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Modelling human perception processes in pedestrian dynamics: a hybrid approach

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ABSTRACT

In this paper, we present a hybrid mathematical model describing crowd dynamics. More specifically, our approach is based on the well-established Helbing-like discrete model, where each pedestrian is individually represented as a dimensionless point and set to move in order to reach a target destination, with deviations deriving from both physical and social forces. In particular, physical forces account for interpersonal collisions, whereas social components include the individual desire to remain sufficiently far from other walkers (the so-called territorial effect). In this respect, the repulsive behaviour of pedestrians is here set to be different from traditional Helbing-like methods, as it is assumed to be largely determined by how they perceive the presence and the position of neighbouring individuals, i.e. either objectively as pointwise/localized entities or subjectively as spatially distributed masses. The resulting modelling environment is then applied to specific scenarios, that first reproduce a real-world experiment, specifically designed to derive our model hypothesis. Sets of numerical realizations are also run to analyse in more details the pedestrian paths resulting from different types of perception of small groups of static individuals. Finally, analytical investigations formalize and validate from a mathematical point of view selected simulation outcomes.

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Analysis of the paths of pedestrian 1 in the presence of a single static individual 2. Panel (a) desired pedestrian path (cross symbols) and pedestrian trajectory in case of a localized perception of individual 2 (filled triangles). Panels (b,c,d) pedestrian paths resulting from a distributed perception of individual 2 as given either by equation (3.17) (b), by equation (3.18) (c) or by equation (3.19) (d). In each image, we plot the trajectory of pedestrian 1 in the cases of R12 equal to 0.25 m (plus symbols), 0.5 m (open circles), 0.75 m (open squares), and 1 m (open triangles).
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RSOS160561F8: Analysis of the paths of pedestrian 1 in the presence of a single static individual 2. Panel (a) desired pedestrian path (cross symbols) and pedestrian trajectory in case of a localized perception of individual 2 (filled triangles). Panels (b,c,d) pedestrian paths resulting from a distributed perception of individual 2 as given either by equation (3.17) (b), by equation (3.18) (c) or by equation (3.19) (d). In each image, we plot the trajectory of pedestrian 1 in the cases of R12 equal to 0.25 m (plus symbols), 0.5 m (open circles), 0.75 m (open squares), and 1 m (open triangles).

Mentions: We finally analyse how, in the case of subjective distributed perceptions, the radius determining the extension of the repulsive region affects individual behaviour. In this respect, a pair of individuals, namely 1 and 2, are placed within an 8 m2 domain Ω, which may represent the planimetry of a room or of a corridor (figure 8). Pedestrian 1 is initially located at x1(0)=(1.83;0.83) m and moves according to equation (3.4). In particular, he/she wants to reach the upper edge of the domain, i.e. for any time t≥0 (cf. figure 8a). During motion, he/she has to avoid individual 2, who is static for the sake of simplicity and situated at x2(t)=x2(0)=(1.83;2.08) m for all t, i.e. between the initial position of walker 1 and his/her target destination. The repulsive behaviour of pedestrian 1 is defined by equation (3.21) with the interaction kernel given in equation (3.22). It is also assumed that no other velocity contribution enters the picture (i.e. for all t≥0). Finally, the gaze of pedestrian 1 extends over the entire domain, so that individual 2 constantly falls within his/her interaction set, i.e. for all t≥0.Figure 8.


Modelling human perception processes in pedestrian dynamics: a hybrid approach
Analysis of the paths of pedestrian 1 in the presence of a single static individual 2. Panel (a) desired pedestrian path (cross symbols) and pedestrian trajectory in case of a localized perception of individual 2 (filled triangles). Panels (b,c,d) pedestrian paths resulting from a distributed perception of individual 2 as given either by equation (3.17) (b), by equation (3.18) (c) or by equation (3.19) (d). In each image, we plot the trajectory of pedestrian 1 in the cases of R12 equal to 0.25 m (plus symbols), 0.5 m (open circles), 0.75 m (open squares), and 1 m (open triangles).
© Copyright Policy - open-access
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC5383809&req=5

RSOS160561F8: Analysis of the paths of pedestrian 1 in the presence of a single static individual 2. Panel (a) desired pedestrian path (cross symbols) and pedestrian trajectory in case of a localized perception of individual 2 (filled triangles). Panels (b,c,d) pedestrian paths resulting from a distributed perception of individual 2 as given either by equation (3.17) (b), by equation (3.18) (c) or by equation (3.19) (d). In each image, we plot the trajectory of pedestrian 1 in the cases of R12 equal to 0.25 m (plus symbols), 0.5 m (open circles), 0.75 m (open squares), and 1 m (open triangles).
Mentions: We finally analyse how, in the case of subjective distributed perceptions, the radius determining the extension of the repulsive region affects individual behaviour. In this respect, a pair of individuals, namely 1 and 2, are placed within an 8 m2 domain Ω, which may represent the planimetry of a room or of a corridor (figure 8). Pedestrian 1 is initially located at x1(0)=(1.83;0.83) m and moves according to equation (3.4). In particular, he/she wants to reach the upper edge of the domain, i.e. for any time t≥0 (cf. figure 8a). During motion, he/she has to avoid individual 2, who is static for the sake of simplicity and situated at x2(t)=x2(0)=(1.83;2.08) m for all t, i.e. between the initial position of walker 1 and his/her target destination. The repulsive behaviour of pedestrian 1 is defined by equation (3.21) with the interaction kernel given in equation (3.22). It is also assumed that no other velocity contribution enters the picture (i.e. for all t≥0). Finally, the gaze of pedestrian 1 extends over the entire domain, so that individual 2 constantly falls within his/her interaction set, i.e. for all t≥0.Figure 8.

View Article: PubMed Central - PubMed

ABSTRACT

In this paper, we present a hybrid mathematical model describing crowd dynamics. More specifically, our approach is based on the well-established Helbing-like discrete model, where each pedestrian is individually represented as a dimensionless point and set to move in order to reach a target destination, with deviations deriving from both physical and social forces. In particular, physical forces account for interpersonal collisions, whereas social components include the individual desire to remain sufficiently far from other walkers (the so-called territorial effect). In this respect, the repulsive behaviour of pedestrians is here set to be different from traditional Helbing-like methods, as it is assumed to be largely determined by how they perceive the presence and the position of neighbouring individuals, i.e. either objectively as pointwise/localized entities or subjectively as spatially distributed masses. The resulting modelling environment is then applied to specific scenarios, that first reproduce a real-world experiment, specifically designed to derive our model hypothesis. Sets of numerical realizations are also run to analyse in more details the pedestrian paths resulting from different types of perception of small groups of static individuals. Finally, analytical investigations formalize and validate from a mathematical point of view selected simulation outcomes.

No MeSH data available.


Related in: MedlinePlus