Prediction of Minimum Spacing between Vehicles with Merge Conflicts Based on Initial and Final Vehicle States

The safety of the lane-changing (LC) process is affected by the merging vehicles and their Surrounding Obstacle Vehicles (SOVs). Most existing studies assume certain driving behaviors of SOVs such as emergency braking during the LC process. However, these assumptions may be overconservative to guarantee safety and may be unrealistic. This study aims to investigate the methodology for predicting the minimum spacing between a merging vehicle and its SOVs based on the initial and final vehicle states during the LC process. A quintic polynomial trajectory model is built to describe the lane-changing (LC) process of a merging vehicle. By determining the trajectory of the potential collision point (PCP), the prediction of the MS is formulated as an optimal control problem for surrounding vehicles. The optimal control model is then transformed into a discrete-time linear optimization model, which can be solved by existing solvers such as Gurobi and Cplex. The proposed model has the potential to improve operational efficiency while ensuring safety, thereby establishing a solid foundation for vehicle trajectory planning.