Fig 1.
Force decomposition in the Headed Social Force Model.
The force , acting along the forward direction, is the projection (along the same direction) of the total force fi resulting from the traditional SFM. The force
, acting along the orthogonal direction, is the projection (along the same direction) of the
force alone.
Fig 2.
Scenario I, alternate motion between two points.
A single pedestrian has to move back and forth between A and B, starting from A, with a desired speed vd = 1.5 ms−1: SFM (red) and HSFM (blue).
Fig 3.
Scenario I, starting with different orientations.
A single pedestrian has to move from A to B, starting with different headings (denoted by the small black dot), at a desired speed vd = 1.5 ms−1: SFM (red) and HSFM (blue).
Fig 4.
Scenario II, Pedestrians in a corridor.
A group of 20 pedestrians walking in the same direction in a 7.5m-wide corridor at a desired speed vd = 1.5 ms−1. Three snapshots of a simulation run of the HSFM, taken at different time instants t.
Fig 5.
Scenario II, Two groups walking in opposite directions.
Two groups of 10 pedestrians each walking in opposite directions in a 5m-wide corridor at a desired speed vd = 1.5 ms−1. Three snapshots of a simulation run of the HSFM, taken at different time instants t.
Fig 6.
Scenario II, Values of for different pedestrian densities.
Average jerk (blue) and
(red) for two groups of N pedestrians each, with N ranging from 5 to 25, walking in opposite directions in a 5m-wide corridor, at a desired speed vd = 1.5 ms−1.
Fig 7.
Scenario III, Pedestrian counter flow through a bottleneck.
Simulation of a metro train boarding process [35]. Pedestrians in red want to get off the train (towards the right), while pedestrians in green are trying to get on it (towards the left). Three snapshots taken at different time instants.
Fig 8.
Scenario III, A visit at the Museum.
Snapshots of a simulation run of the HSFM without the inclusion of group cohesion forces.
Fig 9.
Scenario III, A visit at the Museum.
Snapshots of a simulation run of the HSFM with the inclusion of group cohesion forces.
Fig 10.
Mean distance from the group centroid over time.
Evolution of ξ with cohesive forces (blue) and without cohesive forces (red).
Fig 11.
Effect of ko and kd on the pedestrian trajectories.
A snapshot of the simulation of 20 pedestrians walking in a corridor, for different values of ko and kd [kg ⋅ s−1].
Fig 12.
Effect of ko and kd on trajectory regularity and distribution of the pedestrians.
Average square of the magnitude of the jerk and average distance Δ of a pedestrian from the group centroid for ko = 0.5 (dashed), ko = 1 (solid) and ko = 1.5 (dash-dotted).
Fig 13.
Effect of α on the pedestrian trajectories.
The path followed by a pedestrian passing through the sequence of way-points A-B-C-D, for different values of the parameter α.