Real-Time Crowd Simulation: A Review

Transcription

1 Real-Time Crowd Simulation: A Review Richard Leggett December 2004 Abstract This paper presents a review of current research in the area of real-time crowd simulation. Crowd simulation has many diverse uses, for example in safety modelling, entertainment software, architecture and urban modelling applications. We describe three main approaches to the problem - fluid-based, cellular automata and particle-based, concentrating on the latter. Finally, we describe CrowdSim, a simple but effective implementation of some of the techniques. 1 Introduction In this paper, we present a review of research into the topic of real-time crowd simulation. We also describe the implementation of CrowdSim, a 2-dimensional simulation based upon some of the ideas presented in the paper. We define a crowd to be a collection of pedestrians occupying a common area and with varying degrees of interaction with each other. It is fair to ask the question of why we would want to model crowds. The following are some common reasons: Safety simulation - crowd simulation has been successfully used to model the flow of pedestrians in emergency situations, for example exiting a building on fire ([Helbing et al. 2000]). Architectural simulation - crowd models can be used to test the suitability of building designs and to enhance the realism of pre-construction models. Urban modelling - realistic pedestrians can add to the realism of virtual tourism ([Ulicny and Thalmann 2002]) and can be an aid to town planning. Entertainment software - many modern computer games create virtual worlds for players to inhabit and these are enhanced by the realistic simulation of pedestrians. It s an interesting problem - apart from anything else, the modelling of pedestrians is an interesting mathematical problem. The topic is a large one and it s therefore been necessary to restrict detail in some areas. In particular, we have chosen to focus less on visualisation, as much of the work is equally applicable in 2-dimensional applications as it is in 1

2 three dimensions. Whilst we ve aimed to take a general view, the focus of our interest is the modelling of pedestrians in urban modelling applications, so this will inevitably restrict the detail given to some areas. A review of the literature demonstrates three broad approaches to the simulation of crowds: 1. Fluids - it can be observed that the motion of crowds at a macroscopic level is similar to the flow of fluids. Successful attempts have been made to model pedestrians using the physical laws of fluid dynamics. 2. Cellular automata - discrete, dynamic, systems, which model a lattice of cells and base the state of a cell on the states of the immediately surrounding cells. 3. Particles - probably the majority of the work described in the literature takes this approach, often known as the atomic or particulate approach. Under this scheme, each pedestrian is considered as an individual entity and the interactions between it and the other pedestrians are individually modelled according to physical or social laws. We can think of crowd simulation at both a macroscopic and a microscopic level. At the macroscopic level, we are interested in seeing a mass of people move with a realistic motion, without necessarily being concerned by the movement of an individual. However, when we look at the microscopic level, we are indeed concerned that each individual pedestrian moves in a convincing manner and we may wish to focus on one pedestrian and watch its movement. Depending on the application of the simulation, we may be more or less interested in this microscopic level. As we have stated, our interest is focussed towards urban modelling and for these applications, realistic behaviour at a microscopic level is very much a requirement. Generalising, it is fair to say that fluid-based approaches work best on the macroscopic level. Of the other two approaches, the particle approach is the most popular technique and there is most research in this area. For these reasons, whilst we describe all three approaches, we will pay most attention to the particle approach. 2 Some Observations on Pedestrian Behaviour Before looking at solutions, we begin by noting some observations about the way real pedestrians move and the interactions between them. [Sung et al. 2004] make the point that crowds offer an anonymity. When we look at a crowd, we care about what is happening, not who is doing it. Therefore, the specific actions of individual pedestrians may appear relatively random, but the overall look of the crowd can still be convincing. This ties in with earlier comments on action at the macroscopic level. [Helbing et al. 2001] provide a useful summary of research into real pedestrian motion, mostly obtained from the analysis of video films. The main points are: 1. Pedestrians act automatically - they don t reflect on their strategy in every new situation. Behaviour is an optimised strategy which has been learned over time by trial and error. 2

3 2. Pedestrians show an aversion to taking detours or moving opposite to the desired walking direction (even if the direct route is crowded). 3. Pedestrians normally choose the fastest route to their next destination. 4. If alternative routes are the same length, a pedestrian will most likely choose the one that keeps them going straight ahead for as long as possible. Unless the alternative route is more attractive for other reasons - such as less noise, safer environment, less waiting etc. 5. Pedestrians prefer to walk at their own individual, most comfortable walking speed, so long as it is not necessary to go faster to reach the destination in time. 6. Pedestrians keep a certain distance from other pedestrians and from obstacles. The distance is smaller as the pedestrian hurries and as the crowd density increases. 7. Resting pedestrians are uniformly distributed over the available area if there are no acquaintances among the individuals. 8. Pedestrian density increases (and hence interpersonal distances decrease) around particularly attractive places. 9. Individuals who know each other form groups and these groups can behave as though they were a single entity. [Loscos et al. 2003] make the observation that only around half of pedestrians in any typical scene walk alone, the rest walk in groups of varying sizes. Group behaviour is therefore key to realistic simulations. [Musse et al. 1998] define three main laws for group behaviour: 1. Pedestrians in the same group walk at the same speed 2. Pedestrians in the same group follow the same goals 3. Pedestrians in the same group will wait for each other if one pedestrian is missing In keeping with the Helbing observations, Loscos et al. also note that when congestion occurs, people tend to create flow patterns by following the person in front. Pedestrians don t just walk indefinitely. Their journey usually starts in one building and ends in another, and along the way they may perform various actions. These actions might include window shopping, stopping to talk to another pedestrian or queueing for a bus. For true realism, we also need to model these kinds of behaviour. 3 Three Approaches 3.1 Pedestrians as Fluids Early work by [Henderson 1971] demonstrated that it was possible to model pedestrian flow using the Navier-Stokes equations. These are a set of equations that govern the motion of non-turbulent, Newtonian fluid dynamics. 3

4 Work by Dirk Helbing builds on Henderson s work and in [Helbing et al. 2001], he provides a summary of observations on the similarities between medium and high density pedestrian crowds and the motion of gases and fluids. Comparisons between pedestrian flow and granular flow (eg. sand through an egg timer) are also made. [Hughes 2003] is another example of recent work which models crowd flow according to fluid equations. The author describes crowds as thinking fluids and uses his work to model scenarios as diverse as the Battle of Agincourt and the annual Muslim Hajj. 3.2 Pedestrians as Cellular Automata Cellular automata are discrete dynamic systems, whose behaviour is characterised by local interactions. A CA is made up of a regular lattice of cells, each of which can have one of a finite number of states. In the traditional definition of a CA, each unit of time the state of each cell is re-calculated based on the application of a set of rules to neighbouring cells. The most famous example of this is John Conway s Game of Life [Gardner 1970], where complex organic-like growth patterns can be observed by the application of very simple rules. Extensions to the CA concept allow cells to be influenced not just by neighbouring cells, but by more remote cells also. Initially, these ideas were applied to traffic flow, but later to the more complex problem of pedestrian modelling. Some examples of cellular automata crowd work are [Blue and Adler 2000], [Dijkstra et al. 2000]. 3.3 Pedestrians as Particles The majority of pedestrian simulations take the particulate approach, sometimes called the atomic approach. Early influential work was that of Craig Reynolds [Reynolds 1987] who worked on simulations of flocks of birds, herds of land animals and schools of fish. Each particle, or boid, was implemented as an individual actor which navigates according to its own perception of the environment, the simulated laws of physics, and a simple set of behavioural patterns. Later work ([Reynolds 1999]) extends the concepts to the general idea of autonomous characters, with an emphasis on animation and games applications. [Bouvier et al. 1997] describe a generic particle model and apply it to both the problem of pedestrian simulation and to the apparently distinct problem of airbag deployment. They present software allowing the statistical simulation of the dynamic behaviour of a generic particle system. In their system, the particle system is defined in terms of: the particle types - mass, lifetime, diffusion properties, charge, drag, interactions with surfaces, visualisation parameters the particle sources (or generators) - size, geometry, rate and direction of emission the 3D geometry, including obstacles the evolution of particles within the system 4

5 [Helbing and Molnár 1998] introduce a Social force model for pedestrian dynamics. They suggest that the motion of pedestrians can be described as if they are subject to social forces which are a measure of the internal motivation of individuals to perform certain actions or movements. They describe three essential forces: 1. Acceleration - the velocity of the pedestrian varies over time, as it attempts to reach its optimum speed and as it avoids obstacles. 2. Repulsion - there is a repulsive force from other pedestrians and from obstacles and edges. 3. Attraction - pedestrians are sometimes attracted by other people (eg. friends, street artists) or by other objects (such as window displays). Putting these three forces together, Helbing produces an equation for a pedestrian s total motivation and combining this with a term to allow for fluctuations in behaviour, produces the social force model. He goes on to describe computer models based on the equations, which have been successful in demonstrating various observed phenomena, for example lane formation. In [Helbing et al. 2000], the social force model is applied to the simulation of building escape panic, with impressive results. [Thalmann et al. 1999] model virtual humans according to perception, emotion and behaviour. In each tick of the virtual clock, they model the perception of each virtual human (what they can see, what is happening to them etc.), they model the effect on the emotion and then finally this is translated into behaviour. [Ulicny and Thalmann 2001] build on the work to describe a rules system for individual pedestrians which determines their responses to various situations. An example rule would be: FOR ALL WHEN EVENT = in_danger_area AND ATTRIBUTE fear > 50% THEN BEHAVIOR FLEE [Sung et al. 2004] define a probabilistic model for pedestrians which allows them to move from one state to the next. These work in a similar manner to Finite State Machines, but the state graph and transition matrix are modified at run-time. 4 Deconstructing the Particle Approach In the previous section, we have described the general approaches used by a number of significant contributions to the field. In this section, we break down the particle approach into three broad tasks - decision making and movement, group behaviour and collision avoidance. 4.1 Decision making and movement [Loscos et al. 2003] use a 2-dimensional image map to represent a city layout and automatically assign goals to street corners, based on detection of pavementbuilding-pavement boundaries in the map. The connected goals form a graph 5

6 of the city. The pedestrians are assigned a starting position and a starting goal. When they reach a goal, they are assigned one of the adjacent goals as the next objective. Meanwhile, each pedestrian maintains a store of the last 3 goals visited, so that they don t repeatedly double-back on themselves. In the Loscos model, the flow of crowds also influences the movement of an individual pedestrian. Each time a pedestrian reaches a position on the grid, its direction is stored. This direction field fades over time, but if a new pedestrian reaches the position before it has faded, the direction field is taken into account by the new pedestrian. [Musse et al. 1998] use a similar goal-based approach to the Loscos model, though they have two types - interest points and action points. Interest points are points a pedestrian must pass through, while at action points, the pedestrian is required to perform some form of action, for example stopping. [Sung et al. 2004] use the Probabilistic Road Map as the basis for route selection, a method based upon Dijkstra s shortest path algorithm and commonly known for its use in IP routers. 4.2 Group behaviour [Musse and Thalmann 1997] concentrate on the interactions between groups of people within crowds, and define a rule-based system for the transfer of pedestrians from one group to another. Groups in the Loscos model are defined by a leader and by members. The leader makes all the decisions over direction and goals, with the members following. The members still perform collision detection and avoidance, but their behaviour is heavily influenced by the leader. [Braun et al. 2003] expand Helbing s social force model. In their model, each pedestrian is assigned a family identifier and an altruism level. These act as forces in the model to tend to make some of the pedestrians form groups with others. 4.3 Collision avoidance [Musse and Thalmann 1997] describe two methods of collision avoidance between pedestrians: Type 1: Using simple mathematical equations (the intersection of two lines and distance from two points), we determine future positions and predict a collision event. One of the pedestrians stops, allowing the other to pass. Type 2: The preferred option - instead of waiting, the pedestrian can predict the collision and change direction. However, sometimes, there may be insufficient time to modify direction, so we use type 1 instead. [Loscos et al. 2003] define three types of collision - frontal, following and perpendicular. They further define three collision distances - close, near and far. These factors, together with the behaviour of the other party (waiting or walking), and the pedestrian density (normal or congested) produce an action table for a pedestrian. Actions include varying the angle of the pedestrian s trajectory, it s speed, or stopping entirely. 6

7 Figure 1: CrowdSim running. [Feurtey 2000] introduces a method for collision detection based on projecting future movements onto a cone of (x, y, t) space. He defines a cost function that enables pedestrians to evaluate the cost of moving away from their current trajectory. However, the method is not yet scalable to large numbers of pedestrians. Collision avoidance of static objects, such as buildings, is easier. In 2- dimensions, a common approach is to use a collision map. This is the approach used by Loscos et al., where the authors check for a collision a number of tiles ahead in order to produce smoother avoidance movement. 5 CrowdSim In this section, we describe the design of CrowdSim, a 2-dimensional crowd model, which was designed to explore some of the ideas described in this paper. Figure 1 shows an image of CrowdSim running. It presents a top-down view of a network of city streets and represents individuals by triangles that point in the direction of travel. A GUI allows the simulation to be slowed or paused, pedestrian trails and trajectories to be highlighted, collisions to be highlighted and various other options. 5.1 Overall design The simulation was developed using the Java language and a UML class diagram is shown in figure 2. Each pedestrian is modelled by an instance of the Pedestrian class, whose attributes entirely describe the state, speed and intentions of the pedestrian. The plan of the city is described by a bitmap image, with specific colours used to mark buildings, pavement, road, pedestrian crossings and goals. This bitmap is processed before the simulation begins in order to identify goal positions, crossings and to hide information from the viewer. 7

8 Figure 2: UML diagram showing the class structure of CrowdSim. 5.2 Pedestrian movement The movement from one goal to another governs the basic trajectory of the pedestrians. When a pedestrian reaches its goal, a new goal is chosen from an internal map of goal links (Figure 3). The pedestrian also maintains a memory of previous goals and, where possible, the next goal is chosen so that it is different to all the memory goals. Each time a pedestrian selects a new goal, the angle of the new trajectory is calculated. This is used for collision analysis and for plotting the rotated pedestrian icon. However, individual movement of the pedestrian at each cycle of the simulation is governed by a simple version of the Bresenham straight-line algorithm ([Foley et al. 1994]). 5.3 Collision detection and avoidance Collisions can take place between pedestrians and the scenery (for example buildings) and between pedestrians and other pedestrians. In our definition, collision detection is concerned with behaviour once a collision has occurred, while collision avoidance is concerned with taking actions to ensure a collision doesn t happen in the future. In both cases, CrowdSim creates a temporary goal to direct a pedestrian away from a collision. Once the pedestrian reaches the temporary goal, it is then re-directed back to its original goal. Where a collision has actually occurred, CrowdSim s approach is to vary 8

9 Figure 3: Image showing goals (numbers) and links (lines). the colliding pedestrian s angle of movement by up to 90 degrees, creating a new temporary goal. In the case of collisions with buildings, this strategy tends to pay off. The same is also true of low density concentrations of pedestrians. However, if after a number of attempts, this strategy has not brought success, the pedestrian will stop and wait for a small amount of time. It will again attempt to find a new temporary goal. If this again fails, as can happen in cases of high congestion, the pedestrian will give up and move in the opposite direction. Avoidance behaviour is slightly more sophisticated. At each cycle of the simulation, every pedestrian checks to see if any of the other pedestrians are within a defined radius. For each pedestrian that is, its position over the next n cycles (with, typically, n=30 in our simulation) is calculated and compared with the calculated position of our test pedestrian. If the positions coincide, avoidance action is taken. The avoidance behaviour is dependent upon two factors - the type of collision and the distance from the collision point. As with the Loscos model ([Loscos et al. 2003]), we define three types of collision - frontal, following and perpendicular. And also like Loscos, we define three distances - close, near and far. However, we adopt a slightly simpler model, not considering the movement of the other pedestrian or the density of the crowd. Table 1 describes the actions taken in each situation. The type of collision is decided by the difference in the directional angle between the two pedestrians. If the first pedestrian s trajectory is within 30 degrees either side of the second, then it is considered to be a following collision. If the trajectory is between 150 and 210 degrees different (ie. 180 plus or minus 30 degrees), the collision is considered to be frontal. Anything that falls out of these ranges is considered perpendicular. 6 Conclusions This paper has presented an overview of the current state of crowd simulation research, highlighting the potential shown by particle-based approaches. Ap- 9

10 CollisionT ype Distance Action Front Far Fastest pedestrian takes avoiding action Front Near Fastest pedestrian takes avoiding action Slowest pedestrian slows down, or stops Front Close Fastest pedestrian takes avoiding action Slowest pedestrian stops Following Far Fastest pedestrian takes avoiding action Following Near Fastest pedestrian takes avoiding action and slows down Following Close Fastest pedestrian takes on the speed of the slower pedestrian Perpendicular Far Slowest pedestrian slows down Perpendicular Near Slowest pedestrian slows down Perpendicular Close Slowest pedestrian stops Table 1: CrowdSim collision avoidance actions plying some of these ideas, we have created a useful simulation based on some relatively simple rules. At low to medium pedestrian densities, the techniques used in CrowdSim can produce realistic crowd motion, with pedestrians moving at different speeds, following believable trails and taking sensible avoidance action. At higher densities, the motion of some pedestrians becomes less smooth and further work could be done to improve this. In particular, adopting a more complicated collision avoidance algorithm would improve the situation. Aside from the collision avoidance algorithm, more time would have enabled work on some other aspects of natural human interaction. Grouping of the pedestrians would improve realism, as would greater interaction with scenery - for example window shopping, bus stops and building entrances. References [Blue and Adler 2000] V. Blue, J. Adler, Cellular Automata Microsimulation of Bi-Directional Pedestrian Flows, Journal of the Transportation Research Board, 1678: , [Bouvier et al. 1997] E. Bouvier, E. Cohen, L. Najman, From Crowd Simulation to Airbag Deployment: Particle Systems, a New Paradigm of Simulation, J. Electronic Imaging, 6(1):94-107, [Braun et al. 2003] A. Braun, S. Musse, L. de Oliveira, B. Bodmann, Modeling Individual Behaviors in Crowd Simulation, Proc. of Computer Animation and Social Agents, , [Dijkstra et al. 2000] J. Dijkstra, H. Timmermans, A. Jessurun, A Multi-Agent Cellular Automata System for Visualising Simulated Pedestrian Acitivity, Proc. of the Fourth International Conference on Cellular Automata for Research and Industry, 29-36,

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