1. From Path Planning to Crowd Simulation
Roland Geraerts
3 September 2015
See for more information on our path planning and crowd simulation research.
Our crowd simulation framework is described in the following paper: Wouter G. van Toll, Norman S. Jaklin, Roland Geraerts.
Towards Believable Crowds: A Generic Multi-Level Framework for Agent Navigation. In ICT.OPEN 2015.
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2. Path planning

3. Path planning and crowd simulation
Goal: bring characters from A to B in an environment
Also vehicles, animals, camera, a formation,…
Requirement: fast and flexible
Real-time planning for thousands of characters
Individuals and groups
Dealing with local hazards
Different types of environments
Requirement: realistic paths
For example, the way humans move
Low energy usage (smooth, short, minimal rotation/acceleration)
Keep some distance (clearance) to obstacles
Social behavior and rules (collision avoidance) …

4. Social relevance of simulation
Crowd simulation is needed for
Simulations of the real world
Improving crowd flow, predicting crowd pressures, planning evacuation routes
Replacement of big-scale exercises
Hard and expensive to organize: 500+ people
No impact on environment and surroundings
Populating game worlds
Game world
Rebuilding of train station
Evacuation in sports stadiums
Love Parade in Duisburg, 2010

5. A computational model of human navigation
Challenge: Unify dispersed models for realistic, individual, small group, and collective human movements in interactive, heterogeneous environments.
Dispersed models
Agent-based: individuals, but problems with high densities
Flow-based: no individuals, but good for high densities
Realistic movements
Comprise collaboration, smooth and energy-efficient movement, collision avoidance, and dealing with unrealistic congestions.
Interactive environment
Geometry can change dynamically, and the crowd has to react.
Heterogeneous environment
People need to take logical, distinct, and realistic paths over heterogeneous terrains in the environment.

6. Are we there yet?

7. Path planning errors in games
Networks of waypoints are incorrect
Hand designed
Do not adapt to changes in the environment
Do not adapt to the type of character
Local methods fail to find a route
Keep stuck behind objects
Lead to repeated motion
Groups split up
Not planned as a coherent entity
Paths are unnatural
Not smooth
Stay too close to network/obstacles
Methodology is not general enough to handle all problems
Titan Quest: Immortal throne

8. Path planning algorithms
Method: Flocking
Separation: steer to avoid crowding local units
Alignment: steer towards the average heading of local units
Cohesion: steer to move toward the average position of local units
Advantages
Natural behavior for certain animals
Disadvantages
Coherent group behavior is hard
Trapped in local minima
Flocking (Reynolds): see
Other methods: scripting, cheating
Reynolds, 1987: Flocks, Herds, and Schools: A Distributed Behavioral Model

9. Path planning algorithms
Method: A*
Construction phase: create a grid, mark free/blocked cells
Query phase: use A* to find the shortest path (in the grid)
Advantage
Simple
Disadvantages
Too slow in large scenes
Ugly paths
Little clearance to obstacles
Unnatural motions, e.g. sharp turns
Fixed paths
Predictable motions
Paths resulting from A* algorithms tend to have little clearance to obstacles and can be aesthetically unpleasant, so care must be taken to smooth them.
See for more information/theory on A*.
Major improvements: See e.g.: Field D*: An interpolation-based path planner and replanner (Dave Ferguson and Anthony Stentz)
Hart et al, 1968: A Formal Basis for the Heuristic Determination of Minimum Cost Paths

10. Path planning algorithms
Method: Potential Fields
Goal generates attractive force
Obstacles generate repulsive force
Follow the direction of steepest descent of the potential toward the goal
Advantages
Flexibility to avoid local hazards
Smooth paths
Disadvantages
Expensive for multiple goals
Local minima
Continuum crowds (picture):
Continuum crowds
Treuille et al, 2006: Continuum crowds; Latombe, 1991: Robot motion planning

11. Path planning algorithms
Method: Probabilistic Roadmap Method
Construction phase: build the roadmap
Query phase: query the roadmap
Advantages
Reasonably fast
High-dimensional problems
Disadvantages
Ugly paths
Fixed paths
Predictable motions
Lacks flexibility when environment changes or obstacles are added
Storage can be expensive
Kavraki et al, 1996: Probabilistic roadmaps for path planning in high-dimensional configuration spaces

12. Path planning algorithms
Method: Navigation meshes
Create a representation of the "walkable areas" of a scene
Extract the path
Advantages
General approach
Construction is fast on the GPU
code.google.com/p/recastnavigation
Disadvantages
Often needs much manual editing
Current techniques are imprecise
Bad support for terrains
No automatic annotations (games)
Areas: walk, climb
Places: hiding and sniper spots
Obstacles
Walkable voxels
Raycast navigation code: see
Some open problems
Automatic annotation of the map
Areas: walk, climb, jump, crouch, “avoid” …
Special places: hiding and sniper spots, …
Handle large (dynamic) changes
Efficiently updating the data structure and paths
Improve the efficiency of mesh generation (large scenes)
Wrong coverage/connectivity due to confusing elements
Steep stairs, ramps, hills, curved surfaces, gaps
The mesh is only a data structure storing the walkable areas
How to create visually convincing paths?
Voxel regions
Polygonal regions
Mononen, 2015: Recastnavigation
Convex regions
A path

13. Do we need a new path planning algorithm?
differences
Robotics
Virtual environments
Nr. entities a few robots many characters
Nr. DOFs many DOFs a few DOFs
CPU time much time available little time available
Interaction anti-social social
Type path nice path realistic path
Correctness fool-proof may be incorrect
Path planning has been studied extensively in Robotics

14. Surface-based navigation
We need a paradigm shift
from graph-based to surface-based navigation
Graph-based navigation: little support for route deviation
Hard to avoid expected collision between humans
Hard to support differently sized humans/groups
Costly to deal with dynamic changes in the environment
Hard to efficiently deal with heterogeneous regions
Human navigation is surface-based
A graph is a data structure that can represent the navigable routes in an envi-ronment [7,36,79]. Its nodes represent key positions in the environment which are con-nected through its edges representing routes. Crowd simulation algorithms that are based on this representation suffer from too little support of required deviation from these routes, e.g. to avoid expected collisions between humans, to support differently sized humans/groups, and to deal with dynamic changes in the environment (e.g. a bridge that partially collapses) [73]. In contrast, surface-based representations [24,39,72] handle these problems better because they do support deviation from these routes. In addition, human navigation seems to be surface-based since humans do not walk over imaginary lines but towards areas on a surface.

15. Crowd simulation framework
We need a fast and generic framework
Representation of the environment
Representation environment
Level 5
Plans actions
Level 4
Creates indicative routes
Level 3
Traverses the routes
Yields speed/direction pairs
Level 2
Adapts routes
E.g. to avoid collisions
Level 1
Moves the characters
See N.S. Jaklin, W.G. van Toll, and R. Geraerts. Way to go - A framework for multi-level planning in games. In International Planning in Games Workshop (in ICAPS), pp. 11–14, 2013.
At the top of the hierarchy, event management and action planning (5) generate a set of geometric path planning queries, consisting of start/goal pairs. Next, the global route planning level (4) uses a query to produce an indicative route for a human or group, based on e.g. crowd densities, terrain preferences, visual information, and global coordination. The three lower levels move the crowd in every step of the simulation. On the route following level (3), the global routes are being traversed, yielding preferred velocities (i.e. speed/direction pairs). These are adapted in the local movement level (2) where a human might temporarily deviate from its global route to coordinate its movements and to handle potential collisions with the crowd, yielding a velocity that the animation system (1) uses to move a human.
Van Toll, Jaklin, and Geraerts, Towards Believable Crowds: A Generic Multi-Level Framework for Agent Navigation.

16. Crowd simulation framework
Representation of the environment
Representation environment
Level 5
Plans actions
Level 4
Creates indicative routes
Level 3
Traverses the routes
Yields speed/direction pairs
Level 2
Adapts routes
E.g. to avoid collisions
Level 1
Moves the characters
Van Toll, Jaklin, and Geraerts, Towards Believable Crowds: A Generic Multi-Level Framework for Agent Navigation.

17. Representation of the traversable environment
Comparison of navigation meshes
Triangles
[Kallmann]
Disks
[Pettré et al]
Polygons
[Mononen]
Corridor Map
[Geraerts]
Exact representation x
Linear memory
3D environments
Variable unit widths
Dynamic obstacles
NOT!
Kallmann:
Pettré:
Mononen:
Geraerts:
3D environments  represents the walkable surfaces in a 3D environment

18. Representation of the traversable environment
Requirements
Path existence
100% coverage of the navigable space
All cycles
Flexible: surfaces
Fast computation and small storage
Fast query time during simulation

19. Representation of the traversable environment
Navigation mesh
Voronoi diagram / Medial axis
Voronoi sites: red points
Voronoi sites: red/black lines

20. Representation of the traversable environment
Navigation mesh
Voronoi diagram / Medial axis
From a graph to a surface representation
Closest point annotation

21. Representation of the traversable environment
Navigation mesh
Voronoi diagram / Medial axis
From a graph to a surface representation
Closest point annotation
Computation
Approximation on the GPU
Exact computation on the CPU: Vroni, Boost
Both have to deal with precision issues
GPU computation: see e.g.

22. Representation of the traversable environment
Navigation mesh
Extension to 3D environments
Split environment into 2D layers
Too hard to compute optimally
GPU computation: see e.g.

23. Representation of the traversable environment
Navigation mesh
Extension to 3D environments
Split environment into 2D layers
Too hard to compute optimally
Stitch the navigation meshes on the layers together
Fast to compute: multi-layerd: 46ms; city: 0.3s

24. Representation of the traversable environment
Extension to 2.5D (multi-layered) environments
Technique
Multi-layered environment
Partial medial axes for Li and Lj
Connection scene
Updated medial axes for Li and Lj
Wouter G. van Toll, Atlas F. Cook IV, Roland Geraerts Navigation Meshes for Realistic Multi-Layered Environments. Appears in IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'11), Full text [pdf]

25. Representation of the traversable environment
Result
10 ms
Fast to compute: multi-layerd: 46ms; city: 0.3s

26. Representation of the traversable environment
Navigation mesh
Fast to compute
10 ms
115 ms
3 s

27. Representation of the traversable environment
Can be huge
E.g. 1 km2

28. Representation of the traversable environment
Navigation mesh
Handles dynamic changes
Update costs < 1 ms

29. Representation of the traversable environment
Navigation mesh
Exact representation
Captures 100% of the free space
Captures all homotopically different routes (cycles)
Allows fast extraction of global routes and final paths
Nice mathematical properties
Fast to compute – O(n log n)
Small data structure – O(n)
Nearest obstacle computation – O(1)
2D algorithms also work in ML environments
Fast to compute: multi-layerd: 46ms; city: 0.3s

30. Crowd simulation framework
Representation of the environment
Representation environment
Level 5
Plans actions
Level 4
Creates indicative routes
Level 3
Traverses the routes
Yields speed/direction pairs
Level 2
Adapts routes
E.g. to avoid collisions
Level 1
Moves the characters
See N.S. Jaklin, W.G. van Toll, and R. Geraerts. Way to go - A framework for multi-level planning in games. In International Planning in Games Workshop (in ICAPS), pp. 11–14, 2013.
At the top of the hierarchy, event management and action planning (5) generate a set of geometric path planning queries, consisting of start/goal pairs. Next, the global route planning level (4) uses a query to produce an indicative route for a human or group, based on e.g. crowd densities, terrain preferences, visual information, and global coordination. The three lower levels move the crowd in every step of the simulation. On the route following level (3), the global routes are being traversed, yielding preferred velocities (i.e. speed/direction pairs). These are adapted in the local movement level (2) where a human might temporarily deviate from its global route to coordinate its movements and to handle potential collisions with the crowd, yielding a velocity that the animation system (1) uses to move a human.