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.Acceleration towards desired velocity of motion 2.Repulsive effects 3.Attractive effects 4.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 Deviation

 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?