Self-synchronization of connected vehicles in traffic networks: What happens when we think of vehicles as waves?

In this paper we consider connected and autonomous vehicles (CAV) in a traffic network as moving waves defined by their frequency and phase. This outlook allows us to develop a multi-layer decentralized control strategy that achieves the following desirable behaviors: (1) safe spacing between vehicles traveling down the same road, (2) coordinated safe crossing at intersections of conflicting flows, (3) smooth velocity profiles when traversing adjacent intersections. The approach consist of using the Kuramoto equation to synchronize the phase and frequency of agents in the network. The output of this layer serves as the reference trajectory for a back-stepping controller that interfaces the first-order dynamics of the phase-domain layer and the second order dynamics of the vehicle. We show the performance of the strategy for a single intersection and a small urban grid network. The literature has focused on solving the intersection coordination problem in both a centralized and decentralized manner. Some authors have even used the Kuramoto equation to achieve synchronization of traffic lights. Our proposed strategy falls in the rubric of a decentralized approach, but unlike previous work, it defines the vehicles as the oscillating agents, and leverages their inter-connectivity to achieve network-wide synchronization. In this way, it combines the benefits of coordinating the crossing of vehicles at individual intersections and synchronizing flow from adjacent junctions.