  In a recent series of papers, we proposed a mathematical model for the
dynamics of a group of interacting pedestrians. The model is based on a
non-Newtonian potential, that accounts for the need of pedestrians to keep both
their interacting partner and their walking goal in their vision field, and to
keep a comfortable distance between them. These two behaviours account
respectively for the angular and radial part of the potential from which the
force providing the pedestrian acceleration is derived. The angular term is
asymmetric, i.e. does not follow the third law of dynamics, with observable
effects on group formation and velocity. We successfully compared the
predictions of the model with observations of real world pedestrian behaviour.
We then studied the effect of crowd density on group dynamics. We verified that
the average effect of crowd density may be modelled by adding a harmonic term
to the group potential. The model predictions, which include "phase
transitions" in the group configuration, are again confirmed, at least in the
observed density range, by a comparison with real world data. Until now we had
averaged all pedestrian data collected in a given environmental setting without
differentiating on group composition and social roles. In this work we study
how the group configuration and velocity is affected by inter-pedestrian
relation (family, couples, colleagues, friends), purpose (work, leisure) and
gender. We also show results related to the effect of asymmetric interactions,
that confirm further the non-Newtonian nature of gaze-based angular interaction
in our model.
