Force-based models of pedestrian dynamics

Chraibi, Mohcine; Kemloh, Ulrich; Schadschneider, Andreas; Seyfried, Armin

doi:10.3934/nhm.2011.6.425

Cited by 110 publications

(48 citation statements)

References 44 publications

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“…Their proximity to equations derived from Newton's laws of motion allow direct application of standard numerical methods, such as Euler's method, to solve the equations that are available through toolboxes such as Matlab, Mathematica, or numerical libraries. Nonetheless, scientists and tool users continue to run into trouble when implementing or employing the model [7,8].…”

Section: Introductionmentioning

confidence: 99%

Avoiding numerical pitfalls in social force models

2013

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The social force model of Helbing and Molnár is one of the best known approaches to simulate pedestrian motion, a collective phenomenon with nonlinear dynamics. It is based on the idea that the Newtonian laws of motion mostly carry over to pedestrian motion so that human trajectories can be computed by solving a set of ordinary differential equations for velocity and acceleration. The beauty and simplicity of this ansatz are strong reasons for its wide spread. However, the numerical implementation is not without pitfalls. Oscillations, collisions, and instabilities occur even for very small step sizes. Classic solution ideas from molecular dynamics do not apply to the problem because the system is not Hamiltonian despite its source of inspiration. Looking at the model through the eyes of a mathematician, however, we realize that the right hand side of the differential equation is nondifferentiable and even discontinuous at critical locations. This produces undesirable behavior in the exact solution and, at best, severe loss of accuracy in efficient numerical schemes even in short range simulations. We suggest a very simple mollified version of the social force model that conserves the desired dynamic properties of the original many-body system but elegantly and cost efficiently resolves several of the issues concerning stability and numerical resolution.

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Section: Introductionmentioning

confidence: 99%

Avoiding numerical pitfalls in social force models

2013

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“…Further extension and modifications have been proposed for the original idea of social forces [13,17,18]. Many of these modifications try to mitigate the effects introduced by the physical nature, such as oscillations or inertia [12]. More or less independently of force-based models, several approaches based on cellular automata have been proposed [7][8][9][10][20][21][22].…”

Section: Modelling Approachesmentioning

confidence: 99%

“…Finally, in force-based models [3,[11][12][13]17], the scalar field is interpreted as potential leading to forces and finally to acceleration. The acceleration is integrated to velocity, which is again integrated to obtain the current position.…”

Section: Interpretation Of the Scalar Fieldmentioning

confidence: 99%

“…Conceptionally it seems questionable whether social forces, if we assume they exist, directly translate to physical forces. Using the analogy of physical forces has been shown to be a seminal approach for the simulation of pedestrian dynamics [11,12].…”

Section: Assessment Of Modelling Conceptsmentioning

confidence: 99%

“…Two approaches stand out due to their widespread use: cellular automata [7][8][9][10] and force-based models [3,[11][12][13]. At first glance, these approaches seem to have little in common.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Superposition Principle: A Conceptual Perspective on Pedestrian Stream Simulations

et al. 2016

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Models using a superposition of scalar fields for navigation are prevalent in microscopic pedestrian stream simulations. However, classifications, differences, and similarities of models are not clear at the conceptual level of navigation mechanisms. In this paper, we describe the superposition of scalar fields as an approach to microscopic crowd modelling and corresponding motion schemes. We use this background discussion to focus on the similarities and differences of models, and find that many models make use of similar mechanisms for the navigation of virtual agents. In some cases, the differences between models can be reduced to differences between discretisation schemes. The interpretation of scalar fields varies across models, but most of the time this variation does not have a large impact on simulation outcomes. The conceptual analysis of different models of pedestrian dynamics allows for a better understanding of their capabilities and limitations and may lead to better model development and validation.

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Efficient and validated simulation of crowds for an evacuation assistant

Wagoum

Chraibi

Mehlich

et al. 2012

Computer Animation & Virtual

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To improve safety at mass events, an evacuation assistant that supports security services in case of emergencies is developed. One central aspect is forecasting the emergency egress of large crowds in complex buildings. This requires realistic models of pedestrian dynamics that can be simulated faster than real-time by using methods applied in high performance computing. We give an overview of the project and present the actual results. We also describe the modeling approaches used thereby focusing on the runtime optimization and parallelization concepts.

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Force-based models of pedestrian dynamics

Cited by 110 publications

References 44 publications

Avoiding numerical pitfalls in social force models

Avoiding numerical pitfalls in social force models

The Superposition Principle: A Conceptual Perspective on Pedestrian Stream Simulations

Efficient and validated simulation of crowds for an evacuation assistant

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