Modeling Social Group Structures in Pedestrian Crowds

Transcription

1 Modelng Socal Group Structures n Pedestran Crowds Fasheng Qu, Xaoln Hu, Xue Wang, and Saurav Karmakar Abstract Group structure s an mportant characterstc of socal crowd. However, up to now, the effect of group structure to crowd behavor has not been wdely studed. Ths s partally due to the fact that modelng group-related behavor s a challengng task because of the many factors that need to be consdered. Ths paper presents a unformed framework for modelng dfferent group structures n a pedestran crowd. Both ntra-group structure and nter-group relatonshps are consdered and ther effects on the group behavor are modeled. Crowd behavor smulatons based on two dfferent group structures are developed and promsng results are obtaned. I. INTRODUCTION Smulaton of crowd behavor s an actve research area n recent years. Most of the related work focuses on the mcrolevel analyss on dfferent factors for an ndvdual vrtual pedestran, such as Helbng s socal force model [1], Kaup s modfed HMFV model [2], Frdman s model based on the socal comparson theory [3], and many other models e.g. [4]. Groupng s a common phenomenon n pedestran crowds. For nstance, n a shoppng mall, famly members walk besde each other n a clustered way. Some works studed the group aspect, lke leader-follower group structure [5]. However, there s no common and easy way to buld other types of group structures, such as the clustered groups, the lnear groups, the crcle groups and so on. Here, a group structure refers to the ntra-group structure among agents of the same group, whch s an mportant characterstc accordng to [6]. Besdes havng ntra-group structures, groups may also nfluence each other, resultng n nter-group relatonshps. For example, t s common for a group to follow other nearby groups durng an emergency evacuaton process. Dfferent group structures affect the evacuaton effcency n emergency stuatons, e.g., a leader-follower structure may be more effcent than a clustered structure f a group has a large number of agents. In ths case, a clustered group structure wll result n slow movement, especally n a constraned area [6]. Thus, t s necessary to have an easy way to study dfferent ntra-group structures and nter-group relatonshps, and ther effect on crowd behavor. Unfortunately, t s a challengng task to model group-related behavors due to the many factors that need to be consdered [7] and the heterogenety nature ntroduced by dfferent groups. Ths paper presents an effort of ncorporatng dfferent group structures n smulatng pedestran crowd behavor. The major contrbuton of ths work s a unformed framework that captures the essental features of varous ntragroup structures and nter-group relatonshps so dfferent group structures can be easly modeled. In ths work, smulaton of crowd behavor s based on an agent-based smulaton approach where each ndvdual n the crowd s modeled as an agent, whose movement s based on a behavor-based control model [8, 9]. II. RELATED WORK Crowd behavour smulaton has been studed from dfferent aspects. A well known model s Helbng s physcs and socal force model [1] where the behavor s descrbed as the vector addton of the separate force terms reflectng dfferent envronmental nfluences. Ths model has successfully smulated several mportant features of crowd behavor, such as lane formaton n crowds wth opposte walkng drecton, oscllatons of the crowd passng drecton at a bottleneck, alternatng collectve patterns of moton at ntersectons and so on. Kaup s work [2] extends Helbng s model to produce a more realstc behavor of an ndvdual pedestran under panc or non-panc condtons. Crowd behavor s also smulated for studyng emergency evacuatons and safe egress. The work of [10] developed a prototype system to study some emergent human and socal behavors, such as compettve, queung, and herdng behavors, durng emergency evacuatons. Another feld where crowd behavor smulaton has been researched s computer anmaton and vrtual envronment, for whch a survey can be found n [6]. Crowd smulaton n ths area pays close attentons to real tme 3D anmaton and human computer nteracton. Whle much research has been conducted n crowd behavor smulaton, less work has focused on the aspect of group structures. Frdman[3] et al proposed a crowd behavor model based on Festnger s Socal Comparson Theory, where each agent s modeled wth a set of features and each agent trggers actons to reduce the dfference,.e. poston, drecton and color, wth another most smlar agent. Also they mplemented several crowd behavor scenaros where ndvdual or grouped pedestrans exst. Qngge [5] et al smulated the evacuaton of crowd wth dfferent groups; and each group s based on a Leader-Follower model where the leaders fnd the ext entry and followers follow the nearest follower through a dynamc groupng process based on the A* algorthm. Loscos [11] showed the mportance of group behavor n a realstc crowd smulaton. Musse et al [12] explored an approach based on the relatonshp between the autonomous vrtual humans of a crowd and the emergent behavor orgnated from t.

2 III. THE GROUP-BASED CROWD BEHAVIOR SIMULATION FRAMEWORK Before dscussng how the ntra-group structure and ntergroup relatonshps are modeled, we frst gve an overvew of the group-based crowd behavor smulaton framework. In general, a crowd ncludes multple agents, whch belong to dfferent groups n the crowd. In the current model, each agent can only belong to one group. As a result, a crowd s composed form dfferent groups and each group s composed from dfferent agents. Two specal cases of ths structure are: 1) each group only has one agent and there s no nter-group relatonshp ths s the same case as no group structure s consdered; 2) the whole crowd s a sngle group. A group has a number of agents, each of whch has a unque ID. The total number of agents n the group denotes the group sze. Dfferent groups can have dfferent group szes. We defne that each group has one and only one group leader. The rest of the agents n the group are group members. The group leader s consdered as a specal agent n the group because ths s the only agent who could be nfluenced by agents of other groups due to nter-group relatonshps (see descrpton below). A group member can only be nfluenced by other agents of ts same group. In our framework, two matrxes are used to descrbe the ntra-group structure and nter-group relatonshps. Wthn a group, dfferent agents nfluence each other. These agent-to-agent nfluencng relatonshps are defned by an ntra-group matrx. Besdes agent-to-agent nfluence, dfferent groups may also nfluence each other. The group-to-group relatonshps are defned by an nter-group matrx. These two nfluence matrxes: ntragroup matrx and nter-group matrx defne the most mportant nformaton that s needed to specfy the group structure n a crowd. Each agent represents an ndvdual n a pedestran crowd. Every tme step, t needs to compute a speed vector to govern ts movement. In our smulaton, each agent employs a behavor-based control model [8, 9]. Specfcally, each agent has a set of behavors, such as random move, avod and mantan group. Each of these behavors s excted by some sensory nput. These behavors compete wth each other usng a mutual nhbton mechansm. The wnner behavor controls the agent to carry out the assocated acton for that tme step. More detals of ths behavor-based model can be found n [4, 11]. We note that the mantan group behavor, whch s the man focus of ths paper, s one of the behavors of the agents. Based on the above descrpton, below s a specfcaton of the group-based crowd behavor smulaton system. The crowd s descrbed by <{Groups}, nter-group matrx>, where {Groups} specfy that the crowd contans a set of groups, each of whch has a confgurable group sze; ntergroup matrx s used to model the group-to-group nfluencng relatonshps. Each group can be descrbed as < {Agents}, ntra-group matrx>, where {Agents} s a set of ndvdual agents n the group; ntra-group matrx s used to model the agent-to-agent nfluencng relatonshps. Ether nter-group matrx or ntra-group matrx s a two dmensonal table (see detals n the next secton). Each agent s descrbed by <Role, GP, GD, Speed, GroupNo, ID, DesredDst, CenterDst, SdeDst, PerceptonModel, BehavorBasedModel, >, where Role={group leader, group members}; In the followng sectons, members refer to the group members. GP s the group poston the agent should move to; GD s the average movng drecton of local agents of the same group; Speed specfes the movng speed of the agent; GroupNo specfes whch group ths agent belongs to; ID specfes the order of ths agent n ts group, whch s assgned automatcally; DesredDst, CenterDst and SdeDst are three parameters n modelng the ntra-group structures (see detals n the next secton). PerceptonModel specfes the vsble dstance and range of ths agent. BehavorBasedModel specfes how an agent decdes ts movement. In ths work, each agent has three behavors: CasualMove, Avod and MantanGroup, whch are descrbed blow. CasualMove: movng to a randomly generated destnaton; Avod: avodng collson wth obstacles and other agents; MantanGroup: mantan the group based on the ntragroup structure and the nter-group relatonshp. The ntra-group structure specfes how agents n the group follow each other durng the movement. The nter-group relatonshp specfes how a group leader follows other groups durng a specfc scenaro,.e. emergency stuaton. IV. MODELING THE GROUP BEHAVIOR Each agent s MantanGroup behavor s composed from two aspects of movements: Aggregaton and Followng. They allow the agent to mantan the desred ntra-group structures and nter-group relatonshps. Aggregaton means the agent moves towards other agents of the same group. For a group member, Followng ndcates that the member heads towards the average movement drecton of local agents whch belong to the same group; whle for a group leader, Followng means that the leader follows an agent from another group, to mantan the nter-group relatonshp. Two speed vectors, aggregaton vector and followng vector, are used to represent these two aspects of movements. The sum of these two speed vectors gves the movement drecton of the agent. As wll be shown later, these two vectors can be expressed by the two propertes GP and GD, whch are calculated from the local agents n an agent s percepton range. Next we descrbe the percepton model of each agent, and then show how to calculate GP, GD, and the aggregaton vector and followng vector. A. Percepton Model The percepton model specfes an ellptcal area each agent can perceve, as shown n Fg. 1. The current movng

3 drecton of the agent s ndcated by the arrow labeled wth Drecton. Dst1 and Dst2 represent the maxmum front and sde dstance for vsblty respectvely. Angle ndcates the maxmum vsblty range the agent can detect. Each agent s equpped wth ths percepton model whch s used to detect local (neghborhood) agents. Fg. 1 The Percepton Model. B. Modelng ntra-group structures B1. Intra-group Matrx Each group has an ntra-group matrx whch s a two dmensonal table, where each element s a real number n [0.0, 1.0], whch specfes how much an agent s movement wll be nfluenced by other agents due to the ntra-group structure. 0.0 means that row agent wll not be nfluenced by the column agent (n other words, the column agent has no nfluence to the row agent s movement). 1.0 ndcates that the row agent wll be fully nfluenced by the column agent. Table I shows a sample ntra-group matrx for a group wth three agents wth ID 0, 1, and 2. By default, the frst agent (Agent_0) s the leader n the group. As can be seen from Table I, Agent_1 s nfluenced by Agent_0, and Agent_2 s nfluenced by Agent_1, and Agent_0 (the leader) s not nfluenced by other agents. In other words, the thrd agent follows the second one, whch n turn follows the frst one (the leader). As wll be dscussed later, ths table represents a lnear group structure. TABLE I A SAMPLE INTRA-GROUP MATRIX ID Agent_0 Agent_1 Agent_2 ID Agent_0 N/A Agent_1 1.0 N/A 0.0 Agent_ N/A Besdes the ntra-group matrx, three other parameters are used to descrbe how far (or how close) agents can stay away from each other wthn the same group: SdeDst, CenterDst, and DesredDst SdeDst s the maxmum perpendcular dstance (from the current computng agent to the predecessor s movng drecton), whch the current computng agent can stay away from. CenterDst s the maxmum allowed Eucldan dstance from the current computng agent to the predecessor s poston. DesredDst represents the desred dstance from the current computng agent to the predecessor that the current computng agent wants to mantan. B2. Calculaton of GP and GD Remember that GP s the group poston an agent should move to and GD s the average movng drecton of local agents of the same group. Equaton (1) and (2) show how GP and GD are calculated based on the ntra-group matrx and the poston and speed vector of other agents. Here suppose the ntra-group matrx s labeled wth I (, j) where, j s ID of agent and j. N s the total number of local agents that are n the percepton range (see the percepton model) of agent. Note that only those agents that belong to the same group of agent s counted. CurrentPoston j and SpeedVectorj are the current poston and speed vector of agent j. GP = ( GD = N1 j= 1 N1 j= 1 I (, j)* CurrentPos ton SpeedVector / N j j ) / N (1) (2) For agent, the aggregaton drecton s the drecton from the current poston of agent to GP. If agent s not the group leader, the followng drecton s the drecton ndcated by GD. Otherwse, t s the drecton to the agent from other groups (see descrpton below). Note that (1) apples to both group members and group leaders. However, for the group leader, calculaton of the GD wll be based on nter-group relatonshps. Ths s descrbed n the next secton. C. Modelng nter-group relatonshps C1. Inter-group Matrx Lke the ntra-group matrx, the nter-group matrx s also a two dmensonal table, where each element s a real number n [0.0, 1.0], whch specfes how much a group (specfcally the group leader of that group) wll be nfluenced by agents from other groups. 0.0 means the row group wll not be nfluenced by the column group even when the two groups are close to each other. 1.0 ndcates the row group wll be fully nfluenced by the column group f the two groups are close to each other. Table II shows a sample nter-group matrx for a crowd ncludng four groups wth GroupNo 0, 1, 2 or 3. As can be seen, ths table ndcates all groups can fully nfluence each other. TABLE II A SAMPLE INTER-GROUP MATRIX GroupNo GroupNo Group_0 Group_1 Group_2 Group_3 Group_0 N/A Group_1 1.0 N/A Group_ N/A 1.0 Group_ N/A

4 C2. Calculaton of GD for the Leader As mentoned before, the leader of a group s a specal agent because t wll be nfluenced by agents of other groups. In partcular, the calculaton of the GD varable of the leader s dfferent from that of group members (whch s descrbed n secton B.2). Accordng to Festnger s Socal Comparson Theory [3], n ths work the leader wll follow the agent wth the greatest smlarty value whch s decded by the Eucldan dstance and the nter-group matrx. Specfcally, suppose the element of the nter-group matrx s labeled as E(G(), G(j)), where G(), G(j) s the group number of agent and j respectvely. Suppose agent s a group leader. The procedure for agent to fnd an agent(of other groups) wth the greatest smlarty s shown n Fg. 2. procedure Fnd_Most_Smlar_Agent(Leader ) 1 AgentToFollower Ø; 2 Smlarty 0.0; 3 Temp 0.0; 4 AgentLst all agents that are n the percepton range; 5 for each agent a n AgentLst 6 f a.groupno.groupno and a.destdr =.DestDr 7 Dstance EucldanDstanceBetween(a, ); 8 Temp E(.GroupNo, a.groupno)*100/dstance; 9 f Temp > Smlarty 10 Smlarty Temp; 11 AgentToFollower a; 12 end for; 13 return AgentToFollower; end Fnd Most Smlar Agent. Fg. 2 Pseudo-code of fndng the most smlar agent. DestDr s a property of agents whch ndcates whether an agent moves from east to west or vce versa. The procedure shows that only local agents who belong to the dfferent group (but have the same DestDr) are consdered as canddates. Leader selects the one wth the greatest smlarty value to follow. If a vald AgentToFollower (not Ø) s found, the followng drecton GD for leader s the drecton to AgentToFollower. Otherwse, leader wll not follow any agent from other groups. D. Calculaton of the followng and aggregaton vectors Once the value of GP and GD of an agent s calculated, we can calculate the followng and aggregaton vector for that agent, whch s shown n Fg. 3. Fg. 3 Bref descrpton of two vectors. The black crcle denotes the group poston GPs agent s should move to. sd s the current sde dstance and cd s the current center dstance, from agent s to GP s. v1 and v2 are followng vector and aggregaton vector respectvely. Both vectors are computed through (3). v r = factor* < myspeed* cos( a), myspeed*sn( a) > (3) where myspeed s the speed of agent s. Suppose v r represents the followng vector v1, a s the drecton ndcated by GD s. If agent s s a group leader, factor s computed through (4), where E s E(s.GroupNo,AgentToFollower.GroupNo), and dst s the dstance from agent s to AgentToFollower. factor = E * 20 * DesredDs t / dst Otherwse, factor s 1.0. Whle f suppose v r represents the aggregaton vector v2, a s the drecton from the poston of agent s to GP s. And factor s computed as follows, If cd > CenterDst, factor= cd/centerdst. Otherwse f sd > SdeDst, factor= sd/sdedst. Thus, for agent s, t wll try to move towards GPs to keep wthn DesredDst (not shown n Fg. 3), as well as follow the drecton GD s. In ths way, agent s can mantan the ntragroup structure, as well as the nter-group relatonshp (f agent s s a group leader). V. THE BEHAVIOR MODELS As mentoned before, each agent employs a behavor-based control model [8, 9] and has three behavors. In ths secton, the motvaton of each behavor wll be descrbed, followed by the actons the behavor wll perform. Here, the detal mplementaton wll be skpped for smplcty. Also, the consdered default movng speed, 0.225, s same among all agents and kept unchanged durng the smulaton. (4) Behavor: Casual Move Ths behavor s used to smulate the random movement of each agent. The movng path s the shortest path from the orgn to the destnaton, computed through the Djkast algorthm. And when a specfc destnaton s reached, the

5 agent wll move to another destnaton whch s generated randomly. Exctaton: Ex = 0.6. Acton: If the agent s not at the destnaton area, t walks towards the destnaton accordng to the shortest path. Otherwse f t reaches ts destnaton, t wll move to a new destnaton that s randomly generated. Behavor: AvodObstacle Ths behavor s used to smulate the obstacle avodance n the movement. When an agent s wthn a predefned mnmum dstance from the nearest neghbor agent/obstacle, t wll stay away from t. Exctaton: If the object to be avoded s an obstacle or the agents of the same group, Ex = exp( ( d 9.0) / 3). Otherwse, Ex = exp( ( d 13.5) / 3). If (Ex > 1) Ex = 1. Here d s the dstance from the computng agent to the avodng object. The exponental functon ndcates that as d decreases, the more lkely ths behavor wll be excted. Acton: If the computng agent s n the left sde of the avodng object, t wll turn rght not exceedng 60 degrees. Otherwse, t wll turn left smlarly. In ths process, a basc collson predcton subroutne wll be used to predct f the current computng agent wll collde wth other agents once the turn s fnshed. If the subroutne returns true, the computng agent wll try another tme (the degree of turnng n ths case s 10 degrees less than the angle of the prevous step). If t stll cannot turn, t wll wat at ts current poston. Behavor: MantanGroup Ths behavor mplements the ntra-group structures and the nter-group relatonshp durng the movement. Exctaton: For group members, Ex= exp(( Dst( mypos, GP ) DesredDst) / 3).Whle for group leaders, the exctaton s Ex= max(exp(( Dst( mypos, GP ) DesredDst) / 3), exp( ( Dst( mypos, GP ) 20 * DesredDst) / 3)) (Ex>1) Ex=1. Dst s used to calculate the Eucldan dstance from agent to GP. The exponental functon ndcates that as d decreases, the more lkely ths behavor wll be excted. Acton: GP, GD, and the followng/aggregaton vector are computed on bass of the specfc group structure and nter-group relatonshp, followed by applyng the Parallelogram Law on these two speed vectors to calculate the fnal movng drecton, towards whch the computng agent moves wth the predefned speed.. If under the specfed parameters. We consder two typcal group structures: a lnear structure and a clustered structure. For each structure, we also show how nter-group relatonshps wll affect the overall crowd behavor. In the lnear structure, agents of the same group move n a lne formaton. Each group member follows a predefned predecessor. The ntra-group matrx I s defned n (5), whch ndcates that member wll follow the agent j wth an ID whch s one less than the ID of member. 1.0,! = 0 and j = 1 I (, j) = (5) 0.0, Otherwse In the clustered structure, agents of the same group move n a cluster formaton. Each group member moves closes to ts group center (ndcated by GP ) n the movement. The ntragroup matrx I s defned n (6), whch ndcates that each member wll move close to the center of all group members. 1.0,! = 0 I (, j) = (6) 0.0, Otherwse In both structures, the group leader fnds the path and moves forward. To show the effect of dfferent nter-group relatonshps, for each structure we consder two types of nter-group relatonshps: one wth all elements n the ntergroup matrx beng 1.0 and the other wth elements beng 0.0. Table III shows the crowd behavor smulaton results based on the two group structures. The crowd contans 20 groups, each of whch has 5 agents. Inter-group matrx E=1.0 (or 0.0) ndcates that all elements of E s 1.0 (0.0). Table III clearly shows how the crowd behavour s affected by the ntra-group matrx I and nter-group matrx E. By settng the values of I, dfferent group structures can be defned and result n dfferent group formatons (such as lnear formaton and cluster formaton). By settng the values of E, dfferent nter-group relatonshps can be defned. As shown n Table III, when E=1.0, the crowd moves n a more compact way than when E=0.0 due to the group-to-group nfluence. Ths capablty of ncorporatng dfferent group structures n a unformed framework (as defned by I and E) s desrable for studyng dfferent groups structures n crowd behavours. TABLE III TWO SAMPLE INTRA-GROUP STRUCTURES Structure E Screenshots Lnear 0.0 VI. DEMONSTRATION OF TWO SPECIFIC GROUP STRUCTURES Ths secton demonstrates our crowd model. It shows whether the model can produce the desred group structures

6 1.0 Clustered 0.0 the second fgure shows the lane formaton of ndvdual pedestrans, and 7 lanes are formed. The thrd and fourth fgures show the lane formaton of grouped pedestrans (the group sze s 4 and 10, where 5 and 3 lanes are formed, respectvely). Note that agents belongng to the same lane move n the same drecton (but may not necessarly n the same lne). For example, n the forth fgure n Fg. 4, there are three lanes: a top lane and a bottom lane movng towards left, and a mddle lane movng towards rght. In general, the number of lanes can be counted as the number of alternatng drectons of labels. 1.0 VII. EXPERIMENTS AND ANALYSIS Ths secton shows another experment to further test the effects of group structures on the pedestran crowd. Specfcally, ths experment studes lane formaton (see [14] for detals), whch explores the relatonshp between the number of formed lanes and the wdth of the hallway as well as the group sze. In the experment, the crowd has 20 groups, each of whch s modeled under the developed lnear group structure (wthout consderng the nter-group relatonshp) shown n the last secton. The crowd s stuated at a hallway (whose length s 490), where 10 groups move from east to west and the other 10 groups move from west to east. The ntal poston of each agent s generated randomly. The default movng speed for all agents s Ths experment evaluates whether our crowd model can reproduce the phenomena that, as the lane wdth ncreases, the number of lanes formed by the crowd s also lnearly ncreasng [1]. Also ntutvely, f group structure exsts, the number of lanes should be less than the case that no group structure exsts and contnuously decreasng wth the ncreasng group sze. Generally, the number of lanes wll decrease snce agents are grouped together and each group may follow other groups. Ths experment wll evaluate whether our crowd model can account for ths observaton. Fg. 4 shows one specfc experment envronment (lane wdth s 100) for three dfferent cases, ndvduals, groups wth the sze 4 and groups wth the sze 10. Each agent s labeled wth a number whch s the dentty of the agent. The top fgure shows the ntal poston of each agent. The bottom fgures show the undsturbed lane structures after about fve hundred/thousand smulaton steps. From the top to bottom, Fg. 4 Bdrectonal pedestran movement. Fg. 5 shows the relatonshp between the number of formed lanes (the Y-axs) and the wdth of the hallway (the X- axs). Each data pont s averaged over 10 trals for each wdth. The top curve shows the relatonshp when the crowd contans no group structures. The graph shows that as the wdth ncreases, the number of lanes s also ncreasng almost lnearly. And the bottom curvlnear lnes show the relatonshp when the crowd contans a set of groups. It shows that the number of lanes s less than that of the crowd wth no groups, whch ndcates an mproved flow n ths case. Here we also see that as the group sze ncreases, the number of lanes deceases. Ths experment shows that our crowd model can account for the expected observatons. And nterestngly, f the crowd only contans ndvdual pedestrans (n another word, no group exsts), the number of lanes s ncreasng almost

7 lnearly when the lane wdth s ncreasng. Thus, t s consstent wth Helbng s experments n [1]. Fg. 5 Relatonshp between the number of formed lanes and the wdth of the hallway. [8] X. Hu, Context-Dependent Adaptablty n Crowd Behavor Smulaton, Proc. The 2006 IEEE Internatonal Conference on Informaton Reuse and Integraton (IRI 2006), 2006 [9] F. Qu, X. Hu, BehavorSm: A Learnng Envronment for Behavor-based Agent, Proc. The 10th Internatonal Conference on the SIMULATN OF ADAPTIVE BEHAVIOR (SAB'08), [10] X. Pan, C. S. Han, K. Dauber and K. H. Law. "A Mult-agent Based Framework for Smulatng Human and Socal Behavors durng Emergency Evacuatons," Socal Intellgence Desgn, Stanford Unversty, Stanford, USA, March 24-26, [11] C. Loscos, D. Marchal, A. Meyer, Intutve Crowd Behavour n Dense Urban Envronments usng Local Laws, Proc. Theory and Practce of Computer Graphcs 2003, IEEE Computer Socety, [12] S. R. Musse and D. Thalmann, A Model of Human Crowd Behavor: Group Inter-Relatonshp and Collson Detecton Analyss, Computer Anmaton and Smulatons '97, Proc. Eurographcs workshop, Budapest, Sprnger Verlag, Wen 1997, pp [13] K.Yamor.Gong wth the flow:mcro-macro dynamcs n the macrobehavoral patterns of pedestran crowds. Psychologcal Revew, 105(3): , [14] Daamen, W., and Hoogendoorn, S. P Expermental research of pedestran walkng behavor. Transportaton Research Record VIII. CONCLUSIONS AND FUTURE WORK Group structure s an mportant characterstc of socal crowd. Our work provdes a unformed framework for modelng varous ntra-group structures and the nter-group relatonshp through few model parameters. An agent-based crowd behavor smulaton system s developed where each agent s group behavor s modeled usng the framework. Experment results of crowd behavor smulatons based on two dfferent group structures, a clustered structure and a lnear structure, are developed. The conducted experments (testng the lnear group structure) show that the model s consstent wth an exstng work and other observatons, and the group behavor of the crowd can be controlled through the model parameters. Future work ncludes an mproved model whch consders dfferent group propertes and other ndvdual personaltes. Also comprehensve experments wll be conducted based on the mproved model. REFERENCES [1] D. Helbng, I. J. Farkás, P. Molnár, and T. Vcsek (2002) Smulaton of pedestran crowds n normal and evacuaton stuatons. Pages n: M. Schreckenberg and S. D. Sharma (eds.) Pedestran and Evacuaton Dynamcs (Sprnger, Berln). [2] D.J. Kaup,etc. Crowd Dynamcs Smulaton Research. Proceedngs: 16th Conference on Behavor Representaton n Modelng and Smulaton (BRIMS), [3] Natale Frdman and Gal A. Kamnka. Towards a Cogntve Model of Crowd Behavor Based on Socal Comparson Theory. In Proceedngs of the Twenty-Second Natonal Conference on Artfcal Intellgence (AAAI-07), [4] Low, Davd J Statstcal Physcs: Followng the Crowd. Nature, vol. 407, [5] Qngge JI, Can GAO. Smulatng Crowd Evacuaton wth a Leader- Follower Model. IJCSES Internatonal Journal of Computer Scences and Engneerng Systems, Vol.1, No.4, October [6] Gabrel Santos and Bengno E. Agurre. A Crtcal Revew of Emergency Evacuaton Smulaton Models. NIST Workshop on Buldng Occupant Movement durng Fre Emergences, June 9-10, [7] Adrana Braun, Soraa R. Musse, etc. Modelng Indvdual Behavors n Crowd Smulaton. Proceedngs of the 16th Internatonal Conference on Computer Anmaton and Socal Agents (CASA.03)