  Quantitatively modeling the trajectories and behavior of pedestrians walking
in crowds is an outstanding fundamental challenge deeply connected with the
physics of flowing active matter, from a scientific point of view, and having
societal applications entailing individual safety and comfort, from an
application perspective.
  In this contribution, we review a pedestrian dynamics modeling approach,
previously proposed by the authors, aimed at reproducing some of the
statistical features of pedestrian motion. Comparing with high-statistics
pedestrian dynamics measurements collected in real-life conditions (from
hundreds of thousands to millions of trajectories), we modeled quantitatively
the statistical features of the undisturbed motion (i.e. in absence of
interactions with other pedestrians) as well as the avoidance dynamics
triggered by a pedestrian incoming in the opposite direction. This was
accomplished through (coupled) Langevin equations with potentials including
multiple preferred velocity states and preferred paths. In this chapter we
review this model, discussing some of its limitations, in view of its extension
toward a more complex case: the avoidance dynamics of a single pedestrian
walking through a crowd that is moving in the opposite direction. We analyze
some of the challenges connected to this case and present extensions to the
model capable of reproducing some features of the motion.
