Hexagonal Lattice Formation in Multi-Robot Systems

  • Sailesh PrabhuEmail author
  • William Li
  • James McLurkin
Part of the Springer Tracts in Advanced Robotics book series (STAR, volume 104)


We present an algorithm that arranges a multi-robot system into a regular hexagonal lattice. This configuration provides continuous coverage with the fewest number of robots required. It also has a bounded stretch over a fully-connected graph, producing an efficient multi-hop communications network. Our algorithm uses artificial forces to move each robot to local potential energy wells. A local error correction algorithm detects and corrects most local lattice errors. Both algorithms are fully distributed, requiring local network geometry information, but no global coordinates.We present analysis of the potential energy wells that form the lattice, a proof of the upper bound on the spanning ratio of a hexagonal packing, and the error detecting and correcting algorithm. Simulation results demonstrate the effectiveness of the approach for large populations of robots.


Hexagonal Lattice Triangular Lattice Hexagonal Cell Lattice Error Black Neighbor 
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  1. 1.
    Spears, W.M., Spears, D.F., Hamann, J.C., Heil, R.: Autonomous Robots 17(2), 137 (2004)Google Scholar
  2. 2.
    Spears, W., Spears, W., Heil, R., Heil, R., Spears, D., Zarzhitsky, D.: Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2004, pp. 1528–1529 (2004)Google Scholar
  3. 3.
    Gordon-Spears, D., Spears, W.: Lecture Notes in Computer Science, pp. 193–207 (2003)Google Scholar
  4. 4.
    Spears, W.M., Spears, D.F., Heil, R., Kerr, W., Hettiarachchi, S.: An overview of physicomimetics. In: Şahin, E., Spears, W.M. (eds.) Swarm Robotics 2004. LNCS, vol. 3342, pp. 84–97. Springer, Heidelberg (2005)Google Scholar
  5. 5.
    Mullen, R.J., Monekosso, D., Barman, S., Remagnino, P.: Distributed Autonomous Robotic (2010)Google Scholar
  6. 6.
    Martinson, E., Payton, D.: Lattice formation in mobile autonomous sensor arrays. In: Şahin, E., Spears, W.M. (eds.) Swarm Robotics 2004. LNCS, vol. 3342, pp. 98–111. Springer, Heidelberg (2005), Google Scholar
  7. 7.
    Balch, T., Hybinette, M.: In: Proceedings of the IEEE International Conference on Robotics and Automation, ICRA 2000, vol. 1, pp. 73–80 (2000)Google Scholar
  8. 8.
    Desai, J., Ostrowski, J., Kumar, V.: IEEE Transactions on Robotics and Automation 17(6), 905 (2001)Google Scholar
  9. 9.
    Eikenberry, B., Yakimenko, O., Romano, M.: AIAA Modeling and Simulation Technologies Conference and Exhibit (2006)Google Scholar
  10. 10.
    Hanada, Y., Lee, G., Chong, N.Y.: IEEE Swarm Intelligence Symposium, SIS 2007, pp. 340–347 (2007)Google Scholar
  11. 11.
    Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach, 2nd edn. Prentice Hall (2003)Google Scholar
  12. 12.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning, 1st edn. Addison-Wesley Longman Publishing Co., Inc., Boston (1989)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Rice UniversityHoustonUSA

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