Crowd Path Trajectory Prediction Using Least Action Principle

Due to increasing threats in human crowds, it is crucial to understand how humans react to environmental changes in diverse settings. Many works are targeting the deep analysis of crowd motion, however, the methods rely on massive data collection and require highly sophisticated sensor equipment and computing power. In this paper, we propose a theoretical and practical investigation of pedestrians' natural movement in a confined and well-defined shopping mall region. The modeling for a single pedestrian's motion is relatively easy; however, predicting the path trajectory of a crowd is a complex task. We have focused on creating models that take into account the mechanical features of human motion and predict the trajectory of the crowd with simple mathematical models. In our theoretical investigation, we have employed mean values of the pedestrian characteristics, such as velocity, density, and the presence of numerous barriers. We here present a crowd trajectory prediction system using the least action principle and compare it to the ground truth in the experimental results. The experiment is carried out in a free space shopping mall with installed cameras. We obtained exact trajectories for this experiment, enabling us to measure the dynamics of the crowd. The testing involved 20 recordings spread out over five days, including 30 test subjects. We also created the background of alternative route situations and matched it to the actual trajectories to better understand participants' trajectories. Our model showed a small error between the actual and simulated paths to predict the subjects’ trajectory.