What creates safe and efficient pedestrian–vehicle interactions? a naturalistic study to design human-like behaviour for automated vehicles

Safe and efficient interaction with pedestrians is critical for the successful deployment of autonomous vehicles (AVs). While vehicle speed and acceleration are vital communication signals for this interaction, the ways in which human drivers use these kinematic communication signals remain under-explored. To design motion-based communication for AVs, this study aims to explore how drivers control their speed as a function of initial interaction conditions, and how this translates into more or less successful interaction outcomes. We analysed naturalistic trajectory data of vehicles and pedestrians from two zebra crossings in Leeds, UK, comprising 981 interactions. Partial Least Squares Structural Equation Modelling (PLS-SEM) was applied to quantify the mediating effect of vehicle kinematics on the relationship between initial time gap and interaction outcomes (crossing order, efficiency, and safety). Based on these models, vehicle speed profiles associated with optimal and worst outcomes were identified and compared using Generalized Estimating Equations (GEE). PLS-SEM results confirmed that vehicle kinematics significantly mediate interaction outcomes, exerting a strong influence on efficiency and safety, and a weaker influence on crossing order. Minimum vehicle speed in particular exerted a strong influence on crossing order and safety, suggesting that the speed to which the driver drops is a key communication signal to pedestrians. The mediation results and trajectory analysis revealed that drivers used different strategies to achieve balance between their efficiency and interaction safety: in yielding scenarios (time gap > 3 s), they decelerated early and softly to maintain a low non-zero speed (∼1 m/s) at a far distance (>10 m) to ensure safety while conserving momentum to ensure efficiency; in ambiguous non-yielding scenarios (time gaps ∼ 1 - 3 s), they employed a two-stage strategy: a proactive initial deceleration to prepare for potential danger and reduce uncertainty, followed by an assertive acceleration for efficiency; in unambiguous non-yielding scenarios with a narrow time gap (< 1 s), they sacrificed a small amount of efficiency and adopted proactive deceleration before pedestrians displayed a clear crossing intention to ensure safety. This study expands the understanding of interaction beyond binary yielding choices, offering new insights into the proactive strategies human drivers use to negotiate right-of-way safely and efficiently. Emulating these kinematic strategies can support better integration of AVs into human traffic.