Social Force Model for Pedestrian

Dynamics

Presenter: Robin van Olst

The authors

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

Introduction

How does a social force model work?

Introduction

Consists of 4 parts1. Acceleration towards desired velocity of motion2. Repulsive effects3. Attractive effects4. Fluctuations (randomness)

Path used: the edges of a polygon◦ Why?

Formulation of the SFM

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

Acceleration towards desired velocity of motion

Acquiring the desired direction

Acceleration towards desired velocity of motion

1

Acquiring the acceleration

◦ Actual velocity:

◦ Relaxation term:

Acceleration towards desired velocity of motion

Desired

Deviation

Pedestrian is repelled from:◦ Other pedestrians

Depends on density and speed◦ Borders of obstacles

Repulsive effects

Repulsion from other pedestrians β

◦ Distance from other pedestrians:

◦ is a monotonic decreasing functionwith equipotential lines

Repulsive effects

α

β

Repulsion from other pedestrians β

◦ is a monotonic decreasing functionwith equipotential lines

◦ Semi-minor axis:

Dependant on step width:

◦ Applies gradient:

Repulsive effects

α

β

Repulsion from border B

◦ Distance from border:◦ Point on border closest to α is chosen

Repulsive effects

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

Attractive effects

Repulsive and attractive effects get direction dependent weights:

Repulsive effects:

Attractive effects:

Adding sight

The resulting function:

Almost there..

Add fluctuations◦ Decides on equal decisions

Final touch: limit the pedestrian’s speed by a maximum◦ Cap the desired speed by a maximum speed

The social force model

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

The experiment

Results◦ Pedestrians heading in the same direction form

(dynamically varying) lanes Periodic boundary conditions prevent newly spawned

pedestrians from messing lanes up

The walkway test

Size denotes velocity

Once a pedestrian passes the door, more follow◦ Increasing pressure from the waiting group causes

alternations Matches observations

The narrow door test

Size denotes velocity

Simple model, easy to understand

Describes some realistic behavior◦ Seems open to complex adaptations

Conclusion

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?

Discussion