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In this paper, a unified multi-vehicle formation control framework for Intelligent and Connected Vehicles (ICVs) that can apply to multiple traffic scenarios is proposed. In the one-dimensional scenario, different formation geometries are analyzed and the interlaced structure is mathematically modelized to improve driving safety while making full use of the lane capacity. The assignment problem for vehicles and target positions is solved using Hungarian Algorithm to improve the flexibility of the method in multiple scenarios. In the two-dimensional scenario, an improved virtual platoon method is proposed to transfer the complex two-dimensional passing problem to the one-dimensional formation control problem based on the idea of rotation projection. Besides, the vehicle regrouping method is proposed to connect the two scenarios. Simulation results prove that the proposed multi-vehicle formation control framework can apply to multiple typical scenarios and have better performance than existing methods.