Safety-Oriented Cooperative Control for Connected and Autonomous Vehicle Platoons Using Differential Game Theory and Risk Potential Field

Connected and autonomous vehicle (CAV) platoons face the dual challenge of maintaining longitudinal formation stability while ensuring lateral safety in dynamic traffic environments, yet existing control approaches often address these objectives in isolation. This paper proposes a hierarchical cooperative control framework that integrates a differential game-based longitudinal controller with a risk potential field-driven model predictive controller (MPC) for lateral motion. At the coordination control layer, a differential game formulation models inter-vehicle interactions, with analytical solutions derived for both open-loop Nash equilibrium under predecessor-following (PF) topology and an estimated Nash equilibrium under two-predecessor-following (TPF) topology. The motion control layer employs a risk potential field model that quantifies collision threats from surrounding obstacles and road boundaries, guiding the MPC to perform real-time trajectory optimization. A comprehensive co-simulation platform integrating MATLAB/Simulink, Prescan, and CarSim validates the proposed framework across three representative scenarios: ramp merging with aggressive cut-in maneuvers, emergency braking by a preceding obstacle vehicle, and multi-lane cooperative obstacle avoidance involving multiple dynamic obstacles. Across all scenarios, the CAV platoon achieves safe obstacle avoidance through autonomous decision-making, with spacing errors converging to zero and smooth velocity adjustments that ensure both formation stability and ride comfort. The results demonstrate that the proposed framework effectively adapts to diverse and complex traffic conditions.