Probabilistic Decision-Making for Virtually Coupled Trains Under Uncertainty

The virtually coupled trains present challenges due to the risks associated with small separation. The following train must make appropriate decisions in uncertain and high-risk situations to ensure safety and efficiency. We address uncertainty from sensor noise and unknown preceding train behaviors, establishing a probabilistic decision-making model using a partially observable Markov decision process (POMDP). Collision and risk envelopes are defined using the emergency and full-service braking distance of the following train, considering the “worst-case separation” scenarios, leading to a novel chance-constrained POMDP (CC-POMDP) for the virtually coupled trains. We propose an online planning algorithm, Partially Observable Monte Carlo Planning based on Double Shielding and Progressive Widening (POMCP-DS-PW). The results demonstrate that even without a pre-planned recommended speed curve, the following train can optimize acceleration based on incomplete observations and unknown behaviors of the preceding train, thereby ensuring safety while achieving operational efficiency.