Social Force Model for Pedestrian Dynamics

1. Social Force Model for Pedestrian Dynamics Presenter: Robin van Olst

2. The authors Prof. Dr. Dirk Helbing Heads two divisions of the German Physical Society of the ETH Zurich Ph.D. PéterMolnár Associate Professor of Computer and Information Science at Clark Atlanta University

3. Introduction 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

4. Introduction • How does a social force model work?

5. Formulation of the SFM • Consists of 4 parts • Acceleration towards desired velocity of motion • Repulsive effects • Attractive effects • Fluctuations (randomness) • Path used: the edges of a polygon • Why?

6. Acceleration towards desired velocity of motion • 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

7. Acceleration towards desired velocity of motion • Acquiring the desired direction 1

8. Acceleration towards desired velocity of motion • Acquiring the acceleration • Actual velocity: • Relaxation term: Deviation Desired

9. Repulsive effects • Pedestrian is repelled from: • Other pedestrians • Depends on density and speed • Borders of obstacles

10. Repulsive effects • Repulsion from other pedestrians β • Distance from other pedestrians: • is a monotonic decreasing functionwith equipotential lines α β

11. Repulsive effects • Repulsion from other pedestrians β • is a monotonic decreasing functionwith equipotential lines • Semi-minor axis: • Dependant on step width: • Applies gradient: α β

12. Repulsive effects • Repulsion from border B • Distance from border: • Point on border closest to α is chosen α B

13. Attractive effects • 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

14. Adding sight • Repulsive and attractive effects get direction dependent weights: • Repulsive effects: • Attractive effects:

15. Almost there.. • The resulting function:

16. The social force model • Add fluctuations • Decides on equal decisions • Final touch: limit the pedestrian’s speed by a maximum • Cap the desired speed by a maximum speed

17. The experiment • 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

18. The walkway test • 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

19. The narrow door test • Once a pedestrian passes the door, more follow • Increasing pressure from the waiting group causes alternations • Matches observations Size denotes velocity

20. Conclusion • Simple model, easy to understand • Describes some realistic behavior • Seems open to complex adaptations

21. Discussion • 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?