Control of Vehicle Platoons with Collision Avoidance Using Noncooperative Differential Games

This paper considers a differential game approach to the predecessor-following vehicle platoon control problem without and with collision avoidance. In this approach, each vehicle tries to minimize the performance index (PI) of its control objective, which is reaching consensual velocity with the predecessor vehicle while maintaining a small inter-vehicle distance from it. Two differential games were formulated. The differential game problem for platoon control without collision avoidance is solved for the open-loop Nash equilibrium and its associated state trajectories. The second differential game problem for platoon control with collision avoidance has a non-quadratic PI, which poses a greater challenge to obtaining its open-loop Nash equilibrium. Since the exact solution is unavailable, we propose an estimated Nash strategy approach that is greatly simplified for implementation. An illustrative example of a vehicle platoon control problem was solved under both the without and with collision avoidance scenarios. The results showed the effectiveness of the models and their solutions for both scenarios.