# Generalized Collision-free Velocity Model for Pedestrian Dynamics

The movement of pedestrians is determined by a given speed and a direction. Based on this idea, we propose a collision-free velocity model that is composed of a direction sub-model and a speed sub-model. The direction sub-model calculates an optimal moving direction of a pedestrian according to its desired moving direction which towards its target and the effect from its neighbors. After that, the collision-free speed on the optimal moving direction is calculated, which guarantees that there is no overlap among pedestrians. The model is simple to use and can be further improved.

In this paper paper, we extended the simple model from several aspects. First, a dynamical ellipse is used instead of a constant circle as in the original model to represent the varying 2D space occupied by pedestrians. The axis of the ellipse parallel to the moving direction of the pedestrian is constant, and the axis perpendicular to the moving direction changes with the moving speed.

A better fundamental diagram is obtained with the dynamical ellipse in the corridor scenario compared with the constant circle.

Then a new direction sub-model is proposed to mitigate the usual shaking of pedestrians in the simulation, and to eliminate the backward movement of pedestrians. We adopt a dynamical visual area, a new method to calculate the effect from neighbors, and a new releasing parameter to smooth the turning process of pedestrians. This model leads to a more realistic distribution of pedestrians especially in bottleneck scenarios.