Simulating Crowds Simulating Dynamical Features of Escape Panic & Self-Organization Phenomena in Pedestrian Crowds Papers by Helbing

Why do we care? Easy to use when doing crowds For the layman animator For the layman animator Lots of goodies come for free Lots of goodies come for free Escape panic features Escape panic features Faster-is-slower effect Crowding around doorway Mass behavior Normal pedestrian traffic features Normal pedestrian traffic featuresLanes Waiting at doors Braking rules

How do we learn? Socio-psychological literature Reports in media Empirical investigations Engineering handbooks

What have we learned? People try to move faster than normal People begin pushing and interactions become physical Moving becomes uncoordinated Where does this matter most? Where does this matter most?

What have we learned? Arching and clogging occurs at exits Jams get larger Crowd pressures reach 4,450 N/m Enough to bend steel and break brick walls Enough to bend steel and break brick walls People fall and become obstacles Group mentality sets in and people follow others blindly Alternative exits are underutilized

We want to simulate all this… DynamicsPerception Reflexive actions Cognition Behaviors Behaviors What’s the important stuff to capture? How will we evaluate success?

Helbing’s basic model Generalized force model Pedestrians are like interacting molecules Pedestrians are like interacting molecules People have nominal (desired) velocities People have nominal (desired) velocities People have no other memory People have physical interactions and primitive reactive forces People have physical interactions and primitive reactive forces

Helbing’s basic model Accomplish desired speed and desired heading

gets α to desired velocity, The model closest part of static things, Β, that α should avoid pushes α away from all pedestrians, β pushes α towards certain pedestrians, i These use potential force fields

What are potential force fields? Field around an object that exerts a force on other objects Used by roboticists exponentialsquaredirectional

The model – normal condition Lots of room for choice of potential function Helbing uses an elliptical directional potential β α α α Directional potential: Gradient: directional Force applied on α by β:

What does that do? Lane formation Lane formation Potential force behind leader is low Potential force behind leader is low Leader is moving away (force is not increasing) Leader is moving away (force is not increasing) Turn taking at doorways Turn taking at doorways (it’s a polite model) Turn taking at doorways Easy to follow someone through the door. Easy to follow someone through the door. Eventually pressure from other side builds up and direction changes Eventually pressure from other side builds up and direction changes Rudimentary collision avoidance

Panic !! People are now really close together Body force – counteracts bodily compression Body force – counteracts bodily compression Sliding friction force – people slow down when really close to other people and things Sliding friction force – people slow down when really close to other people and things Desired speed,, has increased Desired speed,, has increased Switch from directional to exponential potential field (but would probably still work with directional) Switch from directional to exponential potential field (but would probably still work with directional)

Helbing’s basic model Pedestrians impact one another Distance between COM Vector from j to i

Helbing’s basic model Pedestrians impact one another If pedestrians touch one another If pedestrians touch one another Push them apart with constant force They tug at one another in direction of travel Difference in velocity Direction of tangent of velocity

Helbing’s basic model Interactions with the wall Just like a pedestrian Just like a pedestrian Bounce off the wall Bounce off the wall Wall slows pedestrian down Wall slows pedestrian down

The model - panic condition distance from α to β g() = 0 if α and β are not touching, otherwise = normal from β to α tangential velocity difference body forcesliding friction force Exponential potential field

What does that do? Faster-is-slower effect Sliding friction term Sliding friction term High desired velocity (panic) High desired velocity (panic) Squishes people together Gaps quickly fill up Exits get an arch-like blockage

Integrating panic with normality Sliding friction and body term can safely be used in all situations Would probably make all scenes look better Panic occurs when everyone’s desired velocity is high and points to same location

Results Exit times for different desired speeds

Results Total leaving time for different desired speeds

Results Widening corridor

Results Solid (measured along corridor) Solid (measured along corridor) Dashed (measured at bump) Dashed (measured at bump)

Mass behavior Confused people will follow everyone else average direction of neighbors j in a certain radius R i individual direction panic probability

Results Finding an alternative exit by following someone

Results Benefits of following (total escaped)

Results Benefits of following (time to escape)

Results Benefits of following (raw difference in number of people through each door)

Problems Possible to go through boundaries Can be fixed by increasing force of boundary Can be fixed by increasing force of boundary Sometimes good Sometimes good Excels at crowds, not individual pedestrian movement When focus is on big crowds and not on individuals, this is good. When focus is on big crowds and not on individuals, this is good.

Future Work Better pedestrian dynamics More realistic collisions Better perception Better behaviors More complex cognition Add more memory More evaluation