# Simulation of Pedestrian Behavior in the Collision-Avoidance Process considering Their Moving Preferences

Authors: Zhilu Yuan; Hongfei Jia; Linfeng Zhang; Lei Bian
Journal: Discrete Dynamics in Nature and Society
 (2017)

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## Abstract

Walking habits can affect the self-organizing movement in pedestrian flow. In China, pedestrians prefer to walk along the right-hand side in the collision-avoidance process, and the same is true for the left-hand preference that is followed in several countries. Through experiments with pedestrian flow, we find that the relative position between pedestrians can affect their moving preferences. We propose a kind of collision-avoidance force based on the social force model, which considers the predictions of potential conflict and the relative position between pedestrians. In the simulation, we use the improved model to explore the effect of moving preference on the collision-avoidance process and self-organizing pedestrian movement. We conclude that the improved model can bring the simulation closer to reality and that moving preference is conducive to the self-adjustment of counterflow.


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## Body

## 1. Introduction

Over the last few decades, research into pedestrian dynamics has attracted many scholars [1–6]. Some researchers use simulation models to analyze pedestrian behavior characteristics and self-organizing phenomena. Understanding the origin of these self-organization phenomena has great significance to evacuation analysis, passenger transport hub design, and pedestrian traffic control. Typical pedestrian self-organized phenomena include arch-like formation, bottleneck oscillation, stripe formation, and lane formation.Lane formation in pedestrian counterflow is an interesting self-organizing phenomenon. “In a counterflow, the motion of the pedestrians tends to self-organize in such a way that dynamically varying lanes are formed where people move in the same direction. This effect is termed lane formation, which is a type of spontaneous symmetry breaking” [7]. In the research field of lane-formation phenomena, most studies concern spatial interaction features or certain types of behavior in the process of collision avoidance. Some types of individual pedestrian behaviors have been analyzed by researchers, such as the following behaviors [7–9]: the walking sideways behavior [10], the “in-advance-avoid behavior” [11], and the right-preference behavior [12–18]. In addition, the collective behavior of pedestrians also attracts a great deal of attention [19–21]. The study of Ma et al. is very representative; they created a k-nearest neighbor (kNN) model based on the cellular automaton model and proposed that the pedestrian interacts with a fixed number of his/her nearest neighbors who are walking from the opposite direction [21].In addition to the above discrete models, some researchers apply the continuous model to study lane formation. The continuous model is represented by the social force model [22–25], in which the walking motivation of pedestrians is expressed in the form of force, the speed of pedestrians can be moved from 0 to the maximum, and the freedom of movement direction is higher than that of the discrete model. Helbing et al. pointed out that the essential effects on lane formation should be the relative velocity of pedestrians walking in opposite directions; the physical interactions caused by the relative velocities make the lane formation happen, even without considering the special walking behavior of pedestrians. Lane formation can also be simulated [26]. Some researchers have pointed out that there are also some drawbacks in using the social force model to study the lane-formation phenomenon; in counterflow situations, the pedestrians do not attempt to avoid the oncoming traffic, and so unrealistic collisions may occur [27]. In follow-up studies of the social force model, the individual decision-making is sufficiently taken into account by researchers. Heliövaara et al. proposed an agent-based crowd model and implemented the model in the social force model: “in the improved model pedestrians observe the walking directions of the agents in front of them and choose their own actions accordingly” [27]. Yuen et al. proposed modifications of the social force model that reflect how overtaking behavior operates in counterflow [28]. Shuaib and Zainuddin introduced an improved tactical aspect of decision-making into the social force model of pedestrian behavior, where the model considers the average density and flow inside such areas and models their effect on the pedestrians’ decisions [29]. Lee et al. proposed a social-force-based pedestrian model; from their simulation results, they pointed out that the “following effect” and “evasive effect” are the main contributors to the lane formation [30].Many factors have been observed and introduced into the study of the lane-formation phenomenon, which shows that there is not a unique cause of this phenomenon. In our view, if pedestrian behaviors or decision-making has broad similarities, self-organization would occur. Pedestrians have a certain similarity of direction choice in the collision-avoidance process: they prefer to walk along the right-hand side in the collision-avoidance process in China, and the same is true for the left-hand preference that is obeyed in several countries. We consider that when the density is relatively low and there is enough choice space for decision-making, they tend to avoid collision in a customary manner. Many scholars have studied the effect of the moving preference of pedestrians on the counterflow, but few studies have explored the factors that affect the moving preference. In the study of Guo [31], they proposed a revised social force model to simulate the pedestrian counterflow through a bottleneck. They considered the position factors to be important influence factors of the moving preference, with the position factors meaning the relative position between the pedestrian and the entrance/exit boundary. Through the analysis of a pedestrian experiment, we find that, under conditions of low density, the relative position between reverse pedestrians can also affect the moving preference in the collision-avoidance process.Thus, the primary objective of this research is to study the collision-avoidance force model of moving preference, which is affected by the prediction of potential conflict and the relative position between pedestrians, and its effects on the the process of collision avoidance and lane formation. This paper is divided into two sections about the designed simulation of the moving preference. The first section analyzes the pedestrian experiment and builds the collision-avoidance force model. The second section presents several cases to study the effect of the moving preference on the self-organizing movement in pedestrian counterflow.


## 2. Pedestrian Moving Preference Simulation Model

### 2.1. The Experiment about Pedestrian Collision-Avoidance Behavior

We define our scope of research to be pedestrian counterflow that is not in crowded conditions. In this case, pedestrians have choice space in their behavior decision.A experiment was performed to study collision-avoidance behavior in October 2016. A group of 50 persons participated, uniformly composed of male students aged around 25 years old. As shown in Figure1, the experimental scenario is that the distance between pedestrians i and j is 8 meters and that they move in the opposite direction. They will keep moving until they reach the initial position of the other pedestrian. The experiment is carried out 7 times in each group, where, each time, the initial relative position between pedestrians is different (the relative positions are shown in 2). We performed 100 groups of independent experiments, from which we calculate the avoid-collision distance, the direction selection of collision avoidance, and the experimental time.Figure 1
The collision-avoidance behavior experiment scenario. The distance between pedestriansi and j is 8 meters. Pedestrian i walks from the left side of the scenario to the right side, and pedestrian j walks from the right side of the scenario to the left side. They keep moving until they reach the initial position of the other pedestrian.(1) Pedestrians usually adjust their direction in advance to avoid collision with the reverse pedestrians, where the size of this avoid-collision distance is determined by the pedestrian’s specific personality factors, which is what some studies have pointed out for use in the potential conflict prediction behavior of pedestrians. The results of the experiment about the avoid-collision distance (the distance between pedestrians at which a pedestrian begins to adjust his/her movement direction) are shown in Figure 3. Most of the time, pedestrians began to adjust their direction of movement when the distance between them was about two meters.(2) The relative position between the pedestrians can affect the direction of collision avoidance. As shown in Figure 4, when the value of lij is relatively small (Patha, Pathb, and Pathc), most pedestrians prefer to move to the right-hand side in the process of collision avoidance. We consider that when lij is small (lij<0.2 m), the relative position between the pedestrians is the “face-to-face” case. In this case, there is no obvious difference between moving to the left-hand side and the right-hand side, and, therefore, the collision-avoidance direction choice depends on the subconscious moving preferences of the pedestrian. In the experiment, the moving preferences are characterized by the right-preference.When the value of|lij| is large (Pathd, Pathe, Pathf, and Pathg), pedestrians tend to maintain the current relative position or make minor adjustments based on the relative position to complete the collision avoidance. We consider that when lij is large (lij≥0.2 m), the relative position between the pedestrians is the “brush past” case. In this case, there is a significant difference between moving to the left-hand side and the right-hand side. In the “brush past” case, the moving preference is not the influencing factor for the direction of collision avoidance, but rather the direction is determined by the relative position.(3) The relative position between pedestrians has a limited effect on the time of the collision-avoidance process. As shown in Figure 5, there is no obvious difference between the experimental times of different paths. Some scholars point out that when a pedestrian going to the right (left) comes face-to-face with a walker going to the left (right), he turns himself sidelong to avoid a collision, where the benefit of this kind of sidling behavior is that pedestrians do not have to slow down substantially [10]. Because of the existence of sidling behavior, the collision-avoidance time in the “face-to-face” case is not significantly higher than that in the “brush past” case. In other words, the change in relative position between the pedestrians would not cause significant fluctuations in the collision-avoidance time.


### 2.2. The Social Force Model

The social force model for traffic flow is as follows [23]:(1)midvidt=fwill+fij+fiw,fwill=mivi0tei0t-vitτi.In the social force model, pedestrian’s movement is affected by three types of force: the will forcefwill that reflects the influence of the moving target on pedestrian, the interaction force fij between pedestrian and his/her nearby pedestrians, and the interaction force fiw between pedestrian and his/her nearby walls or obstacles.The equation of will forcefwill indicates that pedestrian i of mass mi likes to move with a certain desired speed vi0 in a certain direction ei0, generally, which is the destination direction and therefore tends to correspondingly adapt his/her actual velocity vi with a certain characteristic time τi. The function of fwill is to enable the pedestrian to achieve his/her desired speed vi0, and, to make his/her actual motion direction to approach his/her destination direction ei0, the direction of fwill is not the destination direction but vi0(t)ei0(t)-vi(t), which shows that the actual effect of this force is a kind of corrective action.The change of pedestrian motion speed is influenced not only by the will force but also by “interaction forces”fij and fiw. The pedestrian i tends to maintain a velocity-dependent distance from another pedestrian j and walls w. To include this tendency as the interaction forces, fij and fiw are added the social force model:(2)fij=∑j≠ifij=Aiexp⁡rij-dijBi+kgrij-dijnij+κgrij-dijΔvjitij,where Ai and Bi are positive constants, rij is the sum of their radii ri and rj, dij=di-dj denotes the distance between the centers of two pedestrians, and nij is the normalized vector pointing from pedestrian j to i; tij is a tangential direction. The function of gx equals zero if the pedestrians do not touch each other dij>rij and otherwise equals the argument x.(3)fiw=∑fiw=Aiexp⁡ri-diwBi+kgri-diwniw+κgri-diwvi·tiwtiw,where Ai and Bi are positive constants, diw denotes the distance between the wall and pedestrian i, and niw is the normalized vector pointing from the wall to pedestrian i; tiw is a tangential direction. The function of g(x) equals zero if the pedestrians do not touch the wall diw>ri and otherwise equals the argument x.We focus on the collision-avoidance behavior of pedestrians, so we mainly study the interaction force between two pedestrians (fij). fij can be divided into three types of force: the favoidance and the contact force (which contains fextrusion and ffriction).f
a
v
o
i
d
a
n
c
e describe the psychological tendency of two pedestrians i and j to maintain a velocity-dependent distance from each other by a repulsive interaction force favoidance(Aiexp⁡[(rij-dij)/Bi]nij), where Ai and Bi are constants, rij is the sum of their radii ri and rj, dij=di-dj denotes the distance between the pedestrians’ centers of mass, and nij is the normalized vector pointing from pedestrian j to i. dij-rij is the actual distance between pedestrians i and j. The equation of favoidance indicates that the smaller the distance is, the stronger the will for protecting walking space is and the greater favoidance is. When dij≤rij, there is physical contact between pedestrians and fextrusion and ffriction exist.As shown in Figure6, i is the pedestrian who is moving from the right side to the left in the passage. The red area is favoidance search range of i, where j is in the search range and his/her movement direction is opposite to that of i. The collision avoidance between i and j relies on the favoidance between i and j. We divide favoidance into horizontal components favoidance,x and vertical components favoidance,y. Under the action of favoidance,x, the pedestrian i begins to slow down. The direction of favoidance,y determines the direction of collision avoidance, and the direction of favoidance,y is determined by the relative position between the pedestrians. The size of favoidance,y affects the time of the collision-avoidance process.There is no problem when we simulate the “brush past” case with the original social force model, as it can reflect the impact of relative position on the direction of collision avoidance. However, because the direction of collision avoidance is only determined by the relative position between the pedestrians, the social force model is unable to reflect the influence of the moving preference on the direction of collision avoidance. As the relative position of pedestrians becomes closer to the “face-to-face” case, the size offavoidance,y is smaller, which would increase the time of collision avoidance and deviate significantly from reality.


### 2.3. The Collision-Avoidance Force Model considering Moving Preference

We construct a forcefrp based on the social force model, which can reflect the moving preference of the pedestrian.We design the parameters that are used to define the search scope of collision avoidance. The search scope of collision avoidance consists of two parts: the search radius (li) and the search angle. The value of the radius we refer to as the avoid-collision distance is shown in Figure 3. We define the search angle as a 180-degree angle in the current direction of the pedestrian, and we use the angle between the current speed of pedestrian i (vi) and the vector from i to jd→ij to judge whether pedestrian j is in the search angle of pedestrian i. Based on the above analysis, we define ηij,1 and ηij,2 as follows:(4)ηij,1=1dij≤li0dij>liηij,2=1vi·d→ijvi·dij>cos⁡π20others.We use the verticallij (from the center of j to the movement direction of i) to reflect the relative position of pedestrians i and j. As shown in Figure 7(a), when lij>ri+rj, i would not collide with j, i and j do not need to take action to avoid collision, and frp does not exist. As shown in Figure 7(b), when λ<lij≤ri+rj, we consider this relative position to be the “brush past” case. The collision avoidance between the pedestrians can be accomplished by favoidance in the social force model, so we do not introduce frp in this case. As shown in Figure 7(c), when lij≤λ, this relative position is similar to the “face-to-face” case. To reflect the effect of the moving preference, we introduce frp.In the social force model, the pedestrian’s walking space is not discrete, so this is different from the CA or LG models, and there are very few absolute “face-to-face” caseslij=0. Based on the experimental results shown in Figure 4, it is not only in the absolute “face-to-face” cases lij=0 that there is the moving preference. So we design λ as the characteristic value to distinguish between the “brush past” case and the “face-to-face” case. If lij≤λ, whether pedestrian i is on the left or right side of pedestrian j; the same moving preference would affect the individual decision-making. Based on the above analysis, we define ηij,3 as follows:(5)ηij,3=1lij≤λ0lij>λ.We focus on the order offrp. frp and favoidance all reflect the psychological tendency of pedestrians to avoid collision. Therefore, we suppose that frp and favoidance are of the same type; that is, that they are in the same order. We define frp as follows:(6)frp=ϕAiexp⁡rij-dijBiηij,1ηij,2ηij,3nr,where Aiexp⁡[(rij-dij)/Bi] is the order of frp, ϕ is the strength parameter of frp, ηij,n,n=1,2,3 are three nondimensional parameters, and nr is the unit vector perpendicular to the movement direction of i. Based on our experimental results in Figure 4, the moving preference shows a right-preference, so, in our work, nr is the right vertical direction of pedestrian movement.Finally, we addfrp into the social force model:(7)midvidt=fwill+fij+fiw+frp.


## 2.1. The Experiment about Pedestrian Collision-Avoidance Behavior

We define our scope of research to be pedestrian counterflow that is not in crowded conditions. In this case, pedestrians have choice space in their behavior decision.A experiment was performed to study collision-avoidance behavior in October 2016. A group of 50 persons participated, uniformly composed of male students aged around 25 years old. As shown in Figure1, the experimental scenario is that the distance between pedestrians i and j is 8 meters and that they move in the opposite direction. They will keep moving until they reach the initial position of the other pedestrian. The experiment is carried out 7 times in each group, where, each time, the initial relative position between pedestrians is different (the relative positions are shown in 2). We performed 100 groups of independent experiments, from which we calculate the avoid-collision distance, the direction selection of collision avoidance, and the experimental time.Figure 1
The collision-avoidance behavior experiment scenario. The distance between pedestriansi and j is 8 meters. Pedestrian i walks from the left side of the scenario to the right side, and pedestrian j walks from the right side of the scenario to the left side. They keep moving until they reach the initial position of the other pedestrian.(1) Pedestrians usually adjust their direction in advance to avoid collision with the reverse pedestrians, where the size of this avoid-collision distance is determined by the pedestrian’s specific personality factors, which is what some studies have pointed out for use in the potential conflict prediction behavior of pedestrians. The results of the experiment about the avoid-collision distance (the distance between pedestrians at which a pedestrian begins to adjust his/her movement direction) are shown in Figure 3. Most of the time, pedestrians began to adjust their direction of movement when the distance between them was about two meters.(2) The relative position between the pedestrians can affect the direction of collision avoidance. As shown in Figure 4, when the value of lij is relatively small (Patha, Pathb, and Pathc), most pedestrians prefer to move to the right-hand side in the process of collision avoidance. We consider that when lij is small (lij<0.2 m), the relative position between the pedestrians is the “face-to-face” case. In this case, there is no obvious difference between moving to the left-hand side and the right-hand side, and, therefore, the collision-avoidance direction choice depends on the subconscious moving preferences of the pedestrian. In the experiment, the moving preferences are characterized by the right-preference.When the value of|lij| is large (Pathd, Pathe, Pathf, and Pathg), pedestrians tend to maintain the current relative position or make minor adjustments based on the relative position to complete the collision avoidance. We consider that when lij is large (lij≥0.2 m), the relative position between the pedestrians is the “brush past” case. In this case, there is a significant difference between moving to the left-hand side and the right-hand side. In the “brush past” case, the moving preference is not the influencing factor for the direction of collision avoidance, but rather the direction is determined by the relative position.(3) The relative position between pedestrians has a limited effect on the time of the collision-avoidance process. As shown in Figure 5, there is no obvious difference between the experimental times of different paths. Some scholars point out that when a pedestrian going to the right (left) comes face-to-face with a walker going to the left (right), he turns himself sidelong to avoid a collision, where the benefit of this kind of sidling behavior is that pedestrians do not have to slow down substantially [10]. Because of the existence of sidling behavior, the collision-avoidance time in the “face-to-face” case is not significantly higher than that in the “brush past” case. In other words, the change in relative position between the pedestrians would not cause significant fluctuations in the collision-avoidance time.


## 2.2. The Social Force Model

The social force model for traffic flow is as follows [23]:(1)midvidt=fwill+fij+fiw,fwill=mivi0tei0t-vitτi.In the social force model, pedestrian’s movement is affected by three types of force: the will forcefwill that reflects the influence of the moving target on pedestrian, the interaction force fij between pedestrian and his/her nearby pedestrians, and the interaction force fiw between pedestrian and his/her nearby walls or obstacles.The equation of will forcefwill indicates that pedestrian i of mass mi likes to move with a certain desired speed vi0 in a certain direction ei0, generally, which is the destination direction and therefore tends to correspondingly adapt his/her actual velocity vi with a certain characteristic time τi. The function of fwill is to enable the pedestrian to achieve his/her desired speed vi0, and, to make his/her actual motion direction to approach his/her destination direction ei0, the direction of fwill is not the destination direction but vi0(t)ei0(t)-vi(t), which shows that the actual effect of this force is a kind of corrective action.The change of pedestrian motion speed is influenced not only by the will force but also by “interaction forces”fij and fiw. The pedestrian i tends to maintain a velocity-dependent distance from another pedestrian j and walls w. To include this tendency as the interaction forces, fij and fiw are added the social force model:(2)fij=∑j≠ifij=Aiexp⁡rij-dijBi+kgrij-dijnij+κgrij-dijΔvjitij,where Ai and Bi are positive constants, rij is the sum of their radii ri and rj, dij=di-dj denotes the distance between the centers of two pedestrians, and nij is the normalized vector pointing from pedestrian j to i; tij is a tangential direction. The function of gx equals zero if the pedestrians do not touch each other dij>rij and otherwise equals the argument x.(3)fiw=∑fiw=Aiexp⁡ri-diwBi+kgri-diwniw+κgri-diwvi·tiwtiw,where Ai and Bi are positive constants, diw denotes the distance between the wall and pedestrian i, and niw is the normalized vector pointing from the wall to pedestrian i; tiw is a tangential direction. The function of g(x) equals zero if the pedestrians do not touch the wall diw>ri and otherwise equals the argument x.We focus on the collision-avoidance behavior of pedestrians, so we mainly study the interaction force between two pedestrians (fij). fij can be divided into three types of force: the favoidance and the contact force (which contains fextrusion and ffriction).f
a
v
o
i
d
a
n
c
e describe the psychological tendency of two pedestrians i and j to maintain a velocity-dependent distance from each other by a repulsive interaction force favoidance(Aiexp⁡[(rij-dij)/Bi]nij), where Ai and Bi are constants, rij is the sum of their radii ri and rj, dij=di-dj denotes the distance between the pedestrians’ centers of mass, and nij is the normalized vector pointing from pedestrian j to i. dij-rij is the actual distance between pedestrians i and j. The equation of favoidance indicates that the smaller the distance is, the stronger the will for protecting walking space is and the greater favoidance is. When dij≤rij, there is physical contact between pedestrians and fextrusion and ffriction exist.As shown in Figure6, i is the pedestrian who is moving from the right side to the left in the passage. The red area is favoidance search range of i, where j is in the search range and his/her movement direction is opposite to that of i. The collision avoidance between i and j relies on the favoidance between i and j. We divide favoidance into horizontal components favoidance,x and vertical components favoidance,y. Under the action of favoidance,x, the pedestrian i begins to slow down. The direction of favoidance,y determines the direction of collision avoidance, and the direction of favoidance,y is determined by the relative position between the pedestrians. The size of favoidance,y affects the time of the collision-avoidance process.There is no problem when we simulate the “brush past” case with the original social force model, as it can reflect the impact of relative position on the direction of collision avoidance. However, because the direction of collision avoidance is only determined by the relative position between the pedestrians, the social force model is unable to reflect the influence of the moving preference on the direction of collision avoidance. As the relative position of pedestrians becomes closer to the “face-to-face” case, the size offavoidance,y is smaller, which would increase the time of collision avoidance and deviate significantly from reality.


## 2.3. The Collision-Avoidance Force Model considering Moving Preference

We construct a forcefrp based on the social force model, which can reflect the moving preference of the pedestrian.We design the parameters that are used to define the search scope of collision avoidance. The search scope of collision avoidance consists of two parts: the search radius (li) and the search angle. The value of the radius we refer to as the avoid-collision distance is shown in Figure 3. We define the search angle as a 180-degree angle in the current direction of the pedestrian, and we use the angle between the current speed of pedestrian i (vi) and the vector from i to jd→ij to judge whether pedestrian j is in the search angle of pedestrian i. Based on the above analysis, we define ηij,1 and ηij,2 as follows:(4)ηij,1=1dij≤li0dij>liηij,2=1vi·d→ijvi·dij>cos⁡π20others.We use the verticallij (from the center of j to the movement direction of i) to reflect the relative position of pedestrians i and j. As shown in Figure 7(a), when lij>ri+rj, i would not collide with j, i and j do not need to take action to avoid collision, and frp does not exist. As shown in Figure 7(b), when λ<lij≤ri+rj, we consider this relative position to be the “brush past” case. The collision avoidance between the pedestrians can be accomplished by favoidance in the social force model, so we do not introduce frp in this case. As shown in Figure 7(c), when lij≤λ, this relative position is similar to the “face-to-face” case. To reflect the effect of the moving preference, we introduce frp.In the social force model, the pedestrian’s walking space is not discrete, so this is different from the CA or LG models, and there are very few absolute “face-to-face” caseslij=0. Based on the experimental results shown in Figure 4, it is not only in the absolute “face-to-face” cases lij=0 that there is the moving preference. So we design λ as the characteristic value to distinguish between the “brush past” case and the “face-to-face” case. If lij≤λ, whether pedestrian i is on the left or right side of pedestrian j; the same moving preference would affect the individual decision-making. Based on the above analysis, we define ηij,3 as follows:(5)ηij,3=1lij≤λ0lij>λ.We focus on the order offrp. frp and favoidance all reflect the psychological tendency of pedestrians to avoid collision. Therefore, we suppose that frp and favoidance are of the same type; that is, that they are in the same order. We define frp as follows:(6)frp=ϕAiexp⁡rij-dijBiηij,1ηij,2ηij,3nr,where Aiexp⁡[(rij-dij)/Bi] is the order of frp, ϕ is the strength parameter of frp, ηij,n,n=1,2,3 are three nondimensional parameters, and nr is the unit vector perpendicular to the movement direction of i. Based on our experimental results in Figure 4, the moving preference shows a right-preference, so, in our work, nr is the right vertical direction of pedestrian movement.Finally, we addfrp into the social force model:(7)midvidt=fwill+fij+fiw+frp.


## 3. Simulation and Discussion

We take the parameters as in Table1. The simulation results are averaged over 200 independent simulations.Table 1
Parameters in this simulation.
Symbol
Meaning
Value
v
i
0
Desired speed
1.1–1.34 m/s
m
i
Pedestrian mass
80 kg
τ
i
Characteristic time
0.5 s
r
i
Pedestrian radius
0.25 m
A
i
Avoidance force intensity
2
×
1
0
3 N
B
i
Avoidance force range
0.08 m
l
i
Avoid-collision distance
2 m
ϕ
Strength parameter of thefrp
1
k
Body force coefficient
1.2
×
1
0
5
k
g
/
s
2
κ
Friction force coefficient
2.4
×
1
0
5 kg/(m⋅s)
Δ
t
Time step
5
×
1
0
-
3 s
λ
Characteristic value of the relative position
0.2 m
P
a
Pedestrian arrival rate
0.1–0.3 P/(m⋅s)
L
Length of passage
40 m
W
Width of passage
8 m


### 3.1. The Effect of the Moving Preference on the Process of Collision Avoidance

To study the effect of the moving preference on the process of collision avoidance, we explore the relationship between the relative positionlij and the collision-avoidance time (the definition of the collision-avoidance time is shown in Figure 8). In this simulation, there are two reverse pedestrians i and j. We observe the process of collision avoidance between i and j in different relative positions lij and record the collision-avoidance time. The results are shown in Figure 9, which indicate that when there is no frp or when frp is relatively small, in the “face-to-face” case (lij is between −0.2 m and 0.2 m), the collision-avoidance time will have a sharp increase. That means that the pedestrians slow down substantially in the process of collision avoidance, which is not in conformity with the experimental result shown in Figure 5. When the strength parameter of frpϕ = 1, we can find that the collision-avoidance time is relatively stable in the “face-to-face” case.We compare the empirical and simulation results for the moving trajectories. Figure10 is the experimental result of the moving trajectory, in which Figure 10(a) is the “face-to-face” case (lij=0 m) and Figure 10(b) is the “brush past” case (lij=-0.3 m). Figure 11 is the simulation result of the moving trajectories by the original social force model, and Figure 12 is the simulation result of the moving trajectories by the improved model. We find that, by introducing frp, pedestrians move to the right-hand side in the “face-to-face” case, and, in the “brush past” case, the moving trajectories would not change. This is consistent with the original intention of our model design. By comparing the empirical results and the simulation results, we find that the simulation results are closer to the empirical results in the the “face-to-face” case when considering the moving preference.Figure 2
The different relative positions. We use the verticallij (from the center of pedestrian j to the movement direction of pedestrian i) to reflect the relative position of pedestrians i and j. If pedestrian i is to the left of j’s position, we give lij a negative value, and, otherwise, lij has a positive value. In Patha, lij=0; in Pathb, lij=0.1; in Pathc, lij=-0.1; in Pathd, lij=0.2; in Pathe, lij=-0.2; in Pathf, lij=0.3; and in Pathg, lij=-0.3.Figure 3
The investigation results about the avoid-collision distance.Figure 4
Percentage of direction selection in different relative positions between pedestrians.Figure 5
The experimental time in different relative position cases. We define the experimental time as the time when the two pedestrians have both reached the destination.Figure 6
Force analysis of the pedestrian collision-avoidance process in the original social force model.Figure 7
Three types of relative positions between pedestrianslij. In (a) lij>ri+rj, there is no potential conflict between pedestrians. In (b) λ<lij≤ri+rj, this relative position is the “brush past” case. In (c) lij≤λ, this relative position is the “face-to-face” case.
(a)
(b)
(c)Figure 8
The definition of the collision-avoidance time: when pedestrianj walks into the search scope of collision avoidance of pedestrian i and the relative position lij<ri+rj, we record the time T0. When j walks out of the search scope, we record the time T1 and the collision-avoidance time Tca=T1-T0. According to the experimental results, we define the search radius as li=2 m.Figure 9
The collision-avoidance time versus the relative positionlij for different ϕ (strength parameter of the frp).Figure 10
The moving trajectory in the “face-to-face” case and the “brush past” case. (a) is the “face-to-face” case, wherelij=0 m (Patha in Figure 2), and (b) is the “brush past” case, where lij=-0.3 m (Pathg in Figure 2).
(a)
(b)Figure 11
The moving trajectory by the original model. (a) is the “face-to-face” case, wherelij=0 m, and (b) is the “brush past” case, where lij=-0.3 m.
(a)
(b)Figure 12
The moving trajectory by the improved model, which considers the moving preference. (a) is the “face-to-face” case, wherelij=0 m, and (b) is the “brush past” case, where lij=-0.3 m.
(a)
(b)


### 3.2. The Effect of Moving Preference on the Lane-Formation Phenomenon

First, we must emphasize that, even without considering the special walking behavior of pedestrians, the lane formation can also be simulated by the social force model. Therefore, in this section, we are not going to discuss the cause of the lane-formation phenomenon. We just want to determine the effect of moving preference on the lane-formation phenomenon.To study the effect of moving preference on the lane-formation phenomenon, we explore the relationship between the number of lanes and the characteristic value of the relative positionλ. In this simulation, the pedestrians are added into the passage from the left boundary and the right boundary with the same pedestrian arrival rate. We observe the lane formation in the case of different λ; the simulation snapshots are shown in Figure 13. As shown in Figure 13(a), when λ=0.1 m, the number of lanes is 6. As shown in Figure 13(d), when λ=0.4 m, the number of lanes is 2. The results indicate that, with the increase of λ, the number of lanes decreases.Figure 13
The simulation snapshots of lane formation for differentλ. In the simulation, the length of passage L=40 m and the width of passage W=8 m. We use the black and white circles to represent the pedestrian access from both sides of the passage, and we use the black and white lines in front of the circles to represent the current movement direction of pedestrians. The red lines represent the direction of frp. When simulation time t=60 s, we take snapshots for comparison. In (a) λ=0.1 m; in (b) λ=0.2 m; in (c) λ=0.3 m; and in (d) λ=0.4 m.
(a)
(b)
(c)
(d)The video snapshot of the actual lane formation is shown in Figure14(a), and the frequency of the number of lanes formed is shown in Figure 14(b). In the actual situation, there are multilanes formed when pedestrians go across the passage, and, most of the time, there are 4 or 5 lanes. We set the simulation to the same conditions as the actual situation, with the results shown in Figure 15. When λ=0.1 m, most of the time, there are 5 or 6 lanes. When λ=0.3 m, most of time, there are 2, 3, or 4 lanes, and the frequency is the highest for 3 lanes. When λ=0.4 m, most of the time, there are 2 or 3 lanes, and the frequency is the highest for 2 lanes. As shown in Figure 15(b), when λ=0.2 m, most of time, there are about 4 or 5 lanes, and we consider this to be the closest to the actual lane formation that we observed.Figure 14
The actual lane-formation situation. (a) is the video screenshot of lane formation. (b) is the plot of the frequency of number of lanes. The width of the observation area is 8 m, the length of the observation area is 15 m, and the density of the observation area is about 0.38–0.56p/m2. We take 50 screenshots randomly from the video and count the number of the lanes; the results are shown in (b).
(a)
(b)Figure 15
The frequency of number of lanes formed for differentλ. For comparison with the actual data shown in Figure 14, in the simulation, the pedestrians are added into the area from the left boundary and the right boundary with the same pedestrian arrival rate (0.2 P/(m⋅s)), and this arrival rate leads to the same density as in Figure 14.
(a)
(b)
(c)
(d)By this simulation, we find that the moving preference can affect the number of lanes and that the characteristic value of the relative positionλ can affect the accuracy of the simulation.We explore the effect of moving preference on the number of conflicts in the counterflow. In this article, the definition of the conflict is that the distance between two pedestrians with opposite moving directionsdij⩽5 cm and their relative position lij<ri+rj. In the simulation, the pedestrians are added into the passage from the left boundary and the right boundary with the same pedestrian arrival rate, and we count the number of conflicts in 240 s, with the result shown in Figure 16. With the increase in pedestrians, the number of conflicts also increases, and the extent of the increase in conflicts in the case of the right-preference is less than that in the case of no right-preference. Comparing the case of the right-preference with the case of no right-preference, we find that the number of conflicts is significantly decreased. The maximum difference is observed at Pa=0.3, and the number of conflicts is more than doubled (2.13 times). In the case of the right-preference, pedestrians have the same moving preference: when there is a potential conflict before a pedestrian, the pedestrian and the reverse pedestrian all move to the right-hand side so that physical contact between reverse pedestrians can be avoided. In the case of no right-preference, the decision-making of the pedestrian is more random as the number of conflicts is more than in the case of the right-preference.Figure 16
The number of conflicts for different pedestrian arrival rates in 240 s. In this article, the definition of the conflict is that the distance between two pedestrians with opposite moving directionsdij⩽5 cm and their relative position lij<ri+rj.To further study the conflict in counterflow, we analyze the change process of the conflicts in 240 s, with the results shown in Figure17. In the case of the right-preference, when t=22 s, the pedestrian counterflow begins to occur, and the conflicts between pedestrians appear. A relatively sharp increase in conflicts occurs in the adjustment period of about 20 seconds, and, at t=40 s, the increase begins to slow down. Throughout the process, the extent of the increase in conflict is small and stable. In contrast, in the case of no right-preference, the adjustment period is longer and the extent of increase in conflict is bigger. The conflict between pedestrians means a change of lane formation (the position and number of lanes), where the number of conflicts is an important influence factor of the stability of the lane formation. We consider that the moving preference can enhance the stability of lane formation, and it is conducive to self-adjustment of the counterflow.Figure 17
The plot of the number of conflicts versus the time. In the simulation, the pedestrian arrival rate is 0.2 P/(m⋅s),ϕ=1 and λ=0.2 m.To study the effect of moving preference on the efficiency of pedestrians passing, we analyze the change process of the mean speed in 240 s in the counterflow. The result is shown in Figure18, where we can find that the mean speed in the case of the right-preference is faster than in the case of no right-preference. Much as in the situation of conflict, in comparison with the case of no right-preference, after a short period of adjustment, the mean speed in the case of the right-preference maintains a more stable state. To further examine this, we compare the simulation data with actual empirical data; the empirical results were determined by Weidmann [32] and Older [33] for the counterflow under open boundary conditions. The results are shown in Figure 19. The results in the case of right-preference are higher than those in the case of no right-preference and are much more similar to the empirical data. This indicates that the moving preference plays an important role in pedestrian traffic: it can improve the efficiency of pedestrians passing and make it stable.Figure 18
The plot of the mean speed versus the time. In the simulation, the desire speed of pedestrianvi0=1.1 m/s, the pedestrian arrival rate is 0.2 P/(m⋅s), ϕ=1, and λ=0.2 m.Figure 19
Fundamental diagram comparing data. In the simulation,ϕ=1 and λ=0.2 m. For comparison with the actual empirical data, we take the desired speed of pedestrian vi0=1.34 m/s.


## 3.1. The Effect of the Moving Preference on the Process of Collision Avoidance

To study the effect of the moving preference on the process of collision avoidance, we explore the relationship between the relative positionlij and the collision-avoidance time (the definition of the collision-avoidance time is shown in Figure 8). In this simulation, there are two reverse pedestrians i and j. We observe the process of collision avoidance between i and j in different relative positions lij and record the collision-avoidance time. The results are shown in Figure 9, which indicate that when there is no frp or when frp is relatively small, in the “face-to-face” case (lij is between −0.2 m and 0.2 m), the collision-avoidance time will have a sharp increase. That means that the pedestrians slow down substantially in the process of collision avoidance, which is not in conformity with the experimental result shown in Figure 5. When the strength parameter of frpϕ = 1, we can find that the collision-avoidance time is relatively stable in the “face-to-face” case.We compare the empirical and simulation results for the moving trajectories. Figure10 is the experimental result of the moving trajectory, in which Figure 10(a) is the “face-to-face” case (lij=0 m) and Figure 10(b) is the “brush past” case (lij=-0.3 m). Figure 11 is the simulation result of the moving trajectories by the original social force model, and Figure 12 is the simulation result of the moving trajectories by the improved model. We find that, by introducing frp, pedestrians move to the right-hand side in the “face-to-face” case, and, in the “brush past” case, the moving trajectories would not change. This is consistent with the original intention of our model design. By comparing the empirical results and the simulation results, we find that the simulation results are closer to the empirical results in the the “face-to-face” case when considering the moving preference.Figure 2
The different relative positions. We use the verticallij (from the center of pedestrian j to the movement direction of pedestrian i) to reflect the relative position of pedestrians i and j. If pedestrian i is to the left of j’s position, we give lij a negative value, and, otherwise, lij has a positive value. In Patha, lij=0; in Pathb, lij=0.1; in Pathc, lij=-0.1; in Pathd, lij=0.2; in Pathe, lij=-0.2; in Pathf, lij=0.3; and in Pathg, lij=-0.3.Figure 3
The investigation results about the avoid-collision distance.Figure 4
Percentage of direction selection in different relative positions between pedestrians.Figure 5
The experimental time in different relative position cases. We define the experimental time as the time when the two pedestrians have both reached the destination.Figure 6
Force analysis of the pedestrian collision-avoidance process in the original social force model.Figure 7
Three types of relative positions between pedestrianslij. In (a) lij>ri+rj, there is no potential conflict between pedestrians. In (b) λ<lij≤ri+rj, this relative position is the “brush past” case. In (c) lij≤λ, this relative position is the “face-to-face” case.
(a)
(b)
(c)Figure 8
The definition of the collision-avoidance time: when pedestrianj walks into the search scope of collision avoidance of pedestrian i and the relative position lij<ri+rj, we record the time T0. When j walks out of the search scope, we record the time T1 and the collision-avoidance time Tca=T1-T0. According to the experimental results, we define the search radius as li=2 m.Figure 9
The collision-avoidance time versus the relative positionlij for different ϕ (strength parameter of the frp).Figure 10
The moving trajectory in the “face-to-face” case and the “brush past” case. (a) is the “face-to-face” case, wherelij=0 m (Patha in Figure 2), and (b) is the “brush past” case, where lij=-0.3 m (Pathg in Figure 2).
(a)
(b)Figure 11
The moving trajectory by the original model. (a) is the “face-to-face” case, wherelij=0 m, and (b) is the “brush past” case, where lij=-0.3 m.
(a)
(b)Figure 12
The moving trajectory by the improved model, which considers the moving preference. (a) is the “face-to-face” case, wherelij=0 m, and (b) is the “brush past” case, where lij=-0.3 m.
(a)
(b)


## 3.2. The Effect of Moving Preference on the Lane-Formation Phenomenon

First, we must emphasize that, even without considering the special walking behavior of pedestrians, the lane formation can also be simulated by the social force model. Therefore, in this section, we are not going to discuss the cause of the lane-formation phenomenon. We just want to determine the effect of moving preference on the lane-formation phenomenon.To study the effect of moving preference on the lane-formation phenomenon, we explore the relationship between the number of lanes and the characteristic value of the relative positionλ. In this simulation, the pedestrians are added into the passage from the left boundary and the right boundary with the same pedestrian arrival rate. We observe the lane formation in the case of different λ; the simulation snapshots are shown in Figure 13. As shown in Figure 13(a), when λ=0.1 m, the number of lanes is 6. As shown in Figure 13(d), when λ=0.4 m, the number of lanes is 2. The results indicate that, with the increase of λ, the number of lanes decreases.Figure 13
The simulation snapshots of lane formation for differentλ. In the simulation, the length of passage L=40 m and the width of passage W=8 m. We use the black and white circles to represent the pedestrian access from both sides of the passage, and we use the black and white lines in front of the circles to represent the current movement direction of pedestrians. The red lines represent the direction of frp. When simulation time t=60 s, we take snapshots for comparison. In (a) λ=0.1 m; in (b) λ=0.2 m; in (c) λ=0.3 m; and in (d) λ=0.4 m.
(a)
(b)
(c)
(d)The video snapshot of the actual lane formation is shown in Figure14(a), and the frequency of the number of lanes formed is shown in Figure 14(b). In the actual situation, there are multilanes formed when pedestrians go across the passage, and, most of the time, there are 4 or 5 lanes. We set the simulation to the same conditions as the actual situation, with the results shown in Figure 15. When λ=0.1 m, most of the time, there are 5 or 6 lanes. When λ=0.3 m, most of time, there are 2, 3, or 4 lanes, and the frequency is the highest for 3 lanes. When λ=0.4 m, most of the time, there are 2 or 3 lanes, and the frequency is the highest for 2 lanes. As shown in Figure 15(b), when λ=0.2 m, most of time, there are about 4 or 5 lanes, and we consider this to be the closest to the actual lane formation that we observed.Figure 14
The actual lane-formation situation. (a) is the video screenshot of lane formation. (b) is the plot of the frequency of number of lanes. The width of the observation area is 8 m, the length of the observation area is 15 m, and the density of the observation area is about 0.38–0.56p/m2. We take 50 screenshots randomly from the video and count the number of the lanes; the results are shown in (b).
(a)
(b)Figure 15
The frequency of number of lanes formed for differentλ. For comparison with the actual data shown in Figure 14, in the simulation, the pedestrians are added into the area from the left boundary and the right boundary with the same pedestrian arrival rate (0.2 P/(m⋅s)), and this arrival rate leads to the same density as in Figure 14.
(a)
(b)
(c)
(d)By this simulation, we find that the moving preference can affect the number of lanes and that the characteristic value of the relative positionλ can affect the accuracy of the simulation.We explore the effect of moving preference on the number of conflicts in the counterflow. In this article, the definition of the conflict is that the distance between two pedestrians with opposite moving directionsdij⩽5 cm and their relative position lij<ri+rj. In the simulation, the pedestrians are added into the passage from the left boundary and the right boundary with the same pedestrian arrival rate, and we count the number of conflicts in 240 s, with the result shown in Figure 16. With the increase in pedestrians, the number of conflicts also increases, and the extent of the increase in conflicts in the case of the right-preference is less than that in the case of no right-preference. Comparing the case of the right-preference with the case of no right-preference, we find that the number of conflicts is significantly decreased. The maximum difference is observed at Pa=0.3, and the number of conflicts is more than doubled (2.13 times). In the case of the right-preference, pedestrians have the same moving preference: when there is a potential conflict before a pedestrian, the pedestrian and the reverse pedestrian all move to the right-hand side so that physical contact between reverse pedestrians can be avoided. In the case of no right-preference, the decision-making of the pedestrian is more random as the number of conflicts is more than in the case of the right-preference.Figure 16
The number of conflicts for different pedestrian arrival rates in 240 s. In this article, the definition of the conflict is that the distance between two pedestrians with opposite moving directionsdij⩽5 cm and their relative position lij<ri+rj.To further study the conflict in counterflow, we analyze the change process of the conflicts in 240 s, with the results shown in Figure17. In the case of the right-preference, when t=22 s, the pedestrian counterflow begins to occur, and the conflicts between pedestrians appear. A relatively sharp increase in conflicts occurs in the adjustment period of about 20 seconds, and, at t=40 s, the increase begins to slow down. Throughout the process, the extent of the increase in conflict is small and stable. In contrast, in the case of no right-preference, the adjustment period is longer and the extent of increase in conflict is bigger. The conflict between pedestrians means a change of lane formation (the position and number of lanes), where the number of conflicts is an important influence factor of the stability of the lane formation. We consider that the moving preference can enhance the stability of lane formation, and it is conducive to self-adjustment of the counterflow.Figure 17
The plot of the number of conflicts versus the time. In the simulation, the pedestrian arrival rate is 0.2 P/(m⋅s),ϕ=1 and λ=0.2 m.To study the effect of moving preference on the efficiency of pedestrians passing, we analyze the change process of the mean speed in 240 s in the counterflow. The result is shown in Figure18, where we can find that the mean speed in the case of the right-preference is faster than in the case of no right-preference. Much as in the situation of conflict, in comparison with the case of no right-preference, after a short period of adjustment, the mean speed in the case of the right-preference maintains a more stable state. To further examine this, we compare the simulation data with actual empirical data; the empirical results were determined by Weidmann [32] and Older [33] for the counterflow under open boundary conditions. The results are shown in Figure 19. The results in the case of right-preference are higher than those in the case of no right-preference and are much more similar to the empirical data. This indicates that the moving preference plays an important role in pedestrian traffic: it can improve the efficiency of pedestrians passing and make it stable.Figure 18
The plot of the mean speed versus the time. In the simulation, the desire speed of pedestrianvi0=1.1 m/s, the pedestrian arrival rate is 0.2 P/(m⋅s), ϕ=1, and λ=0.2 m.Figure 19
Fundamental diagram comparing data. In the simulation,ϕ=1 and λ=0.2 m. For comparison with the actual empirical data, we take the desired speed of pedestrian vi0=1.34 m/s.


## 4. Conclusion

(1)
A collision-avoidance force modelfrp is proposed to simulate the pedestrian moving preference in the collision-avoidance process. frp considers the prediction for potential conflict and the effect of the relative position between pedestrians on the individual decision-making.
(2)
Addingfrp into the social force model, the collision-avoidance process and the lane-formation phenomenon are simulated by the improved model.
(3)
f
r
p can reduce the collision-avoidance time in the “face-to-face” case, rendering the collision-avoidance process and the lane formation closer to reality.
(4)
If the moving preferences of pedestrians have a wide range of similarity in the counterflow, this type of moving preference is conducive to a self-adjustment of the pedestrian flow and can improve the efficiency of pedestrian passing and make the efficiency more stable.In future work, we will study the moving preferences of pedestrians in other real dynamic scenarios, for example, in the process of merging and separating in T-shaped channels or in the moving process when pedestrians flow through bottleneck. We believe that, in different scenarios, pedestrians have different moving preferences, which can be simulated by constructing an appropriate force base on the social force model.



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*Source: 3678268-2017-05-22.xml*