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Sequencing-enabled Hierarchical Cooperative CAV On-ramp Merging Control with Enhanced Stability and Feasibility

Sixu Li, Yang Zhou, Xinyue Ye, Jiwan Jiang, Meng Wang

TL;DR

The paper addresses safety, stability, and feasibility challenges in on-ramp merging with connected automated vehicles by proposing a sequencing-enabled hierarchical framework. An upper-level mixed-integer linear program determines merging sequences to balance traffic density and efficiency, relaying the result to a two-layer lower-level controller that uses distributed MPC for longitudinal control and a linear MPC for lateral tracking. The longitudinal controller is proven to be asymptotically locally stable and $l_2$-norm string stable, with an expanded initial feasible set compared with conventional terminal-constrained MPC approaches, while the lateral controller maintains lane-keeping on curved ramps. Numerical experiments show the proposed scheme outperforms FIFO sequencing, damps disturbances along vehicle strings, and achieves rapid convergence of lateral deviations, all with real-time computational feasibility. This framework offers a practical, provably stable, and scalable solution for two-dimensional CAV on-ramp merging with potential for real-world ITS deployment.

Abstract

This paper develops a sequencing-enabled hierarchical connected automated vehicle (CAV) cooperative on-ramp merging control framework. The proposed framework consists of a two-layer design: the upper level control sequences the vehicles to harmonize the traffic density across mainline and on-ramp segments while enhancing lower-level control efficiency through a mixed-integer linear programming formulation. Subsequently, the lower-level control employs a longitudinal distributed model predictive control (MPC) supplemented by a virtual car-following (CF) concept to ensure asymptotic local stability, l_2 norm string stability, and safety. Proofs of asymptotic local stability and l_2 norm string stability are mathematically derived. Compared to other prevalent asymptotic local-stable MPC controllers, the proposed distributed MPC controller greatly expands the initial feasible set. Additionally, an auxiliary lateral control is developed to maintain lane-keeping and merging smoothness while accommodating ramp geometric curvature. To validate the proposed framework, multiple numerical experiments are conducted. Results indicate a notable outperformance of our upper-level controller against a distance-based sequencing method. Furthermore, the lower-level control effectively ensures smooth acceleration, safe merging with adequate spacing, adherence to proven longitudinal local and string stability, and rapid regulation of lateral deviations.

Sequencing-enabled Hierarchical Cooperative CAV On-ramp Merging Control with Enhanced Stability and Feasibility

TL;DR

The paper addresses safety, stability, and feasibility challenges in on-ramp merging with connected automated vehicles by proposing a sequencing-enabled hierarchical framework. An upper-level mixed-integer linear program determines merging sequences to balance traffic density and efficiency, relaying the result to a two-layer lower-level controller that uses distributed MPC for longitudinal control and a linear MPC for lateral tracking. The longitudinal controller is proven to be asymptotically locally stable and -norm string stable, with an expanded initial feasible set compared with conventional terminal-constrained MPC approaches, while the lateral controller maintains lane-keeping on curved ramps. Numerical experiments show the proposed scheme outperforms FIFO sequencing, damps disturbances along vehicle strings, and achieves rapid convergence of lateral deviations, all with real-time computational feasibility. This framework offers a practical, provably stable, and scalable solution for two-dimensional CAV on-ramp merging with potential for real-world ITS deployment.

Abstract

This paper develops a sequencing-enabled hierarchical connected automated vehicle (CAV) cooperative on-ramp merging control framework. The proposed framework consists of a two-layer design: the upper level control sequences the vehicles to harmonize the traffic density across mainline and on-ramp segments while enhancing lower-level control efficiency through a mixed-integer linear programming formulation. Subsequently, the lower-level control employs a longitudinal distributed model predictive control (MPC) supplemented by a virtual car-following (CF) concept to ensure asymptotic local stability, l_2 norm string stability, and safety. Proofs of asymptotic local stability and l_2 norm string stability are mathematically derived. Compared to other prevalent asymptotic local-stable MPC controllers, the proposed distributed MPC controller greatly expands the initial feasible set. Additionally, an auxiliary lateral control is developed to maintain lane-keeping and merging smoothness while accommodating ramp geometric curvature. To validate the proposed framework, multiple numerical experiments are conducted. Results indicate a notable outperformance of our upper-level controller against a distance-based sequencing method. Furthermore, the lower-level control effectively ensures smooth acceleration, safe merging with adequate spacing, adherence to proven longitudinal local and string stability, and rapid regulation of lateral deviations.
Paper Structure (20 sections, 4 theorems, 70 equations, 11 figures, 4 tables)

This paper contains 20 sections, 4 theorems, 70 equations, 11 figures, 4 tables.

Table of Contents

  1. INTRODUCTION
  2. PROBLEM FORMULATION
  3. UPPER-LEVEL CONTROLLER
  4. Decision Matrix and Information Vectors
  5. Constraints
  6. Cost Function
  7. LOWER-LEVEL LONGITUDINAL CONTROLLER
  8. Platoon System Dynamics
  9. Optimization Formulation
  10. Local Stability Analysis
  11. String Stability Analysis
  12. Initial Feasibility Analysis
  13. LOWER-LEVEL LATERAL CONTROLLER
  14. Kinematic Bicycle Model
  15. Optimization Formulation
  16. ...and 5 more sections

Key Result

Proposition 4.1

Under the assumption that the leading vehicle CAV1 runs at a constant speed and the safety cost is inactive, for CAV2, for any $\varepsilon>0$, there exists a finite lower bound $\hat{\beta}(\epsilon)={\sum_{k=0}^{N_p-1} \left[ \alpha_l \sum_{j=0}^k \alpha_f^{(k-j)} (\|\gamma_{max} - \gamma_{min}\|_

Figures (11)

  • Figure 1: On-ramp merging scenario and communication
  • Figure 2: Virtual axis mapping in 2 ramp lanes scenario
  • Figure 3: Calculation of $k^*$ using time-space diagram when CAV$i$ and CAV$i-1$ are on different roads
  • Figure 4: String-stable and string-unstable regions in $p$-$q$ space
  • Figure 5: Comparison of initial feasible sets of local-stable MPC controllers with different terminal constraints. (a) Zero-terminal constrained MPC. (b) Invariant set-terminal constrained MPC. (c) Proposed MPC.
  • ...and 6 more figures

Theorems & Definitions (18)

  • Remark 2.1
  • Definition 4.1
  • Definition 4.2
  • Definition 4.3
  • Proposition 4.1
  • proof
  • Proposition 4.2
  • proof
  • Proposition 4.3
  • proof
  • ...and 8 more