Accepted 28 January 2015
Available online 19 February 2015
Pedestrian movement sonal space. State-of-the-art pedestrian motion models automatically reduce speed in last years. Experiidich et al. e new mod ned (Zhen 2009; Smith et al., 2009; Asano et al., 2010; Guo et al., 2011; Lachapelle andWolfram, 2011; Seitz and Köster, 2012; Flö and Lämmel, 2015).
Among the microscopic models cellular automata (Burstedde et al., 2001; Blue and Adler, 2001; Henein and White
Ezaki et al., 2012; Kneidl, 2013) and social force models (Helbing and Molnár, 1995; Helbing et al., 2000; Chraibi et al., 2010; http://dx.doi.org/10.1016/j.trb.2015.01.009 0191-2615/ 2015 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +49 89 1265 3762.
E-mail addresses: firstname.lastname@example.org (I. von Sivers), email@example.com (G. Köster).
Transportation Research Part B 74 (2015) 104–117
Contents lists available at ScienceDirect
Transportation Research Part BModels for macroscopic and microscopic pedestrian transport have been steadily developed over the ments and observations (e.g. Hoogendoorn and Daamen, 2005; Seyfried et al., 2005; Guo et al., 2012; Dav
Hänseler et al., 2014) continue to give new insights into pedestrian dynamics and, thus, not only encourag sometimes make them necessary to capture observed phenomena. Existing models are constantly being refi, 2013; els but g et al., tteröd , 2007;Simulation of pedestrian movement becomes increasingly important to ensure safety for everybody wherever a crowd comes together. Large and dense crowds shape daily urban traffic, not only in areas assigned to walking but also at transfer locations such as train platforms or on shared spaces (Kretz et al., 2013). Thus, pedestrian movement is an integral part of the overall urban transportation problem and adequate modelling of human locomotion in a crowd has become essential to its solution.Crowd dynamics
Optimal Steps Model
Stride length adaptation
Optimisation 1. Introductiondense 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. 2015 Elsevier Ltd. All rights reserved.Dynamic stride length adaptation according to utility and personal space
Isabella von Sivers ⇑, Gerta Köster
Munich University of Applied Sciences, Lothstraße 64, 80335 Munich, Germany a r t i c l e i n f o
Received 7 November 2013
Received in revised form 27 January 2015 a b s t r a c t
Pedestrians 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 perjournal homepage: www.elsevier .com/ locate / t rb
Köster et al., 2013) are prominent and, perhaps, best investigated. But some typical aspects of human movement are still missing in known models, in particular the immediate adaptation of the stride length to the navigational situation. Yet stride
I. von Sivers, G. Köster / Transportation Research Part B 74 (2015) 104–117 105length adaptation is closely connected to at least the latter two of the four most prominent ‘process variables’ of pedestrian traffic listed in Daamen and Hoogendoorn (2003): the free-flow velocity, the walking direction, the crowd density, and the effect of bottlenecks.
When pedestrians navigate a difficult corner or walk within a crowd they reduce their speed. And more than that, they make smaller steps. They do this with foresight, that is, they adapt to the situation before or at the moment they encounter it.
Avoiding collisions is clearly one reason for this. Another one is that pedestrians try to preserve their personal space (Katz, 1937; Sommer, 1959; Hall, 1966) when approaching others who they do not identify with (Novelli et al., 2013) adding a social aspect to their behaviour. The psychological model of personal space introduced by Hall in 1966 (Hall, 1966) is widely accepted and built upon, e.g. (Beaulieu, 2004; Uzzell and Horne, 2006; Evans and Wener, 2007; Kennedy et al., 2009).
Following Seyfried et al. (2010a), smaller strides in dense situations are, at least, one reason for speed reduction. However, most current state-of-the-art pedestrian motion models are only capable of speed adaptation, typically in a reactive way, but do not adjust the stride length. In fact, standard continuous models, based on differential equations, do not even model human steps but rather a smooth sliding motion of particles. Step sizes refer to numeric advances in time without any bio-mechanical meaning. Cellular automaton models only allow ‘hops’ from one cell to the next. Stride adaptation is impossible and the choice of direction is very limited.
Clearly, models of personal space that demand a fine spatial resolution do not make much sense for cellular automata.
However, the concept is also lacking in most of the spatially continuous models of pedestrian traffic. Sterlin et al. (2010) briefly show how it fits into an agent-model but do not give any information on their choice of locomotion model nor simulation results. In robotics, on the other hand, the concept of ‘personal space’ is widely used. The distance robots keep from humans is mostly based on personal spaces according to Hall (1966). They adopt the psychological model to let the robots mimic natural human behaviour – to keep distances from others. The vast variety of articles on ‘personal space’ in robotics cannot be covered here. Important advances in research can be found, e.g., in Tasaki et al. (2004, 2005, 2009, 2013,).