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 

1 st 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 n i = 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 3D mazes

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(n 3 ) to update

2 nd 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 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: ► 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 ► 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) ► 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[] Problem: to move from a (in area A) to b (in area B)

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 ► uitable for patching to reflect changes in the terrain ► 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 3D, shadowed, textured world at 30 frames a second. But for some reason, it appears to.” Alex Zavatone ► Video from: 

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

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 ► PathEngine  ► BioGraphic Technologies AI.implant 

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  MSc.html MSc.html MSc.html ► Map-Based Strategies for Robot Navigation in Unknown Environments, Anthony Stentz  ► A* Explorer demo  ►