Evaluating Safety Envelope for Bus-VRU Interactions: Passenger and VRU Perceived Safety Implication

Paper in proceeding, 2026

Buses are essential for urban transport and generally considered safe. However, accidents involving buses, particularly in urban areas, often result in severe injuries and fatalities for vulnerable road users (VRUs). This study introduces a novel method to compute a safety envelope using reachability analysis and set-volume optimization. The research examines how the size of the safety envelope is influenced by simultaneous steering and braking maneuvers, factoring in perceived risk constraints for both standing bus passengers and VRUs. It also evaluates the relationship between minimum safety distance (MSD) and unsafe distances recorded in real-world bus-VRU collision. Key findings include the impact of VRU-perceived safety risk on a critical zone, with MSD increasing by 5 cm to 4.2 m for different maneuvers and initial speeds. Passenger-perceived safety risk also significantly affects MSD, with increases ranging from 0.05–1 m at 20 km/h to 4.8–12 m at 50 km/h, depending on the lateral offset. A comparison of MSD with crash data reveals that braking distances recorded for most of the crashes, align within the critical zone. Given levels for dangerous VRUs’ and passengers’ risk, the proposed method provides the interval when automated system should engage, as the set difference between the critical zones between the dangerous and highest risk levels.