Voronoi Based Social Force Models

Traditional social force model in corridor.

Voronoi based social force model in bottleneck.

Traditional social force model in corridor.

Voronoi based social force model in bottleneck.

Circle Antipode Simulations

Gif Videos:

Empirical results

Social force model
[1] Helbing D, Molnar P. Social force model for pedestrian dynamics. Phys Rev E. 1995.
[2] Helbing D, Farkas I, Vicsek T. Simulating dynamical features of escape panic. Nature. 2000.

[1] Moussaid M, Helbing D, Theraulaz G. How simple rules determine pedestrian behavior and crowd disasters. PNAS. 2011.

Voronoi based Social force model (Simplified)
[1] Xiao Y, Gao ZY, Qu YC, Li XG. A pedestrian flow model considering the impact of local density: Voronoi diagram based heuristics approach. Transport Res C-Emer. 2016.
[2] Xiao Y, Chraibi M, Qu Y, Tordeux A, Gao Z. Investigation of Voronoi diagram based direction choices using uni- and bi-directional trajectory data. Phys Rev E. 2018.
[3] Qu Y, Xiao Y, Wu J, Tang T, Gao Z. Modeling detour behavior of pedestrian dynamics under different conditions. Physica A 2018.


To reveal the pedestrian motion navigation and conflict reaction mechanism in reality, we organized a series of circle antipode experiments. In the experiments, pedestrians are uniformly initialized on the circle and required to leave for the antipodal positions simultaneously. On one hand, the shortest routes intersect at the center of the circle, and a conflicting area is naturally formulated in the center region during the experiment. Thus, the practical conflict avoidance behaviors can be adequately explored. On the other hand, the experimental conditions of pedestrians are basically symmetric, e.g., symmetric starting points, symmetric destination points, and symmetric surroundings. The symmetric characteristic lays a foundation for further quantitative analyses. Considering these features, several indexes, including the trajectory space distribution, route length, travel time, velocity distribution, and time-series, are defined and investigated. It is found that: (1) Pedestrians prefer the right-hand side during the motion; (2) The route length is as the law of log-normal distribution, while the travel time and speed are normally distributed; (3) Taking the shortest routes unexpectedly cost pedestrians plenty of travel time, while detour seems to be a time-saving decision.

What’s more, the series of experiments can be regarded as a basis for the model evaluation since dealing with the conflicts shall be a most core quality for a pedestrian model. The evaluation framework contains four distribution indexes and two time-series indexes in space and time dimensions, and they are respectively graded according to the K-S test and the DTW method. A traditional social force model and a Voronoi diagram based social force model are proposed for the application of the evaluation framework. The results show that the framework is beneficial to evaluate pedestrian models and even reflects the simple differences between the models.

Original Videos:

Original Trajectories:


Rotated Trajectories Gif: