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Improved Consensus ADMM for Cooperative Motion Planning of Large-Scale Connected Autonomous Vehicles with Limited Communication

Haichao Liu, Zhenmin Huang, Zicheng Zhu, Yulin Li, Shaojie Shen, Jun Ma

TL;DR

The paper addresses cooperative motion planning for large-scale connected autonomous vehicles under limited communications. It develops an improved consensus ADMM that operates on locally connected topologies and introduces a dynamic graph evolution strategy to keep subproblem sizes manageable, achieving $O(N)$ computational complexity by exploiting dual-update sparsity. The method integrates guidance trajectory generation, convexification, and a receding-horizon framework, and demonstrates scalability and real-time feasibility in simulations with up to 80 CAVs in the CARLA environment. The proposed combination of parallel optimization, dynamic subgraph partitioning, and MPC-style receding horizon offers a practical pathway to scalable, safe, and efficient autonomous driving in dense urban scenarios.

Abstract

This paper investigates a cooperative motion planning problem for large-scale connected autonomous vehicles (CAVs) under limited communications, which addresses the challenges of high communication and computing resource requirements. Our proposed methodology incorporates a parallel optimization algorithm with improved consensus ADMM considering a more realistic locally connected topology network, and time complexity of O(N) is achieved by exploiting the sparsity in the dual update process. To further enhance the computational efficiency, we employ a lightweight evolution strategy for the dynamic connectivity graph of CAVs, and each sub-problem split from the consensus ADMM only requires managing a small group of CAVs. The proposed method implemented with the receding horizon scheme is validated thoroughly, and comparisons with existing numerical solvers and approaches demonstrate the efficiency of our proposed algorithm. Also, simulations on large-scale cooperative driving tasks involving 80 vehicles are performed in the high-fidelity CARLA simulator, which highlights the remarkable computational efficiency, scalability, and effectiveness of our proposed development. Demonstration videos are available at https://henryhcliu.github.io/icadmm_cmp_carla.

Improved Consensus ADMM for Cooperative Motion Planning of Large-Scale Connected Autonomous Vehicles with Limited Communication

TL;DR

The paper addresses cooperative motion planning for large-scale connected autonomous vehicles under limited communications. It develops an improved consensus ADMM that operates on locally connected topologies and introduces a dynamic graph evolution strategy to keep subproblem sizes manageable, achieving computational complexity by exploiting dual-update sparsity. The method integrates guidance trajectory generation, convexification, and a receding-horizon framework, and demonstrates scalability and real-time feasibility in simulations with up to 80 CAVs in the CARLA environment. The proposed combination of parallel optimization, dynamic subgraph partitioning, and MPC-style receding horizon offers a practical pathway to scalable, safe, and efficient autonomous driving in dense urban scenarios.

Abstract

This paper investigates a cooperative motion planning problem for large-scale connected autonomous vehicles (CAVs) under limited communications, which addresses the challenges of high communication and computing resource requirements. Our proposed methodology incorporates a parallel optimization algorithm with improved consensus ADMM considering a more realistic locally connected topology network, and time complexity of O(N) is achieved by exploiting the sparsity in the dual update process. To further enhance the computational efficiency, we employ a lightweight evolution strategy for the dynamic connectivity graph of CAVs, and each sub-problem split from the consensus ADMM only requires managing a small group of CAVs. The proposed method implemented with the receding horizon scheme is validated thoroughly, and comparisons with existing numerical solvers and approaches demonstrate the efficiency of our proposed algorithm. Also, simulations on large-scale cooperative driving tasks involving 80 vehicles are performed in the high-fidelity CARLA simulator, which highlights the remarkable computational efficiency, scalability, and effectiveness of our proposed development. Demonstration videos are available at https://henryhcliu.github.io/icadmm_cmp_carla.
Paper Structure (25 sections, 1 theorem, 54 equations, 10 figures, 5 tables, 4 algorithms)

This paper contains 25 sections, 1 theorem, 54 equations, 10 figures, 5 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Notations
  3. Problem Formulation
  4. Representation of CAVs with Graph Theory
  5. Vehicle Model
  6. Cooperative Motion Planning with Communication Limits
  7. Inter-Vehicle Collision Avoidance of CAVs
  8. Cooperative Motion Planning with Limited Communication via Improved Consensus ADMM
  9. Guidance Trajectory Generation and Dynamic Search
  10. Convexification and Reformulation
  11. Improved Consensus ADMM for Cooperative Motion Planning with Limited Communication Range
  12. Dual Update
  13. Primal Update
  14. Cooperative Motion Planning Framework for Large-Scale CAVs
  15. Graph Evolution based on Manhattan Distance
  16. ...and 10 more sections

Key Result

Theorem 1

Given that the dual variables of the CAVs are initialized by same values, for the elements of dual variables with $\forall j\neq i, \forall v\neq i$, $\bm \alpha^{j,k}_{[2,i]} = \bm \alpha^{v,k}_{[2,i]} =\bm \alpha^{k}_{[2,i]}, \bm \alpha\in \{\bm p, \bm s, \bm r,\bm y,\bm x\}, \forall k\in \mathca

Figures (10)

  • Figure 1: Demonstration of the proposed collaborative motion planning strategy for large-scale CAVs in urban driving scenarios. The problem is formulated, where one optimal control problem is constructed within each subgraph (orange region) and solved by the improved consensus ADMM algorithm. The subgraphs are generated by the proposed graph evolution algorithm, in which the edges of the dynamic connectivity graph are created within each blue region centered by each CAV within a specified subgraph.
  • Figure 2: Geometric relationship and transformation for inter-vehicle collision avoidance, in which the two CAVs in a pair are enwrapped with a double circle and an ellipse, respectively. The radius of CAV $i$ is $r^i$, while the length of semi-major and semi-minor axes of CAV $j$ are $a^j$ and $b^j$, respectively. The rotation angle between the global coordinate system and the $a$-paralleled coordinate system is the same as the heading angle of the $\theta^j$. After the above transformation, the collision discriminant becomes judging whether a point is within a unit circle.
  • Figure 3: Smoothed guidance trajectories for cooperative motion planning. We generate these trajectories by sampling the road topology information from the OpenDRIVE map. Each vehicle's trajectory is visually represented by dots of different colors. The plotted guidance trajectories unveil potential collision conflicts that may arise within the intersection area.
  • Figure 4: The minimum distance between all the CAVs at each time step. Different colors represent different methods. All the above methods performed safe cooperative motion planning with a minimum distance greater than 2.5 m.
  • Figure 5: Velocity distribution along all the time steps with different methods. As the reference velocity is 10 m/s, a speed distribution closer to this value indicates better driving performance.
  • ...and 5 more figures

Theorems & Definitions (9)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Theorem 1
  • proof
  • Remark 5
  • Remark 6
  • Remark 7