Generating Pedestrian Trajectories Consistent with the Fundamental Diagram Based on Physiological and Psychological Factors

Narang, Sahil; Best, Andrew; Curtis, Sean; Manocha, Dinesh · 2015 · OpenAlex-citations

DOI: 10.1371/journal.pone.0117856

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Summary

This paper addresses the challenge of generating realistic pedestrian trajectories in crowd simulations that adhere to the Fundamental Diagram, which describes the inverse relationship between crowd density and pedestrian speed. While many existing multi-agent simulators reduce agent speeds in congested areas primarily for collision avoidance, they often fail to capture the natural density-dependent behaviors observed in real-world crowds. The authors propose a novel algorithm that integrates physiological and psychological factors into standard Global-Local Planner (GLP) frameworks to produce trajectories that naturally exhibit these density-speed relationships without significant computational overhead. The method introduces "density-dependent filters" that act as an interface between global path planning and local navigation. These filters adjust an agent’s preferred velocity based on local conditions using two primary factors. The physiological factor relies on biomechanical principles linking stride length and walking speed, defined by a stride factor parameter. The psychological factor models personal space through a "stride buffer" parameter, reflecting the discomfort agents feel when their required space is encroached upon. To estimate available space, the algorithm computes local 2D density by analyzing neighboring agents and obstacles. It uses a Gaussian density function to weigh nearby agents, prioritizing those in front to model elliptical personal space, and calculates contiguous free space around obstacles to account for spatial constraints. At each simulation step, the algorithm samples potential velocities along an arc centered on the global planner’s preferred velocity. It selects a corrected preferred velocity that minimizes the time to reach the goal while respecting the physiological and psychological constraints derived from the local density and free space calculations. This approach allows agents to implicitly choose less congested paths if they offer faster progress, rather than merely reacting to immediate collisions. The system is designed to be general, requiring no assumptions about the specific global planning or local navigation algorithms used, and can be integrated with techniques like reciprocal velocity obstacles or social forces. The authors validate their approach by comparing simulated trajectories with captured real-world crowd data from indoor and outdoor experiments, including corridor and stadium scenarios. The results demonstrate that the algorithm successfully reproduces the Fundamental Diagram’s speed-density relationship, resulting in smoother trajectories and fewer agent-agent collisions compared to traditional methods. The simulation maintains interactive rates for thousands of agents on a single core, offering a computationally efficient solution for generating human-like dense crowd behaviors in applications such as urban design, computer animation, and virtual reality.

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• pedestrian behavior perception