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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
- Less space / time

- Finely granulated
- Can become unwieldy
- Necessary?
- Think of Grand Theft Auto style worlds
- But, allows a more realistic ‘feel’

- Coarsely granulated

Finely granulated

- Prevents some backtracking
- Smoother paths

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 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 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 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

- 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_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*

- 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

- 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

- A* is exponential in worst case
- And requires significant storage
- Depends on heuristic used

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

- 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

- 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

- 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

- High level course nav graph
- Plot general path
- Move to more detailed nav graph
- Good for large environments

Deformable Terrain

- Dynamically changing Nav Graph
- Destroying A Bridge
- Knocking Down a Wall

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 Terrain

- Tony Stentz of Carnegie Mellon
- D* or Dynamic A* algorithm
- Useful under dynamic terrain
- http://www.frc.ri.cmu.edu/~axs/

Navigating Problems

- Determine when you are blocked
- No forward progress
- Or
- Elapsed Time > (Destination.cost / Bot.maxSpeed) + Margin of Error

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