Do walking pedestrians stabily interact inside a large group? Analysis of group and sub-group spatial structure

Do walking pedestrians stabily interact inside a large group? Analysis of group and sub-group spatial structure Francesco Zanlungo (ZANLUNGO@Atr.Jp) Takayuki Kanda (KANDA@Atr.Jp) Intelligent Robotics and Communication Laboratories, ATR, Kyoto, Japan & JSPS CREST, Tokyo, Japan Abstract We combine video recording and laser range tracking to anal- yse the geometrical structure of groups of walking pedestri- ans socially interacting. By recording their relative position and observing their social interaction for a large enough time span we can analyse the stability and universality of their spa- tial structure. We find that while 2-pedestrian and 3-pedestrian groups have a relatively “time stable” and “universal” geomet- rical structure (an abreast formation for pairs, and a “V” for- mation for triads, with the central pedestrian walking slightly behind), no such structure emerges for larger groups. Never- theless, these larger groups result to be composed of time sta- ble two or three people sub-groups with the same “universal” geometrical structure of isolated pairs and triads. Keywords: Group dynamics; proxemics. Introduction The spatial relationship of socially interacting people, i.e proxemics, has been largely studied, starting from the seminal works of (Hall, 1969) and (Kendon, 1990) in which the dis- tances between and spatial distribution of people participating in social activities have been investigated. At the same time other researchers have investigated the size of social groups (by size of a group we mean the number of its components) and the probability distribution of these sizes (James, 1953; Coleman & James, 1961). Many of the aforementioned stud- ies are based on “ecological” observations, i.e. studies in which people are observed in their natural environment while reducing as much as possible the effect of observations on their behaviour. While these studies are obviously based on observations of people behaviour in public spaces, until re- cently they did not focus on one of the main components of public spaces population (at least in modern urban areas), i.e. walking pedestrians. Here by pedestrian we mean a person in a public space moving between two locations for practical or recreational purposes, or even “wandering around” an en- vironment without any particular goal. Pedestrians are often part of social groups with a specific proxemics determined by their dynamical constraints (the fact that they are walking), but the study of these groups has been traditionally made dif- ficult by the fact that they are moving and located inside a crowd, which makes the observation of their behaviour more troublesome. Nevertheless, lately a few works have focused on the behaviour of these groups (Moussa¨id, Perozo, Garnier, Helbing, & Theraulaz, 2010; Costa, 2010), due also to the growing interest in crowd behaviour of which groups are a non negligible component (Aveni, 1977). This interest is due to the necessity of simulating crowd behaviour to design bet- ter pedestrian facilities (Helbing, Farkas, Molnar, & Vicsek, 2002), but also to reproduce faithfully the behaviour of virtual crowds for the entertainment industry (Karamouzas & Over- mars, 2012). While (Moussa¨id et al., 2010) report that the spatial structure of a freely walking (i.e. not environmentally constrained) n- pedestrian group is a line of abreast walking pedestrians, that tends to be bent into “V” or “U” formations (i.e., the pedestri- ans on the sides walk ahead) when the crowd density grows, (Costa, 2010) reports different spatial structures, suggesting for example that the “V” structure is the most occurring one for three people groups (regardless of crowding), and that larger groups tend to split into smaller sub-groups. Never- theless (Costa, 2010) does not analyse the possible effects of environmental constraints on observed behaviours (the width of the sidewalks pedestrians were observed in was compara- ble to the group spatial sizes), and does not provide a quanti- tative study of 2D space structures, nor follows groups for a time interval long enough to analyse their change in time. The difference between these observations leads us to two re- lated problems in walking group proxemics, to which we try to bring insight in this work: • Do n-pedestrian groups (i.e. groups composed of n members) have a prevalent geometrical structure? Here by prevalent we mean universal (common to almost all groups, or at least present in a large majority of them) and time stable (i.e. the positions of pedestrians in an uncon- strained group will be given by small oscillations around those of the prevalent structure). • If such an overall structure does not exist for a n-pedestrian group, is it possible to find it at the sub-group level? In order to analyse these issues, we have to observe pedestri- ans in a situation in which collision avoiding and environ- mental constraints are not very strong (otherwise it would be impossible to identify the “universal” structure). Further- more, we have to combine the need to measure with good detail (and for long enough time) the position of pedestrians, with that of observing their social interactions, in order to analyse the group structure. If a large pedestrian group is divided into smaller sub-groups we may expect social inter- action inside sub-groups to be more frequent than between different sub-groups, and for this reason in many cases the