Abstract
Auction and market-based mechanisms are among the most popular methods for distributed task allocation in multi-robot systems. Most of these mechanisms were designed in a heuristic way and analysis of the quality of the resulting assignment solution is rare. This paper presents a new market-based multi-robot task allocation algorithm that produces optimal assignments. Rather than adopting a buyer’s “selfish” bidding perspective as in previous auction/market-based approaches, the proposed method approaches auctioning from a merchant’s point of view, producing a pricing policy that responds to cliques of customers and their preferences. The algorithm uses price escalation to clear a market of all its items, producing a state of equilibrium that satisfies both the merchant and customers. This effectively assigns all robots to their tasks. The proposed method can be used as a general assignment algorithm as it has a time complexity (\(O(n^3 \text {lg} n)\)) close to the fastest state-of-the-art algorithms (\(O(n^3)\)) but is extremely easy to implement. As in previous research, the economic model reflects the distributed nature of markets inherently: in this paper it leads directly to a decentralized method ideally suited for distributed multi-robot systems.
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Notes
The main algorithm was first presented in the 2013 Robotics: Science and Systems conference (Liu and Shell 2013).
Note that the word pricing is also used in the linear programming literature, in particular for branch-and-bound and cutting plane methods. Therein the term is used to describe the dynamic introduction of new variables. That use is distinct and should not be confused with the economic use in the present paper.
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Liu, L., Shell, D.A. & Michael, N. From selfish auctioning to incentivized marketing. Auton Robot 37, 417–430 (2014). https://doi.org/10.1007/s10514-014-9403-2
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DOI: https://doi.org/10.1007/s10514-014-9403-2