Transcript Robin - Department of Information and Computing Sciences

Presenter: Robin van Olst
Prof. Dr. Dirk Helbing
Heads two divisions of the
German Physical Society of
the ETH Zurich
Ph.D. Péter Molnár
Associate Professor of
Computer and Information
Science at Clark Atlanta
University
Social force: a measure for motivation to move

What is a social force model?
◦ Models the probable motion of a pedestrian
 Only for simple situations
 Follows the gas-kinetic pedestrian model

Why use a social force model?
◦ Comparison to empirical data
◦ Useful for designing big areas

How does a social force model work?

Consists of 4 parts
1.
2.
3.
4.
Acceleration towards desired velocity of motion
Repulsive effects
Attractive effects
Fluctuations (randomness)
Path used: the edges of a polygon

◦
Why?

Pedestrian want to reach his goal comfortably
◦ No detours
◦ Goal is an area, not a point
 Steers towards the closest point of the area
◦ Takes his time to slow down
 I.e. nearing goal or avoiding an obstacle

Acquiring the desired direction
1

Acquiring the acceleration
◦ Actual velocity:
◦ Relaxation term:
Desired

Pedestrian is repelled from:
◦ Other pedestrians
 Depends on density and speed
◦ Borders of obstacles

Repulsion from other pedestrians β
◦ Distance from other pedestrians:
◦
is a monotonic decreasing function
with equipotential lines
α
β

Repulsion from other pedestrians β
◦
is a monotonic decreasing function
with equipotential lines
◦ Semi-minor axis:
 Dependant on step width:
◦ Applies gradient:
α
β

Repulsion from border B
◦ Distance from border:
◦ Point on border closest to α is chosen
α
B

Pedestrians may be attracted to a person or
an object
◦ Friend, street artist, window displays..

Pedestrian loses interest over time
◦ Attraction decreases with time t

Repulsive and attractive effects get direction
dependent weights:

Repulsive effects:

Attractive effects:

The resulting function:

Add fluctuations
◦ Decides on equal decisions

Final touch: limit the pedestrian’s speed by a
maximum
◦ Cap the desired speed by a maximum speed



Large number of pedestrians are used
Pedestrians enter at random positions
Simple setup
◦ No attractive effects or fluctuations are applied

Variables are set
◦ Chosen to match empirical data
 Desired speed: 1.34 ms-1 (std: 0.26 ms-1)
 Max speed: 1.3 * desired speed
 Relaxation time: 0.5
 Decrease for more aggressive walking
 Angle of sight: 200°
 Walkway width: 10 meters

Results
◦ Pedestrians heading in the same direction form
(dynamically varying) lanes
 Periodic boundary conditions prevent newly spawned
pedestrians from messing lanes up
Size denotes velocity

Once a pedestrian passes the door, more
follow
◦ Increasing pressure from the waiting group causes
alternations
 Matches observations
Size denotes velocity

Simple model, easy to understand

Describes some realistic behavior
◦ Seems open to complex adaptations


Repulsive effect doesn’t take the current
velocity into account
Doesn’t handle complex paths at all
◦ Blocked paths, taking alternate routes
 Combine with path planning (corridor based method)

Situations this simple are too rare?
◦ How would it handle under complex situations?