Simulating Crowds

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29 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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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

Lots of goodies come for free



Escape panic features

Faster
-
is
-
slower effect

Crowding around doorway

Mass behavior


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


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

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


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


People have nominal (desired) velocities

People have no other memory


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



e
0
v
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


B
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

β

α

α

α

Directional potential:

Gradient:

directional

Force applied on
α

by
β
:


What does that do?

Lane formation


Potential force behind leader is low


Leader is moving away (force is not
increasing)

Turn taking at doorways
(it’s a polite model)


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


Body force


counteracts bodily compression


Sliding friction force


people slow down when
really close to other people and things


Desired speed, , has increased


Switch from directional to exponential
potential field
(but would probably still work with directional)

0

v
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

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


Bounce off the wall


Wall slows pedestrian down

The model
-

panic condition











t
v
d
r
g
n
d
r
kg
B
A
t
i
d
r
i







)
(
))
(
e
(



r
r
d





radius
radius


r
ij
d
r
r
n









t
v
v
v
t




)
(


d
r

distance from
α

to
β

g() = 0 if
α

and
β

are not touching,
otherwise =

normal from
β

to
α

tangential velocity
difference

body force

sliding friction force

Exponential
potential field

What does that do?

Faster
-
is
-
slower effect


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


Solid (measured

along corridor)


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


Sometimes good

Excels at crowds, not individual pedestrian
movement


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