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Pathfinding and Movement

Pathfinding and Movement. Michael Moll September 29, 2004. 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

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Pathfinding and Movement

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  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. Regular Grids • 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(n2), have to check every node in graph against every other. Imagine a world with a boat load or corners!

  14. Corner Graphs

  15. Corner Graphs

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

  17. Waypoint Graphs • 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(n2) • Path Quality vs. Simplicity • Works poorly in open areas

  18. 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(n2) 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. Navigation Meshes • 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. Transition Table • 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? n2 • …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/Waveren_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_Architecture • Bryan Stout, Smart Moves: Intelligent Pathfinding, 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 • Stefan Baert, Motion Planning Using Potential Fields, http://www.gamedev.net/reference/programming/features/motionplanning/ • John Spletzer, Lecture Notes from An Introduction to Mobile Robotics, 9/16/03

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