http://www.sciencedaily.com/releases/2007/06/070609112916.htm
Robot Exploration with Combinatorial Auctions M. Berhault, H. Huang, P. Keskinocak,  S. Koenig, W. Elmaghraby, P. Griffin,...
Optimal Task Allocation Repeat Auctions  + Combinatorial Auctions + Bidding Strategy = Near Optimal Allocation http://shir...
Repeat Auctions Robot 1 Robot 2 Goal Unknown Terrain Wall
Repeat Auctions Robot 1 Robot 2 Goal Unknown Terrain Wall
Repeat Auctions Robot 1 Robot 2 Goal Wall Wall
Repeat Auctions Robot 1 Robot 2 Goal Wall Wall
Single Item vs. Combinatorial Auctions
Single Item vs. Combinatorial Auctions Possible Bundles: {} {G1} {G2} {G3} {G4} {G1, G2} {G1, G3} {G1, G4} {G2, G3} {G2, G...
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({...
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(...
Bidding Strategies Single Three-Combination Smart-Combination Nearest-Neighbor Graph-Cut http://blog.handbagsmaster.com/in...
Bidding Strategies - Single Same as single item auction
Bidding Strategies - Three-Combination Possible Bundles with 5 Goals: {} {G1} {G2} {G3} {G4} {G5} {G1, G2} {G1, G3} {G1, G...
Bidding Strategies - Smart-Combination Bid on all bundles that have 1 or 2 goals Additionally, bid on the top N bundles co...
Bidding Strategies - Nearest-Neighbor Bid on all "Good Sequences":  * {G i } for all i * If S = {G i , ... G e }...
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 -...
Other Notes When targets are uniformly distributed, all bidding strategies are fairly close wrt travel costs. Nearest-Neig...
The End Questions?
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Robot Exploration with Combinatorial Auctions

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  • Search and rescue robot Problem: unforeseen obstacles/changing environment simple, single-item auctions => tasks allocated with short-sightedness (simple metric - proximity to next task is only consideration)
  • Spirit
  • humans can recognize clusters and allocate appropriately robots using single item auctions allocate with short-sightedness (simple metric - proximity to next task is only consideration)
  • How to find the optimal bundle? Synergies
  • Bidding on the big picture, sacrificing low hanging fruit
  • with all strategies, the value of a goal is a function of the travel distance for the robot
  • Optimistic path - assumes no obstacles in unknown terrain
  • Fancy way of saying bid on goals that are close to the robot and clustered together
  • you can add a goal to a good sequence if the new goal is the nearest neighbor and doesn't make the sequence less attractive
  • Instead of taking all combinations of bundles to calculate utility, bid on a subset
  • with a few exceptions
  • smaller robot utilization allows for less parallelism
  • Robot Exploration with Combinatorial Auctions

    1. 1. http://www.sciencedaily.com/releases/2007/06/070609112916.htm
    2. 2. Robot Exploration with Combinatorial Auctions M. 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
    3. 3. Optimal Task Allocation Repeat Auctions + Combinatorial Auctions + Bidding Strategy = Near Optimal Allocation http://shirt.woot.com/Derby/Entry.aspx?id=30206
    4. 4. Repeat Auctions Robot 1 Robot 2 Goal Unknown Terrain Wall
    5. 5. Repeat Auctions Robot 1 Robot 2 Goal Unknown Terrain Wall
    6. 6. Repeat Auctions Robot 1 Robot 2 Goal Wall Wall
    7. 7. Repeat Auctions Robot 1 Robot 2 Goal Wall Wall
    8. 8. Single Item vs. Combinatorial Auctions
    9. 9. Single Item vs. Combinatorial Auctions Possible 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}
    10. 10. 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})
    11. 11. 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})
    12. 12. 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/
    13. 13. Bidding Strategies - Single Same as single item auction
    14. 14. Bidding Strategies - Three-Combination Possible 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}
    15. 15. 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
    16. 16. Bidding Strategies - Nearest-Neighbor Bid on all "Good Sequences": * {G i } for all i * If S = {G i , ... G e } is a good sequence then S U {G t } is a good sequence if G t is the closest neighbor to G e not in S and the value of S U {G t } ≥ the value of S
    17. 17. Bidding Strategies - Graph Cut
    18. 18. Bidding Strategies - Graph Cut Maximum cuts
    19. 19. 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
    20. 20. 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
    21. 21. The End Questions?

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