Least-effort trajectories lead to emergent crowd behaviors.

Pedestrian crowds often have been modeled as many-particle systems, usually using computer models known as multiagent simulations. The key challenge in modeling crowds is to develop rules that guide how the particles or agents interact with each other in a way that faithfully reproduces paths and behaviors commonly seen in real human crowds. Here, we propose a simple and intuitive formulation of these rules based on biomechanical measurements and the principle of least effort. We present a constrained optimization method to compute collision-free paths of minimum caloric energy for each agent, from which collective crowd behaviors can be reproduced. We show that our method reproduces common crowd phenomena, such as arching and self-organization into lanes. We also validate the flow rates and paths produced by our method and compare them to those of real-world crowd trajectories.