Shielding model for large pedestrian group behaviour

We propose a mathematical framework to turn a cost function able to reproduce the dynamics of a social group composed of two pedestrians walking under low to medium density conditions into a cost function that may reproduce the dynamics of a group of arbitrary size. We first show that simply extending the two pedestrians cost function to a pair-wise n-body one produces completely unrealistic behaviour, while using it as the basis for a first-neighbour one produces more realistic U formations, which are actually observed in human crowds. Nevertheless, for n > 3 these formations are unstable in real crowds, and large groups tend to split into 2 and 3 people sub-groups. We finally show that this more realistic behaviour can be reproduced if we assume that the interaction with the closest partner effectively shields the interaction with the other members of the group.