CS 231. Crowd Simulation. Outline. Introduction to Crowd Simulation. Flocking Social Forces 2D Cellular Automaton Continuum Crowds

Transcription

1 CS 231 Crowd Simulation Outline Introduction to Crowd Simulation Fields of Study & Applications Visualization vs. Realism Microscopic vs. Macroscopic Flocking Social Forces 2D Cellular Automaton Continuum Crowds 1

2 Introduction Crowd simulation attempts to model the motions of objects within an environment. The topic has been researched from several different areas of study: Entertainment Civil Engineering Psychology Computer Science Applications of Crowd Simulation Entertainment and Visual Effects Goal: Create a visually realistic model of crowds for use in movies, television, and video games. Architecture and Civil Engineering Goal: Study the flow of people/vehicles through environments. Analyze road network efficiency. Building evacuation characteristics. Psychology Goal: Validate behavior models of the human mind under different environmental conditions (ex. panic). Computer Science Goal: Help out in any of the three areas above with algorithmic know- how. Study AI models and behavior. 2

3 Visualization vs. Realism The various crowd simulation techniques can generally be divided into two categories: Visualization Entertainment and Visual Effects Realism Architecture and Civil Engineering Psychology Techniques have begun to merge over the last decade. Crowd Visualization Goal: Create a visually realistic model of crowds. Simulation does not have to be physically accurate. Techniques may have to integrate with motion captured animations. Algorithms frequently exploit Level-of of-detail. Movies and television applications can afford offline processing as long as simulation time is reasonable. Video games have real-time requirements. 3

4 Crowd Visualization Disney s Lion King (1994). Lord of the Rings Trilogy ( ). Using the tool Massive. Crowd Realism Goal: Study the flow of people/vehicles through environments. Must be as physically accurate as possible. Studies constantly compare simulation results with empirical data. Simple visualizations such as a single point per object. 4

5 Crowd Realism Simulation of a ship evacuation, using the tool EXODUS. Paths of pedestrian exploration driven by space syntax architectural concepts. Microscopic vs. Macroscopic Simulations techniques can also be categorized as microscopic vs. macroscopic. Microscopic techniques simulate the individual object. Crowd behavior is an emergent property of the microscopic-level algorithms driving the simulation. Macroscopic techniques simulate groups of objects. Example: Treating a transit system as a flow problem.. 5

6 Flocking Flocking technique introduced by Craig W. Reynolds and his Boids. Techniques to simulate animal flocking, herds, and schooling. Sets the stage for further study into crowd simulation. Each agent in the simulation is called a boid. Big Idea: Complex crowd behaviors can be achieved through individual agents following simple rules. Flocking Geometry in Flight Each boid has its own local coordinate system: X axis is left/right Y axis is up/down Z axis is ahead/back Rotations too: Rotation about X is pitch Rotation about Y is yaw Rotation about Z is roll 6

7 Flocking Geometry in Flight For realism in the simulation Momentum is conserved. Speed damping achieved by setting a maximum speed and acceleration. Gravity is used for banking of boids. Banking orientation a function of path curvature and direction of gravity. Not physically realistic. Does not capture that traveling up is harder than traveling down. Flocking Steering Behaviors Flocking is closely related to particle systems. Forces between particles cause motion. Interactions take place within a local neighborhood of each Boid. Three basic steering behaviors: Separation Alignment Cohesion Each steering behavior directs thrust in a desired direction. 7

8 Flocking Steering Behaviors Separation Boids steer to avoid crowding local flockmates. Collision avoidance. Keeps boids a realistic distance apart. Flocking Steering Behaviors Alignment (AKA Velocity Matching) Boids attempt to match the velocity of their neighbors. Complements separation. Causes boids to move in the same general direction. 8

9 Flocking Steering Behaviors Cohesion Boids steer to move towards the average position of local flockmates. Stay together in a local flock. Allows flocks to both merge and bifurcate. Flocking Boid Brain Each steering behavior may yield a different thrust vector. The Boid Brain combines, prioritizes, and arbitrates between potentially conflicting urges. 9

10 Flocking Boid Brain Averaging (and weighted averaging) of steering vectors works but can yield poor behavior in cases where steering urges are in opposite directions. Hesitation or indecision can lead to collisions with obstacles. INSTEAD: Steering vectors are processed in order of priority with a weighted average. Priorities may be reassigned dynamically. Flocking Boid Brain Better Solution: A fixed amount of acceleration is available to each boid each simulation iteration. Steering vectors are processed in order of priority with a weighted average. Priorities may be reassigned dynamically. Steering vectors are processed until all acceleration credits have been used up. The last processed vector is attenuated to keep within acceleration credit limits. 10

11 Flocking Simulated Perception Perception is limited to a local field of view. Local neighborhood is a spherical zone of sensitivity centered around a boid s origin. Sensitivity is weighted with the inverse of distance square, 1/r 2. Linear weighting yields unrealistic spring- like animations. Additional parameters can be used to simulated bias: Extra weighting in forward direction to increase awareness of what is ahead. Flocking Simulated Perception Implications of local perception: Flocks of boids are allowed to bifurcate as groups of boids may break away from others and still satisfy the cohesion steering behavior. Global cohesion/centering models were used early in Boids development. Generated unusual effects causing all members of a scattered flock to simultaneously converge towards the flock s centroid. 11

12 Video Break 12

13 Social Forces Developed by Dirk Helbing and Peter Molnar in 1995 with several advancements since A frequently referenced piece of work Widely successful because it elegantly reproduces many common features observed in pedestrian movement Social Forces Social Forces are not exerted by the environment on a pedestrian s s body, but rather a quantity that describes the motivation to act: Respect personal space Follow others at a safe distance Avoid getting too close to walls and obstacles Can be thought of as a developed model of flocking for humans as pedestrians follow a set of social rules that guide their movement 13

14 Social Forces One equation describes all forces acting on an individual agent: Desired Motion Obstacle Avoidance Social Force Attractive Forces Social Forces Acceleration towards a goal. Given current location, desired location, current speed, and desired speed Acceleration towards the destination is given by: Where e α is a vector towards the destination The τ α term is a relaxation value that controls timing 14

15 Social Forces Pedestrians will keep a certain distance from others that depends upon the pedestrian density and desired speed Implemented as a repulsive force with equipotential lines having the form of an ellipse that is in the direction of motion Elliptical range allows for an agent to leave room for their own subsequent steps Social Forces Respect the personal space of others Pedestrians have a limited cone of vision, so forces from agents outside an agent s s immediate attention should be attenuated. Inter-agent forces to not cross between obstacles. For example, agents on opposite sides of a wall should not affect each other. 15

16 Social Forces Avoid colliding with obstacles. Pedestrians keep a certain distance from buildings, walls, obstacles, etc. This behavior can be described by repulse force with: Where monotonic decreasing potential. The r αb denotes the distance between the agent and the nearest portion of the obstacle. Social Forces Social Forces also allows attractive forces Examples: Friends Street Performers Window Displays The equation for these forces has the same form as the inter-agent repulsive forces This force is also attenuated with a field of attention 16

17 Social Forces Final Social Force equation The social force model is now defined by: The fluctuation term takes into account random variations in behavior which enhances realism. Social Forces Simulations Two pedestrian phenomena are observed with social forces model: Lane Formation Door Oscillation 17

18 Social Forces Simulations Lane Formation The empty circles and full circles have desired direction of motion in opposite directions. Circle diameter reflects actual velocity. Social Forces Simulations Door Oscillation If one pedestrian has been able to pass a narrow door, other pedestrians with the same desired walking direction can follow easily. Others wait. The door can be captured as pressure on the opposite side builds up, allowing pedestrians in the other direction to pass. 18

19 Social Forces Additions Several additions to Social Forces appear Example, evacuation and panic: People move or try to move considerably faster than normal. Individuals start pushing each other (violating repulsive forces from earlier work). Moving becomes uncoordinated. Arching and clogging appears at exits. Jams build up. Physical interactions in jams can build up to dangerous pressures, s, injuring people and breaking of obstacles. Injured people become obstacles to the rest of the crowd. People show a tendency towards mass behavior. Alternative exits are often overlooked or not efficiently used. Social Forces (II) Equations Revised inter-agent force equation is given by: Body force counteracts body compression. k is a large constant. Sliding friction force impedes relative tangential motion if pedestrians come too close. Κ is another large constant. Inspired by granular interactions. 19

20 Social Forces (II) Simulations Arching/Clogging at exits: Corridor widening can lead to bottlenecks: Social Forces Results Below shows the effects of fire, which is said to have a socio-psychological strength 10x greater than a normal wall. 20

21 Social Forces Results Breaking of a corridor doorway into two helps in lane formation and avoid door clogging and oscillation. Social Forces Results Placing a column in front of an exit can alleviates problems due to arching by reducing pressure. More efficient egress. Fewer or no injuries. 21

22 2D Cellular Automata Cellular automaton (plural: cellular automata) A regular grid of cells,, each in one of a finite number of states.. Time is also discrete, updates based on neighbors form last timestep. Neighbors are a selection of cells relative to the specified cell, and do not change (though the cell itself may be in its neighborhood, it is not usually considered a neighbor). 22

23 2D Cellular Automata 2D CA system for modeling pedestrian crowds: Goal to replicate the phenomena generated by Social Forces. Lane formation Door oscillations Arching and clogging By replicating these phenomena, they hope to prove CA is a valid approach to pedestrian modeling. (Historical Note: Most cellular automata solutions are 1D and in the domain of traffic analysis.) 2D Cellular Automata The 2D CA pedestrian model presented here breaks an environment (floor plan) down into a grid of cells. Each cell may be occupied by one particle (agent) or by an obstacle. Particles move through the environment by moving to adjacent unoccupied cells. 23

24 2D Cellular Automata Particles may move in 1 of 9 directions with probabilities denoted by M ij. (Or one is to stay put.) Each particle may have its own local probability grid. If the target cell is occupied, the particle stays put. 2D Cellular Automata Lane Formation Two different species of pedestrians traveling in different directions across the screen. 24

25 2D Cellular Automata Arching/Clogging Pedestrians exit the room. Arching is clearly visible around the exit. 2D Cellular Automata A full simulation: Lecture hall evacuation. 25

26 Continuum Crowds Treuille et al. 26

27 Continuum Crowds - motivation Most previous methods are agent-based This is a (macroscopic) continuum approach 27

28 Goal G Speed f Discomfort g Cost C Potential Ф Goal G G 28

29 Speed - Topography Height Discomfort 29

30 Cost Assumption: People always choose the path P to the goal which minimizes: distance time discomfort Potential Goal 30

31 Potential Group 1 Group 2 Group 3 31

32 32 Cost Cost C Potential Potential Ф Goal Goal G Discomfort Discomfort g Speed Speed f Cost Cost C Potential Potential Ф Goal Goal G Discomfort Discomfort g Speed Speed f Cost Cost C Potential Potential Ф Goal Goal G Discomfort Discomfort g Speed Speed f Cost Cost C Potential Potential Ф Goal Goal G Discomfort Discomfort g Speed Speed f Cost Cost C Potential Potential Ф Goal Goal G Discomfort Discomfort g Speed Speed f Cost Cost C Potential Potential Ф Goal Goal G Discomfort Discomfort g Speed Speed f Results Results

33 Video Break Conclusion Path planning for large groups of people at interactive rates Unify overall path planning and collision avoidance Captures emergent phenomena Model adaptable to many situations 33

34 LOD in Crowds 34

35 LOD in Crowds While not explicitly related to simulation, fast rendering allows for more time to be spent performing simulation. There are several techniques that are commonly used to speed up crowd rendering. LOD in Crowds Geometric & Animation LOD Reduce the number of polygons in the model at different LOD steps. At a certain LOD, stop animating bones of figure and use static-keyframe meshes instead. May continue to reduce polygons in the model. At the farthest LOD, stop using static meshes and use 2D billboards. May be a simple sprite animation. Or more complex polyposter [Kavan]] which is a collection of 2D deformable textured polygons. 35

36 Geometric LOD Geometric LOD A 2D billboard from different views can be generated dynamically. Billboards can be used to dramatically increase crowd size. 36

37 Geometric LOD Polyposter approximation of a full mesh animation. 37

38 Crowd Interfaces Crowds brush Video Break 38