Robot Exploration with Combinatorial Auctions

http://www.sciencedaily.com/releases/2007/06/070609112916.htm

Robot Exploration

with Combinatorial AuctionsM. Berhault, H. Huang, P. Keskinocak,

S. Koenig, W. Elmaghraby, P. Griffin, A. Kleywegt

http://www.news.cornell.edu/releases/rover/Mars.update8-19-04.html

Corey A. Spitzer - CSCI 8110 04-20-2010

Optimal Task Allocation

Repeat Auctions

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Combinatorial Auctions

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Bidding Strategy

=

Near Optimal Allocation

http://shirt.woot.com/Derby/Entry.aspx?id=30206

Repeat Auctions

Robot1

Robot2

Goal

UnknownTerrain

Wall

Repeat Auctions

Robot1

Robot2

Goal

UnknownTerrain

Wall

Repeat Auctions

Robot1

Robot2

Goal

Wall

Wall

Repeat Auctions

Robot1

Robot2

Goal

Wall

Wall

Single Item vs. Combinatorial Auctions

Single Item vs. Combinatorial AuctionsPossible Bundles:

{}

{G1}

{G2}

{G3}

{G4}

{G1, G2}

{G1, G3}

{G1, G4}

{G2, G3}

{G2, G4}

{G3, G4}

{G1, G2, G3}

{G1, G2, G4}

{G1, G3, G4}

{G2, G3, G4}

{G1, G2, G3, G4}

Task Synergies - Positive

Travel Distance for R1: T(S)

T({G3}) = 4

T({G4}) = 4

T({G3, G4}) = 7

T({G3, G4}) ≤ T({G3}) + T({G4})

Task Synergies - Negative

Travel Distance for R1: T(S)

T({G3}) = 4

T({G1}) = 8

T({G3, G1}) = 16

T({G3, G1}) ≥ T({G3}) + T({G1})

Bidding Strategies

Single

Three-Combination

Smart-Combination

Nearest-Neighbor

Graph-Cut

http://blog.handbagsmaster.com/index.php/2009/09/eleven-auction-terms-you-should-know/

Bidding Strategies - Single

Same as single item auction

Bidding Strategies - Three-CombinationPossible Bundles with 5 Goals:{}{G1}{G2}{G3}{G4}{G5}{G1, G2}{G1, G3}{G1, G4}{G1, G5}{G2, G3}{G2, G4}{G2, G5}{G3, G4}{G3, G5}{G4, G5}{G1, G2, G3}{G1, G2, G4}{G1, G2, G5}{G1, G3, G4}

{G1, G3, G5}{G1, G4, G5}{G2, G3, G4}{G2, G3, G5}{G2, G4, G5}{G3, G4, G5}{G1, G2, G3, G4}{G1, G2, G3, G5}{G1, G2, G4, G5}{G1, G3, G4, G5}{G2, G3, G4, G5}{G1, G2, G3, G4, G5}

Bidding Strategies - Smart-Combination

Bid on all bundles that have 1 or 2 goals

Additionally, bid on the top N bundles containing more than 2 goals.

Given k clusters of s goals (where s is in the set S of cluster sizes >2), N = |S| * max(S) * k.

Goal

Goal Goal

Goal

Goal Goal

Goal

Goal Goal

Goal Goal

Goal

Bidding Strategies - Nearest-Neighbor

Bid on all "Good Sequences":

* {Gi} for all i

* If S = {Gi, ... Ge} is a good sequence then S U {Gt} is a good sequence if Gt is the closest neighbor to Ge not in S and the value of S U {Gt} ≥ the value of S

Bidding Strategies - Graph Cut

Bidding Strategies - Graph Cut

Maximum cuts

Summary of Experimental Results

Generally Best Performing Bidding Strategies wrt:

Travel Costs -- Graph-Cut

Travel Times -- Three-Combination

Smallest Number of Bids -- Single, then Graph-Cut

Smallest Robot Utilization -- Graph-Cut

Important Factors:

Goal distribution (uniform or clustered), number of clusters, prior knowledge of the terrain

Other Notes

When targets are uniformly distributed, all bidding strategies are fairly close wrt travel costs.

Nearest-Neighbor and Graph-Cut tend to have large bundle sizes => smaller number of active robots

Smaller robot utilization => smaller travel costs, but larger travel times

The End

Questions?