Semi-centralized Reconstruction of Robot Swarm Topologies - The Largest Laplacian Eigenvalue and High Frequency Noise are used to Calculate the Adjacency Matrix of an Underwater Swarm from Time-series

Vincenzo Fioriti, Stefano Chiesa, Fabio Fratichini

2013

Abstract

An important task in underwater autonomous vehicle swarm management is the knowledge of the graph topology, to be obtained with the minimum possible communication exchanges and amid heavy interferences and background noises. Despite the importance of the task, this problem is still partially unsolved. Recently, the Fast Fourier Transform and the addition of white noise to consensus signals have been proposed independently to determine respectively the laplacian spectrum and the adjacency matrix of the graph of interacting agents from consensus time series, but both methodologies suffer technical difficulties. In this paper, we combine them in order to simplify calculations, save energy and avoid topological reconstruction errors using only the largest eigenvalue of the spectrum and instead of white noise, a high frequency, low amplitude noise. Numerical simulations of several swarms (random, small-world, pipeline, grid) show an exact reconstruction of the configuration topologies.

References

  1. Ren, J., Wang, W.-X., Li, B., and Lai, Y.-C., 2010. Noise Bridges Dynamical Correlation and Topology in Coupled Oscillator Networks, Phys. Rev. Lett., 104 pp. 058701.
  2. Olfati-Saber, R., and Murray, R. M., 2004. Consensus Problem in Networks of Agents with Switching Topology and Time-Delays, IEEE Trans. Aut. Contr., 49 (9) pp. 1520-1531.
  3. Olfati_Saber, R., 2005. Ultrafast Consensus, Proceedings of the American Control Conference IEEE. pp. 2371- 2378, Los Alamitos, CA.
  4. Olfati_Saber, R., Fax, J., Murray, R. M., 2007. Consensus and Cooperation in Networked Multi-Agent Systems. Proceedings of IEEE, 95, 1, Jan.2007.
  5. Dousse, O., Baccelli, F., and Thiran, P., 2005. Impact of Interferences on Connectivity in Ad Hoc Networks, IEEE ACM Trans. Networking, 13 (2) 425.
  6. Franceschelli, M., Gasparri, A., Giua, A., Seatzu, C.,2012. Decentralized Estimation of Laplacian Eigenvalues in Multi-Agent Systems, http://arxiv.org/pdf/1206.4509. pdf.
  7. Cucker, F. and Smale, S., 2007, On the mathematics of the emergence, Jnp. J. Math., 2 (1) pp. 197-227.
  8. Camperi, M., Cavagna, A., Giardina, I., Parisi, G., and Silvestri, E., 2012, Spatially balanced topological interaction grants optimal cohesion in flocking models. http://rsfs.royalsocietypublishing.org/content/ early/2012/08/07/rsfs.2012.0026.
  9. Yang, P., Freeman, R. A., Gordon, G., Lynch, K., Srinivasa, S., and Sukthankar, R, 2008. Decentralized estimation and control of graph connectivity in mobile sensor networks. American Control Conference.
  10. Van Dam, E., and Haemers, W., 2003, Which graphs are determined by their spectrum?, Linear Algebra and its Applications, 373 pp.241-272.
  11. Dell'Erba, R., and Moriconi, C., 2012. The Localization problem for Harness: a Multipurpose Robotic Swarm. SENSORCOMM 2012 Sixth International Conference on Sensor Technologies and Applications.
  12. Pompili, D. and Melodia, T., 2005. Three-dimensional routing in under water acoustic sensor network. PESWASUN 7805 ACM Conference 1-59593, Montreal, Quebec, Canada.
  13. Ballerini, M., et al., 2008, Interaction ruling animal collective behavior depends on topological rather than metric distances: evidence from a field study, Proc. Nat. Acad. Sci. USA, 105 pp. 1232-1237.
  14. Chiesa, S. and Taraglio, S., 2012. Flock Formation Control through Parameter Tuning in Underwater Swarms. ICINCO'12 Conference Rome, pp. 313-316.
  15. Kibangou, A., Commault, C., 2012. Decentralize Laplacian Eigenvalues Estimation and Collaborative Network Topology Identification. 3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems, NecSys 7812, Santa Barbara.
  16. Wang, W. X., Ren, J., Lai, Y. C., Li. B., 2012. Reverse engineering of complex dinamic networks in the presence of time-delayed interaction based on timeseries. Chaos, 22 033131.
  17. Nawaz, S., Hussain, M., Watson, S., Trigoni, N., and Green, P. N., 2009. An Underwater Robotic Network for Monitoring Nuclear Waste Storage Pools. 1st International ICST Conference on Sensor Systems and Software.
  18. Joordens, M. And Ponds, W., 2010. Consensus Control for a System of Underwater Swarm Robots. IEEE Systems Journal, 4 (1).
  19. Appala Raju, Y., Devee Prasan, U., 2012, Network Layer Analysis & Novel Recommendations Regarding Feasibility towards UWSN, Int. J. Eng. Res. Dev. 4 (10) pp. 1-7.
  20. Traverso, F., Trucco, A. , Vernazza, G., 2012. Simulation of non-White and non-Gaussian Underwater Ambient Noise. OCEANS'12 MTS/IEEE Yeosu Conference, Yeosu South Korea.
  21. Tanner, H., Jadbabaie, A., and Pappas, 2003. G., Stable flocking of mobile agents, part I: Fixed topology. Proceedings of the 42nd IEEE Conference on Decision and Control DC2003), vol. 2, Dec. 2003, pp. 2010-2015.
  22. Bullo, F. Cortes, J., and Martinez, S. 2009. Distributed Control of Robotic Networks, ser. Applied Mathematics Series. Princeton University Press.
  23. Xi, J., Shi, Z., Zhong, Y., 2012. Consensus and consensualization of high-order swarm systems with time delays and external disturbances, J. Dyn. Sys. Meas. 134 4.
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Paper Citation


in Harvard Style

Fioriti V., Chiesa S. and Fratichini F. (2013). Semi-centralized Reconstruction of Robot Swarm Topologies - The Largest Laplacian Eigenvalue and High Frequency Noise are used to Calculate the Adjacency Matrix of an Underwater Swarm from Time-series . In Proceedings of the 10th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-8565-70-9, pages 74-81. DOI: 10.5220/0004421800740081


in Bibtex Style

@conference{icinco13,
author={Vincenzo Fioriti and Stefano Chiesa and Fabio Fratichini},
title={Semi-centralized Reconstruction of Robot Swarm Topologies - The Largest Laplacian Eigenvalue and High Frequency Noise are used to Calculate the Adjacency Matrix of an Underwater Swarm from Time-series},
booktitle={Proceedings of the 10th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2013},
pages={74-81},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004421800740081},
isbn={978-989-8565-70-9},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 10th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Semi-centralized Reconstruction of Robot Swarm Topologies - The Largest Laplacian Eigenvalue and High Frequency Noise are used to Calculate the Adjacency Matrix of an Underwater Swarm from Time-series
SN - 978-989-8565-70-9
AU - Fioriti V.
AU - Chiesa S.
AU - Fratichini F.
PY - 2013
SP - 74
EP - 81
DO - 10.5220/0004421800740081