An anytime assignment algorithm: From local task swapping to global optimality
 Lantao Liu,
 Dylan A. Shell
 … show all 2 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
The assignment problem arises in multirobot taskallocation scenarios. Inspired by existing techniques that employ task exchanges between robots, this paper introduces an algorithm for solving the assignment problem that has several appealing features for online, distributed robotics applications. The method may start with any initial matching and incrementally improve the current solution to reach the global optimum, producing valid assignments at any intermediate point. It is an anytime algorithm with a performance profile that is attractive: quality improves linearly with stages (or time). Additionally, the algorithm is comparatively straightforward to implement and is efficient both theoretically (complexity of \(O(n^3\lg n)\) is better than many widely used solvers) and practically (comparable to the fastest implementation, for up to hundreds of robots/tasks). The algorithm generalizes “swap” primitives used by existing task exchange methods already used in the robotics community but, uniquely, is able to obtain global optimality via communication with only a subset of robots during each stage. We present a centralized version of the algorithm and two decentralized variants that trade between computational and communication complexity. The centralized version turns out to be a computational improvement and reinterpretation of the littleknown method of Balinski–Gomory proposed half a century ago. Thus, deeper understanding of the relationship between approximate swapbased techniques—developed by roboticists—and combinatorial optimization techniques, e.g., the Hungarian and Auction algorithms—developed by operations researchers but used extensively by roboticists—is uncovered.
Inside
Within this Article
 Introduction
 Related work
 Problem description and preliminaries
 Task swapping and optimality
 An optimal swapbased primal method
 Distributed variants
 Experiments
 Discussion and future work
 Conclusion
 References
 References
Other actions
 Akgül, M. (1992). The linear assignment problem. In M. Akgiil & S. Tufecki (Eds.), Combinatorial optimization (pp. 85–122). Berlin: Springer. CrossRef
 Balinski, M. L., & Gomory, R. E. (1964). A primal method for the assignment and transportation problems. Management Science, 10(3), 578–593. CrossRef
 Berhault, M., Huang, H., Keskinocak, P., Koenig, S., Elmaghraby, W., Griffin, P., & Kleywegt, A. J. (2003). Robot Exploration with Combinatorial Auctions (pp. 1957–1962). In Proceedings of the IROS.
 Bertsekas, D. P. (1990). The auction algorithm for assignment and other network flow problems: A tutorial. Interfaces, 20(4), 133–149. CrossRef
 Burkard, R., Dell’Amico, M., & Martello, S. (2009). Assignment problems. New York, NY: Society for Industrial and Applied Mathematics. CrossRef
 Cao, Y. U., Fukunaga, A. S., & Kahng, A. B. (1997). Cooperative mobile robotics: Antecedents and directions. Autonomous Robots, 4, 226–234. CrossRef
 Chaimowicz, L., Campos, M. F. M., & Kumar, V. (2002). Dynamic role assignment for cooperative robots (pp. 293–298). In Proceedings of the IEEE International Conference on Robotics and Automation.
 Cunningham, W., & Marsh, A. B, I. (1978). A primal algorithm for optimum matching. Mathematical Programming Study, 8, 50–72.
 Dantzig, G. (1963). Linear programming and extensions. Princeton: Princeton University Press.
 Dias, M.B., & Stentz, A. (2002). Opportunistic optimization for marketbased multirobot control (pp. 2714–2720 ). In Proceedings of the IROS.
 Dias, M. B., Zlot, R., Kalra, N., & Stentz, A. (2006). Marketbased multirobot coordination: A survey and analysis. In Proceedings of the IEEE.
 Edmonds, J., & Karp, R. M. (1972). Theoretical improvements in algorithmic efficiency for network flow problems. Journal of the ACM, 19(2), 248–264. CrossRef
 Farinelli, A., Iocchi, L., Nardi, D., & Ziparo, V. A. (2006). Assignment of dynamically perceived tasks by token passing in multirobot systems. In Proceedings of the IEEE, Special Issue on Multirobot Systems.
 Gerkey, B. P., & Matarić, M. J. (2004). A formal analysis and taxonomy of task allocation in multirobot systems. International Journal of Robotics Research, 23(9), 939–954. CrossRef
 Giordani, S., Lujak, M., & Martinelli, F. (2010). A distributed algorithm for the multirobot task allocation problem. LNCS: Trends in Applied Intelligent Systems, 6096, 721–730. CrossRef
 Goldberg, A. V., & Kennedy, R. (1995). An efficient cost scaling algorithm for the assignment problem. Mathematics Programs, 71(2), 153–177. CrossRef
 Golfarelli, M., Maio, D., & Rizzi, S. (1997). Multiagent path planning based on taskswap negotiation (pp. 69–82). In Proceedings of the UK Planning and Scheduling Special Interest Group, Workshop.
 Koenig, S., Keskinocak, P., & Tovey, C. A. (2010). Progress on agent coordination with cooperative auctions. In Proceedings of the AAAI.
 Kuhn, H. W. (1955). The Hungarian method for the assignment problem. Naval Research Logistic Quarterly, 2, 83–97. CrossRef
 Lagoudakis, M. G., Markakis, E., Kempe, D., Keskinocak, P., Kleywegt, A., Koenig, S., et al. (2005). Auctionbased multirobot routing. In Robotics: Science and Systems. Cambridge: MIT Press.
 Liu, L., & Shell, D. (2011). Assessing optimal assignment under uncertainty: An intervalbased algorithm. International Journal of Robotics Research, 30(7), 936–953. CrossRef
 Liu, L., & Shell, D. (2012a). A distributable and computationflexible assignment algorithm: From local task swapping to global optimality. In Proceedings of Robotics: Science and Systems, Sydney, Australia.
 Liu, L., & Shell, D. (2012b). Largescale multirobot task allocation via dynamic partitioning and distribution. Autonomous Robots, 33(3), 291–307. CrossRef
 Nanjanath, M., & Gini, M. (2006). Dynamic task allocation for robots via auctions (pp. 2781–2786). In Proceedings of the ICRA.
 Parker, L. E. (2008). Multiple mobile robot systems. In B. Siciliano & O. Khatib (Eds.), Handbook of robotics chapter 40. Berlin: Springer.
 Sandholm, T. (1998). Contract types for satisficing task allocation: I Theoretical results (pp. 68–75). In Proceedings of the AAAI Spring Symposium: Satisficing Models.
 Sariel, S., & Balch, T. (2006). A distributed multirobot cooperation framework for real time task achievement. In Proceedings of Distributed Autonomous Robotic Systems.
 Stone, P., Kaminka, G. A., Kraus, S., & Rosenschein, J. S. (2010). Ad Hoc autonomous agent teams: Collaboration without precoordination. In Proceedings of the AAAI.
 Thomas, L., Rachid, A., & Simon, L. (2004). A distributed tasks allocation scheme in multiUAV context (pp. 3622–3627). In Proceedings of the ICRA.
 Wawerla, J., & Vaughan, R. T. (2009). Robot task switching under diminishing returns (pp. 5033–5038). In Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems, IROS’09.
 Zavlanos, M. M., Spesivtsev, L., & Pappas, G. J. (2008). A distributed auction algorithm for the assignment problem. In Proceedings of the CDC.
 Zheng, X., & Koenig, S. (2009). Kswaps: cooperative negotiation for solving taskallocation problems (pp. 373–378). In Proceedings of the International Joint Conferences on Artificial Intelligence (IJCAI).
 Zilberstein, S. (1996). Using anytime algorithms in intelligent systems. AI Magazine, 17(3), 73–83.
 Title
 An anytime assignment algorithm: From local task swapping to global optimality
 Journal

Autonomous Robots
Volume 35, Issue 4 , pp 271286
 Cover Date
 20131101
 DOI
 10.1007/s1051401393512
 Print ISSN
 09295593
 Online ISSN
 15737527
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Multirobot task allocation
 Decentralized assignment
 Anytime algorithms
 Task swapping
 Industry Sectors
 Authors

 Lantao Liu ^{(1)}
 Dylan A. Shell ^{(1)}
 Author Affiliations

 1. Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA