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
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. 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
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. 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
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
