# Vision-based macroscopic pedestrian models

@article{Degond2013VisionbasedMP, title={Vision-based macroscopic pedestrian models}, author={Pierre Degond and C{\'e}cile Appert-Rolland and Julien Pettr'e and Guy Theraulaz}, journal={Kinetic and Related Models}, year={2013}, volume={6}, pages={809-839} }

We propose a hierarchy of kinetic and macroscopic models for a system consisting of a large number of interacting pedestrians. The basic interaction rules are derived from [44] where the dangerousness level of an interaction with another pedestrian is measured in terms of the derivative of the bearing angle (angle between the walking direction and the line connecting the two subjects) and of the time-to-interaction (time before reaching the closest distance between the two subjects). A mean…

## 62 Citations

### A Hierarchy of Heuristic-Based Models of Crowd Dynamics

- Computer Science
- 2013

A hierarchy of kinetic and macroscopic models is derived from a noisy variant of the heuristic behavioral Individual-Based Model of Ngai et al. where pedestrians are supposed to have constant speeds to seek the best compromise between navigation towards their target and collisions avoidance.

### Pedestrian Models based on Rational Behaviour

- BiologyArXiv
- 2018

This work will consider a model for pedestrian dynamics that attempts to reproduce the rational behaviour of individual agents through the means of anticipation, and discusses the validity of this game theoretical-based model in regimes with varying degrees of congestion.

### A local version of the Hughes model for pedestrian flow

- Computer Science
- 2015

A modification of the Hughes model to include local effects, namely limited vision, and a conviction towards decision making, is presented, which enables smooth turning and temporary waiting behavior.

### Comparing first-order microscopic and macroscopic crowd models for an increasing number of massive agents

- Physics
- 2016

A comparison between first-order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number of pedestrians, finding that the two types of models approach one another in the limit, provided the strength and/or the domain of pedestrian interactions are properly modulated by at either scale.

### Kinetic description of collision avoidance in pedestrian crowds by sidestepping

- Physics
- 2018

In this paper we study a kinetic model for pedestrians, who are assumed to adapt their motion towards a desired direction while avoiding collisions with others by stepping aside. These minimal…

### A pedestrian flow model with stochastic velocities: Microscopic and macroscopic approaches

- Physics
- 2017

We investigate a stochastic model hierarchy for pedestrian flow. Starting from a microscopic social force model, where the pedestrians switch randomly between the two states stop-or-go, we derive an…

### A meshfree particle method for a vision-based macroscopic pedestrian model

- PhysicsInternational Journal of Advances in Engineering Sciences and Applied Mathematics
- 2018

In this paper we present numerical simulations of a macroscopic vision-based model (Degond et al. in Kinet Relat Models AIMs 6(4):809–839, 2013) derived from microscopic situation rules described in…

### A meshfree particle method for a vision-based macroscopic pedestrian model

- Physics
- 2018

This model describes an approach to collision avoidance between pedestrians by taking decisions of turning or slowing down based on basic interaction rules, where the dangerousness level of an interaction with another pedestrian is measured in terms of the derivative of the bearing angle and of the time-to-interaction.

### A unified multiscale vision of behavioral crowds

- PhysicsMathematical Models and Methods in Applied Sciences
- 2019

A multiscale vision to human crowds is proposed which provides a consistent description at the three possible modeling scales, namely, microscopic, mesoscopic, and macroscopic.

### Microscopic and Macroscopic Models for Vehicular and Pedestrian Flows

- Environmental ScienceOrder, Disorder and Criticality
- 2020

In this chapter we develop and study microscopic and macroscopic models for car and pedestrian ﬂows. After a general introduction on the basic features of the ﬂows under consideration, we develop our…

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