A simplified force model and enhanced steering for a quantitative description of pedestrian dynamics

Publication Type:

Conference Paper

Source:

Pedestrian and Evacuation Dynamics PED 2012 (2012)

Abstract:

Force-based models are a very popular approach for modeling pedestrian dynamics which assumes that pedestrian‘s movement is a consequence of exterior forces acting on pedestrians. In this work we propose a space continuous force based model to describe the movement of pedestrians in 2D-space by means of forces and torques. Furthermore, the model incorporates a foresight mechanism allowing pedestrians to react on the actual as well as on a predicted situation. Formally the movement of pedestrians is defined by N differential equations. The equation of motion is given by superposition of repulsive and driving forces. While repulsive forces keep pedestrians away from each other and other obstacles, driving forces lead them to a chosen exit with a preferred velocity. In most force-based models [2-11] pedestrians are modeled as circles or mass points. Since the forces act on the center of mass of each pedestrian and given the point symmetry of pedestrians, the torques are zero. Therefore the movement of pedestrians is restricted to accelerations and decelerations without the ability to avoid other pedestrians. In general these avoidance maneuvers are introduced in force-based model in form of algorithmic solutions. In this work we model the shape of pedestrians as elliptical disks and enhance the generalized centrifugal force model [1]. With a proper choice of the acting point of the forces taking into account the actual volume exclusion, the direction of pedestrians is determined, by means of the aforementioned forces but also by torques that those forces produce in time. Thus, no extra procedures to manage collisions or avoidance maneuvers are necessary. This approach leads to a realistic description of volume exclusion and short termed evasion maneuvers. For the steering on a tactical level a new method to choose the desired direction is investigated and tested in geometries with 90° and 180° corners. The method is based on identifying automatically in a given geometry corners and set lines rotated with a certain angle around them. To avoid congestions around the corner, each line is assigned points weighted decreasingly away from the corner. In case of low densities, pedestrians are guided towards the corner. If the density gets high, pedestrians get, thanks of the weights, directed away from the corner. Qualitative and quantitative comparisons among several experimental data and measurement methods are used to validate the steering model. The model for the volume exclusion and steering contains only two free parameters, which benefits this procedure and facilitates its calibration. For the sake of validation of the model for the volume exclusion we reproduce empirical data in several geometries with one set of parameter. The GCFM was successfully validated in narrow and wide corridors. For bottlenecks, corners, T-junctions and generally geometries that necessitate maneuvering, the need to model the desired direction is especially more highlighted. With the enhancements, we introduce in this work, it is possible to simulate more challenging geometries without the need of tuning and changing parameters. In summary the proposed model reflects three aspects:
1. The repulsive force reflects the elliptical shape of pedestrians. Its magnitude is proportional to the overlapping area with other pedestrians.
2. The repulsive force engender a torque, allowing pedestrians to change easily direction.
3. The forces depend not only on the actual situation but also on an educated guess how the situation changes in the future.
4. The desired direction is modeled to enable maneuvering in complex geometries.