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Accelerating Time-Optimal Trajectory Planning for Connected and Automated Vehicles with Graph Neural Networks

Viet-Anh Le, Andreas A. Malikopoulos

TL;DR

The paper tackles real-time cooperative trajectory planning for multiple CAVs at unsignalized intersections by learning a mapping from problem parameters to optimal exit times using GraphSAGE. It combines a rigorous time-optimal framework with a learning-based warm-start to accelerate computation while enforcing all state, control, and safety constraints. The key contribution is a GNN-based predictor that estimates the optimal terminal times ${t_i^f}$, paired with an accelerated numerical solver that respects feasibility, enabling replanning at every time step. The results demonstrate significant computational speedups and travel-time improvements, highlighting the method's potential for scalable, real-time coordination in connected vehicle systems, and suggesting future extension to mixed-traffic scenarios.

Abstract

In this paper, we present a learning-based framework that accelerates time- and energy-optimal trajectory planning for connected and automated vehicles (CAVs) using graph neural networks (GNNs). We formulate the multi-agent coordination problem encountered in traffic scenarios as a cooperative trajectory planning problem that minimizes travel time, subject to motion primitives derived from energy-optimal solutions. The effectiveness of this framework can be further improved through replanning at each time step, enabling the system to incorporate newly observed information. To achieve real-time execution of such a multi-agent replanning scheme, we employ a GNN architecture to learn the solutions of the time-optimal trajectory planning problem from offline-generated data. The trained model produces online predictions that serve as warm-start solutions for numerical optimization, thereby enabling rapid computation of minimal exit times and the associated feasible trajectories. This learning-augmented approach substantially reduces computation time while ensuring that all state, input, and safety constraints are satisfied.

Accelerating Time-Optimal Trajectory Planning for Connected and Automated Vehicles with Graph Neural Networks

TL;DR

The paper tackles real-time cooperative trajectory planning for multiple CAVs at unsignalized intersections by learning a mapping from problem parameters to optimal exit times using GraphSAGE. It combines a rigorous time-optimal framework with a learning-based warm-start to accelerate computation while enforcing all state, control, and safety constraints. The key contribution is a GNN-based predictor that estimates the optimal terminal times , paired with an accelerated numerical solver that respects feasibility, enabling replanning at every time step. The results demonstrate significant computational speedups and travel-time improvements, highlighting the method's potential for scalable, real-time coordination in connected vehicle systems, and suggesting future extension to mixed-traffic scenarios.

Abstract

In this paper, we present a learning-based framework that accelerates time- and energy-optimal trajectory planning for connected and automated vehicles (CAVs) using graph neural networks (GNNs). We formulate the multi-agent coordination problem encountered in traffic scenarios as a cooperative trajectory planning problem that minimizes travel time, subject to motion primitives derived from energy-optimal solutions. The effectiveness of this framework can be further improved through replanning at each time step, enabling the system to incorporate newly observed information. To achieve real-time execution of such a multi-agent replanning scheme, we employ a GNN architecture to learn the solutions of the time-optimal trajectory planning problem from offline-generated data. The trained model produces online predictions that serve as warm-start solutions for numerical optimization, thereby enabling rapid computation of minimal exit times and the associated feasible trajectories. This learning-augmented approach substantially reduces computation time while ensuring that all state, input, and safety constraints are satisfied.

Paper Structure

This paper contains 11 sections, 16 equations, 3 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Coordination of Connected and Automated Vehicles
  3. Problem Formulation
  4. Time-Optimal Trajectory Planning
  5. Replanning Mechanism
  6. Learning to Coordinate with Graph Neural Networks
  7. GraphSAGE Networks
  8. GNN-based Accelerated Numerical Algorithm
  9. Simulation Studies
  10. Results and Discussions
  11. Conclusion

Figures (3)

  • Figure 1: An intersection scenario with 4 lanes.
  • Figure 2: Comparison of computation times across different traffic volumes for the baseline (Algorithm \ref{['alg:optimal_exit_time']}) and GNN-based solver (Algorithm \ref{['alg:gnn-solver']}).
  • Figure 3: Position and speed trajectories for $20$ vehicles in a simulation example using different methods. Different colors represent the trajectories of vehicles traveling on different lanes.

Theorems & Definitions (4)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4