Realistic Crowd Simulation
with Density-Based
Path Planning
Wouter G. van Toll
Atlas F. Cook IV
Roland Geraerts
ICT.OPEN / ASCI
October 22nd, 2012
Introduction
Path planning in virtual environments (e.g. games)
Global planning:
find a main route
Local planning:
variety, collision avoidance
Many characters at once:
crowd simulation
Problem: in a crowd, short
routes are not always good
Collision avoidance cannot
solve everything
Other routes are unused
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Overview
We use crowd density information for global planning
Stored in a navigation mesh (Explicit Corridor Map)
Planning algorithm: time-based A*
Periodic replanning
Results
Characters take detours around congested areas
Crowd spreads over different routes
Efficient: tens of thousands of characters in real-time
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Sneak preview
Before:
After:
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Navigation Meshes / Crowd Density
Preliminaries
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Navigation meshes
Characters need to find paths through an environment
Navigation graph: 1D edges
Not flexible enough for crowds
Navigation mesh: 2D polygons
Global path: sequence of polygons
Local planning during movement
Common in modern games / simulations
“Crowd simulation has been solved!”
Assumptions in the navigation mesh / crowd
General framework?
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Explicit Corridor Map
An exact and flexible navigation mesh
Medial axis
Closest-obstacle annotations
A* on the medial axis  path
+ corridor
Shortest paths with clearance
Collision avoidance
Multi-layered environments
Dynamic updates
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Crowd density
Fraction of a region Ri that is occupied by characters
Often in persons per m²
Often in levels and colors
For us: value ρi between 0 and 1
(allows multiple character sizes)
F
E
Practical studies
Time-based path planning?
D
C
B
A
avg. walking speed
When the density is high,
people walk more slowly
Density-speed function
v(ρ) : [0,1]  [0, vmax]
crowd density
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Density Map / Density-Based Path Planning
Method
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Density map
ECM divides the environment
into non-overlapping regions
Each region maps
to an ECM edge
Each region stores its
local density
Updated in real-time
Density of a region
 Expected walking speed
within the region
 Expected traversal time
of the edge
 Expected delay
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Density-based path planning
A* search on the medial axis
A character wants a “fast path”, not necessarily the shortest
Each ECM edge ei has a density ρi
tmin(ei): traversal time at speed v(0) = vmax
tdens(ei): traversal time at speed v(ρi)
tdelay(ei) = tmin(ei) - tdens(ei)
cost(ei) = tmin(ei) + w • tdelay(ei)
Controlling the sensitivity to delays
w = 0: shortest path
w = 1: “fastest path” (Höcker et al., 2010)
w > 1: more eager to take detours
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Replanning
Densities change all the time
Characters should re-check their paths
“We cannot see crowds that are far away”
Density viewing distance D along the medial axis
A*: if the path length > D, assume ρ = 0
 Path has a visible and an invisible part
Partial replanning: re-use invisible parts
Character has moved
More points are visible
At a mutually invisible point, A* can stop
 Speed vs. knowledge
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Realistic Crowds in Real-Time
Results
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Experimental results
Varying the cost weight w
w = 0  congestions
w = 1, no replanning  periodic effect
w = 1, replanning  realistic crowd flow
 longer but faster paths
w > 1  larger detours, indecisive crowd
 Useful in other environments?
Varying the viewing distance
D=0
∞m m
350
Real-time periodic replanning
replanning time
1 - 2 ms in a large city
Multi-threading: steering 50K characters in 30 ms/frame
70 ms/frame left for e.g. replanning
# path vertices
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Conclusions / Future work
Closing Comments
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Conclusions
The ECM navigation mesh serves as a density map
Non-overlapping, exact, always defined
Region densities map to “edge speeds”
Updated in real-time
Characters use density-based A*
Short paths with little expected delay
Sensitivity to delay can be set
(Partial) replanning
Result: More realistic crowds
Characters spread over routes
Characters avoid congestions
Emergent: global effects due to individual choices
(Still) real-time performance for large crowds
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Future work
New questions
Use flow information? (speed + direction)
Use actual visibility?
Event-based vs. periodic replanning
Plan with terrain information?
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More information
Poster
Contact us
W.G.vanToll@uu.nl
R.J.Geraerts@uu.nl
http://people.cs.uu.nl/roland/
Questions?
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