Stochastic fluctuations of diluted pedestrian dynamics along curved paths.

As we walk towards our destinations, our trajectories are constantly influenced by the presence of obstacles and infrastructural elements; even in the absence of crowding our paths are often curved. Since the early 2000s 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 a Langevin-like social-force model quantitatively compatible with both averages and fluctuations of the walking dynamics. 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.