial $f(x)$ of degree $n$, such that $f(x_i) = y_i$ for all $i = 1, \ldots, n+1$.

Figures (5)

  • Figure 1: Schematic of the intersection showing the control zone, conflict points, and paths.
  • Figure 2: Snapshot of a CAV entering the Intersection
  • Figure 3: Relationship between minimum rear-end and lateral time headways
  • Figure 4: CAV trajectories defined only from Problem 2.
  • Figure 5: CAV trajectories defined from both Problem 2 and 3.

Theorems & Definitions (14)

  • Remark 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Lemma 1
  • proof
  • Theorem 3
  • proof
  • Remark 2
  • ...and 4 more