  As we walk towards our destinations, our trajectories are constantly
influenced by the presence of obstacles and infrastructural elements: even in
absence of crowding our paths are often curved. Over the last two decades
pedestrian dynamics have been extensively studied aiming at quantitative models
with both fundamental and technological relevance. Walking kinematics along
straight paths have been experimentally investigated and quantitatively modeled
in the diluted limit (i.e. in absence of pedestrian-pedestrian interactions).
It is natural to expect that models for straight paths may be an accurate
approximations of the dynamics even for paths with curvature radii much larger
than the size of a single person. Conversely, as paths curvature increase one
may expect larger and larger deviations. As no clear experimental consensus has
been reached yet in the literature, here we accurately and systematically
investigate the effect of paths curvature on diluted pedestrian dynamics.
Thanks to a extensive and highly accurate set of real-life measurements
campaign, we derive and validate via a Langevin-like social-force model capable
of quantitatively describing both averages and fluctuations. Leveraging on the
differential geometric notion of covariant derivative, we generalize previous
work by some of the authors, effectively casting a Langevin social-force model
for the straight walking dynamics in a curved geometric setting. We deem this
the necessary first step to understand and model the more general and
ubiquitous case of pedestrians following curved paths in the presence of crowd
traffic.
