Local Dynamics Models for Crowd Simulation

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Local Dynamics Models for Crowd Simulation

• Yeh, Hengchin

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Outline

• Introduction
• Optimal Velocity Model
• Helbings Model and Extensions
• Rule Based and Others
• HiDAC in More Detail
• References

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Introduction Definition

• Narrow
• Helbings social forces.

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Introduction Definition

• Narrow
• Helbings social forces.
• Broad
• Forces
• Change of positions an velocities
• According to local environment
• Everything not Global (planning, navigation and
  so on)

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Introduction Design flow

• Observation
• Choose the macroscopic phenomena you want to
  reproduce.

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Introduction Design flow

• Observation
• Choose the macroscopic phenomena you want to
  reproduce.
• Design the form of (microscopic) forces.
• Highly arbitrary and heuristic.
• Analogous to physics.

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Introduction Design flow

• Observation
• Choose the macroscopic phenomena you want to
  reproduce.
• Design the form of (microscopic) forces.
• Highly arbitrary and heuristic.
• Analogous to physics.
• Simulation
• Fix the problems.

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Introduction - Examples

• Domain
• Roadmaps
• Cellular automata
• Continuous space
• etc.
• Methods
• Particle dynamics and potential field
• Rule based, eg. flocking
• Special, eg. RVO.

CA Very popular in Statistical Physics (eg.
Physica A), but not in Graphics
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1D-Optimal Velocity Model (OVM)

• From Transportation Science
• 1D traffic flow.
• Imaging driving on highway
• A car will keep the maximum speed with enough the
  distance to the next car.
• A car tries to run with optimal velocity
  determined by the distance to the next car.
• Safety distance

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1D-OVM

• Formula
• a How fast the car wants to accelerate to the
  desired speed.
• V optimal (desired) speed.
• b, c constants

Distance to the next car
tanh? Any monotonic increasing function with
upper/lower bounds suffice.
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1D-OVM

• Demo
• Phenomena Congestion, phase transition
• The uniform flow becomes unstable when a lt 2
  V(L/N).
• Intuition lag in response time magnifies
  fluctuations.

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2D-OVM

• Similar ideas
• For
• Only attraction
• For
• Both attraction and repulsion

?
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2D-OVM

• _
• Anything that models (approximates) the
  anisotropic nature of human perception /
  reaction.
• For example
• Self driving force
• Range of consideration

?
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2D-OVM

• Similar phenomena
• Lane formation in low density.
• Congestion in high density

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Helbings Forces

• Helbing and Molnar 1995
• Social force model for pedestrian dynamics
• Helbing et al. 2000
• The paper, published in Nature.
• Helbing et al. 2002
• Lakoba and Kaup 2005
• Helbing et al. 2005
• Helbing et al. 2007
• Crowd turbulence the physics of crowd disasters
• Yu and Johansson 2007
• Modeling Crowd Turbulence by Many-Particle
  Simulation

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Helbing 2000

• Main equation
• Add features or modify this equation.
• Example
• HiDAC
• AERO

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Self-Driven Force

• First term
• Deviation of current velocity from preferred
  velocity
• p panic parameter (in)dependence
• preferred velocity own velocity.
• average velocity within a radius around
  the agent himself collective velocity.

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Self-Driven Force

• First term
• Deviation of current velocity from preferred
  velocity
• p panic parameter (in)dependence
• preferred velocity own velocity.
• average velocity within a radius around
  the agent himself collective velocity.
• Compared to OVM
• No distance dependence for preferred velocity.
• No concept of safety distance. Can be added.

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Interactive Forces

• Second Term

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Interactive Forces

• Social force
• Baseline, almost in every paper
• A, B, dij

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Interactive Forces

• Pushing force
• Kernel
• k, elasticity, spring constant

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Interactive Forces

• Frictional force relative velocity
• But no static friction, alternative

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Agent-Obstacle Force

• Analogously
• Or, again

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Summary of Helbing 2000

• The social force do not have a physical source.
• Body force and sliding friction forces do.
• But rather simple
• no ground friction
• no dynamic constraint
• Details Qualitative vs quantitative.

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Summary of Helbing 2000

• Phenomena
• Nick talked about them
• Pressure buildup (Pressure discussed later)
• Clogging at bottleneck
• Jamming at widening
• Faster is slower
• Inefficient use of alternative exits (due to
  panicking and herding)

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Lakoba and Kaup 2005

• Title Modifications of the Helbing-Molnár-Farkas-
  Vicsek Social Force Model for Pedestrian
  Evolution
• HMFV later on.
• Fix some counterintuitive results of HMFV,
• by changing numerical values
• as well as modifying the model

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Problem 1 of HMFV

• Overlapping
• HMFV allows overlapping, it NEEDS overlapping for
  pushing forces and frictional forces.
• But no limit.

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Overlapping

• There should be a core which is not
  penetratable.

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Overlapping

• There should be a core which is not
  penetratable.
• Maximum overlapping or squeezing
• Smax, say, 20 of the radius.
• Collision Elimination

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Methods for Handling Overlapping

• HMFV use high k in
• Problem In order to prevent overlapping ? makes
  humans very stiff springs or bouncy balls.
• 5cm ? 5000 N, or 7G
• Potential Barrier
• for
• approaches infinity as dij ? Rij 2 Smax

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Potential Barrier

• Numerically, Stiff equation
• Since
• f unbounded, very large.
• In order to be stable, (i.e. x not blowing off)
  only very small time step can be used.
• Runs forever.
• Implicit integration is expensive too
• Lakoba Kaup OEA

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Overlap-Eliminating Algorithm (OEA)

• n total number of pedestrians count 0
• While (overlapping occurs count lt n)
• Find the most overlapped pedestrian pi.
• If (pi intersects with the wall)
• Move pi away from the wall
• set vi,n ? 0 vi ,t stays the same.
• make pi stationary
• end if
• Move all pjs away from pi.
• Set vj ? vi
• end while

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OEA

• Set vj ? vi this only works for uni-goal system,
  such as egress.
• Still no guarantee.
• But probability very low.
• Can we do better?
• What if the only collision free configuration is
  a packing one?
• Finite packing? HARD

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OEA time step

• Determine the maximum allowable time step by
  letting each pedestrian to move
• No less than Smax.
• Can be even bigger if all (obstacles and
  pedestrians) are at least d gt Smax apart.

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OEA time step

• OEA is a physical process. Need time.
• Deduce the needed time from change of momentum
  and feasible force.

time left for other physical processes
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fOE

• fOE
• a free parameter, how hard he can bounce away
  from overlapping objects.
• Related to skeleton elasticity, c.f. k for
  muscle elasticity.

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Problem 2 of HMFV

• Too small B
• 8 cm 1.4G
• or say, 50 cm for less then a weight of a
  baseball.
• Consider walking toward a wall.
• Too bouncy.
• Oscillation expected.

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Density Effects of the Social Force

• Since B is larger now
• need to suppress the social repulsion as the
  person approaches a dense crowd density is high.

K0 0.3 K1 gt1
Normalized density
D0 diameter of pedestrian
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Orientational Dependence of the Social Force

• Face-to-back W1
• Give extra weight to Face-to-face W2

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Orientational Dependence of the Social Force

• Face-to-back W1
• Give extra weight to Face-to-face W2

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Helbing 05

• Add some more features
• Impatience
• average speed into the desired direction
  of motion.
• Long waiting times decrease the actual velocity
  compared to the desired one, which increases the
  desired velocity

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More features

• Fluctuation
• Orientational effects

0.2
0.8
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Helbing 05 Interesting Suggestions
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Helbing 05 Interesting Suggestions
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What is left in this lecture

• Examples of method-specific local dynamics
• in AERO
• in Autonomous Pedestrians Shao and Terzopoulos
  05
• HiDAC in more details
• following Nicks lecture.

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Local Dynamics in AERO
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Local Dynamics in AERO

• New face Roadmap force field

lk
p
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Autonomous Pedestrians

• Rule-based.
• local rules
• A B D E F collision avoidance.
• C Modified Potential field. To maintain
  separation in a moving crowd.

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Autonomous Pedestrians

• Temporary Crowd
• Moving in similar directions
• Situated within a parabolic region in front of H.
• ri repulsiveness
• di distance to Ci

fi
di
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HiDAC

• Position for agent i is

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Avoidance Forces

• f F not force. but unit directional vector.
• Used to direct the speed (scalar).

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Avoidance Forces

• desired attractor (FiAt)
• walls w (FwiWa)
• obstacles k(FkiOb) and
• other agents j (FjiOt)
• trying to keep its previous direction of
  movement to avoid abrupt changes in its
  trajectory (FiTon -1).

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Avoiding Obstacles
Rectangle of influence

• Perpendicular to dki or nw
• Tangent.

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Avoiding Agents

• Tangent
• distance factor
• orientation factor

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Repulsion Force

• Recall
• Dimension displacement
• Use directly move the agent out of the
  overlapping situation
• 0.3 priorities between agents and walls or
  obstacles.

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Repulsion Force (Displacement)
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Note

• Unlike Helbings model. More like RVO.
• Directly manipulate velocities. No real forces.
• Speed never blows off. Decide directions
  mostly.
• Stops and waits next page.

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Resolving Shaking

• Stopping rule
• If others push against you and you are not
  panicking, you stop.
• To avoid deadlock, a timer is set.
• alpha becomes zero can change position only if
  pushed by others.

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Resolving Shaking

• Waiting rule
• If another agent j walking in the same direction
  falls within the disk.
• Timer too.
• Until the condition no longer holds.

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Pushing

• Waiting rule
• If another agent j walking in the same direction
  falls within the disk.
• Timer too.
• Until the condition no longer holds.

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Panic

• High level
• Communication
• Low level
• crowd density goes up.
• pushing occurs frequently.

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References

• OVM
• A. Nakayama and Y. Sugiyama. Two-Dimensional
  Optimal Velocity Model for Pedestrians and
  Biological Motion. AIP Conference Proceedings
  2003661107
• A. Nakayama and Y. Sugiyama. Group Formation of
  Organisms in 2-Dimensional OV Model. Traffic and
  Granular Flow 03 2005399-404
• A. Nakayama, Katsuya Hasebe and Y. Sugiyama.
  Instability of Pedestrian Flow and Phase
  Structure, Physical Review E 200571036121
• Social Force
• D. Helbing, I. Farkas, and T. Vicsek, "Simulating
  Dynamical Features of Escape Panic,"
  cond-mat/0009448, September 2000.
• D. Helbing et al., "Self-Organized Pedestrian
  Crowd Dynamics Experiments, Simulations, and
  Design Solutions," Transportation Science, vol.
  39, pp. 1-24, 2005.
• T.I. Lakoba, D.J. Kaup, and N.M. Finkelstein,
  "Modifications of the Helbing-Molnar-Farkas-Vicsek
  Social Force Model for Pedestrian Evolution,"
  SIMULATION, vol. 81, pp. 339, 2005.
• D. Helbing, A. Johansson, and H.Z. Al-Abideen,
  "Dynamics of crowd disasters An empirical
  study," Physical Review E, vol. 75, pp. 46109,
  2007.
• W. Yu and A. Johansson, "Modeling crowd
  turbulence by many-particle simulations,"
  Physical Review E, vol. 76, pp. 46105, 2007.
• Crowd Simulation in Graphics
• W. Shao and D. Terzopoulos, "Autonomous
  pedestrians," Proceedings of the 2005 ACM
  SIGGRAPH/Eurographics symposium on Computer
  animation, pp. 19-28, 2005.
• N. Pelechano, J.M. Allbeck, and N.I. Badler,
  "Controlling individual agents in high-density
  crowd simulation," Proceedings of the 2007 ACM
  SIGGRAPH/Eurographics symposium on Computer
  animation, pp. 99-108, 2007.
• A. Sud et al, "Real-time navigation of
  independent agents using adaptive roadmaps,"
  Proceedings of the 2007 ACM symposium on Virtual
  reality software and technology, pp. 99-106, 2007.