social force model for pedestrian dynamics
Post on 31-Dec-2015
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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
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