Simulating CrowdsSimulating CrowdsSimulating Dynamical Features of Escape Panic & Simulating Dynamical Features of Escape Panic & Self-Organization Phenomena in Pedestrian CrowdsSelf-Organization Phenomena in Pedestrian Crowds

Papers by HelbingPapers by Helbing

Why do we care?Why do we care?

Easy to use when doing crowdsEasy to use when doing crowds For the layman animatorFor the layman animatorLots of goodies come for free Lots of goodies come for free Escape panic featuresEscape panic features

Faster-is-slower effectFaster-is-slower effectCrowding around doorwayCrowding around doorwayMass behaviorMass behavior

Normal pedestrian traffic featuresNormal pedestrian traffic featuresLanesLanesWaiting at doorsWaiting at doorsBraking rulesBraking rules

How do we learn?How do we learn?

Socio-psychological literatureSocio-psychological literatureReports in mediaReports in mediaEmpirical investigationsEmpirical investigationsEngineering handbooksEngineering handbooks

What have we learned?What have we learned?

People try to move faster than normalPeople try to move faster than normalPeople begin pushing and interactions People begin pushing and interactions become physicalbecome physicalMoving becomes uncoordinatedMoving becomes uncoordinated Where does this matter most?Where does this matter most?

What have we learned?What have we learned?

Arching and clogging occurs at exitsArching and clogging occurs at exitsJams get largerJams get largerCrowd pressures reach 4,450 N/mCrowd pressures reach 4,450 N/m Enough to bend steel and break brick wallsEnough to bend steel and break brick walls

People fall and become obstaclesPeople fall and become obstaclesGroup mentality sets in and people follow Group mentality sets in and people follow others blindlyothers blindlyAlternative exits are underutilizedAlternative exits are underutilized

We want to simulate all this…We want to simulate all this…

DynamicsDynamicsPerceptionPerceptionReflexive actionsReflexive actionsCognitionCognition BehaviorsBehaviors

What’s the important stuff to capture?

How will we evaluate success?

Helbing’s basic modelHelbing’s basic model

Generalized force modelGeneralized force model Pedestrians are like interacting moleculesPedestrians are like interacting molecules People have nominal (desired) velocitiesPeople have nominal (desired) velocities

People have no other memoryPeople have no other memory People have physical interactions and People have physical interactions and

primitive reactive forcesprimitive reactive forces

Helbing’s basic modelHelbing’s basic model

Accomplish desired speed and desired Accomplish desired speed and desired headingheading

gets α to desired velocity,

The modelThe model

e0v

closest part of static things, Β, that α

should avoid

pushes α away from all

pedestrians, β pushes α towards

certain pedestrians, i

These use potential force fields

B

What are potential force fields?What are potential force fields?

Field around an object that exerts a force Field around an object that exerts a force on other objectson other objectsUsed by roboticists Used by roboticists

exponential square directional

The model – normal conditionThe model – normal condition

Lots of room for choice of potential functionLots of room for choice of potential functionHelbing uses an elliptical directional potentialHelbing uses an elliptical directional potential

βα

αα

Directional potential:

Gradient:

directional

Force applied on α by β:

What does that do?What does that do?

Lane formation Lane formation Potential force behind leader is lowPotential force behind leader is low Leader is moving away (force is not Leader is moving away (force is not

increasing)increasing)Turn taking at doorways Turn taking at doorways (it’s a polite model)(it’s a polite model)

Easy to follow someone through the door.Easy to follow someone through the door. Eventually pressure from other side builds up Eventually pressure from other side builds up

and direction changesand direction changesRudimentary collision avoidanceRudimentary collision avoidance

Panic !!Panic !!

People are now really close togetherPeople are now really close together Body force – counteracts bodily compressionBody force – counteracts bodily compression Sliding friction force – people slow down when Sliding friction force – people slow down when

really close to other people and thingsreally close to other people and things Desired speed, , has increasedDesired speed, , has increased Switch from directional to exponential Switch from directional to exponential

potential field potential field (but would probably still work with directional)(but would probably still work with directional)

0v

Helbing’s basic modelHelbing’s basic model

Pedestrians impact one anotherPedestrians impact one another

Distance between COM

Vector from j to i

Helbing’s basic modelHelbing’s basic model

Pedestrians impact one anotherPedestrians impact one another If pedestrians touch one anotherIf pedestrians touch one another

Push them apart with constant forcePush them apart with constant force

They tug at one another in direction of travelThey tug at one another in direction of travel

Difference in velocity Direction of tangent of velocity

Helbing’s basic modelHelbing’s basic model

Interactions with the wallInteractions with the wall Just like a pedestrianJust like a pedestrian Bounce off the wallBounce off the wall Wall slows pedestrian downWall slows pedestrian down

The model - panic conditionThe model - panic condition

tvdrgndrkgBA t

i

dr

i

)())(e(

rrd radiusradius r

ijdrrn

tvvv t )(

dr distance from α to β g() = 0 if α and β

are not touching, otherwise =

normal from β to αtangential velocity difference

body force sliding friction forceExponential

potential field

What does that do?What does that do?

Faster-is-slower effectFaster-is-slower effect Sliding friction termSliding friction term High desired velocity (panic)High desired velocity (panic)

Squishes people togetherSquishes people togetherGaps quickly fill upGaps quickly fill up

Exits get an arch-like blockageExits get an arch-like blockage

Integrating panic with normality Integrating panic with normality

Sliding friction and body term can safely Sliding friction and body term can safely be used in all situationsbe used in all situationsWould probably make all scenes look Would probably make all scenes look betterbetterPanic occurs when everyone’s desired Panic occurs when everyone’s desired velocity is high and points to same locationvelocity is high and points to same location

ResultsResults

Exit times for different desired speedsExit times for different desired speeds

ResultsResults

Total leaving time for different desired Total leaving time for different desired speedsspeeds

ResultsResults

Widening corridorWidening corridor

ResultsResults

Widening corridorWidening corridor Solid (measured Solid (measured

along corridor)along corridor) Dashed (measured Dashed (measured

at bump)at bump)

Mass behaviorMass behavior

Confused people will follow everyone elseConfused people will follow everyone else

average direction of neighbors j in a certain radius Ri

individual direction

panic probability

ResultsResults

Finding an alternative exit by following Finding an alternative exit by following someonesomeone

ResultsResults

Benefits of following (total escaped)Benefits of following (total escaped)

ResultsResults

Benefits of following (time to escape)Benefits of following (time to escape)

ResultsResults

Benefits of following (raw difference in Benefits of following (raw difference in number of people through each door)number of people through each door)

ProblemsProblems

Possible to go through boundariesPossible to go through boundaries Can be fixed by increasing force of boundaryCan be fixed by increasing force of boundary Sometimes goodSometimes good

Excels at crowds, not individual pedestrian Excels at crowds, not individual pedestrian movementmovement When focus is on big crowds and not on When focus is on big crowds and not on

individuals, this is good.individuals, this is good.

Future WorkFuture Work

Better pedestrian dynamicsBetter pedestrian dynamicsMore realistic collisionsMore realistic collisionsBetter perceptionBetter perceptionBetter behaviorsBetter behaviorsMore complex cognitionMore complex cognitionAdd more memoryAdd more memoryMore evaluationMore evaluation