Multi-emotion crowd motion simulation method based on fractional-order potential field model

Abstract

The present invention belongs to the field of crowd modeling and simulation, and discloses a multi-emotion crowd motion simulation method based on a fractional-order potential field model. The present invention divides the emotional state of an individual into four states: Calm, Anxiety, Panic, and Hysteria, based on the different emotional states that pedestrians may produce due to factors such as the environment during the movement, and divides the corresponding visual range for different emotional states. The fractional-order potential field model is redefined as an emotional field that conforms to the law of crowd movement, and the emotional force between individuals is obtained according to the area, movement state, and emotional state of other individuals. Newton's second law is used to simulate the interaction between individuals and the environment and other individuals. The method of the present invention can effectively simulate the mutual influence between individuals and surrounding individuals under the influence of emotions. Pedestrians in different emotional states present different forms of interaction during the evacuation process. It has the advantages of being novel, simple to understand, and simple and effective in calculation.

Description

Technical Field

[0001] The invention belongs to the field of crowd modeling and simulation, and in particular relates to a multi-emotion crowd motion simulation method based on a fractional-order potential field model. Background Art

[0002] Crowd motion modeling and simulation is a research hotspot in computer graphics, safety science and artificial intelligence, and has been used in many application areas, such as crowd evacuation, digital entertainment and social security. Crowd simulation can well reproduce the self-organization phenomenon of crowd motion, and at the same time, combined with various uncertain factors such as individual physiological characteristics and social factors, it can more accurately simulate the evacuation behavior of crowds in emergency situations.

[0003] In real life, emergencies often cause pedestrians to be nervous. These negative emotions can easily spread among the crowd, and may eventually lead to large-scale crowd riots. Because emotions are a kind of psychological activity generated by the cognition and consciousness of an individual, they not only affect the behavior of the individual, but also can affect the behavior of other individuals through emotional contagion. Therefore, simulating the evacuation of the crowd under the influence of emotions is a very challenging problem. A large number of workers have different studies on emotional factors. Some introduced the SIR model into the cellular automaton model and developed the "CA-SIRS model". By simulating the emotional contagion of the crowd in static and moving conditions, it was found that individual movement would increase the speed of emotional contagion and increase the proportion of pedestrians who were eventually infected. Some combined the P-SIS model with the social force model and found that the model can simulate crowd evacuation more realistically. Others explored the dynamics of the emotional contagion process in dense crowds and studied the influence of factors such as the proportion of pedestrians with initial negative emotions and the emotional influence radius on the overall emotional transformation of the crowd.

[0004] Looking at the current research, we can find that most studies focus on the spread of emotions, while few studies focus on the impact of individual behavior on the whole under different emotions. Obviously, the differences in the specific behaviors of individuals under different emotions will also affect the spread of emotions and the evacuation of the crowd. Therefore, it is crucial to explore the impact of individual emotional factors on individual behavior and even the evacuation of the entire crowd.

[0005] The fractional-order potential field model is applied in the field of robot control. It reflects the changes in the magnitude of forces of different degrees through the changes in the order. If we map the fractional-order potential field to crowd movement and combine the impact of emotional changes on pedestrian vision, the differences in pedestrian behavior under different emotions can be described with the help of the fractional-order potential field model, which is of guiding significance for realistic simulation of crowd movement. Summary of the invention

[0006] The purpose of the present invention is to provide a multi-emotion crowd motion simulation method based on a fractional-order potential field model to solve the above-mentioned technical problems.

[0007] In order to solve the above technical problems, the present invention combines the behavioral characteristics of crowd evacuation and the fractional-order potential field model, defines the behavioral criteria that conform to crowd movement, and simulates the behavior of the crowd during movement. The specific technical solution is as follows:

[0008] A multi-emotion crowd motion simulation method based on a fractional-order potential field model comprises the following steps:

[0009] Step 1: Divide the crowd according to their different emotional states during exercise;

[0010] Step 2: Based on the emotional state of pedestrian evacuation and the corresponding visual field division, the fractional-order potential field is redefined as an emotional field model that conforms to the law of crowd movement;

[0011] Step 3: Based on step 2, the emotional interaction force between individuals is calculated according to the area, movement state, emotional state and visual field of other individuals;

[0012] Step 4: Combine emotional simulation to simulate the interaction between individuals and the environment and other individuals.

[0013] Furthermore, the specific steps of step 1 are to divide the emotional state into four states: Calm, Anxiety, Panic, and Hysteria, and at the same time divide the anxiety level range for pedestrians in the four different emotional states, and set the maximum expected speed and viewing range for pedestrians in the four different emotional states.

[0014] Furthermore, the step 2 includes the following specific steps:

[0015] Step 2.1: Starting from the field strength generated by a point charge in a vacuum, the electric field formula is:

[0016]

[0017] Where ε is the dielectric constant in vacuum, r represents the distance from charge q, and integrating it once can give the first-order potential field V1(r), and the potential field formula is:

[0018]

[0019] Where ε is the dielectric constant in vacuum, r represents the distance from the charge q;

[0020] Step 2.2: The second-order potential field V2(r) is obtained by quadratic integration. The potential field formula is:

[0021]

[0022] Where ε is the dielectric constant in vacuum, r represents the distance from the charge q;

[0023] Step 2.3: Obtain any integer-order potential field and fractional-order potential field through calculation. The fractional-order potential field is given by Weyl fractional integration, and the formula is:

[0024]

[0025] Where n>0, Γ(n) is the gamma function, ε is the dielectric constant in vacuum, and r represents the distance from the charge q.

[0026] By transformation, the equation can be written as follows:

[0027]

[0028] Where n>0, Γ(n) is the gamma function, ε is the dielectric constant in vacuum, and r represents the distance from the charge q;

[0029] Step 2.4: Normalize the potential field, where the potential at r min Take 1 at r max When 0 is taken, it can be simplified to obtain the final emotional field. The emotional field formula is:

[0030]

[0031] Among them U drep (r) represents the emotional field, where n is the order of the fractional order, which can also represent the degree of anxiety or urgency. The larger the n, the higher the degree of anxiety. max Indicates the maximum effective distance of emotional force, r min It represents the minimum effective distance of emotional force, and r represents the distance between two pedestrians.

[0032] Furthermore, the step 3 includes the following specific steps:

[0033] Calculate the emotional interaction between an individual and other individuals within the field of view, and the emotional interaction between an individual and other individuals within the field of view Defined as the negative gradient of the emotion field, the formula is:

[0034]

[0035] Where n represents the anxiety level of the pedestrian, r min and r max represents the minimum influence radius and the maximum influence radius, is a unit vector, and its direction is from individual j to individual i.

[0036] Furthermore, step 4 includes the following specific steps:

[0037] Step 4.1: According to Newton's second law, calculate the force on individuals during crowd movement. The formula is:

[0038]

[0039] in, Driving force for the destination, is the repulsive force of the obstacle, The repulsion between individuals, The uncertain force that the crowd is subjected to during movement;

[0040] Step 4.2: The interaction between individuals and the environment and other individuals is simulated by simulating the repulsive force between individuals, the driving force of the destination, the repulsive force of obstacles and the emotional force between individuals. The simulation method is verified by simulation platform unity3D.

[0041] The multi-emotion crowd motion simulation method based on the fractional-order potential field model of the present invention has the following advantages: the present invention divides the emotional state of an individual into four states: Calm, Anxiety, Panic, and Hysteria, based on the different emotional states that pedestrians may have due to factors such as the environment during motion, and divides the corresponding visual range for different emotional states, redefines the fractional-order potential field model as an emotional field that conforms to the law of crowd motion, obtains the emotional force between individuals according to the area, motion state, and emotional state of other individuals, and uses Newton's second law to simulate the interaction between individuals and the environment and other individuals. The method of the present invention can effectively simulate the mutual influence between individuals and surrounding individuals under the influence of emotions, and pedestrians in different emotional states present different forms of interaction during the evacuation process, which has the advantages of being novel, simple to understand, and simple and effective in calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic diagram of the process of the present invention;

[0043] Figure 2 It is a schematic flow chart of specific implementation steps of the method of the present invention;

[0044] Figure 3 is the emotion classification diagram in the method of the present invention;

[0045] Figure 4 This is a schematic diagram of analyzing the motion situation under the influence of emotions in the method of the present invention;

[0046] Figure 5 is the emotion field curve diagram of the method of the present invention;

[0047] Figure 6 A schematic diagram of a local scene of the method of the present invention;

[0048] Figure 7 It is a schematic diagram of individual position distribution during the evacuation process under a single exit of the method of the present invention;

[0049] Figure 8 A schematic diagram of a dual-export scenario of the method of the present invention;

[0050] Fig. 9 A schematic diagram of a three-exit scenario of the method of the present invention;

[0051] Fig.10 A schematic diagram of a four-exit scenario of the method of the present invention; DETAILED DESCRIPTION

[0052] In order to better understand the purpose, structure and function of the present invention, the following is a further detailed description of a multi-emotion crowd motion simulation method based on a fractional-order potential field model of the present invention in conjunction with the accompanying drawings.

[0053] like Figure 1 , Figure 2 As shown, the multi-emotion crowd motion simulation method based on the fractional-order potential field model of the present invention comprises the following steps:

[0054] Step 1: Divide the crowd according to their different emotional states during exercise, such as Figure 3 As shown in the figure, the emotional state is divided into four states: Calm, Anxiety, Panic, and Hysteria. At the same time, the anxiety level range is divided for pedestrians in different emotional states, and the maximum expected speed and visual range are set for pedestrians in different emotional states. Combined with the actual situation, a schematic diagram of the movement under the influence of emotions can be obtained, as shown in Figure 4 As shown in the figure, it can be seen that the pedestrian in the emotional state of Calm has the largest detour radius and the widest attention range, which is 180° in the current emotional state; when the emotional state is anxiety, the detour radius gradually decreases, and the attention gradually narrows, and the attention range at this time is 135°; as the anxiety level increases, when the emotional state is Panic, the attention range is 90°, and at the same time the detour radius is further reduced; finally, when the emotional state is Hysteria, the attention range is the narrowest, which is 45°, and the pedestrian is almost detoured by the pedestrian in front. As the anxiety level increases, the attention range narrows, and the pedestrian's attention gradually gathers in front of him. At this time, although the individual's travel speed increases, the probability of collision with surrounding pedestrians also increases.

[0055] Step 2: Since the traditional model cannot show the difference in pedestrian behavior under different emotions, in order to correctly describe the movement differences of pedestrians under different emotions, we modify the traditional model based on the behavioral characteristics of pedestrian evacuation and the division of individual emotional states and movement conditions. Fractional-order potential fields are widely used in the field of robot path planning due to their elegant mathematical analysis and expression. We redefine fractional-order potential fields as an emotional field model that conforms to the laws of crowd movement. Step 2.1: In order to obtain an emotional field of any order, we can start from the field strength generated by a point charge in a vacuum. The electric field formula is:

[0056]

[0057] Where ε is the dielectric constant in vacuum, and r represents the distance from charge q. Integrating it once gives the first-order potential field V1(r), and the potential field formula is:

[0058]

[0059] where ε is the dielectric constant of a vacuum and r is the distance from the charge q.

[0060] Step 2.2: The second-order potential field V2(r) is obtained by quadratic integration. The potential field formula is:

[0061]

[0062] where ε is the dielectric constant of a vacuum and r is the distance from the charge q.

[0063] Step 2.3: Through calculation, we can obtain any integer-order potential field, or even fractional-order potential field. The fractional-order potential field is given by Weyl fraction integral, and the formula is:

[0064]

[0065] Where n>0, Γ(n) is the gamma function, ε is the dielectric constant in vacuum, and r represents the distance from the charge q.

[0066] By transformation, the equation can be written as follows:

[0067]

[0068] Where n>0, Γ(n) is the gamma function, ε is the dielectric constant in vacuum, and r represents the distance from the charge q;

[0069] Step 2.4: Normalize the potential field, where the potential at r min Take 1 at r max When , it is taken as 0, and it can be simplified to obtain the final emotional field emotional field formula:

[0070]

[0071] Among them U drep (r) represents the emotional field, where n is the order of the fractional order, and can also represent the degree of anxiety or urgency. The larger the n, the higher the degree of anxiety. max Indicates the maximum effective distance of emotional force, r min It represents the minimum effective distance of emotional force, and r represents the distance between two pedestrians;

[0072] In this way, we get the formula of the emotion field. It can be seen that in the process of calculating the emotion field, no integration is required. The shape of the emotion field depends only on the order of the fractional order. Its final form has a beautiful mathematical form and is very concise. Figure 5 From the emotional field curve, we can see that when the distance r is small, the smaller n is, the steeper the potential field line is, and the greater the emotional force is at this time. As the distance between pedestrians continues to shorten, for emotionally stable pedestrians, the potential field line becomes steeper and steeper, and the emotional force they are subjected to increases dramatically, indicating that pedestrians with stable emotions tend to maintain a more comfortable spatial distance; while for unstable pedestrians, the growth rate of emotional force gradually slows down, and the potential field line transitions from a concave function to a convex function, which indicates that pedestrians begin to reduce their demand for self-space. When the anxiety level reaches a certain value, pedestrians will give up the pursuit of comfortable space in order to reach the target location as quickly as possible. At this time, the potential field line presents an obvious convex function shape, and the emotional force at this time becomes smaller and smaller as the distance shortens. As shown in the figure below: Figure 6 , which is a schematic diagram of a local scene of the method of the present invention.

[0073] Step 3: Calculate the emotional interaction between individuals based on the area, movement state and emotional state of other individuals;

[0074] According to the crowd interaction principle and interaction behavior, the emotional force between individuals and other individuals within the field of view is calculated. Since the interaction between individuals and other individuals within the field of view changes with the change of emotions, there is an emotional force between individuals and the emotional force between individuals and other individuals within the field of view. Defined as the negative gradient of the emotion field, the formula is:

[0075]

[0076] Where n represents the anxiety level of the pedestrian, r min and r max represents the minimum influence radius and the maximum influence radius, is a unit vector, and its direction is from individual j to individual i.

[0077] Step 4: Calculate the force on individuals in crowd movement, and use Newton's second law to simulate the interaction between individuals and the environment and other individuals;

[0078] Step 4.1: According to Newton's second law, calculate the force on individuals during crowd movement. The formula is:

[0079]

[0080] in, Driving force for the destination, is the repulsive force of the obstacle, The repulsion between individuals, The uncertain force that the crowd is subjected to during movement;

[0081] Step 4.2: The interaction between individuals and the environment and other individuals is simulated by simulating the repulsive force between individuals, the driving force of the destination, the repulsive force of obstacles, and the emotional force between individuals. The simulation method is verified by simulation platform unity3D, such as Figure 7-10 As shown in the figure, in local, single-exit, double-exit, triple-exit and quad-exit scenarios, the individual evacuation simulation is analyzed from the individual's position distribution. It can be seen from the figure that this method can effectively simulate the mutual influence between individuals and surrounding individuals under the influence of emotions, and pedestrians in different emotional states present different forms of interaction during the evacuation process.

[0082] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A multi-emotion crowd motion simulation method based on a fractional-order potential field model, characterized in that: The steps include: Step 1: Divide the crowd according to their different emotional states during exercise; Step 2: Based on the emotional state of pedestrian evacuation and the corresponding visual field division, the fractional-order potential field is redefined as an emotional field model that conforms to the law of crowd movement; Step 2.1: Starting from the field strength generated by a point charge in a vacuum, the electric field formula is: Where ε is the dielectric constant in vacuum, r represents the distance from charge q, and integrating it once gives the first-order potential field V1(r). The potential field formula is: Where ε is the dielectric constant in vacuum, r represents the distance from the charge q; Step 2.2: The second-order potential field V2(r) is obtained by quadratic integration. The potential field formula is: Where ε is the dielectric constant in vacuum, r represents the distance from the charge q; Step 2.3: Obtain the potential field of any integer order and fractional order through calculation. The fractional order potential field is given by Weyl fractional integration, and the formula is: Where n>0, Γ(n) is the gamma function, ε is the dielectric constant in vacuum, and r represents the distance from the charge q. By transformation, the equation can be written as follows: Where n>0, Γ(n) is the gamma function, ε is the dielectric constant in vacuum, and r represents the distance from the charge q; Step 2.4: Normalize the potential field, where the potential at r min Take 1 at r max When , take 0 and simplify it to get the final emotional field. The emotional field formula is: Among them U drep (r) represents the emotional field, where n is the order of the fractional order, indicating the degree of anxiety or urgency. The larger the n, the higher the degree of anxiety. max Indicates the maximum effective distance of emotional force, r min It represents the minimum effective distance of emotional force, and r represents the distance between two pedestrians; Step 3: Based on step 2, the emotional interaction force between individuals is calculated according to the area, movement state, emotional state and visual field of other individuals; Calculate the emotional interaction between an individual and other individuals within the field of view, and the emotional interaction between an individual and other individuals within the field of view Defined as the negative gradient of the emotion field, the formula is: Where n represents the anxiety level of the pedestrian, r min and r max represents the minimum influence radius and the maximum influence radius, is a unit vector, with the direction from individual j to individual i; Step 4: Combine emotional simulation to simulate the interaction between individuals and the environment and other individuals; Step 4.1: According to Newton's second law, calculate the force on individuals during crowd movement. The formula is: in, Driving force for the destination, is the repulsive force of the obstacle, The repulsion between individuals, The uncertain force that the crowd is subjected to during movement; Step 4.2: The interaction between individuals and the environment and other individuals is simulated by simulating the repulsive force between individuals, the driving force of the destination, the repulsive force of obstacles and the emotional force between individuals. The simulation method is verified by simulation platform unity3D.

2. The multi-emotion crowd motion simulation method based on the fractional-order potential field model according to claim 1 is characterized in that: The specific steps of step 1 are to divide the emotional state into four states: Calm, Anxiety, Panic, and Hysteria, and at the same time divide the anxiety level ranges for pedestrians in the four different emotional states, and set the maximum expected speed and visual range for pedestrians in the four different emotional states.

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