Stochastic Time-Optimal Trajectory Planning for Connected and Automated Vehicles in Mixed-Traffic Merging Scenarios

Addressing safe and efficient interaction between connected and autonomous vehicles (CAVs) and human-driven vehicles (HDVs) in a mixed-traffic environment has attracted considerable attention. In this article, we develop a framework for stochastic time-optimal trajectory planning for coordinating multiple CAVs in mixed-traffic merging scenarios. We present a data-driven model, combining Newell's car-following model with Bayesian linear regression (BLR), for efficiently learning the driving behavior of human drivers online. Using the prediction model and uncertainty quantification, a stochastic time-optimal control problem is formulated to find robust trajectories for CAVs. We also integrate a replanning mechanism that determines when deriving new trajectories for CAVs is needed based on the accuracy of the BLR predictions. Finally, we demonstrate the performance of our proposed framework using a realistic simulation environment.