Experimental characterization of collision avoidance in pedestrian dynamics

In the present paper, the avoidance behavior of pedestrians was characterized by controlled experiments. Several conflict situations were studied considering different flow rates and group sizes in crossing and head-on configurations. Pedestrians were recorded from above, and individual two-dimensional trajectories of their displacement were recovered after image processing. Lateral swaying amplitude and step lengths were measured for free pedestrians, obtaining similar values to the ones reported in the literature. Minimum avoidance distances were computed in two-pedestrian experiments. In the case of one pedestrian dodging an arrested one, the avoidance distance did not depend on the relative orientation of the still pedestrian with respect to the direction of motion of the first. When both pedestrians were moving, the avoidance distance in a perpendicular encounter was longer than the one obtained during a head-on approach. It was found that the mean curvature of the trajectories was linearly anticorrelated with the mean speed. Furthermore, two common avoidance maneuvers, stopping and steering, were defined from the analysis of the acceleration and curvature in single trajectories. Interestingly, it was more probable to observe steering events than stopping ones, also the probability of simultaneous steering and stopping occurrences was negligible. The results obtained in this paper can be used to validate and calibrate pedestrian dynamics models.

Figure 1

Snapshots of avoidance experiments. The arrows indicate the pedestrians' direction of motion. (a) One pedestrian avoiding another arrested pedestrian, which can be considered as an elliptical obstacle. (b) One to one head-on pedestrian avoidance. (c) One to one perpendicular crossing. (d) and (e) Two groups of two (d) and three (e) pedestrians in a perpendicularly crossing situation. (f) Two lines of pedestrians in a perpendicular crossing. The average flow of each line is 0.9 pedestrian/s. (g) and (h) Two groups of ten pedestrians in a perpendicular crossing (g) and in a counterflow configuration (h). (i) Parallel white ropes separated by 0.5 m, placed at 1.7 m from the floor for correcting lens deformation and calibrating distance units.

Figure 2

Recovered trajectories. (a) Two representative recovered trajectories (circles) and their NN fitting $\mathbf{r}$ (solid line). (b) Lateral swaying: definition of the amplitude $\left(A\right)$ and period $\left(L\right)$. The solid line corresponds to the smoothed trajectory $\mathbf{r}$, and the dashed one represents the main direction of motion determined using the quadratic fitting $\left({\mathbf{r}}^{\prime }\right)$. The ellipse at $(x,y)=(0,0)$ represents an arrested pedestrian. (c) Another trajectory displaying less lateral swaying (lower $A)$.

Figure 3

Instantaneous speeds of two-pedestrian experiments. Histogram obtained from 74 trajectories corresponding to the configurations shown in Figs. 1– 1. The mean value is $\langle v\rangle =1.66\mathrm{m}/\mathrm{s}$, and the standard deviation is $\sigma =0.24\mathrm{m}/\mathrm{s}$.

Figure 4

Definition of angle $\theta \left(t\right)$ to characterize the curvature of trajectories.

Figure 5

Key variables derived from one representative trajectory of a free pedestrian. The upper left panel depicts the trajectory, and the arrow indicates the forward direction; the upper right panel shows the speed evolution, and the lower panels display the acceleration and curvature, respectively. The solid and dashed lines represent the mean and threshold values that are explained below (see Fig. 7).

Figure 6

Relationship between curvature and speed for pedestrian trajectories. Each symbol represents the average and standard deviation for all trajectories corresponding to each experimental configuration shown in Fig. 1. (a) Angular change rate versus speed. (b) Maximum angular change rate for each trajectory versus the difference between extreme values of the velocity normalized by its mean value.

Figure 7

Time evolution of acceleration and angular velocity for three trajectories. In all cases, the solid line represents the mean value, and the dashed line is the threshold value of $2.8\times \sigma$ as explained in the text. (a) One steering event and no stopping one. (b) Stopping event but not a steering one. (c) Stopping and steering events occurring simultaneously. Vertical arrows indicate events, i.e., values beyond thresholds. The dashed and tilted arrows indicate the start of the maneuver.

Figure 8

Approximate probabilities of having avoidance events for the different configurations studied. (I) Experiments described in Figs. 1–1, (II) Fig. 1, (III) Fig. 1, (IV) Fig. 1, (V) Fig. 1, and (VI) Fig. 1. The configurations are ordered by increasing the number of total events (rhombus).