Title slide

1
Title slide
University of Central Florida
Institute for Simulation Training
Continuous time-space simulations of
pedestrian crowd behavior
T.I. Lakoba, D.J. Kaup, and N.M.
Finkelstein with Simulation Technology
Center, Orlando, FL
Acknowledgement Research supported in part by
STRICOM Contract N61339-02-C-0107
2
Overview of recent work

• Two main types of crowd models
• Cellular Automata (discrete space) models
• - A. Schadschneider et al (Koln, Germany)
• - V. Blue, J. Adler (DOT, USA)
• - J. Dijkstra et al (Eindhoven, Netherlands)
• - M. Batty et al (CASA _at_ UCL, UK)
• - M. Schreckenberg et al (Duisburg, Germany)
• Continuous-space models
• - D. Helbing et al (Dresden, Germany)
• social-forces physical forces
• - S. AlGadhi et al (El-Riyadh, Saudi Arabia)
• continuous-mechanics equations
• - S. Hoogendoorn et al (Delft, Netherlands)
• specifies way-finding mechanisms.

• Phenomena which these
• models can reproduce
• - Lane formation in 2-way traffic
• - Observed speed-density relation
• - Clogging/arching at doors
• - Periodic change of direction
• when two crowds try to pass
• through the same door
• in two opposite directions.

3
Objectives of this work

• We build upon Helbing et al s social-force
  model
• To quantitatively correctly reproduce collective
  behavior,
• they assumed unrealistic parameters for
  individual behavior
• too short an interaction range, gt
• too high deceleration/acceleration of
  individual pedestrians.
• We find values of parameters for Helbings model
• that correctly reproduce both collective
  and individual behaviors.

Social forces physical
forces (repulsion/attraction) (pushing,
friction)

4
Outline of presentation

• Describe equations of the model
• Motivate need for new parameter values for the
  model
• Highlight new features compared to Helbings
  model
• The equations are numerically stiff
• We propose an original algorithm that partially
  overcomes stiffness while using an explicit
  first-order Euler method
• Show movies of pedestrians exiting a room

5
Equations of the model

Social forces Physical
forces (repulsion/attraction,
(pushing, friction) preferred velocity)

Achieves or not his walking goal gt loses/gains
excitement Has/has not seem exit/obstacle
recently gt gains/loses memory Recognizes how
dense crowd is gt adjusts repulsion to density.

6
Equations of the modelSocial forces

Tendency to keep preferred speed
Repulsion (tendency to keep distance from
others, and from boundaries)
Attraction to exit(s)
D attr gtgt D rep (non-infinite D attr plays role
when a person decides which exit to head)
As panic increases,
7
Equations of the modelPhysical forces

Pushing and Friction (when pedestrians come in
contact with each other)

• Note
• Physical forces do not depend on
• relative orientation of pedestrians
• - By themselves, the pushing forces
• do NOT prevent pedestrians from
• walking through each other !

8
Helbings et al parameter values for the model

m/s (normal walking) m/s (moderate panic) m/s
(extreme panic)
m 80 kg,
0.5 s,
Helbing et al Nature, 407, p.487 (2000)
N m kg/s2
! ?
Yet, results of simulations, found at
http//angle.elte.hu/panic, show remarkably
realistic dynamics of many ( 200) pedestrians.
9
Desired parameter values

• Find
  that lead to accelerations of no more than 0.3
  0.5 g
• when considering few pedestrians.
• What are the ranges of corresponding parameters?
• Expect that the model needs to be made more
  complex to include more features that help
  reflect realistic human behavior.
• What are the other features needed ?

10
Ranges for parametersCriteria for few-ped
dynamics

• is found by considering a fit
  to measurements
• gt

• new to
• Helbings
• model

11
Ranges for parametersCriterion for multi-ped
dynamics
The model should reproduce the faster is slower
effect.
The faster is slower effect
People trying to leave a room too fast get
stuck at the door and end up getting out slower
than they would have been able to do if they
had walked with a normal speed.
12
Essential new featurescompared to Helbing et
als model

• Equations are stiff ? Code has to resolve
  two disparate scales
• LARGE distances about the size of the room (
  10 m), and
• Small distance between peds when they
  come into contact ( 1 cm).
• New algorithm detects and eliminates
  overlaps among pedestrians.
• This allows one to keep bounded
  from below
• while using the explicit 1st-order Euler
  method.
• Ability to learn and forget about location of an
  exit and walls.
• The knowledge about their locations is used
  to determine
• Direction to which a pedestrian is looking, gt
• Attraction force to the exit (similarly,
  repulsion from walls).

13
Overlap-eliminating algorithm

• Find a pedestrian who is overlapped with, the
  most.
• If he is overlapped with a wall,
• 2a. Move him away from wall so that
  
• 2b. Then, move pedestrians overlapping with him,
  away,
• and set their new velocities to coincide.
• If he is overlapped, but not with a wall, do
  Part 2b only.
• Repeat steps 1 3 until no overlapped
  pedestrians are found,
• but no more times than the total number
  of pedestrians.
• Time spent on one round of O-E
  
• During this time, coordinates of a
  pedestrian
• who is being un-overlapped, are not
  updated
• (i.e. he is preoccupied with
  overlap-elimination only).

free parameter
14
Results

• Simulations show presence of the faster is
  slower effect.
• Results are obtained as a function of
  parameters characterizing magnitude of the
  repulsive force among pedestrians.

Solid Vpref1.5 m/s Dashed Vpref3
m/s Dotted Vpref4.5m/s
15
View Video of the Simulation

• The video runs 3 different velocities, of one
  minute each.
• Illustrates that faster is slower.
• Shade of blue indicates excitement level.
• Click here to watch the video.