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Robust Optimal Lane-changing Control for Connected Autonomous Vehicles in Mixed Traffic

Anni Li, Andres S. Chavez Armijos, Christos G. Cassandras

TL;DR

The paper tackles robust time- and energy-efficient lane changes for a Connected Autonomous Vehicle operating in mixed traffic with Human-Driven Vehicles. It develops a threshold-based policy that decides whether a CAV should merge ahead of a human-driven vehicle or ahead of a cooperating CAV, and it formulates this decision within a bilevel, game-theoretic framework solved by an Iterated Best Response (IBR) method. Safety is guaranteed via Control Barrier Functions, while a detailed longitudinal and lateral planning scheme is developed for both merging scenarios, including a monotonicity analysis that underpins the threshold policy. Simulation results show substantial improvements in cost and minimal disruption to traffic flow, validating the approach and highlighting robustness to HDV behavior; the work also demonstrates significant benefits of CAV cooperation over HDV-only baselines.

Abstract

We derive time and energy-optimal policies for a Connected Autonomous Vehicle (CAV) to execute lane change maneuvers in mixed traffic, i.e., in the presence of both CAVs and Human Driven Vehicles (HDVs). These policies are also shown to be robust with respect to the unpredictable behavior of HDVs by exploiting CAV cooperation which can eliminate or greatly reduce the interaction between CAVs and HDVs. We derive a simple threshold-based criterion on the initial relative distance between two cooperating CAVs based on which an optimal policy is selected such that the lane-changing CAV merges ahead of a cooperating CAV in the target lane; in this case, the lane-changing CAV's trajectory becomes independent of HDV behavior. Otherwise, the interaction between CAVs and neighboring HDVs is formulated as a bilevel optimization problem with an appropriate behavioral model for an HDV, and an iterated best response (IBR) method is used to determine an equilibrium. We demonstrate the convergence of the IBR process under certain conditions. Furthermore, Control Barrier Functions (CBFs) are implemented to ensure the robustness of lane-changing behaviors by guaranteeing safety in both longitudinal and lateral directions despite HDV disturbances. Simulation results validate the effectiveness of our CAV controllers in terms of cost, safety guarantees, and limited disruption to traffic flow. Additionally, we demonstrate the robustness of the lane-changing behaviors in the presence of uncontrollable HDVs.

Robust Optimal Lane-changing Control for Connected Autonomous Vehicles in Mixed Traffic

TL;DR

The paper tackles robust time- and energy-efficient lane changes for a Connected Autonomous Vehicle operating in mixed traffic with Human-Driven Vehicles. It develops a threshold-based policy that decides whether a CAV should merge ahead of a human-driven vehicle or ahead of a cooperating CAV, and it formulates this decision within a bilevel, game-theoretic framework solved by an Iterated Best Response (IBR) method. Safety is guaranteed via Control Barrier Functions, while a detailed longitudinal and lateral planning scheme is developed for both merging scenarios, including a monotonicity analysis that underpins the threshold policy. Simulation results show substantial improvements in cost and minimal disruption to traffic flow, validating the approach and highlighting robustness to HDV behavior; the work also demonstrates significant benefits of CAV cooperation over HDV-only baselines.

Abstract

We derive time and energy-optimal policies for a Connected Autonomous Vehicle (CAV) to execute lane change maneuvers in mixed traffic, i.e., in the presence of both CAVs and Human Driven Vehicles (HDVs). These policies are also shown to be robust with respect to the unpredictable behavior of HDVs by exploiting CAV cooperation which can eliminate or greatly reduce the interaction between CAVs and HDVs. We derive a simple threshold-based criterion on the initial relative distance between two cooperating CAVs based on which an optimal policy is selected such that the lane-changing CAV merges ahead of a cooperating CAV in the target lane; in this case, the lane-changing CAV's trajectory becomes independent of HDV behavior. Otherwise, the interaction between CAVs and neighboring HDVs is formulated as a bilevel optimization problem with an appropriate behavioral model for an HDV, and an iterated best response (IBR) method is used to determine an equilibrium. We demonstrate the convergence of the IBR process under certain conditions. Furthermore, Control Barrier Functions (CBFs) are implemented to ensure the robustness of lane-changing behaviors by guaranteeing safety in both longitudinal and lateral directions despite HDV disturbances. Simulation results validate the effectiveness of our CAV controllers in terms of cost, safety guarantees, and limited disruption to traffic flow. Additionally, we demonstrate the robustness of the lane-changing behaviors in the presence of uncontrollable HDVs.
Paper Structure (24 sections, 7 theorems, 82 equations, 9 figures, 4 tables, 1 algorithm)

This paper contains 24 sections, 7 theorems, 82 equations, 9 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Vehicle Dynamics
  4. Safety Constraints
  5. Traffic Disruption
  6. Optimal pre-interaction trajectory for CAV C
  7. CAV $C$ Merges Ahead of HDV
  8. Optimal Longitudinal Motion for $C$ and $H$ Interaction
  9. Estimate HDV Trajectory (OCP-HDV)
  10. Update CAV C Trajectory (OCP-CAVC)
  11. Update CAV 1 Trajectory (OCP-CAV1)
  12. Convergence Analysis of IBR Process
  13. Optimal Lateral Motion Planning
  14. CAV C Merges Ahead of CAV 1
  15. Optimal Longitudinal Trajectory Planning
  16. ...and 9 more sections

Key Result

Lemma 1

If the optimal trajectory of HDV $H$ or CAV $C$ remains the same in two consecutive iterations, i.e., $x_{i,k}^*(t)=x_{i,k+1}^*(t)$, $t\in[t_1^*,t_f^*],i\in\{C,H\},k\in\mathbb{N}_+$, the Iterated Best response (IBR) process converges in a finite number of iterations.

Figures (9)

  • Figure 1: The basic lane-changing maneuver process.
  • Figure 2: Elliptical safe region in lane-changing maneuvers.
  • Figure 3: The relative position of triplet from $t_0$ to $t_1$
  • Figure 4: Bilevel optimization problem solved by CAV $C$. Initialization provides $t_1^*$ obtained from the pre-interaction process and the solution of \ref{['eq:OCP_cavC']} to get $t_f^*,x_C^*(t),v_C^*(t)$. In addition, $x_1^*(t)=x_1(t_1^*)+v_1(t_1^*)(t_f^*-t_1^*),v_1^*(t)=v_1(t_1^*)$. Upon convergence, the lane change maneuver is executed with the final $x_C^*(t),v_C^*(t),t\in[t_1^*,t_f^*]$.
  • Figure 5: The illustration of the constrained case
  • ...and 4 more figures

Theorems & Definitions (7)

  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Theorem 1
  • Lemma 4
  • Lemma 5
  • Theorem 2