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Modelling human perception processes in pedestrian dynamics: a hybrid approach

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.


Pedestrian behaviour in the case of selected distributed perceptions of the three individuals strolling within the left lane, i.e. in equation (3.21), λ1j=1 for j=2,3,4 and for all t≥0. In particular, (a) reports a walker representative path resulting from w1j=w (j=2,3,4) as defined in equation (3.17), (b) reports a pedestrian representative trajectory resulting from w1j=w (j=2,3,4) as defined in equation (3.18), while (c) finally reports a walker representative path resulting from w1j=w (j=2,3,4) as defined in equation (3.19). In all cases, area of influence of each individual within the left lane is defined in equation (3.16), with R1j=Rw=1.5 m for j=2,3,4.
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RSOS160561F6: Pedestrian behaviour in the case of selected distributed perceptions of the three individuals strolling within the left lane, i.e. in equation (3.21), λ1j=1 for j=2,3,4 and for all t≥0. In particular, (a) reports a walker representative path resulting from w1j=w (j=2,3,4) as defined in equation (3.17), (b) reports a pedestrian representative trajectory resulting from w1j=w (j=2,3,4) as defined in equation (3.18), while (c) finally reports a walker representative path resulting from w1j=w (j=2,3,4) as defined in equation (3.19). In all cases, area of influence of each individual within the left lane is defined in equation (3.16), with R1j=Rw=1.5 m for j=2,3,4.

Mentions: As reproduced in figures 5 and 6, the empirical observations relative to the experimental settings S2(b,c) are not computationally reproduced when w is a probability distribution (i.e. when w is given by equation (3.17) or by equation (3.18)): in these cases, the walking individual still in fact prefers to pass within the left lane. This result is consistent with the fact that, as already stated, such a type of perception function models only the uncertainty that a pedestrian has of the position of his/her surrounding individuals, but does not imply psychological arguments.Figure 6.


Modelling human perception processes in pedestrian dynamics: a hybrid approach
Pedestrian behaviour in the case of selected distributed perceptions of the three individuals strolling within the left lane, i.e. in equation (3.21), λ1j=1 for j=2,3,4 and for all t≥0. In particular, (a) reports a walker representative path resulting from w1j=w (j=2,3,4) as defined in equation (3.17), (b) reports a pedestrian representative trajectory resulting from w1j=w (j=2,3,4) as defined in equation (3.18), while (c) finally reports a walker representative path resulting from w1j=w (j=2,3,4) as defined in equation (3.19). In all cases, area of influence of each individual within the left lane is defined in equation (3.16), with R1j=Rw=1.5 m for j=2,3,4.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
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getmorefigures.php?uid=PMC5383809&req=5

RSOS160561F6: Pedestrian behaviour in the case of selected distributed perceptions of the three individuals strolling within the left lane, i.e. in equation (3.21), λ1j=1 for j=2,3,4 and for all t≥0. In particular, (a) reports a walker representative path resulting from w1j=w (j=2,3,4) as defined in equation (3.17), (b) reports a pedestrian representative trajectory resulting from w1j=w (j=2,3,4) as defined in equation (3.18), while (c) finally reports a walker representative path resulting from w1j=w (j=2,3,4) as defined in equation (3.19). In all cases, area of influence of each individual within the left lane is defined in equation (3.16), with R1j=Rw=1.5 m for j=2,3,4.
Mentions: As reproduced in figures 5 and 6, the empirical observations relative to the experimental settings S2(b,c) are not computationally reproduced when w is a probability distribution (i.e. when w is given by equation (3.17) or by equation (3.18)): in these cases, the walking individual still in fact prefers to pass within the left lane. This result is consistent with the fact that, as already stated, such a type of perception function models only the uncertainty that a pedestrian has of the position of his/her surrounding individuals, but does not imply psychological arguments.Figure 6.

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.