Publication Type: Conference Paper
In the frame of a French project (PEDIGREE) involving four teams (IMT-Toulouse, INRIA-Rennes, CRCA-Toulouse, LPT-Orsay), we have performed several experiments to study the dynamics of pedestrians in various geometries.
Experiments were performed in-door, and each pedestrian was equipped with 4 markers which were detected by a VICON system (infra-red cameras). As a result, the full 3D trajectory of each pedestrian could be reconstructed, with a frequency of 120 frames/s.
In the frame of this project, several experiments were performed, including:
1 - 1d-motion along a circle [1,2,3].
2 - mono-directional and bi-directional flow in a ring corridor .
3 - oscillations at a bottleneck.
4 - Interactions between 2 or 3 individual trajectories.
5 - Interactions between incoming lines of pedestrians.
Then, as an illustration of the type of results that can be obtained from these experiments, we shall concentrate on the analysis of the 1d circle experiment.
Participants were asked to walk in a natural way along a circular path, without passing each other. Two different circular paths were used, with different radii (respectively 2.4 and 4.1 meters). The number of pedestrians was varied from 8 to 28, resulting in a global density ranging from 0.31 to 1.86 ped/m. However, the local densities could be lower or higher due to spontaneous formation of spatial inhomogeneities.
Before the start of the experiment, pedestrians were placed either at equal distances around the circle, or packed all together. Each experiment lasted 1mn (or slightly more for higher densities), and several replicas (up to 8) were realized for the same set of parameters, if possible with different sets of participants.
First some comparison with previous experiments [5,6] will be presented. Here, the fundamental diagram can be defined in several ways, depending whether the density and the velocity are taken as global, locally averaged or instantaneous quantities . The initial conditions (homogeneous or jammed) turn out to have a short lived influence. The contributions to the fundamental diagram of stationary behavior or transient behavior due to rapid fluctuations will be discussed.
In previous experiments, the velocity-spatial headway relation was found to be linear. However, our experiment has allowed us to cover a much larger range of densities.
One of our main result is to show that there exist two clear transitions in the behavior of pedestrians, separating 3 dynamical phases :
- Free flow regime: for a spatial headway larger than 3 meters, pedestrians walk with their preferred velocity;
- Weakly constrained regime: for a spatial headway between 1.1 and 3 meters, the velocity depends only weakly on the spatial headway.
- Strongly constrained regime: for a spatial headway less than 1.1 meter, the velocity depends strongly on the spatial headway.
In each phase, the velocity-spatial headway relation is linear, but the slope is differs from one phase to the other. This finding could open new perspectives in terms of modeling.
The transition between the weakly and strongly constrained regimes was already partially visible in previous experiments but was not interpreted as such, as lower densities were not explored. It has consequences on the way comparisons between different experiments should be performed, in order to extract some cultural influence on the walking behavior as in .
The oscillations of the radial coordinate allow to detect steps. We shall present systematically how the step frequency or amplitude vary with the parameters of the experiment, and extract some simple laws . We show also that, as expected, synchronization of the steps may occur at high densities, but that this is not a general feature.
The knowledge of the full individual trajectories allows also to extract the stop and go waves that are produced at high densities. We can extract not only the propagation velocity of the waves, but also the damping of the signal inside the wave, the width of the wave, the characteristics of the pedestrians inside the wave, etc... The possibility to localize precisely the waves will enrich the discussion about the fundamental diagram.
The analysis of the following behavior observed for pairs of successive pedestrians has led to the proposal of a microscopic model . It is possible to compare models and experiments either at the microscopic level, or at a macroscopic level, based on the characteristics of stop and go waves.
The data obtained from this experiment will be made available for the scientific community on a web platform in 2012.