Advertisement

Autonomous Robots

, Volume 37, Issue 4, pp 417–430 | Cite as

From selfish auctioning to incentivized marketing

  • Lantao Liu
  • Dylan A. Shell
  • Nathan Michael
Article

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.

Keywords

Task Allocation Combinatorial Auction Auction Algorithm Price Increment Utility Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Agmon, N., Kaminka, G. A., Kraus, S., & Traub, M. (2010). Task reallocation in multi-robot formations. Journal of Physical Agents, 4(2), 1–10.Google Scholar
  2. Bertsekas, D. P. (1979). A distributed algorithm for the assignment problem. Cambridge: Laboratory for Information and Decision Systems Report, MIT.Google Scholar
  3. Bertsekas, D. P. (1990). The auction algorithm for assignment and other network flow problems: A tutorial. Interfaces, 20(4), 133–149.CrossRefGoogle Scholar
  4. Bertsekas, D. P. (1992). Auction algorithms for network flow problems: A tutorial introduction. Computational Optimization and Applications, 1, 7–66.MathSciNetCrossRefzbMATHGoogle Scholar
  5. Bradley, S., Hax, A., & Magnanti, T. (1977). Applied mathematical programming. Reading: Addison-Wesley.Google Scholar
  6. Burkard, R. E., Dell’Amico, M., & Martello, S. (2009). Assignment problems. New York, NY: Society for Industrial and Applied Mathematics.CrossRefzbMATHGoogle Scholar
  7. Derigs, U. (1985). The shortest augmenting path method for solving assignment problems: Motivation and computational experience. Annals of Operations Research, 4, 57–102.MathSciNetCrossRefGoogle Scholar
  8. Dias, M. B., & Stentz, A. (2002). Opportunistic optimization for market-based multirobot control. In Proceedings of the IROS (pp. 2714–2720).Google Scholar
  9. Dias, M. B., Zlot, R., Kalra, N., & Stentz, A. (2006). Market-based multirobot coordination: A survey and analysis. Proceedings of the IEEE, 94(7), 1257–1270.CrossRefGoogle Scholar
  10. Dinic, E. A., & Kronrod, M. A. (1969). An algorithm for the solution of the assignment problem. Soviet Mathematics Doklady, 10, 1324–1326.zbMATHGoogle Scholar
  11. Gerkey, B. P. & Matarić, M. J. (2000). Murdoch: Publish/subscribe task allocation for heterogeneous agents. In Fourth International Conference on Autonomous Agents (pp. 203–204).Google Scholar
  12. Gerkey, B. P., & Matarić, M. J. (2002). Sold!: auction methods for multirobot coordination. IEEE Transactions on Robotics and Automation, 18(5), 758–768.CrossRefGoogle Scholar
  13. Gerkey, B. P., & Matarić, M. J. (2004). A formal analysis and taxonomy of task allocation in multi-robot systems. International Journal of Robotics Research, 23(9), 939–954.CrossRefGoogle Scholar
  14. Giordani, S., Lujak, M., & Martinelli, F. (2010). A distributed algorithm for the multi-robot task allocation problem. LNCS: Trends in Applied Intelligent Systems, 6096, 721–730.Google Scholar
  15. Goldberg, D., Cicirello, V. A., Dias, M. B., Simmons, R. G., Smith, S. F., & Stentz, A. (2003). Task allocation using a distributed market-based planning mechanism. In Proceedings of the International Joint Conference on Autonomous Agents & Multiagent Systems, (AAMAS), Melbourne (pp. 996–997).Google Scholar
  16. Koenig, S., Keskinocak, P., & Tovey, C. A. (2010). Progress on agent coordination with cooperative auctions. In Proceedings of the AAAI.Google Scholar
  17. Kuhn, H. W. (1955). The Hungarian method for the assignment problem. Naval Research Logistic Quarterly, 2, 83–97.CrossRefGoogle Scholar
  18. Lagoudakis, M. G., Markakis, E., Kempe, D., Keskinocak, P., Kleywegt, A., Koenig, S., et al. (2005). Auction-based multi-robot routing. In Robotics: Science and Systems.Google Scholar
  19. Liu, L., & Shell, D. A. (2012a). A distributable and computation-flexible assignment algorithm: From local task swapping to global optimality. In Proceedings of Robotics: Science and Systems.Google Scholar
  20. Liu, L., & Shell, D. A. (2012b). Large-scale multi-robot task allocation via dynamic partitioning and distribution. Autonomous Robots, 33(3), 291–307.CrossRefGoogle Scholar
  21. Liu, L., & Shell, D. A. (2013). Optimal market-based multi-robot task allocation via strategic pricing. In Proceedings of Robotics: Science and Systems, Berlin, Germany.Google Scholar
  22. Luo, L., Chakraborty, N., & Sycara, K. (2013). Distributed algorithm design for multi-robot task assignment with deadlines for tasks. In ICRA.Google Scholar
  23. Mankiw, N. (2011). Principles of economics. Economics series. Melbourne: Cengage Learning.Google Scholar
  24. McLurkin, J., & Yamins, D. (2005). Dynamic task assignment in robot swarms. In Proceedings of Robotics: Science and Systems.Google Scholar
  25. Michael, N., Zavlanos, M. M., Kumar, V., & Pappas, G. J. (2008). Distributed multi-robot task assignment and formation control. In IEEE International Conference on Robotics and Automation, Pasadena, CA.Google Scholar
  26. Nanjanath, M. & Gini, M. (2006). Dynamic task allocation for robots via auctions. In Proceedings of the ICRA (pp. 2781–2786).Google Scholar
  27. Parker, L. E. (1998). Alliance: An architecture for fault-tolerant multi-robot cooperation. IEEE Transactions on Robotics and Automation, 14(2), 220–240.CrossRefGoogle Scholar
  28. Pentico, D. W. (2007). Assignment problems: A golden anniversary survey. European Journal of Operational Research, 176, 774–793.MathSciNetCrossRefzbMATHGoogle Scholar
  29. Sandholm, T. (2002). Algorithm for optimal winner determination in combinatorial auctions. Artificial Intelligence, 135(1–2), 1–54.MathSciNetCrossRefzbMATHGoogle Scholar
  30. Smith, S. L. & Bullo, F. (2007a). A geometric assignment problem for robotic networks. In Modeling, Estimation and Control: Festschrift in Honor of Giorgio Picci on the Occasion of his 65 Birthday (Vol. 364, pp. 271–284).Google Scholar
  31. Smith, S. L. & Bullo, F. (2007b). Target assignment for robotic networks: Asymptotic performance under limited communication. In American Control Conference (pp. 1155–1160).Google Scholar
  32. Turpin, M., Michael, N., & Kumar, V. (2012). Trajectory planning and assignment in multirobot systems. In International Workshop on the Algorithmic Foundations of Robotics (WAFR).Google Scholar
  33. Vail, D., & Veloso, M. (2003). Multi-robot dynamic role assignment and coordination through shared potential fields. In A. Schultz, L. Parker, & F. Schneider (Eds.), Multi-robot systems. Dordrecht: Kluwer.Google Scholar
  34. Vincent, R., Fox, D., Ko, J., Konolige, K., Limketkai, B., Morisset, B., et al. (2008). Distributed multirobot exploration, mapping, and task allocation. Annals of Mathematics and Artificial Intelligence, 52(2–4), 229–255.MathSciNetCrossRefzbMATHGoogle Scholar
  35. Wolfstetter, E. (1994). Auctions: An introduction. Journal of Economic Surveys, 10(4), 367–420.CrossRefGoogle Scholar
  36. Zavlanos, M. M., Spesivtsev, L., & Pappas, G. J. (2008). A distributed auction algorithm for the assignment problem. Proceedings of the IEEE Conference on Decision and Control (pp. 1212–1217). Mexico: Cancun.Google Scholar
  37. Zhang, Y., & Parker, L. E. (2013). Considering inter-task resource constraints in task allocation. Autonomous Agents and Multi-Agent Systems, 26(3), 389–419.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.The Robotics InstituteCarnegie Mellon UniversityPittsburghUSA
  2. 2.Department of Computer Science and EngineeringTexas A&M UniversityCollege StationUSA

Personalised recommendations