# Competitive target search with multi-agent teams: symmetric and asymmetric communication constraints

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## Abstract

We study a search game in which two multi-agent teams compete to find a stationary target at an unknown location. Each team plays a mixed strategy over the set of search sweep-patterns allowed from its respective random starting locations. Assuming that communication enables cooperation we find closed-form expressions for the probability of winning the game as a function of team sizes and the existence or absence of communication within each team. Assuming the target is distributed uniformly at random, an optimal mixed strategy equalizes the expected first-visit time to all points within the search space. The benefits of communication enabled cooperation increase with team size. Simulations and experiments agree well with analytical results.

## Keywords

Multi-agent system Competitive search Search and rescue Search game## Notes

### Acknowledgements

We would like to thank Colin Ward, Corbin Wilhelmi, and Cyrus Vorwald for their help in facilitating the mixed platform experiments.

## Supplementary material

## References

- Beard, R. W., & McLain, T. W. (2003). Multiple uav cooperative search under collision avoidance and limited range communication constraints. In
*Proceedings of 42nd IEEE conference on decision and control, 2003*, Vol. 1, pp. 25–30Google Scholar - Bertuccelli, L. F., & How, J. P. (2005). Robust UAV search for environments with imprecise probability maps. In
*44th IEEE conference on decision and control, 2005 and 2005 European control conference. CDC-ECC ’05*, pp. 5680–5685, https://doi.org/10.1109/CDC.2005.1583068 - Bhattacharya, S., Khanafer, A., & Başar, T. (2016). A double-sided jamming game with resource constraints. Springer International Publishing, pp. 209–227Google Scholar
- Chandler, P., & Pachter, M. (2001). Hierarchical control for autonomous teams. In
*Proceedings of the AIAA guidance, navigation, and control conference*, pp. 632–642Google Scholar - Choset, H., & Pignon, P. (1998). Coverage path planning: The boustrophedon cellular decomposition. In
*Field and service robotics*(pp. 203–209). SpringerGoogle Scholar - Chung, T. H., Hollinger, G. A., & Isler, V. (2011). Search and pursuit-evasion in mobile robotics.
*Autonomous Robots*,*31*(4), 299–316.CrossRefGoogle Scholar - Demaine, E. D., Fekete, S. P., & Gal, S. (2006). Online searching with turn cost.
*Theoretical Computer Science*,*361*(2), 342–355.MathSciNetCrossRefMATHGoogle Scholar - Dias, M. B. (2004). Traderbots: A new paradigm for robust and efficient multirobot coordination in dynamic environments. PhD thesis, Carnegie Mellon University PittsburghGoogle Scholar
- 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 - Feinerman, O., Korman, A., Lotker, Z., Sereni, J. S. (2012). Collaborative search on the plane without communication. In
*Proceedings of the 2012 ACM symposium on principles of distributed computing, PODC ’12*(pp. 77–86). ACM, New York https://doi.org/10.1145/2332432.2332444, - Flint, M., Polycarpou, M., & Fernandez-Gaucherand, E. (2002). Cooperative control for multiple autonomous uav’s searching for targets. In
*Proceedings of the 41st IEEE Conference on Decision and Control*, Vol. 3, pp. 2823–2828Google Scholar - Forsmo, E. J., Grotli, E. I., Fossen, T. I., & Johansen, T. A. (2013). Optimal search mission with unmanned aerial vehicles using mixed integer linear programming. In
*International conference on unmanned aircraft systems (ICUAS)*, pp. 253–259, https://doi.org/10.1109/ICUAS.2013.6564697 - Gerkey, B. P., Thrun, S., & Gordon, G. (2005). Parallel stochastic hill-climbing with small teams. In
*Multi-robot systems. From swarms to intelligent automata*Volume III (pp. 65–77). SpringerGoogle Scholar - Hollinger, G. A., Yerramalli, S., Singh, S., Mitra, U., & Sukhatme, G. S. (2015). Distributed data fusion for multirobot search.
*IEEE Transactions on Robotics*,*31*(1), 55–66.CrossRefGoogle Scholar - Hopcroft, J. E., & Karp, R. M. (1971). A n5/2 algorithm for maximum matchings in bipartite. In
*IEEE 12th annual symposium on switching and automata theory*, pp. 122–125Google Scholar - Hu, J., Xie, L., Lum, K. Y., & Xu, J. (2013). Multiagent information fusion and cooperative control in target search.
*IEEE Transactions on Control Systems Technology*,*21*(4), 1223–1235. https://doi.org/10.1109/TCST.2012.2198650.CrossRefGoogle Scholar - Huang, A. S., Olson, E., & Moore, D. C. (2010). Lcm: Lightweight communications and marshalling. In
*IEEE/RSJ international conference on, intelligent robots and systems (IROS)*, pp. 4057–4062Google Scholar - Huang, H., Ding, J., Zhang, W., & Tomlin, C. J. (2015). Automation-assisted capture-the-flag: A differential game approach.
*IEEE Transactions on Control Systems Technology*,*23*(3), 1014–1028.CrossRefGoogle Scholar - Kim, M. H., Baik, H., & Lee, S. (2013). Response threshold model based uav search planning and task allocation.
*Journal of Intelligent & Robotic Systems*,*75*(3), 625–640. https://doi.org/10.1007/s10846-013-9887-6.Google Scholar - Koopman, B. (1956). The theory of search. II Target detection.
*Operations Research*,*4*(5), 503–531.MathSciNetCrossRefGoogle Scholar - Kwak, D. J., & Kim, H. J. (2014). Policy improvements for probabilistic pursuit-evasion game.
*Journal of Intelligent & Robotic Systems*,*74*(3–4), 709–724. https://doi.org/10.1007/s10846-013-9857-z.CrossRefGoogle Scholar - Lynen, S., Achtelik, M. W., Weiss, S., Chli, M., Siegwart, R. (2013). A robust and modular multi-sensor fusion approach applied to mav navigation. In
*2013 IEEE/RSJ international conference on intelligent robots and systems*, pp. 3923–3929Google Scholar - Mangel, M. (1989). Marcel Dekker, New YorkGoogle Scholar
- Noori, N., & Isler, V. (2013). Lion and man with visibility in monotone polygons.
*The International Journal of Robotics Research*p 0278364913498291Google Scholar - Otte, M., Kuhlman, M., & Sofge, D. (2016). Competitive two team target search game with communication symmetry and asymmetry. In
*International workshop on the algorithmic foundations of robotics (WAFR)*, San Francisco, USAGoogle Scholar - Sato, H., & Royset, J. O. (2010). Path optimization for the resource-constrained searcher.
*Naval Research Logistics (NRL)*,*57*(5), 422–440.MathSciNetMATHGoogle Scholar - Spieser, K., & Frazzoli, E. (2012). The cow-path game: A competitive vehicle routing problem. In
*IEEE 51st annual conference on decision and control (CDC)*, pp. 6513–6520Google Scholar - Spires, S. V., & Goldsmith, S. Y. (1998). Exhaustive geographic search with mobile robots along space-filling curves. In
*Collective robotics*(pp. 1–12). SpringerGoogle Scholar - Sujit, P. B., & Ghose, D. (2004). Multiple agent search of an unknown environment using game theoretical models. In
*Proceedings of the American control conference*, 2004, Vol. 6, pp. 5564–5569Google Scholar - Sujit, P. B., & Ghose, D. (2009). Negotiation schemes for multi-agent cooperative search.
*Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering*,*223*(6), 791–813.CrossRefGoogle Scholar - Sydney, N., Paley, D. A., Sofge, D. (2015). Physics-inspired motion planning for information-theoretic target detection using multiple aerial robots.
*Autonomous Robots*pp 1–11Google Scholar - Trummel, K., & Weisinger, J. (1986). Technical note the complexity of the optimal searcher path problem.
*Operations Research*,*34*(2), 324–327.MathSciNetCrossRefMATHGoogle Scholar - Vidal, R., Shakernia, O., Kim, H. J., Shim, D. H., & Sastry, S. (2002). Probabilistic pursuit-evasion games: theory, implementation, and experimental evaluation.
*IEEE Transactions on Robotics and Automation*18(5):662–669, https://doi.org/10.1109/TRA.2002.804040 - Vincent, P., & Rubin, I. (2004). A framework and analysis for cooperative search using uav swarms. In
*Proceedings of the 2004 ACM symposium on applied computing*, SAC ’04. ACM, New York, pp. 79–86, https://doi.org/10.1145/967900.967919, - Waharte, S., & Trigoni, N. (2010). Supporting search and rescue operations with uavs. In
*International conference on emerging security technologies (EST)*, 2010, pp. 142–147Google Scholar - Zhu, M., Frazzoli, E. (2012). On competitive search games for multiple vehicles. In
*IEEE 51st annual conference on decision and control (CDC)*, 2012, pp. 5798–5803, https://doi.org/10.1109/CDC.2012.6426371