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CSCI 4310. Lecture 8: Path Planning. Book. Buckland Ch. 8. Navigation. How to represent the areas that an agent can occupy in the world. Navigation Graph (NavGraph) Some More Sophisticated Methods. Nav Graph. Works in 2 or 3 dimensions Trade-off Coarsely granulated Easier to manage

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csci 4310

CSCI 4310

Lecture 8: Path Planning

slide2
Book
  • Buckland Ch. 8
navigation
Navigation
  • How to represent the areas that an agent can occupy in the world.
  • Navigation Graph (NavGraph)
  • Some More Sophisticated Methods
nav graph
Nav Graph
  • Works in 2 or 3 dimensions
  • Trade-off
    • Coarsely granulated
      • Easier to manage
      • Less space / time
    • Finely granulated
      • Can become unwieldy
      • Necessary?
      • Think of Grand Theft Auto style worlds
      • But, allows a more realistic ‘feel’
finely granulated
Finely granulated
  • Prevents some backtracking
  • Smoother paths
path smoothing
Path smoothing
  • Required with inverse proportion to granularity of the nav graph
  • With a course graph, we may go backwards to find the nearest “source” node
  • This looks unrealistic
path smoothing1
Path smoothing
  • Dijkstra or A* returns A-B-C because there is no A-C link in the underlying Nav Graph
  • Our agent is not precisely constrained by the Nav Graph,
  • So… if A-C is feasible (we don’t hit any obstacles) take it

B

C

A

path smoothing2
Path smoothing
  • Raven_PathPlanner::SmoothPathEdges
  • Can check adjacent edges (quicker)
  • Or all edge combinations (slower but more precise)
  • bool Raven_Bot::canWalkBetween (Vector2D from, Vector2D to)

B

C

A

nav graph1
Nav Graph
  • Can select a data structure that allows additional information at nodes or edges
    • “Cost” of traversing the edge, to bias A* or Dijkstra
    • Crossing water is more expensive, so choose a slightly longer path that avoids water
    • Books refers to this as annotation
    • Can also use information to determine state of player (swimming, running, etc.)
spatial partitioning
Spatial Partitioning
  • Often need to know…
    • Which node is closest to me
    • Which node is closest to my destination
    • Which health pack is closest to me
    • Etc.
  • Track each entity or track each location
  • Spatial partition tracks entities at each location
raven path planning details
Raven Path Planning Details
  • Raven_PathPlanner class
  • 1. Find the closest node to the bot’s current location
  • 2. Find the closest node to the desired location (or item)
  • 3. Use a search algorithm to find the least cost path between the two.
  • * notice we did not say shortest
dijkstra vs a
Dijkstra vs. A*
  • If we have a good heuristic, A* works well
    • When plotting a path from source to destination, we usually have a good distance estimate
  • If no heuristic, can save some overhead with Dijkstra
    • Such as when searching for the nearest power-up.
    • We may not know where it is
raven details
Raven Details
  • Request a path

// Given an item type, this method determines the closest reachable graph node

// to the bot\'s position and then creates a instance of the time-sliced

// Dijkstra\'s algorithm, which it registers with the search manager

bool RequestPathToItem(unsigned int ItemType);

// Given a target, this method first determines if nodes can be reached from

// the bot\'s current position and the target position. If either end point

// is unreachable the method returns false.

//

// If nodes are reachable from both positions then an instance of the time-

// sliced A* search is created and registered with the search manager. the

// method then returns true.

bool RequestPathToPosition(Vector2D TargetPos);

implementation
Implementation
  • A* is exponential in worst case
  • And requires significant storage
    • Depends on heuristic used
implementation1
Implementation
  • Book has several search speed-ups
  • Given fixed cycles for path planning per game loop iteration
  • Pre-Calculated Paths
  • Time-Sliced Search
  • Hierarchical Search
pre calculated paths
Pre-Calculated Paths
  • Dynamic programming

A path from B

To D should

First Go To

Node C

Need to store

Both sides if

We are using

A directed Nav

Graph

(A to B may

Be different than

B to A)

pre calculated paths in raven
Pre-Calculated Paths in Raven
  • Methods to call to build tables
  • CreateAllPairsTable(const graph_type& G)
    • Returns a 2-D Vector of ints
  • Can also have pre-calculated costs
    • Useful in goal evaluation in Chapter 9
  • Pre-calculated paths time space tradeoff
time sliced path planning
Time-Sliced Path Planning
  • Modify search algorithm to allow a single iteration
  • Call as many iterations as time allows
  • Can incrementally request search paths to reduce burden on CPU
hierarchical path planning
Hierarchical Path Planning
  • High level course nav graph
  • Plot general path
  • Move to more detailed nav graph
  • Good for large environments
deformable terrain
Deformable Terrain
  • Dynamically changing Nav Graph
  • Destroying A Bridge
  • Knocking Down a Wall
deformable terrain1
Deformable Terrain
  • Requires a modifiable Nav Graph
  • Fully deformable terrain has not come about yet because
    • No pre-calculated paths can be generated (or they can, but many more are required and must be tied to state of the world)
    • Increases in time for path request
deformable terrain2
Deformable Terrain
  • Tony Stentz of Carnegie Mellon
  • D* or Dynamic A* algorithm
  • Useful under dynamic terrain
  • http://www.frc.ri.cmu.edu/~axs/
navigating problems
Navigating Problems
  • Determine when you are blocked
  • No forward progress
  • Or
  • Elapsed Time > (Destination.cost / Bot.maxSpeed) + Margin of Error
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