1. 2.3 – Path Look-Up Tables Owen Cummings

2. William van der Sterren  Company CGF-AI specializes in tactical AI for 3D virtual worlds: autonomous AI squads and individuals, squad maneuvers and team tactics, dynamic response to threats, smart use of the terrain, human-like situational awareness, and interpretation of combat situations. CGF-AI specializes in tactical AI for 3D virtual worlds: autonomous AI squads and individuals, squad maneuvers and team tactics, dynamic response to threats, smart use of the terrain, human-like situational awareness, and interpretation of combat situations. CGF-AI  Products William is contributing to the AI for Guerrilla's Killzone (PlayStation2, 2004, published by Sony (SCEE / SCEA)). Killzone already collected an IGN Award "PlayStation 2 Best of Show" and another IGN Award "Best Shooter" at the May 2004 E3 conference / trade show. William is contributing to the AI for Guerrilla's Killzone (PlayStation2, 2004, published by Sony (SCEE / SCEA)). Killzone already collected an IGN Award "PlayStation 2 Best of Show" and another IGN Award "Best Shooter" at the May 2004 E3 conference / trade show.GuerrillaKillzone"PlayStation 2 Best of Show""Best Shooter"GuerrillaKillzone"PlayStation 2 Best of Show""Best Shooter" William contributed to the AI used in Guerrilla's Shellshock: Nam '67 (PlayStation2, Xbox, PC, 2004, published by Eidos Interactive). William contributed to the AI used in Guerrilla's Shellshock: Nam '67 (PlayStation2, Xbox, PC, 2004, published by Eidos Interactive).GuerrillaShellshock: Nam '67GuerrillaShellshock: Nam '67

3. Why use Path Look-Up Tables?  Path Look-Up tables can be 10 to 200 times faster than searching with A*  However, the amount of memory required for the tables often prohibits using them for anything other than small levels  Also they have problems reflecting changes in terrain

4. Path Look-Up Matrix  For N waypoints, the matrix has size NxN  Each entry in the matrix contains, for the corresponding source and destination pair, the next neighboring waypoint to visit or a no path available marker.

5. Simple Example 1 2 3 4 567 8 9 Start End A(2,9) = 1 A(1,9) = 3 A(3,9) = 5 A(5,9) = 6 A(6,9) = 7 A(8,9) = 9 A(7,9) = 8 Success! A(2,9) = No path sentinel Failure! So this means that we know right away with one memory access and without searching that a path does not exist from node 2 to node 9

6. Problems with Path Look-Up Matrices  Memory Consumption Increase quadratically with number of waypoints Increase quadratically with number of waypoints Typical number of waypoints between 256 and 65535 so 2 bytes per entry Typical number of waypoints between 256 and 65535 so 2 bytes per entry For 1000 waypoints -> 2MBFor 1000 waypoints -> 2MB For 2000 waypoints -> 8MBFor 2000 waypoints -> 8MB This limits the use of these tables to small levels This limits the use of these tables to small levels

7. Problems continued  Static representation of terrain Can only reflect changes via update or patch Can only reflect changes via update or patch Updating the table is an O(n 3 ) operation Updating the table is an O(n 3 ) operation Patching also problematic Patching also problematic To handle a central door being unlocked for a 1000 waypoint level, the full 2MB table would have to be replacedTo handle a central door being unlocked for a 1000 waypoint level, the full 2MB table would have to be replaced

8. Smaller Indexed Path Look-Up Matrix  Replace the 2 byte next waypoint to visit by a 4 bit index in the waypoint’s list of outgoing waypoints  Assumes a maximum of 15 outgoing waypoints per waypoint  Memory Consumption N*N*0.5 for the matrix + N*15*2.0 for the outgoing waypoint list N*N*0.5 for the matrix + N*15*2.0 for the outgoing waypoint list 542KB for 1000 waypoints 542KB for 1000 waypoints 4MB for 2000 waypoints 4MB for 2000 waypoints

9. Smaller Indexed Path Look-Up Matrix  Pros Memory consumption reduced by a factor of 4 Memory consumption reduced by a factor of 4 Can deal with 4 times as much terrain for the same amount of memory, at a mere 5-percent reduction in performance Can deal with 4 times as much terrain for the same amount of memory, at a mere 5-percent reduction in performance  Cons Still scales quadratically with number of waypoints Still scales quadratically with number of waypoints Still hard to accommodate terrain changes Still hard to accommodate terrain changes

10. But…  Using 1 MB for path look-up tables is not an option on many game platforms  So we need a different solution…

11. Area-Based Path Look-Up Table  Area-Based Approach Do path look-up at two levels Do path look-up at two levels Set of portalsSet of portals Clusters of waypoints (“areas”)Clusters of waypoints (“areas”)

12. How it works  To get from waypoint a to waypoint b Determine the nearby portals for a and b Determine the nearby portals for a and b Determine the shortest path between these portals using a portal path look up table Determine the shortest path between these portals using a portal path look up table Translate this portal path into a waypoint path, for each pair of portals on the portal path, retrieve the waypoint path between them using the look-up table of the area connecting this portal pair Translate this portal path into a waypoint path, for each pair of portals on the portal path, retrieve the waypoint path between them using the look-up table of the area connecting this portal pair

13. How to Partition the Terrain?  Areas Should consist of co-located waypoints with good interconnectivity Should consist of co-located waypoints with good interconnectivity Small borders to neighboring areas Small borders to neighboring areas Optimal area size is sqrt(N) Optimal area size is sqrt(N)  Portals Waypoints that connect the areas Waypoints that connect the areas Try to keep portals per area < 10 for faster and smaller look up tables Try to keep portals per area < 10 for faster and smaller look up tables

14. When the number of areas is tripled, the memory consumption of the area based look up tables is 3.3 times larger as opposed to 3 2 as large for the other LUTs This is because the portal table increases by a factor of 3 2 and the area tables only increase by a factor of 3 and because the portal table is much smaller this only results in a total memory increase of 3.3

15. The Algorithm in more detail  To look up a path from a (in area A) to b (in area B) If A = B, retrieve the local path from area A’s own look-up matrix and we are done If A = B, retrieve the local path from area A’s own look-up matrix and we are done If A ≠ B do the following If A ≠ B do the following For source area A, retrieve the outgoing connections ApFor source area A, retrieve the outgoing connections Ap For destination area B, retrieve the incoming portals BpFor destination area B, retrieve the incoming portals Bp Pick the pair (Ap o, Bp i ) that yields the shortest path (a - Ap o - Bp i -b)Pick the pair (Ap o, Bp i ) that yields the shortest path (a - Ap o - Bp i -b) For the pair Ap o, Bp i, retrieve a path consisting of inter-area connectionsFor the pair Ap o, Bp i, retrieve a path consisting of inter-area connections Finally, retrieve and construct the detailed waypoint path, by retrieving the in-area path for each area on the pathFinally, retrieve and construct the detailed waypoint path, by retrieving the in-area path for each area on the path

16. What do we need to do this?  For each area, we need to record how to travel from any waypoint in this area to another waypoint also in the area  Need to record all connections from that area to other areas  For every connection between two areas, we need to record the cost and shortest path to any other inter-area connection

17. Demo  Show the demo program

18. Terrain Representation issues  For a map with 1,500 waypoints and 20 areas, there might be some 300 waypoints lying on the border of connected areas  Find the minimal set of waypoints that together still represent all inter-area connections Typically 60 – 75% smaller Typically 60 – 75% smaller More efficient look-up at higher level More efficient look-up at higher level Smaller inter-area travel info matrix Smaller inter-area travel info matrix

19. Per Area Information  Waypoints within the area, and the connected portals (2 bytes per waypoint)  Incoming and outgoing waypoints in dedicated arrays (2 bytes per waypoint)  All in-area paths, as a matrix containing the index to the next neighbor. Index is a 1-byte index into the array of area waypoints.  Travel time to the outgoing portal, for every combination of waypoint, outgoing portal (1 byte per entry)  Travel time from the incoming portal, for every combination of incoming portal, waypoint (1 byte per entry)

21. Portal Path Information  Matrix that contains for every pair of portal waypoints (p i, p o ): Travel time from p i to p o or no path (2 bytes) Travel time from p i to p o or no path (2 bytes) Next portal to visit to get to p o (2 bytes) Next portal to visit to get to p o (2 bytes) Next area to traverse to get from p i to the next portal (2 bytes) Next area to traverse to get from p i to the next portal (2 bytes)

22. Performance Comparison Short Paths – 0 to 16 waypoints Long Paths – 17+ waypoints Far Travel Costs – costs of paths longer than 16 waypoints. AI typically compares travel costs when selecting the nearest item or power up to fetch. Path look-up matrices offer 50 to 150 times better performance than A*, and 2 to 5 times better than area based Area based look-up tables provide a speed up of 10 to 80 times

23. Pesky Dynamic Terrain  Area based look up tables are much more suitable for handling terrain changes because of the partitioning  Worst case the patch consists of several tens of KB when the portal table and an area table have to be changed  More complicated when several portals can be opened or closed in arbitrary order. Have to compute various patches for all sequences

24. Quake 3  Quake 3 Arena uses an approach similar to the area-based look-up tables, but for volume-based (as opposed to waypoints) navigation data. Link to pdf Link to pdf Link to pdf Link to pdf Section 6 and 12 Section 6 and 12 Very in depth, very technical, very confusing Very in depth, very technical, very confusing

25. 2.4 - An Overview of Navigation Systems  This “exciting” chapter goes over software engineering strategies to implement a navigation system  What is a navigation system? A navigation system is a separate component responsible for synthesizing movement behaviors. A navigation system is a separate component responsible for synthesizing movement behaviors.

26. Levels of Abstraction  Choosing the level of abstraction mostly depends on the complexity of the agent AI Planner : Only the shortest path algorithm is abstracted out and implemented separately. Agent is responsible for making the path request and interpreting the result Planner : Only the shortest path algorithm is abstracted out and implemented separately. Agent is responsible for making the path request and interpreting the result Pathfinder : Gives slightly more responsibility to the navigation system, the pathfinder would deal with the execution of plans. Pathfinder : Gives slightly more responsibility to the navigation system, the pathfinder would deal with the execution of plans. Sub-architecture : It’s possible to use an AI architecture specifically for navigation. This will generally be composed of different movement behaviors and planning abilities, including the terrain model Sub-architecture : It’s possible to use an AI architecture specifically for navigation. This will generally be composed of different movement behaviors and planning abilities, including the terrain model

27. Navigation Interfaces  Agent AI has a certain level of complexity in the desires and motivations  Creating intelligent movement involves transmitting these motivations to the navigation system  The interface allows information about these motivations to be expressed

28. Interface Expressiveness  Choosing an interface involves making a compromise between focus and flexibility Highly focused – can be better tuned to a specific problem Highly focused – can be better tuned to a specific problem Flexible – can have the expressiveness to handle a wider variety of scenarios Flexible – can have the expressiveness to handle a wider variety of scenarios

29. Different levels of expressiveness  Existing paradigms Single Pair : Two points are specified in the world (origin and destination), and the shortest path between them is returned Single Pair : Two points are specified in the world (origin and destination), and the shortest path between them is returned Weighted Destinations : Instead of limiting the requests to one destination, this can be extended to multiple goals, each with its own reward coefficient. An optimal path that maximizes the tradeoff between reward and cost Weighted Destinations : Instead of limiting the requests to one destination, this can be extended to multiple goals, each with its own reward coefficient. An optimal path that maximizes the tradeoff between reward and cost Spatial Desires : Abstracting out space, it’s possible to specify the movement by passing the motivations from the agent to the navigation system (e.g. get armor or a weapon) Spatial Desires : Abstracting out space, it’s possible to specify the movement by passing the motivations from the agent to the navigation system (e.g. get armor or a weapon)

30. AI Paradigms for Movement  Reactive Behaviors Takes sensory input and performs direct mapping to determine output Takes sensory input and performs direct mapping to determine output Possible Behaviors – obstacle avoidance, seeking, fleeing Possible Behaviors – obstacle avoidance, seeking, fleeing Perfect for simple situations Perfect for simple situations Can’t handle traps or complex layouts Can’t handle traps or complex layouts  Deliberative Planning Provably optimal paths Provably optimal paths Higher-level of spatial intelligence; plans made according to terrain representation Higher-level of spatial intelligence; plans made according to terrain representation  Hybrid Systems Combine common sense of reactive behaviors with intelligence of planning Combine common sense of reactive behaviors with intelligence of planning

31. Implementation  Reactive Behaviors Steering behaviors based on highly explicit mathematical equations Steering behaviors based on highly explicit mathematical equations Two problems : integration of multiple behaviors and realism Two problems : integration of multiple behaviors and realism Prioritize behaviors and use fuzzy logic to simulate realism Prioritize behaviors and use fuzzy logic to simulate realism  Deliberative Planning Not necessarily a search, other techniques can be more efficient Not necessarily a search, other techniques can be more efficient Precompute everything (like the look-up tables) Precompute everything (like the look-up tables) Reactive approximation techniques to build near optimal paths without a search Reactive approximation techniques to build near optimal paths without a search Dynamic environments make things tricky Dynamic environments make things tricky Trigger a replan when the conditions have changed sufficientlyTrigger a replan when the conditions have changed sufficiently “Quality of service” algorithms“Quality of service” algorithms

32. Conclusion  The development of a navigation system takes more than understanding a heuristic search algorithm  Numerous issues involved in synthesizing realistic movement in games  Ignoring these can lead to a suboptimal solution, unnecessarily complex code, and visible problems with the behaviors