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Coordinated Control of Autonomous Vehicles for Traffic Density Reduction at a Signalized Junction: An MPC Approach

Rudra Sen, Subashish Datta

TL;DR

This work tackles traffic density at signalized junctions by coordinating connected autonomous vehicles (CAVs) through a dual-mode model predictive control (MPC) framework. It combines reference-velocity generation tied to junction signal timings with a linearized collision-avoidance scheme and a cooperative lane-change strategy, all under a formal stability and feasibility guarantee provided by an online maximal control invariant terminal set. The MPC design minimizes set-point tracking errors to a junction-oriented reference while enforcing polyhedral state and input constraints, and uses a maximal invariant terminal set to ensure recursive feasibility and convergence via a matrix inequality for the terminal cost $P$. Numerical simulations with 20 AVs across three lanes show effective congestion mitigation near red phases, safe lane-change maneuvers, and satisfaction of all constraints, highlighting the approach’s potential for real-time traffic optimization in urban environments.

Abstract

The effective and safe management of traffic is a key issue due to the rapid advancement of the urban transportation system. Connected autonomous vehicles (CAVs) possess the capability to connect with each other and adjacent infrastructure, presenting novel opportunities for enhancing traffic flow and coordination. This work proposes a dual-mode model predictive control (MPC) architecture that tackles two interrelated issues: mitigating traffic density at signalized junctions and facilitating seamless, cooperative lane changes in high-density traffic conditions. The objective of this work is to facilitate responsive decision-making for CAVs, thereby enhancing the efficiency and safety of urban mobility. Moreover, we ensure recursive feasibility and convergence of the proposed MPC scheme by the integration of an online-calculated maximal control invariant terminal set. Finally, the efficacy of the proposed approach is validated through numerical simulation.

Coordinated Control of Autonomous Vehicles for Traffic Density Reduction at a Signalized Junction: An MPC Approach

TL;DR

This work tackles traffic density at signalized junctions by coordinating connected autonomous vehicles (CAVs) through a dual-mode model predictive control (MPC) framework. It combines reference-velocity generation tied to junction signal timings with a linearized collision-avoidance scheme and a cooperative lane-change strategy, all under a formal stability and feasibility guarantee provided by an online maximal control invariant terminal set. The MPC design minimizes set-point tracking errors to a junction-oriented reference while enforcing polyhedral state and input constraints, and uses a maximal invariant terminal set to ensure recursive feasibility and convergence via a matrix inequality for the terminal cost . Numerical simulations with 20 AVs across three lanes show effective congestion mitigation near red phases, safe lane-change maneuvers, and satisfaction of all constraints, highlighting the approach’s potential for real-time traffic optimization in urban environments.

Abstract

The effective and safe management of traffic is a key issue due to the rapid advancement of the urban transportation system. Connected autonomous vehicles (CAVs) possess the capability to connect with each other and adjacent infrastructure, presenting novel opportunities for enhancing traffic flow and coordination. This work proposes a dual-mode model predictive control (MPC) architecture that tackles two interrelated issues: mitigating traffic density at signalized junctions and facilitating seamless, cooperative lane changes in high-density traffic conditions. The objective of this work is to facilitate responsive decision-making for CAVs, thereby enhancing the efficiency and safety of urban mobility. Moreover, we ensure recursive feasibility and convergence of the proposed MPC scheme by the integration of an online-calculated maximal control invariant terminal set. Finally, the efficacy of the proposed approach is validated through numerical simulation.

Paper Structure

This paper contains 16 sections, 2 theorems, 31 equations, 9 figures, 5 algorithms.

Table of Contents

  1. Introduction
  2. Notations
  3. Vehicle Model and Problem Formulation
  4. Vehicle Model
  5. MPC Formulation for Control Action for AVs
  6. Reference Velocity Generation
  7. Linear Approximation of Collision Avoidance Constraint
  8. Computation of Terminal Set
  9. Cost Function and MPC formulation
  10. Lane Change Maneuver
  11. Recursive Feasibility and Stability Analysis
  12. Recursive Feasibility
  13. Stability Analysis
  14. Computation of terminal cost weight matrix P
  15. Numerical Example
  16. ...and 1 more sections

Key Result

Lemma 1

Assume that there exists a nonempty terminal set $\mathscr{X}^i_{\mathbb{T}_k}\subseteq\mathscr{X}^i$ such that the predicted terminal state $x^i_{N|k}\in\mathscr{X}^i_{\mathbb{T}_k}$. If the optimization $\mathbb{OP}$ is feasible at time step $k$, then it will be feasible for any future time step $

Figures (9)

  • Figure 1: Dynamic Model of AV
  • Figure 2: Linearized collision avoidance constraint: (a) The active hyperplane (solid red) when $j^{th}$ AV is ahead on the same lane, (b) The active hyperplane when $j^{th}$ AV is on the right lane, (c) The active hyperplane when $j^{th}$ AV is on the left lane.
  • Figure 3: Lane change scenario
  • Figure 4: Longitudinal Positions of all AVs ($20$ AVs) crossing $SJ$. Horizontal red lines (solid) denote red signal duration, and horizontal green lines (dashed) denote green signal duration.
  • Figure 5: Longitudinal Velocity of all AVs ($20$ AVs). Horizontal red lines (dashed) denote maximum and minimum velocity bounds.
  • ...and 4 more figures

Theorems & Definitions (4)

  • Remark 1
  • Lemma 1
  • Lemma 2
  • Remark 2