Social chamber behavior motion simulation method based on ORCA model

Abstract

The invention discloses a social small group behavior motion simulation method based on an ORCA model, and the method comprises the steps: firstly constructing an intimacy function, and quantifying the intimacy among internal members through considering different social relationships and spatial distances thereof, thereby dynamically reflecting the intimacy change of the relationships among the members; meanwhile, the behavior of the group is restrained by combining an alignment and aggregation rule so as to simulate the aggregation behavior in the social small group. Secondly, the roles are modeled based on a five-personality model, and corresponding leader capabilities are divided for different individuals so as to simulate following behaviors in the group. And finally, integrating the small group internal gathering behavior and the leader following behavior into an ORCA algorithm to jointly drive the crowd to move. Based on the method, the Unity3D engine is adopted for simulation, and compared with an original model, the method can show the influence of mutual constraint and leader force in the group in the crowd motion simulation process.

Description

Technical Field

[0001] The invention belongs to the technical field of crowd simulation modeling, and in particular relates to a social small group behavior motion simulation method based on an ORCA model. Background Art

[0002] As a simulation technology that integrates multidisciplinary knowledge such as computer science, mathematical modeling, sociology and psychology, crowd motion simulation technology aims to explore and predict the behavior and movement patterns of crowds in various environments. It is crucial to the optimization of public safety, urban planning, and emergency response mechanisms. At present, crowd motion simulation technology is mainly divided into two categories: micro models and macro models. Micro models focus on the accurate simulation of individual behaviors, while macro models study the overall movement trends and characteristics of crowds from a holistic perspective. The RVO (Reciprocal Velocity Obstacle) model is a micro model that solves the problem of intelligent body collision in a dynamic environment. The algorithm avoids collisions by predicting potential collisions and adjusting the intelligent body path accordingly. However, when two individuals walking towards each other choose the same side to avoid collision, there will be a risk of collision. As an improved version of RVO, the ORCA (Optimal Reciprocal Collision Avoidance) algorithm introduces the "optimal reciprocity" principle and improves the obstacle avoidance efficiency in complex environments. However, in terms of group behavior interaction in complex environments, it is difficult to reflect the specific impact of the interaction within a small group on individual behavior, which in turn affects the authenticity and reliability of the simulation.

[0003] Swarm behavior simulation is an important method for studying the collective behavior of human society, animal groups or microscopic particles. It is usually based on simple rules followed by individuals and local interactions, resulting in complex global behaviors. In the simulation, individuals are usually affected by other individuals in the group, resulting in the formation of collective behavior patterns for the entire group. Swarm behavior simulation includes models such as bird flocks, fish schools, animal migration, crowd evacuation and traffic flow, among which aggregation behavior and leader-follower behavior are important aspects. In addition, the social attributes of individuals and their social relationships with each other must also be considered in the study of group behavior. Different attributes and social relationships will affect the interaction mode and behavior choices between individuals. Summary of the invention

[0004] The purpose of the present invention is to provide a method for integrating the aggregation behavior and leadership behavior within a small group into the framework of the Optimal Reciprocal Collision Avoidance (ORCA) algorithm to simulate the interaction behavior within a small social group in a crowd.

[0005] To achieve the above-mentioned purpose, the technical solution of the present invention is as follows: first, an intimacy function is constructed to quantify the intimacy between internal members by considering different social relationships and their spatial distances, thereby dynamically reflecting the changes in the closeness of the relationships between members. At the same time, the alignment and aggregation rules are combined to constrain the behavior of the group to simulate the aggregation behavior within a small social group. Secondly, the roles are modeled based on the five-personality model, and corresponding leadership capabilities are divided for different individuals to simulate the following behavior in the group. Finally, the aggregation behavior within the small group and the leader-following behavior are integrated into the ORCA algorithm to jointly drive the crowd movement. The results show that the invention can show the mutual constraints within the group and the influence of leadership during the crowd movement simulation process.

[0006] The present invention has the following beneficial effects:

[0007] 1. The present invention improves the ORCA model by introducing small group behavior into the model to influence individual speed decisions, thereby realizing the combination of collision avoidance behavior and group coordinated motion, and improving the applicability of the original model.

[0008] 2. The present invention constructs a group behavior aggregation model based on the two behavioral rules of alignment and aggregation, and describes the social relations between groups through a dynamically changing intimacy model, which can simulate the interaction and dynamic interaction between small group members during the aggregation process.

[0009] 3. The present invention constructs a leader-follower model that reflects leadership, and describes the leadership traits of individuals through five personality dimensions, forming a role modeling based on the five personality models. The combination of the leader-follower model and the ORCA algorithm can show the influence of leaders on groups when simulating group behavior.

[0010] The present invention improves the applicability of the ORCA algorithm, making it more realistic when simulating crowd behavior. Simulation experiments verify that the method of the present invention is effective. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 It is a flow chart of the small group behavior motion simulation method based on the ORCA model of the present invention;

[0012] Figure 2 This is a diagram showing the dynamic changes in the intensity of intimacy in small group social relationships;

[0013] Figure 3 For the leader-follower model diagram;

[0014] Figure 4a and Figure 4b A collision avoidance speed decision diagram for ORCA that incorporates group behavior;

[0015] Figure 5a-5dis the crowd location distribution diagram at different times during evacuation (α=0.5);

[0016] Figure 6a-6d This is a graph showing the changes in distance and intimacy of different social relationships during the evacuation process;

[0017] Figure 7a-7c is the pedestrian evacuation trajectory during the evacuation process (α=0.3,β=0.3) DETAILED DESCRIPTION

[0018] The technical solution of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0019] The invention discloses a social small group behavior movement simulation method based on an ORCA model. Figure 1 This is a flow chart of the social small group behavior motion simulation method based on the ORCA model of the present invention. The specific steps include:

[0020] Step 1: formulate the speed rules of the gathering behavior within the small group, and define the intensity function of the intimacy between small groups to quantify the social intimacy between individuals, based on which the gathering behavior model is established;

[0021] Step 2: Model the leadership role based on the five-personality model, identify the leader of the group, and establish a leadership-following behavior model;

[0022] Step 3, combine the two group behaviors into the ORCA algorithm to realize group behavior interaction and avoid collision;

[0023] Step 1.1, using the alignment rule, calculate the alignment speed;

[0024] Each individual will try to keep pace with the average speed and direction of its neighbors. When most of its neighbors move in a certain direction, the individual will also adjust its speed to match that direction. For individual i in the group, assume that its neighbor set is N (i) , n is the number of surrounding neighbors, v j is the speed of the jth neighbor, then the alignment behavior of individual i can be expressed by the following formula:

[0025]

[0026] in represents the speed that needs to be adjusted based on the alignment rule. This formula effectively calculates the speed adjustment of individual i so that its speed tends to the average speed of its neighbors, thereby promoting the coordinated movement of the entire group.

[0027] Step 1.2, calculate the aggregation speed using the aggregation rule;

[0028] Individuals tend to move to the average position of their neighbors, thus promoting the overall cohesion of the group. For individual i in the group, its position is represented by p i ,Assume that n is the number of neighbors of individual i, and the set of neighbors is N(i), the aggregation rule can be expressed by the following formula:

[0029]

[0030] in is the speed that needs to be adjusted based on the aggregation rule, p i and p j are the positions of the current individual and its neighbors, respectively. When there are neighbor individuals, the formula calculates the speed towards the average position of the neighbors. When there are no neighbors, the speed is adjusted to 0. This ensures that the individual maintains the current state when there are no companions around, and moves towards the center of the group when there are companions.

[0031] Step 1.3, calculating the aggregation speed based on two behavior rules;

[0032] Finally, the speed of individual i at time t+Δt is adjusted by the current speed and the speed based on the aggregation and alignment-based speed adjustments Together, the position at time t+Δt is determined by the current position plus the velocity change within this time step Δt.

[0033]

[0034] p i (t+Δt)=p i (t)+v i (t+Δt) (4)

[0035] where v i (t+Δt) is the velocity of individual i in the next time step, p i (t+Δt) is the position of individual i in the next time step, and Δt is the length of the next time step. Equations (3) and (4) constitute the basic dynamic model describing group behavior, where the speed update reflects the individual's response to the movement of its neighbors, and the position update is the cumulative result of these speed changes.

[0036] Step 1.4, define an intimacy intensity function I ij (x) to quantify the intimacy between simulated individuals;

[0037] Where i and j represent different individuals, and x represents the distance between them. The intimacy strength can be represented by a Gaussian function:

[0038]

[0039] where a ij Indicates the peak value of intimacy; b ij represents the distance between two individuals when their intimacy reaches its peak; c ij Describes how quickly intimacy decays.

[0040] In pedestrian simulations, there is usually a so-called “social distance” within which the intimacy between individuals increases as the distance decreases, and once a certain distance (i.e., b ij ), intimacy will begin to decrease.

[0041] Table 1 Intimacy parameter settings

[0042]

[0043] As shown in Table 1, according to Hall's theory, the social distance between people can be divided into family, friends, and general relationships, and the corresponding parameters are set. ij The larger the value, the greater the intimacy between individuals; parameter b ij is smaller, indicating that the distance between the two is closer when the intimacy reaches its peak; for c ij , a larger value means that the intimacy decays more slowly, reflecting the continuity of intimacy. Its dynamic change trend is as follows Figure 2 shown.

[0044] In step 1.5, individual i considers the effect of intimacy when gathering with other individuals in the group.

[0045] Update according to formula (3), assuming that the intimacy strength between individuals i and j at time t is I ij (t,x), the distance x is |p j -p i |. Then the individual speed affected by the gathering behavior of small social groups is:

[0046]

[0047] Step 2.1, use the five-personality model to define pedestrian roles;

[0048] First, the OCEAN model is used to model the personality characteristics of pedestrians. It includes five main dimensions: Openness to Experience, Conscientiousness, Extraversion, Agreeableness, and Neuroticism. The five dimensions together constitute a model for describing personality traits, and the score on each dimension reflects the individual's tendency and behavior pattern in that trait.

[0049] There is a relationship between leadership and the five personality traits of conscientiousness C, agreeableness A, and neuroticism N. Among them, C and A are positively correlated with leadership ability, while N is negatively correlated with leadership ability. Based on these three dimensions, role modeling is performed using ψ c , a , n Represent the three dimensions of the model respectively. The individual personality trait differences are represented by the Gaussian distribution function G, with a mean of μ and a standard deviation of σ 2 .

[0050] ψ ε =G(μ,σ 2 ) (7)

[0051] where μ∈(0,1),σ 2 ∈[0,0.1],ε∈(C,A,N). Therefore, the leadership tendency of an individual is α leader It can be expressed as

[0052] α leader =ω c ψ C +ω a ψ A +ω n (1-ψ N ) (8)

[0053] where ω c ,ω a ,ω n is the weight of the eigenvalues ​​of each dimension, ω c ,ω a ,ω n ∈[0,1].

[0054] Step 2.2, calculate the leader-follower behavior speed;

[0055] like Figure 3 As shown in the figure, the behavior of pedestrians is affected by the leader in two ways. On the one hand, followers tend to move towards the leader's position, reflecting their tendency to imitate the leader's behavior. On the other hand, the movement direction of followers is consistent with that of the leader, reflecting the tendency to actively adjust their own behavior to keep pace with the leader.

[0056] The speed v at which individual i is influenced by its leader il It can be calculated by the following formula:

[0057] v il =ρv l +(1-ρ)n il (9)

[0058] where v lrepresents the speed of the leader of individual i, n il Represents the direction vector of individual i pointing to its leader.

[0059] The distance d between individual i and its leader ij Determines the value of the impact factor ρ, and its calculation formula is:

[0060]

[0061] Where δ is a constant. ij When d is larger, ρ is smaller, indicating that individual i tends to move toward the leader. ij When is smaller, ρ is larger, and individual i tends to move in the direction of the leader’s speed.

[0062] Then the speed at which individual i is affected by the leader factor can be further expressed as:

[0063]

[0064] α leader The larger the value, the stronger the influence of the leader, and the leader's movement or behavior decisions are more attractive to followers.

[0065] Step 3, combine the two group behaviors into the ORCA algorithm to realize group behavior interaction and avoid collision;

[0066] Step 3.1, calculate the collision avoidance half-plane of all neighboring agents through the ORCA algorithm;

[0067] ORCA is an efficient multi-agent system collision avoidance algorithm that can handle complex dynamic environments well and is suitable for scenarios such as crowd simulation and robot group collaboration. Its core idea is to transform the crowd collision avoidance problem into the optimal speed problem on a half-plane. By considering the individual collision avoidance behavior and the corresponding feasible speed set, the speed direction is limited to the half-plane. As long as the individual speed falls within the half-plane, collision can be avoided.

[0068] (1) Velocity Obstacle: Based on the information (position, speed) of the neighboring agents, the velocity obstacles (VO) of all neighboring agents are calculated. For agents A and B, the velocity obstacle It is defined as the set of velocities that can lead to a collision within time τ.

[0069]

[0070] Where D(p B -p A ,r A +r B) indicates that the radius is r A +r B , the center is p B -p A Open disk; r A 、r B are the radii of agents A and B respectively; p A 、p B are position vectors, i.e., the positions of agents A and B in space.

[0071] (2) Optimal reciprocal collision avoidance speed: Agent A is based on Generate a set of optional velocities for each neighbor that avoids collisions, i.e. Half plane.

[0072]

[0073] Where n is Previous point v A -v B +u is the normal vector, u is the shortest velocity vector that needs to be offset to avoid collision with the relative velocity, and 1 / 2 means both parties bear half the responsibility.

[0074] (3) Calculate the new speed: the set of feasible speeds for agent A It is composed of the intersection of the half-plane of the collision-free velocity domain of all adjacent agents and the maximum velocity domain.

[0075] Static obstacles in the environment can be regarded as neighboring agents with a speed of 0. Assume that the set of all neighbors of agent A is {AO k |k=1,2,…,n}, the set of all static obstacles is {CO k |k=1,2,…,m}. Then the ORCA set of optional collision-free velocity domains for agent A is:

[0076]

[0077] The speeds in this set represent the speed range in which the agent can move safely in the current time step. max is the maximum speed of the agent. Agent A will choose The speed closest to its expected speed is taken as the new speed, and the next speed of the individual is:

[0078]

[0079] where v pref is the desired velocity of the agent, and v is the velocity in the collision-free velocity domain.

[0080] like Figure 4aAs shown, the shaded area represents the collision avoidance ORCA plane and the allowed speed of the neighboring intelligent body calculated by the ORCA algorithm. When the agent's velocity is in this region, it ensures that it will not collide with neighboring agents in the next time step, while being as close to the desired velocity v as possible. pref .

[0081] Step 3.2, integrate group behavior into the ORCA algorithm to jointly influence speed decision;

[0082] In order to achieve coordinated movement of group behavior and collision avoidance behavior, group behavior is integrated into the ORCA algorithm, and the influence of group behavior is taken into account when selecting the next time speed. During the speed update process, the current collision avoidance area and the expected speed v towards the target are considered. pref , and the speed decision v generated by group behavior factors g 、v l (determined by equation (6) and equation (11) respectively) on the speed selection, such as Figure 4b The new speed should be determined according to the following principles: Under the premise of ensuring collision avoidance, select a speed closest to v pref 、v g 、v l The speed of the weighted sum is used to achieve coordinated movement of individuals in a group.

[0083] Update based on formula (15). The speed update formula of the agent in the next time step is as follows:

[0084] v new′ = arg min v∈ORCA ||v-[(1-γ-β)v pref +γv g +βv l ]|| (16)

[0085] where v g 、v l They represent the speed decision made under the influence of small group behavior, reflecting the influence of gathering behavior and leader-follower behavior. γ and β are weight coefficients, which adjust the influence of gathering behavior and leader-follower behavior on speed update. The increase of coefficients γ and β means that the agent is more driven by group consciousness in speed selection and shows a stronger group behavior tendency. The simulation evacuation situation is as follows Figure 5a-5d , Figure 6a-6d , Figure 7a-7c shown.

Claims

1. A social small group behavior motion simulation method based on the ORCA model, characterized by The following steps are involved: Step 1: formulate the speed rules of the gathering behavior within the small group, and define the intensity function of the intimacy between small groups to quantify the social intimacy between individuals, based on which the gathering behavior model is established; Step 2: Model the leadership role based on the five-personality model, identify the leader of the group, and establish a leadership-following behavior model; Step 3: Combine the two group behaviors within the small group into the ORCA algorithm to achieve interaction of group behaviors while avoiding collisions.

2. A social small group behavior motion simulation method based on ORCA model according to claim 1, characterized in that: The specific method of step 1 is as follows: Step 1.1, calculate the alignment speed using the alignment rule; According to the speed of individual neighbors, the alignment speed of the individual tends to keep the same speed as the neighbors is calculated. For individual i in the group, assuming that its neighbor set is N (i) , n is the number of surrounding neighbors, v j is the speed of the jth neighbor, then the alignment behavior of individual i can be expressed by the following formula: in Indicates the speed that needs to be adjusted based on the alignment rules; Step 1.2, calculate the aggregation speed using the aggregation rule; According to the average position of all neighboring individuals, the aggregation speed of individuals based on the group is calculated. For individual i in the group, its position is represented by p i ,Assume that n is the number of neighbors of individual i, and the set of neighbors is N(i), the aggregation rule can be expressed by the following formula: in is the speed that needs to be adjusted based on the aggregation rule, p i and p j are the positions of the current individual and its neighbors respectively; Step 1.3, calculating the aggregation speed based on two behavior rules; Finally, the speed of individual i at time t+Δt is adjusted by the current speed and the speed based on the aggregation and alignment-based speed adjustments Together, the position at time t+Δt is determined by the current position plus the velocity change within this time step Δt. p; (t+△t)=p; (t)+t2; (t+At)(4) where v i (t+Δt) is the velocity of individual i in the next time step, p i (t+Δt) is the position of individual i at the next time step, and Δt is the length of the next time step; Step 1.4, define an intimacy intensity function I ij (x) to quantify the intimacy between simulated individuals; Where i and j represent different individuals, and x represents the distance between them. The intimacy strength is represented by a Gaussian function: where a ij Indicates the peak value of intimacy; b ij represents the distance between two individuals when their intimacy reaches its peak; c ij Describes how quickly intimacy decays. In step 1.5, individual i considers the effect of intimacy when gathering with other individuals in the group. Assume that the intimacy strength between individuals i and j at time t is I ij (t, x), the distance x is |p j -p i |. Then the individual speed affected by the gathering behavior of small social groups is: in represents the individual alignment speed, v i (t) represents the current speed of the individual, and n represents the number of neighbors.

3. A social small group behavior motion simulation method based on ORCA model according to claim 2, characterized in that: The specific method of step 2 is as follows: Step 2.1, use the five-personality model to define pedestrian roles; The OCEAN model is used to model the personality characteristics of pedestrians. Leadership is positively correlated with responsibility C and agreeableness A among the five personality traits, and negatively correlated with neuroticism N. Based on these three dimensions, role modeling is performed using ψ c , a , n Represent the three dimensions of the model respectively. The individual personality trait differences are represented by the Gaussian distribution function G, with a mean of μ and a standard deviation of σ 2 : ψ ε =G(μ,σ 2 ) (7) where μ∈(0,1),σ 2 ∈[0, 0.1], ε∈(C, A, N). Therefore, the leadership tendency of an individual is α leader It can be expressed as a leader =ω c ψ C +oh a ψ A +oh n (1-ψ N ) (8) where ω c ,ω a ,ω n is the weight of the eigenvalues ​​of each dimension, ω c ,ω a ,ω n ∈[0, 1]. Step 2.2, calculate the leader-follower behavior speed, and divide the influence of the leader on pedestrian behavior into two aspects: on the one hand, the follower tends to move towards the leader's position, and on the other hand, the follower's movement direction is consistent with the leader's movement direction; The speed v at which individual i is influenced by its leader il It can be calculated by the following formula: v il =ρv l +(1-p)n il (9) where v l represents the speed of the leader of individual i, n il Represents the direction vector of individual i pointing to its leader. The distance d between individual i and its leader ij Determines the value of the impact factor ρ, and its calculation formula is: Among them, is a constant. The speed at which individual i is affected by the leader factor can be further expressed as:

4. A social small group behavior motion simulation method based on ORCA model according to claim 3, characterized in that: The specific method of step 3 is as follows: Step 3.1, calculate the collision avoidance half-plane of all neighboring agents through the ORCA algorithm; (1) Speed ​​barrier: Based on the information perceived by the neighboring agents, the speed barriers of all neighboring agents are calculated. For agents A and B, the speed barrier It is defined as the set of velocities that can lead to a collision within time τ. Where D(p B -p A , r A +r B ) indicates that the radius is r A +r B , with the center at p B -p A Open disk; r A 、r B are the radii of agents A and B respectively; p A 、p B are position vectors, i.e., the positions of agents A and B in space; (2) Optimal reciprocal collision avoidance speed: Agent A is based on Generate a set of optional velocities for each neighbor that avoids collisions, i.e. Half plane: Where n is Previous point v A -v B +u is the normal vector, where u is the shortest velocity vector that needs to be offset to avoid collision, and 1 / 2 means both parties bear half of the responsibility; (3) Calculate the new speed: the set of feasible speeds for agent A It is composed of the intersection of the half-plane of the collision-free velocity domain of all adjacent agents and the maximum velocity domain; Static obstacles in the environment can be regarded as neighboring agents with a speed of 0. Assume that the set of all neighbors of agent A is {AO k |k=1,2,...,n}, the set of all static obstacles is {CO k |k=1,2,...,m}; then the ORCA set of optional collision-free velocity domains for agent A is: The speeds in this set represent the speed range in which the agent can move safely in the current time step; where v max is the maximum speed of the agent; agent A will choose The speed closest to its expected speed is taken as the new speed, and the next speed of the individual is: where v pref is the expected velocity of the agent, v is the velocity in the collision-free velocity domain; Step 3.2, integrate group behavior into the ORCA algorithm to jointly influence speed decision; During the velocity update process, the current collision avoidance area and the desired velocity v towards the target are considered. pref , and the speed decision v generated by group behavior factors g 、v l The influence of speed selection, the determination of the new speed should follow: under the premise of ensuring collision avoidance, select a speed closest to v pref 、v g 、v l The speed of the weighted sum to achieve coordinated movement of individuals in a group; Update based on formula (15). The speed update formula of the agent in the next time step is as follows: v new′ =arg min v∈ORCA ||v-[(1-γ-β)v pref +γv g +βv l ]|| (16) where v g 、v l They represent the speed decision made under the influence of small group behavior, reflecting the influence of gathering behavior and leader-follower behavior. γ and β are weight coefficients, which regulate the influence of gathering behavior and leader-follower behavior on speed update.

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