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Swarm Interpolation Using an Approximate Chebyshev Distribution

  • Joshua Kirby
  • Marco A. Montes de Oca
  • Steven Senger
  • Louis F. Rossi
  • Chien-Chung Shen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7461)

Abstract

In this paper, we describe a novel swarming framework that guides autonomous mobile sensors into a flexible arrangement to interpolate values of a field in an unknown region. The algorithm is devised so that the sensor distribution will behave like a Chebyshev distribution, which can be optimal for certain ideal geometries. The framework is designed to dynamically adjust to changes in the region of interest, and operates well with very little a priori knowledge of the given region.

For comparison, we interpolate a variety of nontrivial fields using a standard swarming algorithm that produces a uniform distribution and our new algorithm. We find that our new algorithm interpolates fields with greater accuracy.

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References

  1. 1.
    Battles, Z., Trefethen, L.N.: An extension of matlab to continuous functions and operators. SIAM J. Sci. Comput. 25(5) (May 2004), http://dx.doi.org/10.1137/S1064827503430126
  2. 2.
    Bertozzi, A., Kemp, M., Marthaler, D.: Determining environmental boundaries: Asynchronous communication and physical scales. LNCIS, vol. 309, pp. 403–405 (2005)Google Scholar
  3. 3.
    Cortes, J., Martinez, S., Karatas, T., Bullo, F.: Coverage control for mobile sensing networks. IEEE Trans. on Robotics and Automation 20(2), 243–255 (2004)CrossRefGoogle Scholar
  4. 4.
    Cui, X., Hardin, T., Ragade, R.K., Elmaghraby, A.S.: A swarm-based fuzzy logic control mobile sensor network for hazardous contaminants localization. In: 2004 IEEE Int. Conf. on Mobile Ad-hoc and Sensor Systems, pp. 194–203 (October 2004)Google Scholar
  5. 5.
    Fasshauer, G.E.: Meshfree Approximation Methods with MATLAB. Interdisciplinary Math. Sci., vol. 6. World Scientific Publishing, Singapore (2007)zbMATHGoogle Scholar
  6. 6.
    Kadrovach, B.A., Lamont, G.B.: A particle swarm model for swarm-based networked sensor systems. ACM, New York (2002)Google Scholar
  7. 7.
    Kalantar, S., Zimmer, U.: Distributed shape control of homogeneous swarms of autonomous underwater vehicles. Autonomous Robots 22(1), 37–53 (2007)CrossRefGoogle Scholar
  8. 8.
    Krause, A., Singh, A., Guestrin, C.: Near-optimal sensor placements in gaussian processes: Theory, efficient algorithms and empirical studies. J. Mach. Learn. Res. 9, 235–284 (2008), http://dl.acm.org/citation.cfm?id=1390681.1390689 zbMATHGoogle Scholar
  9. 9.
    Trefethen, L.: Spectral Methods in MATLAB. SIAM, Philadelphia (2000)zbMATHCrossRefGoogle Scholar
  10. 10.
    Turduev, M., Atas, Y., Sousa, P., Gazi, V., Marques, L.: Cooperative chemical concentration map building using decentralized asynchronous particle swarm optimization based search by mobile robots. In: 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 4175–4180 (October 2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Joshua Kirby
    • 1
  • Marco A. Montes de Oca
    • 2
  • Steven Senger
    • 2
  • Louis F. Rossi
    • 2
  • Chien-Chung Shen
    • 1
  1. 1.Department of Computer and Information SciencesUniversity of DelawareNewarkUSA
  2. 2.Department of Mathematical SciencesUniversity of DelawareNewarkUSA

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