Simulation of Crowd Motion Based on Boids Flocking Behavior and Social Force Mod

ZHANG Xuguang, ZHU Yanna

(School of Communication Engineering, Hangzhou Dianzi University, Hangzhou, China)

Abstract: In the process of crowd movement, pedestrians are often affected by their neighbors. In order to describe the consistency of adjacent individuals and collectivity of a group, this paper learns from the rules of the flocking behavior, such as segregation, alignment and cohesion, and proposes a method for crowd motion simulation based on the Boids model and social force model. Firstly, the perception area of individuals is divided into zone of segregation, alignment and cohesion. Secondly, the interactive force among individuals is calculated based upon the zone information, velocity vector and the group information. The interactive force among individuals is the synthesis of three forces: the repulsion force to avoid collisions, the alignment force to keep consistent with the velocity direction, and the attractive force to get close to the members of group. In segregation and alignment areas, the repulsion force and alignment force among pedestrians are limited by visual field factors. Finally, the interactive force among individuals, the driving force of destination and the repulsion force of obstacles work together to drive the behavior of crowd motion. The simulation results show that the proposed method can not only effectively simulate the interactive behavior between adjacent individuals but also the collective behavior of group.

Keywords: Collective Behavior, Crowd Motion Simulation, Social Force Model, Boids Model

1 Introduction

Crowd motion modeling and simulation is a research hotspot in computer graphics[1], safety science[2]and artificial intelligence[3-5], which has been used in many application fields such as crowd evacuation[6],digital entertainment[7]and social security[8-9]. Crowd simulation[10]can well reproduce the self-organization phenomenon of crowd movement. At the same time,combined with various uncertain factors such as physiological characteristics of individuals, social factors and psychological factors, it can more accurately simulate evacuation behavior and emergency decision of crowd in emergency.

A crowd is not simply a collection of individuals.The behavior of an individual may be affected by other pedestrians in a crowd, which may depend on various physiological, psychological and social factors. These factors contribute to several typical characteristics in crowd evacuation, including the following:

(1) Herding Behavior:

Herd behavior refers to the behavior that pedestrians spontaneously show similar behavior to adjacent individuals. When walking, pedestrians tend to keep the same speed direction as the surrounding individuals[11]. When choosing the evacuation exit,the nearby pedestrians prefer to choose the same exit[12].

(2) Non-adaptive Behavior:

In emergency situations, individuals may react irrationally. It may lead to pushing each other, congestion at the exit, and even the crowd swarmed to cause disaster[13].

(3) Grouping Behavior:

In evacuating a large-scale crowd, individuals often tend to form a group with other pedestrians, and the members of a group have a close relationship with them, such as family, colleagues and friends. The degree of aggregation in a group is related to the relationship between the members in a group[14].

The common models of crowd simulation include social force model[15-17], cellular automaton model[18-21]and agent model[22-23]. Among them, social force model,through solving Newton’s equation to determine the position of each individual, can simulate the characteristics of pedestrian flow such as the ‘faster-is-slower’and the ‘arch of the exit’. It is a very classic model in crowd simulation. However, the social force model still needs to be further mined in the performance of group behavior. It is very important to embody more crowd characteristics in simulation model. This paper improves the social force model from the following aspects:

(1) Strengthen the movement consistency between individuals:

As individuals often have herd psychology in the crowd, in addition to mutual exclusion, the following and herding behavior affected by herd psychology should be added.

(2) Strengthen the influence of group behavior:

Pedestrians often do not walk in isolation when they move, sometimes they appear in the form of groups[24]. The behaviors of group members will influence each other. It is better integrate the group attribute to the traditional social force model.

(3) With the influence of visual field factors:

Human visual field is limited, and pedestrians can only be affected by the external environment in the field of vision. The reaction of pedestrians to other individuals in and out of the field of view will be different.

Therefore, based on the idea of biological group behavior model, this paper modifies the original social force model, and proposes a crowd movement simulation method based on Boids model. The Boids model[25], proposed by Reynolds, concludes three rules of collective motion, including segregation, alignment and cohesion. Segregation rule helps flock to avoid mutual collisions, alignment rule can smooth the velocities to similar values, and cohesion rule is the tendency of flock to stay in the center of the flock. This paper obtains the idea from the above rules and extends it to crowd motion simulation. Firstly, we learn from the rules of the flocking behavior in Boids model and design crowd movement simulation rules. Secondly,we define the perception zone of the individual, and divide it into three parts: zone of segregation, zone of alignment and zone of cohesion. Thirdly, the corresponding interaction behavior of individuals is defined in different regions: the individuals in zone of segregation, exert repulsion force to avoid collision based on the rule of segregation; the individuals in zone of alignment, exert the alignment force to reflect the consistency of adjacent individuals based on the rule of alignment; the members of group in zone of cohesion,exert the attractive force to keep the group members together based on the rule of cohesion. Furthermore,for the zone of segregation and alignment, we take into account the effective field of vision. In the calculation of group attractive forces, we ignore the factor of view field. Based upon the zone information, velocity vector and the group information, the interactive force among individuals can be calculated, i.e., the sum of the repulsion force, the alignment force and the attractive force. Finally, the interactive force among individuals,the driving force of destination, and the repulsion force of obstacles are integrated together to drive the behavior of crowd motion.

The remainder of this paper is organized as follows. Section 2 indicates the related works. Section 3 introduces the theory of social force model. In Section 4 a method of crowd simulation based on Boids model is introduced in detail. Section 5 discusses the conducted simulation experiments to show the efficiency of the proposed method. Section 6 concludes the paper and presents the future research focus.

2 Related Work

2.1 Social Force Model

Social force model (SFM), proposed by Helbing and Molnár[13]in 1995, is a classic continuous space microscopic model. Four kinds of force are included in this model: driving force toward the desired target,repulsive force from the neighbor pedestrian, repulsive force from the obstacle and the disturbing force, so it can qualitatively reproduce many self-organizing phenomenon like lane formation and arching. Many scholars have modified social force model in many factors such as psychological characteristics[26], psychological characteristics[27], decision-making behaviors[28]and path planning[29]. Liang et al.[30]paid attention to the parameter of the desired speed of social force model and proposed three more strategies of assigning desired speed for the first time. Besides, the recommendations are given on choosing the strategies of assigning the desired speed according to the different background of applications. The fuzzy logic method[31], is adopted to solve the multiple-choice problem including guide selection by informed followers and exit selection by guides during the guided crowd evacuation. Khamis et al.[32]combined an Artificial Bee Colony (ABC) optimization algorithm on the basis of social force model, and found that this method can tune less control parameters in finding the most optimal exit door locations. Cao et al.[33]studied the psychological characteristics of crowd and established a P-SIS model based on social force model to simulate emotional contagion during crowd evacuation.

2.2 The Boids Model

Crowd motion is a kind of collective motion. In addition to human beings, there are many collective movements in nature and biology, such as fish schools[34], robot groups[35]and so on. Biological groups use the interaction and coordination of information to achieve collective behavior. Through observing the cluster phenomenon of biological groups and using the models of different disciplines to analyze and summarize, there are many valuable models and methods are formed to describe the collective movement in nature, such as Boids model[25]. Boids model is to describe the collective movement of organisms, especially the movement of birds and fish. In Boids model, individuals mainly follow three rules of biological movement: Segregation, Alignment and Cohesion (SAC).

SAC rules are of fundamental significance to the research of flocking motion. After it is clearly summarized by Reynolds in 1987[25], researchers use different experimental methods to propose a variety of flocking models. In 2002, Couzin[36]established a three-layer flocking motion model on the basis of Boids rule. By changing the size of segregation area,alignment area and cohesion area, it can better simulate the movement of different biological flocking under different conditions. Keigo[37]developed a control method of swarm agents using Boids model. The swarm agents are considered as uncontrollable targets,and they are controlled by a small number of user-control agents with introducing communication to specific agent to the swarm agent. T. Choi[38]adopted the three rules of Boids model to build an art production framework that generates images using multi-agents with chaotic dynamics features.

3 The Principle of Social Force Model

4 Calculation of Pedestrian Interactive Force Based on Boids Model

The Boids model is extended to crowd motion simulation in this paper. Based on the behavior characteristics of crowd and the three rules of collective motion[25], the behavior rules of the crowd motion simulation are designed in our work.

4.1 Design of Crowd Movement Simulation Rules

Learning from the rules of the flocking behavior in Boids model, and taking into account the physiological and psychological characteristics of the crowd,the crowd movement simulation rules are designed as follows:

(1) Segregation Rule:

In order to avoid physical collision, pedestrians usually prefer to keep a certain distance from nearby buildings, obstacles or other pedestrians during walking[39], which meets the segregation rule of the Boids model.

(2) Alignment Rule:

In collective evacuation, pedestrians are easily affected by other nearby pedestrians in the field of vision. When choosing the evacuation direction, pedestrians try to conform with others, and even may produce the phenomenon of following and herding,which meets the alignment rule of the Boids model.

(3) Cohesion Rule:

For the rule of cohesion, individuals without group information may make different choices in the process of motion, while the group members are usually close to each other to maintain the integrity of the group.

4.2 Division of Individual’s Perception Zone

In the process of movement, pedestrian perception of the surrounding environment will be affected by location and space factors[40]. Within the scope of perception, pedestrians will have different behaviors according to the distance. Therefore, this paper divides the space around pedestrians into different perception areas when simulating crowd movement. Based on the three crowd motion rules above, we further divide‘perception area’ into zone of segregation, alignment and cohesion. Since there is a blind area in visual field of human being, assuming that the pedestrian's visual angle isα, the zone of segregation and alignment will be limited in the circular arc with the center angle ofα. As for the zone of cohesion, members of the same group will communicate with each other, so they need not be limited by their visual field. The perceptual zone can be divided into three regions, and the hierarchical relationship among the three regions is shown in Fig.1.The area of gray, yellow, and orange refers to the zone of segregation, alignment and cohesion area respectively.

Combined the rules of crowd movement with division of ‘perception zone’, the behavior of the pedestrian can be described: For the individuals in zone of segregation, the pedestrian keeps appropriate distance from them based on the rule of segregation; For the individuals in zone of alignment, the pedestrian adjusts the velocity to keep the consistency of adjacent individuals based on the rule of alignment; For the members of group in zone of cohesion, the pedestrian maintains the group members together based the rule of cohesion.

4.3 The Calculation of Interactive Forces

According to the rules of crowd’s interaction, the interactive force between individuals can be calculated as three parts, i.e., repulsion force, alignment force and attractive force. The analysis of the interactive force of pedestrianiis shown in Fig.1.

(1) Repulsion Force:

Fig.1 The sketch of Perception Zone and Interactive Forces

The interactive force among individuals is the sum of the repulsion force, the alignment force and the attractive force, as shown in formula (16):

According to Newton's second law, the interactive force among individuals, the driving force of destination, the repulsion force of obstacles, external attractive force and the disturbing force determine the position and velocity of pedestrianiin the next time, as shown in formula (17) and (18). In this paper, we do not consider the influence of external factors on pedestrian movement, such as window display. Thus, the external attraction and interference are ignored.

5 Simulation Experiment

Based on unity 3D simulation platform, we construct the evacuation scenarios of single exit and multi-exit to simulate crowd motion using the proposed method, and compare with the social force model to verify the effectiveness of the proposed method.

5.1 Single Exit Evacuation Scene

The evacuation scene is set as a 15×20m2single exit room, where the exit width is 1.0m. The total number of pedestrians in the scene is 200, of which the number of pedestrians belong to a small group is 55,including three kinds of relationships of family,friends and colleagues, and the remaining 145 are individual pedestrians without group information.The members of the same group are represented as the same color, while the individuals without group information are represented by black. Pedestrian mass is set at 60kg, while maximum speed is limited between 0.98m/s and 1.25m/s. The radius of the segregation, alignment, and cohesion region are 0.5m, 1m and 5m respectively. Other parameter variables are shown as below:v0=1.34m/s,κ=4 ×1 04kg ∙ m-1∙ s-1,K =6 × 1 04kg ∙ s-2,Ar=150N,Br=0.08m,Aa=200N,Ba=0.4m,At=300N,Bt=0.8m.

(1) Distribution of Pedestrians’ Location

In order to explore the difference of crowd movement driven by the traditional social force model and the proposed method, we simulate crowd evacuation behavior under single exit and show four distribution states at t=0s, t=3s, t=10s, and t=22s. Fig.2 and Fig.3 show the location distribution of individuals during the evacuation process has significant differences for the SFM and the proposed method.

Fig.2 Location Distribution of SFM at Different Times: (a) t=0s; (b) t=3s; (c) t=10s; (d) t= 22s.

Fig.3 Location Distribution of the Proposed Method at Different Times: (a) t = 0s; (b) t = 3s; (c) t = 10s; (d) t = 22s.

As shown in Fig.2 (a) and Fig.3 (a), the initial position of each individual is the same. However, due to the attraction among the group members in the proposed model, individuals in the same group are mutual approaching during the evacuation process,and there is an obvious gathering phenomenon, as shown in Fig.2 (b) and Fig.3 (b). With the progress of the evacuation process, the number of pedestrians in the scene gradually decreases. At t = 22s, the number of pedestrians remaining in the evacuation scene driven by social force model is obviously more than that by the proposed method, which can be seen from Fig.2 (d) and Fig.3 (d). It is worth mentioning that the efficiency of evacuation is related to some parameters,such as the number of pedestrians and initial location in the crowd. When the number of pedestrians and initial location in the crowd change, the crowd evacuation efficiency of this method and the traditional social force model may change.

(2) Evacuation Trajectories of Individuals

In order to reveal the crowd movement process in a period of time, we visualize the evacuation trajectory from the initial state to the time of t = 0s, t = 2s, t = 5s and t = 17s. The evacuation trajectories of independent individuals are represented by gray lines, while the same group members are represented by the same color.

As shown in Fig.4, there is no obvious convergence phenomenon in the trajectory of SFM at all times(Fig.4 (b), (c) and (d)). However, the evacuation trajectories of the proposed model, when t=2s, has obvious convergence points, as shown in Fig.5 (b).Moreover, with the progress of the evacuation process,the group trajectories maintain the aggregation state.This is because in the proposed simulation model, the individual's motion state is more affected by the group members and the surrounding pedestrians.

In order to further analyze the influence of repulsion force, alignment force and attractive force on pedestrian movement, we visualize the complete trajectories of group and individual members in single exit pedestrian movement, as shown in Fig.6, where (a)and (b) are the movement trajectories of group members, and (c) and (b) are the evacuation trajectories of individual members.

As can be seen from Fig.6 (c) and Fig.6 (d),compared with the traditional social forces, the pedestrian trajectory simulated by this method is more orderly. Since individual members are not affected by group attractive force, it shows that repulsion force and alignment force in the proposed simulation model play a role in expressing the interaction between individuals.Pedestrians driven by traditional social forces will be repelled by the surrounding pedestrians. However, the model proposed in this paper can restrict the repulsion among individuals to a certain extent. It can be seen from Fig.6 (b) that the movement of group members has a more obvious aggregation effect and the trajectory changes are more abundant when using the method proposed in this paper. This is because compared with individuals, group members are affected by attractive force.

Fig.4 Evacuation Trajectory of SFM: (a) t = 0s; (b) t = 2s; (c) t = 5s; (d) t = 17s

5.2 Multi-exit Evacuation Scene

This paper constructs three evacuation scenarios with 2, 3, and 4 exits, in order to simulate and verify the behaviors of crowd movement under the multi-exit scenario. In the three evacuation scenarios, the initial position of pedestrians is same as the single exit scene in Section 5.1.

In the case of multi-exit scenario, we set the members of the same group to choose the same exit to eliminate the influence of exit selection, while individuals without groups choose the exit closest to themselves. In the Fig.7, the position distribution of crowds at t = 2s are represented respectively when the number of evacuation exits is 2, 3, 4. Among them, (a),(c) and (e) is driven by the proposed method, while (b),(d) and (f) is driven by the traditional social force model.

Fig.5 Evacuation Trajectory of this Method: (a) t = 0s; (b) t = 2s; (c) t = 5s; (d) t = 17s.

Fig.6 Evacuation Trajectories of Small Groups and Individual: (a) small groups in SFM; (b) small groups in proposed model; (c) individuals in SFM; (d) individuals in proposed model.

Fig.7 The Number of Evacuation Exits Is 2, 3, 4 Respectively

It can be seen from Fig.7 that no matter the number of exits is 2, 3 or 4, the group members driven by this method have obvious aggregation phenomenon in the evacuation process. This is consistent with the attractive force of group and alignment force of individuals designed in this paper. In addition, with the increase of the number of exits, the evacuation efficiency of the two methods is significantly improved,while the difference of evacuation efficiency based on traditional social force model and the proposed method is significantly reduced.

6 Conclusion

In this paper, we propose a method for crowd motion simulation based on the rules of Boids model.Three rules (segregation, alignment and cohesion) are used to simulate the interaction behavior of crowd.Firstly, the perception area of individuals is divided into zone of segregation, alignment and cohesion.Secondly, the interactive forces among individuals are calculated based on the zone information, velocity vector and the group information. The interactive force among individual is the synthesis of three forces: the repulsion force to avoid collisions, the alignment force to reflect the consistency of adjacent individuals, and the attractive force to keep the group members together.Finally, the interactive force among individuals, the driving force of destination and the repulsion force of obstacles work together to drive the behavior of crowd motion. The experimental results of simulation show that the proposed method can not only effectively simulate the interactive behavior between adjacent individuals but also the collective behavior of group. In the future work, we will divide more abundant relationships among groups and explore group behavior more deeply.