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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.

No MeSH data available.


Representation of a generic pedestrian i and of his/her interaction set , defined in equation (3.13). In particular, the walker i approaches the individual 1 as he/she is, i.e. a localized obstacle. The pedestrian i instead subjectively considers the field individuals 2, 3 and 4 as distributed entities, whose presence is psychologically perceived to be extended over the regions  (with j=2,3,4) and locally measured by the corresponding function wij, given in equation (3.17), in equation (3.18) or in equation (3.19), respectively.
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RSOS160561F3: Representation of a generic pedestrian i and of his/her interaction set , defined in equation (3.13). In particular, the walker i approaches the individual 1 as he/she is, i.e. a localized obstacle. The pedestrian i instead subjectively considers the field individuals 2, 3 and 4 as distributed entities, whose presence is psychologically perceived to be extended over the regions (with j=2,3,4) and locally measured by the corresponding function wij, given in equation (3.17), in equation (3.18) or in equation (3.19), respectively.

Mentions: In this respect, it is consistent to first assume that a pedestrian is only influenced by persons that are sufficiently near, i.e. those falling within a given region around his/her actual position. For each walker i, we indeed define his/her interaction set3.13Si(t)={j=1,…,N: j≠i, /xj(t)−xi(t)/≤Ri, xj(t)−xi(t)/xj(t)−xi(t)/⋅gi(t)≥cos⁡θi}.The above equation states that a pedestrian i accounts for only the presence of the group of individuals j (called again field individuals) located within a circular sector, centred at his/her position xi and symmetrically enlarged from his/her gazing direction gi, with overall angular span 2θi and radius Ri (figure 3). It is worth noticing that the definition of may allow a pedestrian to react to the presence of individuals behind structural elements (for instance, walls or columns): in a first approximation, this is consistent as a walker can perceive another person also by hearing his/her voice. However, reasonable reductions of the pedestrian interaction set may be required in specific scenarios or geometries of the domain (e.g. the presence of soundproofed and/or of opaque walls), not accounted for, for the sake of simplicity, in this work. It is useful to remark that, hereafter, we assume that the extension of the interaction set is equal for all pedestrians: in particular, we fix θi=1.48 rad (≃85°) and Ri=50 m for all i=1,…,N, as done in [28,36,44].Figure 3.


Modelling human perception processes in pedestrian dynamics: a hybrid approach
Representation of a generic pedestrian i and of his/her interaction set , defined in equation (3.13). In particular, the walker i approaches the individual 1 as he/she is, i.e. a localized obstacle. The pedestrian i instead subjectively considers the field individuals 2, 3 and 4 as distributed entities, whose presence is psychologically perceived to be extended over the regions  (with j=2,3,4) and locally measured by the corresponding function wij, given in equation (3.17), in equation (3.18) or in equation (3.19), respectively.
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Related In: Results  -  Collection

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

RSOS160561F3: Representation of a generic pedestrian i and of his/her interaction set , defined in equation (3.13). In particular, the walker i approaches the individual 1 as he/she is, i.e. a localized obstacle. The pedestrian i instead subjectively considers the field individuals 2, 3 and 4 as distributed entities, whose presence is psychologically perceived to be extended over the regions (with j=2,3,4) and locally measured by the corresponding function wij, given in equation (3.17), in equation (3.18) or in equation (3.19), respectively.
Mentions: In this respect, it is consistent to first assume that a pedestrian is only influenced by persons that are sufficiently near, i.e. those falling within a given region around his/her actual position. For each walker i, we indeed define his/her interaction set3.13Si(t)={j=1,…,N: j≠i, /xj(t)−xi(t)/≤Ri, xj(t)−xi(t)/xj(t)−xi(t)/⋅gi(t)≥cos⁡θi}.The above equation states that a pedestrian i accounts for only the presence of the group of individuals j (called again field individuals) located within a circular sector, centred at his/her position xi and symmetrically enlarged from his/her gazing direction gi, with overall angular span 2θi and radius Ri (figure 3). It is worth noticing that the definition of may allow a pedestrian to react to the presence of individuals behind structural elements (for instance, walls or columns): in a first approximation, this is consistent as a walker can perceive another person also by hearing his/her voice. However, reasonable reductions of the pedestrian interaction set may be required in specific scenarios or geometries of the domain (e.g. the presence of soundproofed and/or of opaque walls), not accounted for, for the sake of simplicity, in this work. It is useful to remark that, hereafter, we assume that the extension of the interaction set is equal for all pedestrians: in particular, we fix θi=1.48 rad (≃85°) and Ri=50 m for all i=1,…,N, as done in [28,36,44].Figure 3.

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.