Distributed Kuramoto Self-Synchronization of Vehicle Speed Trajectories in Traffic Networks

Abstract

This paper presents a distributed synchronization strategy for connected and automated vehicles in traffic networks. The strategy considers vehicles traveling from one intersection to the next as waves. The phase angle and frequency of each wave map to its position and velocity, respectively. The goal is to synchronize traffic such that intersecting traffic waves are out of phase at every intersection. This ensures the safe collective navigation of intersections. Vehicles share their phase angles through the V2X infrastructure, and synchronize these angles using the Kuramoto equation. This is a classical model for the self-synchronization of coupled oscillators. The mapping between phase and location for vehicles on different roads is designed such that Kuramoto synchronization ensures safe intersection navigation. Each vehicle uses a constrained optimal control policy to achieve its desired target Kuramoto phase at the upcoming intersection. The overall outcome is a distributed traffic synchronization algorithm that simultaneously tackles two challenges traditionally addressed independently, namely: coordinating crossing at an individual intersection, and harmonizing traffic flow between adjacent intersections. Simulation studies highlight the positive impact of this strategy on fuel consumption and traffic delay time, compared to a network with traditional traffic light timing.