Multi-Vehicle Trajectory Planning at V2I-enabled Intersections based on Correlated Equilibrium

TL;DR

This paper tackles multi-vehicle coordination at V2I-enabled intersections by replacing traditional Nash equilibrium planning with a correlated-equilibrium framework. An Intersection Manager collects vehicle-specific trajectory libraries and preference data, then computes a CE-consistent recommendation distribution that vehicles sample from to construct a safety corridor and refined, feasible trajectories. The approach preserves rationality while enabling consensus and safer, more efficient intersection crossing, demonstrated through simulations and hardware experiments against NE-based and MPC baselines. The work offers a scalable, infrastructure-assisted solution for real-time, multi-vehicle trajectory planning in urban intersections with potential for broader application to fixed-path scenarios.

Abstract

Generating trajectories that ensure both vehicle safety and improve traffic efficiency remains a challenging task at intersections. Many existing works utilize Nash equilibrium (NE) for the trajectory planning at intersections. However, NE-based planning can hardly guarantee that all vehicles are in the same equilibrium, leading to a risk of collision. In this work, we propose a framework for trajectory planning based on Correlated Equilibrium (CE) when V2I communication is also enabled. The recommendation with CE allows all vehicles to reach a safe and consensual equilibrium and meanwhile keeps the rationality as NE-based methods that no vehicle has the incentive to deviate. The Intersection Manager (IM) first collects the trajectory library and the personal preference probabilities over the library from each vehicle in a low-resolution spatial-temporal grid map. Then, the IM optimizes the recommendation probability distribution for each vehicle's trajectory by minimizing overall collision probability under the CE constraint. Finally, each vehicle samples a trajectory of the low-resolution map to construct a safety corridor and derive a smooth trajectory with a local refinement optimization. We conduct comparative experiments at a crossroad intersection involving two and four vehicles, validating the effectiveness of our method in balancing vehicle safety and traffic efficiency.

Figures (13)

• Figure 1: At traffic intersections, the IM collects the preference probability distributions of vehicles over the trajectory library and computes recommendation probability with a CE constraint that aligns with the interests and rationality of all vehicles. The experimental details are provided in Sect. VI. The video is available at https://www.bilibili.com/video/BV1MZ421e7L7/?spm_id_from=333.337.search-card.all.click&vd_source=b35525d31a331a616aa4def5c50e002b.
• Figure 2: Framework Flowchart.
• Figure 3: Trajectory generation diagram.
• Figure 4: Representation of trajectory library in spatial-temporal grid map.
• Figure 5: The schematic diagram of information is contained in the spatial-temporal grid map.