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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.

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Path look up tables an overview of navigation systems

Path Look-up Tables & An Overview of Navigation Systems

Hai Hoang


Path look up tables 2 3
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
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


1 st type of path look up table
1st 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 n0 for (a , b)

      • Followed by next neighbor n1 for (n0 , b)

      • Repeat until ni = b


  • 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 3D mazes


  • Hug memory consumption

    • Increases quadratically with the number of waypoints

    • Typically, each entry is 2 bytes

      • For 1,000 waypoints – 2MB

      • For 2,000 waypoints – 8MB

  • Contains only static representation of terrain

    • Can only reflect changes via an update or patch

    • O(n3) to update

2 nd type of path look up table
2nd 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

Memory consumption
Memory Consumption

  • Memory consumed for the 4 bit index look-up matrix is:

    • N x 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 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 changes

    • Still grows very fast

3 rd type of path look up table
3rd 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

Look up at top level pseudo code
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 b to path[]

Benefits over matrix indexed look up table
Benefitsover 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,

    • a2 + b2 < (a + b)2

  • More suitable for patching to reflect changes in the terrain

    • Can open or close portals

    • Patch an area


  • 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
Memory Consumption & Performance Relative to A*

Quake 3 arena
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
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 3D, shadowed, textured world at 30 frames a second. But for some reason, it appears to.” Alex Zavatone

  • Video from:


Fast graphics
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

Navigation system
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
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
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
AI Paradigms for Movement

  • Reactive Behaviors

  • Deliberative Planning

  • Hybrid Systems

Ai paradigms for movement1
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
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 cont1
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
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
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


  • 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
Examples of Navigation Systems

  • PathEngine


  • BioGraphic Technologies AI.implant


D simplified
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
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


  • 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


  • A* Explorer demo