#### Transcript Robin - Department of Information and Computing Sciences

```Presenter: Robin van Olst
Prof. Dr. Dirk Helbing
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:
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:

◦ 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?
```