Safety envelope of pedestrians upon motor vehicle conflicts identified via active avoidance behaviour

Human reaction plays a key role in improved protection upon emergent traffic situations with motor vehicles. Understanding the underlying behaviour mechanisms can combine active sensing system on feature caption and passive devices on injury mitigation for automated vehicles. The study aims to identify the distance-based safety boundary (“safety envelope”) of vehicle–pedestrian conflicts via pedestrian active avoidance behaviour recorded in well-controlled, immersive virtual reality-based emergent traffic scenarios. Via physiological signal measurement and kinematics reconstruction of the complete sequence, we discovered the general perception-decision-action mechanisms under given external stimulus, and the resultant certain level of natural harm-avoidance action. Using vision as the main information source, 70% pedestrians managed to avoid the collision by adapting walking speeds and directions, consuming overall less “decision” time (0.17–0.24 s vs. 0.41 s) than the collision cases, after that, pedestrians need enough “execution” time (1.52–1.84 s) to take avoidance action. Safety envelopes were generated by combining the simultaneous interactions between the pedestrian and the vehicle. The present investigation on emergent reaction dynamics clears a way for realistic modelling of biomechanical behaviour, and preliminarily demonstrates the feasibility of incorporating in vivo pedestrian behaviour into engineering design which can facilitate improved, interactive on-board devices towards global optimal safety.


I. Experimental data
Supplementary Table 1. Reaction time and relative distance from the vehicle in the cases where the pedestrians perceived the coming bullet vehicle before collision. Visual, kinematics and location information of 17 complete experimental cases were presented. Dp(tps), Dp(tpa), Dv(tps), Dv(tpa) and vp (tps), vp(tpa), vv(tps), vv(tpa) represent the the relative location and moving velocity of the pedestrian and the "bullet vehicle" at tps (danger perceived) and tpa (decision made), with the centre of the vehicle front-end taken as the origin.

II. Estimation of the distance-based safety envelopes
We propose four simplified conditions (I, II Table 2). We made an example to show the calculation result of safety envelope; the distance-based safety envelope was calculated based on the average pedestrian avoidance ability and a group of representative parameters of the vehicle and the pedestrian ( Figure 6; Supplementary  Figure 4 in the main text).
Supplementary Table 3. Assumptions of the representative interaction conditions between the vehicle and the pedestrian detected by vehicle sensing system.
From the front-left of vehicle and vertical to vehicle moving direction where . is the maximum longitudinal acceleration of the vehicle; . is the maximum lateral acceleration; 0 is initial moving velocity, 0 is the distance between the vehicle and the potential collision venue (Figure 7 in the main text).
The four interaction conditions and the calculation of the safety envelope are explained as below: (I) Both the pedestrian and vehicle notice each other: pedestrians would be moving to the "collision venue" with natural avoidance behaviour; vehicle would be moving to the "collision venue" at the maximum braking (no steering included).
Solving the time of vehicle to potential collision venue ( ) based on the initial velocity ( 0 ), braking deceleration ( . ) and the distance from vehicle to potential collision venue ( 0 ) (Figure 7).
For the backward avoidance, backward avoidance velocity ( . ) and distance ( . ) of the pedestrian during avoidance can be determined based on its moving velocity (eq. 2) and the pedestrian-vehicle interaction (Supplementary Table 2).
where . represents the velocity of the pedestrian during backward avoidance, . represents the pedestrian moving distance in the process of backward avoidance.
For the forward avoidance, forward avoidance velocity ( . ) and avoidance distance ( . ) of the pedestrian during avoidance can be determined based on its moving velocity (equation (2) in the main text) and the pedestrian-vehicle interaction (Supplementary Table 2). where . represents the velocity of pedestrian during forward avoidance, .a represents the distance of pedestrian moving in the process of forward avoidance.
Determining the hazard distance of the pedestrian to the centreline of the vehicle (equation (S1)-(S5) and (5) In order to maintain the stability of the vehicle body, the minimum turning radius of the vehicle ( . ) depends on the vehicle velocity and the maximum lateral acceleration. Solving the minimum turning radius of vehicle at , Forward moving distance of the vehicle at , ( ), in the process of maximum braking was calculated based on the initial velocity ( 0 ) and braking deceleration ( . ), The steering angle of the vehicle ( . ) at is calculated based on the geometric relationship between vehicle steering radius and moving distance per unit time, i.e., the accumulation of the steering angle in the previous time. (S10) Moving displacement of vehicle front-end to the right ( . ) at in the process of maximum braking is calculated based on the steering angle and the moving distance per unit time, where . represent the moving displacement of vehicle front-end to the right.
Determining the hazard distance of pedestrian to centreline of vehicle (equation (S11) and (S2)~(S5)): Similarly, scenario (I**) denotes the condition that vehicle would be moving at maximum braking and left steering. Moving displacement of vehicle front-end to the left ( . ) at in the process of maximum braking is calculated based on steering angle and moving distance of the vehicle per unit time (eq. (S7)~(S10)) (S13) Determining the hazard distance of pedestrian to centreline of vehicle (equation (S13) and (S2)~(S5)): (II) Pedestrian notice the coming vehicle and would be moving to the "collision venue" at avoiding velocity ( . ); vehicle do not notice the moving pedestrian and would move with the initial-driving velocity.
Solving the time of vehicle to potential collision venue ( ) based on the vehicle initial velocity ( 0 ) and distance of vehicle arrive at potential collision venue ( 0 ) (Figure 7).
Determining the hazard distance of pedestrian to centreline of vehicle (equation (S15) and (S2)~(S5)): (III) Pedestrian do not notice the coming vehicle and would be moving to the "collision venue" with the initialwalking velocity; vehicle notice the moving pedestrian and would move at the maximum braking (no steering included).
Pedestrian would be moving to the "collision venue" at initial-walking velocity. Solving the pedestrian moving distance ( ).

III. Movie showing the pedestrian reactions in the experiments
Movie S1. In the movie, we provide animations of the experimental platform and records in the present study to aid the reader in visualizing the pedestrian reactions (Supplementary Figure 1). The video shows the view of the scenario from both the pedestrian and a third-party (i.e., the experimenter), the real in-lab subject motion of the subject, the parallel virtual interaction with the vehicle via VR device, and animations of the kinematic reconstructions of the pedestrian. Supplementary