Limits...
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.


(a) Modulus of the velocity contribution vwalliw due to the pedestrian desire to maintain a sufficient distance from a non-walkable element w, e.g. a structural element or a domain border, see equation (3.9). (b) Moduli of the contact velocity components, introduced in equation (3.10). (c) Modulus of the repulsive interaction kernel, as defined in equation (3.22). (d) Representation of the angle γi defining the gazing direction gi of a generic pedestrian i, as described in equation (3.24).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSOS160561F2: (a) Modulus of the velocity contribution vwalliw due to the pedestrian desire to maintain a sufficient distance from a non-walkable element w, e.g. a structural element or a domain border, see equation (3.9). (b) Moduli of the contact velocity components, introduced in equation (3.10). (c) Modulus of the repulsive interaction kernel, as defined in equation (3.22). (d) Representation of the angle γi defining the gazing direction gi of a generic pedestrian i, as described in equation (3.24).

Mentions: The second velocity component in equation (3.5) instead describes the intention of the individual i to stay sufficiently away from (i) obstacles and structural elements within the domain; (ii) parts of the domain borders that do not represent his/her target destinations and (iii) non-walkable areas. As reproduced in figure 2a, such a contribution in individual dynamics can be implemented by a distance-decaying repulsive term that is active only when the pedestrian is close enough to one of them:3.8viwall(t)=∑w=1Wviwwall(t),where3.9viwwall(t)={−Aiexp⁡((Rb−diww(xi(t)))Bi)niww(xi(t)),if diww(xi(t))≤Lw;0,otherwise;where is the distance from the actual position of pedestrian i to the nearest point of a non-walkable element w (with w=1,…,W), while is the corresponding unit vector (see for instance [25,28,41]). Furthermore, Ai and Bi are constants equal to 1 m s−1 and 0.01 m for any individual i, respectively (as estimated in [28] with a proper sensitivity analysis), and Rb=0.25 m is the body radius of a medium-size pedestrian (as proposed in [28,36,42,43]). Finally, Lw=1 m is a reasonable threshold value above which the repulsive term from domain structural elements vanishes.Figure 2.


Modelling human perception processes in pedestrian dynamics: a hybrid approach
(a) Modulus of the velocity contribution vwalliw due to the pedestrian desire to maintain a sufficient distance from a non-walkable element w, e.g. a structural element or a domain border, see equation (3.9). (b) Moduli of the contact velocity components, introduced in equation (3.10). (c) Modulus of the repulsive interaction kernel, as defined in equation (3.22). (d) Representation of the angle γi defining the gazing direction gi of a generic pedestrian i, as described in equation (3.24).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSOS160561F2: (a) Modulus of the velocity contribution vwalliw due to the pedestrian desire to maintain a sufficient distance from a non-walkable element w, e.g. a structural element or a domain border, see equation (3.9). (b) Moduli of the contact velocity components, introduced in equation (3.10). (c) Modulus of the repulsive interaction kernel, as defined in equation (3.22). (d) Representation of the angle γi defining the gazing direction gi of a generic pedestrian i, as described in equation (3.24).
Mentions: The second velocity component in equation (3.5) instead describes the intention of the individual i to stay sufficiently away from (i) obstacles and structural elements within the domain; (ii) parts of the domain borders that do not represent his/her target destinations and (iii) non-walkable areas. As reproduced in figure 2a, such a contribution in individual dynamics can be implemented by a distance-decaying repulsive term that is active only when the pedestrian is close enough to one of them:3.8viwall(t)=∑w=1Wviwwall(t),where3.9viwwall(t)={−Aiexp⁡((Rb−diww(xi(t)))Bi)niww(xi(t)),if diww(xi(t))≤Lw;0,otherwise;where is the distance from the actual position of pedestrian i to the nearest point of a non-walkable element w (with w=1,…,W), while is the corresponding unit vector (see for instance [25,28,41]). Furthermore, Ai and Bi are constants equal to 1 m s−1 and 0.01 m for any individual i, respectively (as estimated in [28] with a proper sensitivity analysis), and Rb=0.25 m is the body radius of a medium-size pedestrian (as proposed in [28,36,42,43]). Finally, Lw=1 m is a reasonable threshold value above which the repulsive term from domain structural elements vanishes.Figure 2.

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.