  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.
