Reconnection with the Ideal Tree A New Approach to Real-Time Search - - PowerPoint PPT Presentation

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Reconnection with the Ideal Tree A New Approach to Real-Time Search - - PowerPoint PPT Presentation

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Search Designing a solution The FRIT Algorithm Results Future work Reconnection with the Ideal Tree A New Approach to Real-Time Search Le on Illanes Department of Computer Science School of Engineering Pontificia Universidad Cat

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SLIDE 1

Search Designing a solution The FRIT Algorithm Results Future work

Reconnection with the Ideal Tree

A New Approach to Real-Time Search Le´

  • n Illanes

Department of Computer Science School of Engineering Pontificia Universidad Cat´

  • lica de Chile

Santiago, Chile

January 10, 2014

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 2

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Agent-centered Search

Search in initially unknown environments.

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 3

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Agent-centered Search

Search in initially unknown environments. Search in dynamic environments.

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 4

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Agent-centered Search

Search in initially unknown environments. Search in dynamic environments. Real-time search.

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 5

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Agent-centered Search

Search in initially unknown environments. Search in dynamic environments. Real-time search.

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 6

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

The LRTA* Algorithm

Learning Real-Time A* Local A*-like search around the agent Move towards the best state in the local region

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 7

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

1 2 1 2 3 2 3 4

Learning Real Time A*

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 8

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

1 2 1 2 3 2 3 4

Learning Real Time A*

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 9

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

1 2 1 2 3 2 3 4

Learning Real Time A*

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 10

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

1 2 1 2 3 2 3 4

Learning Real Time A*

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 11

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

1 2 1 4 3 2 3 4

Learning Real Time A*

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 12

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

1 2 1 4 3 2 3 4

Learning Real Time A*

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 13

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

1 2 1 4 5 2 3 4

Learning Real Time A*

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 14

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

1 2 1 4 5 2 3 4

Learning Real Time A*

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 15

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

1 2 1 4 5 2 3 4

Learning Real Time A*

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 16

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 2 4 3

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 17

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 2 4 3

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 18

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 2 4 3

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 19

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 4 4 3

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 20

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 4 4 3

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 21

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 4 4 5

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 22

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 4 4 5

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 23

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 6 4 5

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 24

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 6 4 5

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 25

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 6 6 5

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 26

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 6 6 7

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 27

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 8 6 7

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 28

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 8 6 7

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 29

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 5 8 6 7

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 30

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 7 8 6 7

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 31

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 7 8 8 7

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 32

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 7 8 8 9

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 33

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 7

10

8 9

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 34

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

Heuristic learning (` a la LRTA*)

1 2 3 4 6 5 1 2 4 2 4 5 1 3 3 7

10

8 9

Path finding in an unknown environment (w/ free-space assumption)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 35

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

How do we avoid erratic movements?

More lookahead More learning Pruning states

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 36

Search Designing a solution The FRIT Algorithm Results Future work Agent-centered Search Issue: Heuristic Depressions

How do we avoid erratic movements?

More lookahead More learning Pruning states

We asked ourselves: Anything simpler?

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 37

Search Designing a solution The FRIT Algorithm Results Future work Design principles

Design principles

1 2 Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 38

Search Designing a solution The FRIT Algorithm Results Future work Design principles

Design principles

1

Avoid expensive computation

Sorting Learning

2 Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 39

Search Designing a solution The FRIT Algorithm Results Future work Design principles

Design principles

1

Avoid expensive computation

Sorting Learning

2

Exploit the heuristic

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 40

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

The FRIT Algorithm

Follow and Reconnect with the Ideal Tree

Le´

  • n Illanes

Reconnection with the Ideal Tree

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Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

The Ideal Tree

Definition (Ideal Tree) For a problem graph G with goal g and free-space assumption graph GM, we define an Ideal Tree to be any spanning tree for GM rooted at g.

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 42

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

The Ideal Tree

Definition (Ideal Tree) For a problem graph G with goal g and free-space assumption graph GM, we define an Ideal Tree to be any spanning tree for GM rooted at g. In practice: parent(s) = argmin

u:(s,u)∈E(GM)

c(s, u) + h(u)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 43

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

The Ideal Tree

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 44

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

The Ideal Tree

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 45

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT

Input: Given the free-space assumption graph GM, a goal g, and a starting node s0. s ← s0 // Set the current state to s0 while s = g do

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 46

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT

Input: Given the free-space assumption graph GM, a goal g, and a starting node s0. s ← s0 // Set the current state to s0 while s = g do Observe the environment around s and remove non-existent arcs from GM.

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 47

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT

Input: Given the free-space assumption graph GM, a goal g, and a starting node s0. s ← s0 // Set the current state to s0 while s = g do Observe the environment around s and remove non-existent arcs from GM. if s has no parent node then Reconnect:

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 48

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT

Input: Given the free-space assumption graph GM, a goal g, and a starting node s0. s ← s0 // Set the current state to s0 while s = g do Observe the environment around s and remove non-existent arcs from GM. if s has no parent node then Reconnect: Follow:

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 49

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT

Input: Given the free-space assumption graph GM, a goal g, and a starting node s0. s ← s0 // Set the current state to s0 while s = g do Observe the environment around s and remove non-existent arcs from GM. if s has no parent node then Reconnect: Follow: s ← parent(s) // Move the agent to the parent of s

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 50

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT

Input: Given the free-space assumption graph GM, a goal g, and a starting node s0. s ← s0 // Set the current state to s0 while s = g do Observe the environment around s and remove non-existent arcs from GM. if s has no parent node then Reconnect: Locally search around s to find any state s′ connected to g. Update the Ideal Tree to include the path from s to s′. Follow: s ← parent(s) // Move the agent to the parent of s

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 51

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 52

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 53

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 54

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 55

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 56

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 57

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 58

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 59

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 60

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 61

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 62

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 63

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

FRIT by example Observe Follow Reconnect

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 64

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 65

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 66

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 67

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 68

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 69

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 70

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 71

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 72

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 73

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 74

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 75

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 76

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 77

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 78

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 79

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 80

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 81

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

A better example

Le´

  • n Illanes

Reconnection with the Ideal Tree

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Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

Video!

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 83

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

The Real-Time Property

As described, FRIT is not a Real-Time Search Algorithm. We need a bound on the amount of states visited while reconnecting.

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 84

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

The Real-Time Property

As described, FRIT is not a Real-Time Search Algorithm. We need a bound on the amount of states visited while reconnecting. What to do when the bound is surpassed?

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 85

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

Two approaches

1 2 Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 86

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

Two approaches

1

Standard FRIT: Do nothing. . . [RIBH13, RIBH14]

2 Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 87

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

Two approaches

1

Standard FRIT: Do nothing. . . [RIBH13, RIBH14]

2

FRITRT: Use a Real-Time Search Algorithm for

  • Reconnection. [RIBH14]

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 88

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

Complexity

Follow is O(1)

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  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 89

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

Complexity

Follow is O(1) Reconnect can be O(|V |)

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 90

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

Complexity

Follow is O(1) Reconnect can be O(|V |) Reconnect can be O(|V |). Using BFS as the local search algorithm, we check at most |V | nodes to see if they are connected to the goal. This check can be done as a recursive function with no side effects and can thus be memoized, ensuring that for each reconnection search we do at most |V | comparisons.

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 91

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

Complexity

Follow is O(1) Reconnect can be O(|V |) Reconnect can be O(|V |). Using BFS as the local search algorithm, we check at most |V | nodes to see if they are connected to the goal. This check can be done as a recursive function with no side effects and can thus be memoized, ensuring that for each reconnection search we do at most |V | comparisons. Additionally, we prove correcteness and completeness for both FRIT and FRITRT, while giving an explicit upper bound of (|V |+1)2

4

moves for FRIT and O(|V |3) moves for FRITRT.

Le´

  • n Illanes

Reconnection with the Ideal Tree

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Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

Convergence

FRIT immediately converges to a suboptimal solution

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 93

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

Convergence

FRIT immediately converges to a suboptimal solution

Le´

  • n Illanes

Reconnection with the Ideal Tree

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SLIDE 94

Search Designing a solution The FRIT Algorithm Results Future work The Ideal Tree Follow and Reconnect FRIT and Real-Time Search Properties

Convergence

FRIT immediately converges to a suboptimal solution

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Search Designing a solution The FRIT Algorithm Results Future work FRITRT FRIT with BFS Comparison between approaches

Games: FRITRT halves daRTAA*’s solutions

1000 10000 100000 1000000 10000000 20 40 60 80 100 120 140 Average Solution Cost (log-scale) Average time per planning episode (us) FRIT_rt(RTAA) FRIT_rt(daRTAA) RTAA daRTAA

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Search Designing a solution The FRIT Algorithm Results Future work FRITRT FRIT with BFS Comparison between approaches

Mazes: Similar tendencies

1000 10000 100000 1000000 10000000 20 40 60 80 100 120 Average Solution Cost (log-scale) Average time per planning episode (us) FRIT_rt(RTAA) FRIT_rt(daRTAA) RTAA daRTAA

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Search Designing a solution The FRIT Algorithm Results Future work FRITRT FRIT with BFS Comparison between approaches

Games: FRIT dominates for very small t

1000 10000 100000 1000000 10000000 100 200 300 400 500 600 Average Solution Length (log-scale) Average time per planning episode (us) FRIT(BFS) RA* AA*

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Search Designing a solution The FRIT Algorithm Results Future work FRITRT FRIT with BFS Comparison between approaches

Mazes: Again, similar tendencies

1000 10000 100000 1000000 10000000 100 200 300 400 500 600 Average Solution Length (log-scale) Average time per planning episode (us) FRIT(BFS) RA* AA*

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Search Designing a solution The FRIT Algorithm Results Future work FRITRT FRIT with BFS Comparison between approaches

FRIT(BFS) obtains better solutions

1000 10000 100000 1000000 10000000 10 20 30 40 50 60 Average Solution Length (log-scale) Average time per planning episode (us) FRIT_rt(daRTAA) FRIT(BFS)

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Search Designing a solution The FRIT Algorithm Results Future work

Future work

Other applications Optimizing for pathfinding in grids [RIB14] Moving-target search Dense graphs (e.g.: Airport networks)

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Search Designing a solution The FRIT Algorithm Results Future work

Summary

We presented a family of real-time search algorithms which: Are easy to implement Avoid expensive computations Converge to suboptimal solutions in the second trial Significantly outperform standard real-time search algorithms when time constraints are tight

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Search Designing a solution The FRIT Algorithm Results Future work

Bibliography

Nicol´ as Rivera, Le´

  • n Illanes, and Jorge A. Baier, Real-time

pathfinding in unknown terrain via reconnection with an ideal tree, Proceedings of the 14th Ibero-American Conference on Artificial Intelligence (IBERAMIA) (Santiago, Chile), November 2014, To appear. Nicolas Rivera, Leon Illanes, Jorge A. Baier, and Carlos Hern´ andez, Reconnecting with the ideal tree: An alternative to heuristic learning in real-time search, Proceedings of the 6th Symposium on Combinatorial Search (SoCS), 2013. Nicol´ as Rivera, Le´

  • n Illanes, Jorge A. Baier, and Carlos

Hern´ andez, Reconnection with the ideal tree: A new approach to real-time search, Journal of Artificial Intelligence Research 50 (2014).

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Reconnection with the Ideal Tree

A New Approach to Real-Time Search Le´

  • n Illanes

Department of Computer Science School of Engineering Pontificia Universidad Cat´

  • lica de Chile

Santiago, Chile

January 10, 2014

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FRIT(BFS) AA* k

  • Avg. Its

Time/ep No moves

  • Avg. Its

Time/ep No moves (µs) (%) (µs) (%) 1 1508631 0.0430 99.80 1144680 0.4152 99.84 5 303483 0.2148 99.01 229967 2.0727 99.25 10 152858 0.4283 98.03 115628 4.1376 98.51 50 32401 2.0940 90.71 24156 20.378 92.86 100 17370 4.0678 82.67 12723 40.004 86.44 500 5449 16.115 44.74 3607 172.41 52.15 1000 4035 24.840 25.38 2583 274.35 33.20 5000 3073 39.316 2.046 1854 474.29 6.904 10000 3026 40.487 0.501 1775 514.88 2.764 50000 3011 40.851 0.030 1728 524.55 0.117 100000 3011 40.869 0.007 1726 543.66 0.014

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Memoizing the tree component

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