Path%20Look-up%20Tables%20

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Path Look-up Tables An Overview of Navigation
Systems

• Hai Hoang
• 10/4/2004

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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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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.generation5.org/content/2002/ase.asp

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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

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Path Look-Up Matrix Example
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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 3D mazes

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Problems

• 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

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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

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Example of Indexed Look-Up Table
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Example of Indexed Look-Up Table(cont.)
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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

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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

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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

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Designing Portal Path Table
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(No Transcript)
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Look-Up at Top Level (pseudo-code)
Problem to move from a (in area A) to b
(in area B)

• if (AB) 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

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In Area Look-Up
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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,
• a2 b2 lt (a b)2
• More suitable for patching to reflect changes in
  the terrain
• Can open or close portals
• Patch an area

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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

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Memory Consumption Performance Relative to A
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Area-Based Look-Up Table???
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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

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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
• http//www.planetquake3.net/

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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/buildArticle.php?id
152
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An Overview of Navigation Systems (2.4)
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Navigation System

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

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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

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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)

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AI Paradigms for Movement

• Reactive Behaviors
• Deliberative Planning
• Hybrid Systems

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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

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AI Paradigms for Movement (cont)

• Deliberative Planning
• Reactive behaviors cant 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

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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

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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

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Implementing Deliberate Planning

• Planning doesnt 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

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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

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Examples of Navigation Systems

• PathEngine
• http//www.pathengine.com
• BioGraphic Technologies AI.implant
• http//www.biographictech.com

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D Algorithm
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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

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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

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References

• Game AI Programming Wisdom 2, Steve Rabin, 2004
• The Quake III Arena Bot, J. P. v. Waveren
• http//www.kbs.twi.tudelft.nl/Publications/MSc/200
  1-VanWaveren-MSc.html
• Map-Based Strategies for Robot Navigation in
  Unknown Environments , Anthony Stentz
• http//www.frc.ri.cmu.edu/axs/doc/aaai96.pdf
• A Explorer demo
• http//www.generation5.org/content/2002/ase.asp
• http//www.director-online.com/buildArticle.php?id
  152