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Braking control, especially in an emergency, is a key technology that is needed to ensure safety in vehicle platoons. However, delays in vehicle platoons can severely affect braking control. This paper proposes an optimized braking control to reduce the standstill spacing and braking duration during delays so that a platoon will stop within a short time frame with a reduced length, thus improving road utilization while ensuring both inter-vehicle and in-vehicle safety. However, two challenges need to be addressed. First, due to the delay in car-following interactions and the nonlinearity of the control law, an analysis model is needed to quantize the duration and distance during an emergency braking with delays. Second, the optimization of these control parameters is an NP-hard problem. Therefore, delay differential equations are introduced to model the braking process, and a crossing criterion is introduced to establish the relationship between the control law and the braking process. The propositions of standstill spacing and braking duration are then derived based on the Runge-Kutta method. According to these criteria, a particle swarm optimization (PSO) based on a lexicographic method with a penalty function is introduced to provide a solution framework with polynomial complexity. Simulation results verify the accuracy of the braking modeling process. Moreover, the results verify the performance of the proposed algorithm and provide a reference for platoon control.

Reducing the Standstill Spacing and Duration of Safe Braking Control in Vehicle Platoons With Delays