Spacetime metric for pedestrian movement

TL;DR

This paper introduces a novel spacetime metric model for pedestrian movement that accounts for environmental factors, allowing the visualization of pedestrian paths as geodesics influenced by a variable feeling of time.

Contribution

It defines a new spacetime metric for pedestrian dynamics, visualizes the geometry over time, and introduces a time factor parameter reflecting pedestrians' subjective time perception.

Findings

Spacetime geometry visualizations for pedestrian movement.

A new parameter quantifying pedestrians' feeling of time.

A differential equation model for collision avoidance.

Abstract

This paper will present a model for pedestrian motion by defining a spacetime metric. This model considers the factors that are effective in the movement of pedestrians (such as obstacles, walls and other pedestrians) by defining a proper metric. In fact, the surrounding environment that affects the motion of pedestrians changes the flat(Euclidean) spacetime metric and, therefore, the shortest possible path to their destination. This change is such that pedestrians have a different feeling of time at any point and moment in the environment. Based on this feeling, they adjust their route to the destination so that they travel the shortest possible route in curved spacetime, which follows a geodesic. The contributions are :1. Defining spacetime metric for pedestrian movement.2. Visualizing the spacetime geometry for several timesteps.3. Introducing a parameter called the time factor and its physical meaning in terms of the pedestrian feeling of time. According to this paper formulation, pedestrians feel time differently at each position and moment, and the time factor measures this feeling of time. 4. Proposing a simple model with differential equations suitable for data assimilation methods while preserving the essential feature of collision avoidance behaviour.