Platooning on highways with connected and automated vehicles (CAVs) has attracted considerable attention, while how to mange and coordinate platoons in urban networks remains largely an open question. This scientific gap mainly results from the maneuver complexity on urban roads, making it difficult to model the platoon formation process. Inspired by flocking behaviors in nature, this paper proposed a two-dimensional model to describe CAV group dynamics. The model is formulated based on potential fields in planar coordinates, which is composed of the inter-vehicle potential field and the cross-section potential field. The inter-vehicle potential field enables CAVs to attract each other when vehicle gaps are larger than the equilibrium distance, and repel each other otherwise. It also generates incentives for lane change maneuvers to join a platoon or to comply with the traffic management layer. The cross-section potential field is able to mimic lane keeping behavior and it also creates resistance to avoid unnecessary lane changes at very low incentives. These modeling principles can also be applied to human-driven vehicles in the mixed traffic environment. Behavioral plausibility of the model in terms of car-following rationality and car-following safety is demonstrated analytically and further verified with simulation in typical driving scenarios. The model is computationally efficient and can provide insights into platoon operations in urban networks.
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