Control-Theoretic Multi-Agent Modeling of Crowd Dynamics with Physical and Psychological Interactions

We propose a multi-agent model framework for crowd dynamics in pedestrian environments. The model integrates physical and psychological interactions among agents and with the environment, accounting for physical and social forces based on inter-agent and obstacle distances. It improves the physical characteristics of an agent by modeling the agent's active and reactive torso rotation. These features capture an agent's rotational and lateral movement induced by torque interactions between the agents and enable phenomena such as shouldering and navigating narrow corridors. The physical layer also includes a feedback control force, specifically Proportional-Integral (PI) feedback control, that enables the agent to track a desired velocity profile, reflecting directional intention and determination. The authority of this control force is determined by using upper limits on the allowable force magnitude, which is determined by the competitive index characteristic of each agent. The psychological layer models agent competitiveness, incorporating inter-agent interactions and responses to environmental hazards. The physical and psychological layers are coupled by the inter-agent distances and the psychological state, determining the feedback control authority on each agent's pushing force and motion. To illustrate the novel behavior enabled by this model, we present extensive simulation scenarios highlighting the model's layers and how the different parameters influence the crowd's behavior.