1. Pathfinding and Movement Michael Moll September 29, 2004

2. A Character Has to Move Amount of processing time per cycle for AI is low While movement is obviously a vital part of a game, it’s not exactly the most interesting task performed With A* as an example, plenty of algorithms to find paths, but probably less considered, but more important is How will we represent space we move through??

3. Overview Alternative Search Space Representations –Grids –Graphs –Meshes… Ok, we know what the world looks like, how can we move through it? –A* –Precomputed Pathfinding with Navigation Sets –Potential Fields

4. Search Space Considerations Scope of articles in book and presentation are 2- D worlds Main consideration for search spaces are memory requirements and if they facilitate fast searches (using whatever algorithm we choose) Since all of these are basically graphs, bigger worlds will require more nodes, more edges  more memory, longer searches

5. Path Optimality

6. More Considerations Representation must take into account way an character moves (size, etc) How will we create the search space? Can they be automatically generated? Scripting paths should use different structure

7. Regular Grids

8. How do we generate? Advantages –Random access lookup (O(1)) to determine what tile lies at any coordinate –Complete Negatives –Usually requires large number of nodes to accurately represent world –Path Quality -Agent can only walk in four cardinal directions? That’s no fun. -Let them walk diagonals! Still not much fun

9. Regular Grids NWSE Diagonals String-Pulling Catmull-Rom Spline

10. Grids as Graphs Everything else we look at will be a graph Grids are graphs too –Each cell is a node and edges are adjoining cells Maybe we should just handle grid as a graph –Undirected graph could tell us about topography, etc, whereas array can’t

11. Grids as Graphs

12. Corner Graphs Waypoints around obstacles

13. Corner Graphs How do we generate? –Identify convex corners, can character walk in straight line between? Add edge if possible Advantages –Less memory –Faster generation Negatives –Character will “walk on a rail” hugging edges of obstacles instead of walking through open space –And what about different sized characters? –Lookup is O(n 2 ), have to check every node in graph against every other. Imagine a world with a boat load or corners!

14. Corner Graphs

16. Waypoint Graphs Place nodes in middle of rooms instead of at convex corners

17. How do we generate? –Place nodes wherever we want (suits 3-D worlds But requires hand tuning to be effective  ) Advantages –Reduce memory footprint from regular grids, reduce wall hugging from corner graphs –Work well in “human” architectures Negatives –Still O(n 2 ) –Path Quality vs. Simplicity –Works poorly in open areas Waypoint Graphs

19. Circle-Based Waypoint Graphs Add radius parameter to indicate open space near waypoint

20. Circle-Based Waypoint Advantages –Only look at overlapping circles, alleviating O(n 2 ) problem from before –Easier to obtain optimal paths –Works well in open terrain Negatives –Doesn’t work as well in human architectures that aren’t circle friendly

21. Space-Filling Volumes Use rectangles or 3-D Boxes instead of circles

22. Space-Filling Volumes How do we generate? –Seed and Grow –Make Grid and Merge Very similar to circle-based, but handles angles better

23. Navigation Meshes Enough with the graphs already! Let’s try and cover walk able surfaces with convex polygons Character can travel between adjoining polygons

24. Navigation Meshes

25. How do we generate? –By hand (time consuming) Automated tools to analyze and optimize geometry of world Too complex and not represented as a single polygon mesh, instead may be overlapping, etc

26. Navigation Meshes Advantages –Quickly find optimal paths independent of character shapes and capabilities –Handle indoor and outdoor terrains well Negatives –Can become complex and expensive memory wise –Difficult to generate

27. Problem with N-Sided Meshes

28. Interacting with Pathfinding What about dynamic objects in world? All the representations discussed have been static and obviously can’t handle a dynamic world directly These representations need to be able to provide information to system determining path –Waypoint Graphs and Corner Graphs don’t illustrate walk able surfaces –Meshes and Grids do map every walk able surface –Space-filling volumes and Circle Waypoints provide some representation of walk able areas

29. Further Options for Representation Any other ideas of what we can do to make job of path finding algorithm easier? Prof. Munoz has mentioned this before…. Hierarchical Representations –Choose most suitable scheme for given world, and break up into more manageable pieces Any other ideas of what we can do to make job of path finding algorithm easier? Prof. Munoz has mentioned this before…. Hierarchical Representations –Choose most suitable scheme for given world, and break up into more manageable pieces

30. Path finding Now that we have world represented, how do we plan movement? –A*, Depth-First, Dijkstra Dynamic path finding is expensive –Precompiled solutions can eliminate runtime cost, but memory expensive Article suggests technique of Navigation Set Hierarchy

31. Transition Table Main element in pre computed solutions is a lookup table Each entry represents next step to take from one node to some goal node

32. Transition Table

33. Do not need full search of nodes at run time, just series of lookups Fast, but becomes memory expensive as size of world grows –How expensive? n 2 …solution to shrink transition tables? Hierarchy!

34. Navigation Set Self-contained collection of nodes that requires no links to external nodes to complete a path Nodes can be members of more than one set Goal: Find someway to partition large Navigation Sets into smaller ones

35. Complete Hierarchy

36. Interface Nodes and Sets Need to account for paths that cross navigation sets Any node that connects to a node in another navigation set is an interface node Have a second layer of nodes in addition to navigation sets, called interface set Interface set itself is a navigation set –Therefore, can make transition table for it too

37. Complete Hierarchy 21 nodes –1 Navigation Set = 441 Table Entries (21*21) –4 Navigation Sets = 183 Table Entries (7*7 + 7*7 + 7*7 + 6*6)

38. Constructing the Hierarchy Two goals to process –How many tables to create? Amount of data needed is 1/n of original size + interface set As size of navigation sets increase, cost of interface set becomes less a factor –Where to place boundaries? Keep interface nodes as low as possible

39. Constructing the Hierarchy

40. Path finding Determine best paths leading from source node to boundary of source set Determine best path from source set boundary to goal set boundary Determine best path from goal set boundary to goal node Compile list of complete paths and choose one with least cost

41. Cost Amount of searching is limited to number of interface nodes in goal and source sets only Cost of searching between sets does not scale up with increases in navigation set size –Dependent on number of interface nodes

42. Applications of Navigation Set Hierarchy Interfacing heterogeneous navigation regions Navigation data on demand Extending beyond two tiers

43. Potential Fields Used by Scared Little Girl in Robocode Reactive approach to path finding –Setup virtual potential or force field around objects –Must define field and agents reaction to field Interactions in general are explicitly stated and movement “emerges” –Paths are not planned explicitly

44. Potential Fields Think of world as matrix –Each point tells has value to represent strength of field under it –Possibly assign potential based on distance from goal Might get stuck behind obstacle –Result/Goal: “Glide down gradient/path of least resistance”

45. Potential Fields Advantages? –Works in continuous space! No need to make grid, place waypoints, etc Disadvantages? –Can be trapped in local minima –It’s emergent, not sure what it will do

46. Commercial Implementations How advanced is Half-Life 2's path finding? Is it still based around triangulations, or is it more focused on waypoints, or both... or? Steve Bond: I guess the best answer to this question is "A character who wants to get somewhere will find a way to get there". Half-Life 2's path finding supports swimming, flying, jumping, climbing ladders, and opening doors.

47. Commercial Implementations Unreal Tournament –Waypoints with pre computed paths Navigation Points placed throughout world –Assumes world is generally static Run local path finding on top of global path finding Local path finder constants queries physics engine to find dynamic objects

48. Commercial Implementations Area Awareness System –Designed for Quake 3, used in Doom 3 –Does not use waypoints, instead 3-D bounded hulls, called areas Cost of moving from one point to another within a hull (reachable area) is minimal Reachability can also be determined if a hull touches another –http://www.kbs.twi.tudelft.nl/docs/MSc/2001/W averen_Jean-Paul_van/thesis.pdfhttp://www.kbs.twi.tudelft.nl/docs/MSc/2001/W averen_Jean-Paul_van/thesis.pdf

49. Commercial Implementations Half Life 2 –Waypoint Based Call of Duty –Based off of Quake 3 AAS –Path finding handled by Conduit Engine

50. Sources AI Game Programming Wisdom 2 H. Munoz-Avila & T. Fisher, Strategic Planning for Unreal Tournament Bots. First Person Shooter Architecture AI, http://wiki.beyondunreal.com/wiki/First_Person_Shooter_AI_Architec ture http://wiki.beyondunreal.com/wiki/First_Person_Shooter_AI_Architec ture Bryan Stout, Smart Moves: Intelligent Pathfinding, http://www.gamasutra.com/features/19970801/pathfinding.htm http://www.gamasutra.com/features/19970801/pathfinding.htm JMP van Wavern, The Quake III Arena Bot, http://www.kbs.twi.tudelft.nl/docs/MSc/2001/Waveren_Jean- Paul_van/thesis.pdf http://www.kbs.twi.tudelft.nl/docs/MSc/2001/Waveren_Jean- Paul_van/thesis.pdf Stefan Baert, Motion Planning Using Potential Fields, http://www.gamedev.net/reference/programming/features/motionpla nning/ http://www.gamedev.net/reference/programming/features/motionpla nning/ John Spletzer, Lecture Notes from An Introduction to Mobile Robotics, 9/16/03