Robot Exploration with Combinatorial Auctions
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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 Robot Exploration with Combinatorial Auctions Presentation Transcript

  • 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, 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 + Combinatorial Auctions + Bidding Strategy = Near Optimal Allocation http://shirt.woot.com/Derby/Entry.aspx?id=30206
  • 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, 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-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}
  • 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": * {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
  • 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?