Path Lookup Tables An Overview of Navigation Systems

Path Look-up Tables & An Overview of Navigation Systems Hai Hoang 10/4/2004

Path Look-up Tables (2. 3) ► Outline: § Why Use Look-up Tables? § 3 types of look-up tables ►Path look-up matrix ►Indexed path look-up matrix ►Area-based look-up table § Design and Performance of each

Why Use Path-Look Up Tables? ► A* is a popular path search algorithm, but slow. ► Fastest way to find a path § NOT to search § but to look up a path from a precomputed table ► Free up the CPU for other AI decisions ► How much faster? § 10 to 200 times faster, depending on implementation and terrain ► A* Explorer demo § http: //www. generation 5. org/content/2002/ase. asp

st 1 Type of Path Look-Up Table ► Using a matrix § For N waypoints, the matrix size is N x N § Each cell stores ►The next neighboring waypoint to visit on the path ►Or the “no path available” marker § To look up path from a to b ►Retrieve next neighbor n 0 for (a , b) ►Followed by next neighbor n 1 for (n 0 , b) ►Repeat until ni = b

Path Look-Up Matrix Example

Benefits ► Fast path retrieval ► Predictable path ► Low CPU consumption ► Path retrieval performance is not influenced by terrain layout § Unlike A* - as efficiently with deserted plains as with 3 D mazes

Problems ► Hug memory consumption § Increases quadratically with the number of waypoints § Typically, each entry is 2 bytes ►For 1, 000 waypoints – 2 MB ►For 2, 000 waypoints – 8 MB ► Contains only static representation of terrain § Can only reflect changes via an update or patch § O(n 3) to update

nd 2 Type of Path Look-Up Table ► Using an Indexed Path Look-up Matrix § Reduce memory consumption by factor of 4 by: ► using 1 matrix to store an index, ► another to store the outgoing waypoints ► Replace the 2 bytes “next waypoint to visit” with a 4 -bit index into the waypoint list of outgoing waypoints ► Assumption: § Reduce the waypoint graph so each waypoint use a maximum of only 15 outgoing waypoints ► By trimming away outgoing waypoints best approximated by another link or via a shorter path

Example of Indexed Look-Up Table

Example of Indexed Look-Up Table(cont. )

Memory Consumption ► Memory consumed for the 4 bit index lookup matrix is: § N x. 5 (. 5 byte is 4 bits) ► For the 15 outgoing waypoints look-up matrix: § N x 15 x 2 ► For 1, 000 waypoints: 542 kb ► For 2, 000 waypoints: 4 MB

Benefits and Problems ► Benefits: ► 4 times a much terrain for the same amount of memory as regular path-look up matrix ►Only about 5% reduction in performance ► 2 to 5 times better than area-based matrix ► Problem: ►Hard to update for terrain ►Still grows very fast changes

rd 3 Type of Path Look-Up Table ► Using Area-Based look-up matrix § Divide terrain up into areas § Move from area to area using portals § Path look-up is performed on two levels

Designing Portal Path Table

Look-Up at Top Level (pseudo-code) Problem: to move from a (in area A) to b (in area B) if (A==B) then both waypoints in the same area, just look in the area table ► If (A!=B) - 2 different areas ► § Retrieve portal for area A , call it Pa ► Stores § § § the path from a to Pa in path[] Retrieve portal for area B, call it Pb Find the shortest path from Pa to Pb From Pa to Pb, there might be portals in between ► If there is, find path from Pa to Pi ► Translate the portal path into waypoints moves and add to path[] ► until Pi == Pb § Finally, add path from Pb to path[]

In Area Look-Up

Benefits over Matrix & Indexed Look-up Table ► Using many smaller tables, 1 for portals paths, several for the path with in each area. § Save lots of memory, especially for larger numbers of waypoints § Since look-up tables are quadratic, § a 2 + b 2 < (a + b)2 ► More suitable for patching to reflect changes in the terrain § Can open or close portals § Patch an area

Problems? ► Memory consumption depends on the quality of the area and the size of areas interconnection ► And the reason: open areas § More memory if not partitioned well § Larger area interconnections – needs more portals § Could be harder to patch

Memory Consumption & Performance Relative to A*

Area-Based Look-Up Table? ? ?

Quake 3 Arena ► Used a technique similar to area look-up table ► Map is divided into convex hulls called areas Minimal navigation complexity, such as walk or swim Maps with 5000 or more areas are common. Moving from one area to another depends on reachability § Quake uses a real-time dynamic routing algorithm § The routing data is caches for fast look-up § The idea of portals are used for teleporting between areas § § §

Does it make you wonder? ► How graphics are rendered fast enough. ► Handle multi-players – added delay ► CPU Time left for AI for bots ► “If you're a fan of Quake like I am, you're surely aware that your computer is not able to render that entire 3 D, shadowed, textured world at 30 frames a second. But for some reason, it appears to. ” Alex Zavatone ► Video from: § http: //www. planetquake 3. net/

Fast graphics? ? ? ► What it is doing is taking data from a prerendered world and turning that into a textured, shadowed realistic looking environment. That's possible because the information has already been calculated and is stored in some sort of look up tables. “ Alex Zavatone http: //www. director-online. com/build. Article. php? id=152

An Overview of Navigation Systems (2. 4)

Navigation System ►A Navigation System is a separate component responsible for synthesizing movement behaviors. ► By encapsulating navigation into a component, it’s simpler to craft behaviors and movements. ► Purpose is to provide modularity in AI programming.

3 Levels of Abstraction ► Planner: § Only the shortest path algorithm abstracted and implemented in the navigation system § The agent has to make the request and interpret the result. ► Pathfinder: § The pathfinder would deal with the execution of the plans § The agent still has direct control of the paths ► Sub-architecture: § Planning abilities and composing different movement behaviors

Navigation Interfaces Allows agent to send information to the navigation system ► When designing the interface the programmer must decide between a focused or flexible interface ► Existing paradigms for navigation interfaces (starting with the most focused) ► § Single pair: Two points are specified, the shortest path is returned. § Weighted destinations: Can have multiple destinations, each with its own reward coefficient. § Spatial desires: Specifying the movement by passing the motivation from the agent to the navigation system (e. g. get armor or get weapon)

AI Paradigms for Movement ► Reactive Behaviors ► Deliberative Planning ► Hybrid Systems

AI Paradigms for Movement ► Reactive Behaviors (reactive steering): § Takes sensory input and performs a direct mapping to determine output § Example: takes in local info about obstacles and outputs commands as to where to move § Possible behaviors include obstacles avoidance, seeking, and fleeing. § Cannot handle traps , complex layout, intricate scenarios, and human-level movement with these behaviors

AI Paradigms for Movement (cont) ► Deliberative Planning: § Reactive behaviors can’t handle traps , complex layout, intricate scenarios, and human-level movement § Planning can formulate suitable paths in the world before used to solve these problems § Plans are made according to the terrain representation

AI Paradigms for Movement (cont) ► Hybrid Systems: § Simple obstacles can be handled by reactive behaviors, no need to waste a lot of time on finding paths that could be handled straightforwardly § Planned is need to optimized between speed or quality of movement § Solution is to use both paradigms

Implementing Reactive Behavior ► Simplest technique is steering behaviors § Using mathematical equations to decide where to steer next § Problem with: ►Integration of multiple behaviors § Fixed by prioritize behaviors ►Realism § Fuzzy logic – blend the behaviors together to make it look more realistic

Implementing Deliberate Planning ► Planning doesn’t necessary mean search § Precompute everything § Use reactive approximation to build near optimal path § Use threshold to trigger replan § Use D* to research the tree from A* § Use quality of service algorithm

Conclusion ► Choose the right navigation architecture is important § Improve quality of the behaviors § Increase performance § Make it easier for Agent to integrate with your navigation system

Examples of Navigation Systems ► Path. Engine § http: //www. pathengine. com ► Bio. Graphic Technologies AI. implant § http: //www. biographictech. com

D* Algorithm

D* Simplified ►S = Start state ► G = Goal state ► X = Current state ► M = Current map ► 1) Store all known, approximate, estimated, and believed information about the environment in M ► 2) Let X = S

D* Simplified (cont. ) ► 3) Plan an optimal path from X to G using M -terminate with failure if no path found ► 4) Follow path found in 3 until find G or find discrepancy in M and the environment ► 5) Update M to include new sensor info, then go to 3 to replan

References ► Game AI Programming Wisdom 2, Steve Rabin, 2004 ► The Quake III Arena Bot, J. P. v. Waveren ► Map-Based Strategies for Robot Navigation in Unknown Environments , Anthony Stentz § http: //www. kbs. twi. tudelft. nl/Publications/MSc/2001 -Van. Waveren. MSc. html § http: //www. frc. ri. cmu. edu/~axs/doc/aaai 96. pdf ► A* Explorer demo ► http: //www. director-online. com/build. Article. php? id=152 § http: //www. generation 5. org/content/2002/ase. asp