Transcript Simulating Crowds

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
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For the layman animator
Lots of goodies come for free 
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Escape panic features
Faster-is-slower effect
Crowding around doorway
Mass behavior
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Normal pedestrian traffic features
Lanes
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
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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
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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…
Dynamics
Perception
Reflexive actions
Cognition
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Behaviors
What’s the important stuff
to capture?
How will we evaluate success?
Helbing’s basic model
Generalized force model
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Pedestrians are like interacting molecules
People have nominal (desired) velocities
People have no other memory
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People have physical interactions and
primitive reactive forces
Helbing’s basic model
Accomplish desired speed and desired
heading
The model
gets α to desired
0
velocity, v e
closest part of static
things, Β, that α
should avoid
pushes α away
from all
pedestrians, β
pushes α towards
certain pedestrians, i

B
These use potential force fields
What are potential force fields?
Field around an object that exerts a force
on other objects
Used by roboticists
exponential
square
directional
The model – normal condition
Lots of room for choice of potential function
Helbing uses an elliptical directional potential
directional
Directional potential:
Gradient:
α
Force applied on α by β:
β
α
α
What does that do?
Lane formation
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Potential force behind leader is low
Leader is moving away (force is not
increasing)
Turn taking at doorways (it’s a polite model)
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Easy to follow someone through the door.
Eventually pressure from other side builds up
and direction changes
Rudimentary collision avoidance
Panic !!
People are now really close together
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Body force – counteracts bodily compression
Sliding friction force – people slow down when
really close to other people and things
Desired speed, v0 , has increased
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
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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
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Just like a pedestrian
Bounce off the wall
Wall slows pedestrian down
The model - panic condition
Exponential
potential field
body force
sliding friction force
r  d
t
 ( Ai e
 kg(r  d )) n  g (r  d )v
t
Bi
g() = 0 if α and β
are not touching,
otherwise = r  d
distance from α to β
r  radius   radius 
d  r  r
normal from β to α
n 
r  r
d ij
tangential velocity
difference
t
v
 (v  v )  t
What does that do?
Faster-is-slower effect
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Sliding friction term
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
Widening corridor
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Solid (measured
along corridor)
Dashed (measured
at bump)
Mass behavior
Confused people will follow everyone else
individual direction
panic probability
average direction of
neighbors j in a
certain radius Ri
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
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Can be fixed by increasing force of boundary
Sometimes good
Excels at crowds, not individual pedestrian
movement
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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