Dynamic stride length adaptation according to utility and personal space

Abstract

a b s t r a c tPedestrians adjust both speed and stride length when they navigate difficult situations such as tight corners or dense crowds. They try to avoid collisions and to preserve their personal space. State-of-the-art pedestrian motion models automatically reduce speed in dense crowds simply because there is no space where the pedestrians could go. The stride length and its correct adaptation, however, are rarely considered. This leads to artefacts that impact macroscopic observation parameters such as densities in front of bottlenecks and, through this, flow. Hence modelling stride adaptation is important to increase the predictive power of pedestrian models. To achieve this we reformulate the problem as an optimisation problem on a disk around the pedestrian. Each pedestrian seeks the position that is most attractive in a sense of balanced goals between the search for targets, the need for individual space and the need to keep a distance from obstacles. The need for space is modelled according to findings from psychology defining zones around a person that, when invaded, cause unease. The result is a fully automatic adjustment that allows calibration through meaningful social parameters and that gives visually natural results with an excellent fit to measured experimental data.

The Superposition Principle: A Conceptual Perspective on Pedestrian Stream Simulations

“…Movement of agents in cellular automata can be emulated if the numerical solution for the optimisation is chosen in a specific way [25]. When the next position is chosen on the whole disk, smaller steps are possible allowing for smoother movement and stream behaviour [44].…”

“…For cellular automata, the values of the adjacent cells simply have to be compared. In the optimal steps model, a similar approach can be taken with placing a grid on the circle or disc [25,27], or, alternatively, employing a numerical optimisation scheme [44]. In probabilistic cellular automata, a random variable has to be drawn from the probability distribution, which is constructed based on the scalar field.…”

“…In the optimal steps model, locomotion is not continuous but rather in continuous space, thus allowing for a free motion process. New opportunities to study pedestrians' real stepping behaviour may result from this modelling approach [27,44].…”

“…The introduction of psychological or physiological aspects, such as a field of vision, can lead to discontinuities in the scalar field over time. These discontinuities can be a problem for models based on differential equations and some optimisation schemes [44,45]. On the other hand, extensions developed for one model based on scalar fields can easily be adopted for other models within the superposition paradigm.…”

Parsimony versus Reductionism: How Can Crowd Psychology be Introduced into Computer Simulation?

“…Hence, in order to accurately simulate different types of crowds, While the importance of crowd psychology for engineering has been noted (Aguirre, El-Tawil, Best, Gill, & Fedorov, 2011;Sime, 1995), theories of crowd psychology have only been minimally incorporated into mathematical modelling and computer simulations, and from a psychological point of view, these are out-dated (Templeton, Drury, & Philippides, 2015). A more promising direction of research are proxemics (Baum & Paulus, 1987;Hall, 1966), which describe the social distances individuals keep from one another and has been used for the study of crowd behaviour (Costa, 2010;von Sivers & Köster, 2015;Zanlungo, Ikeda, & Kanda, 2014). Although there have been some attempts to introduce small groups within the larger crowd behaviour to simulation models such as families, friends or other predefined groups (Köster, Seitz, Treml, Hartmann, & Klein, 2011;Moussaïd, Perozo, Garnier, Helbing, & Theraulaz, 2010;Singh et al, 2009;Yang, Zhao, Li, & Fang, 2005), these models do not consider the social structure or dynamic of the whole crowd (for a comprehensive review, see (Templeton et al, 2015)).…”