Skip to main content
Springer Nature Link
Log in

Optimotaxis: A Stochastic Multi-agent Optimization Procedure with Point Measurements

  • Conference paper
Hybrid Systems: Computation and Control (HSCC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4981))

Included in the following conference series:

Abstract

We consider the problem of seeking the maximum of a scalar signal using a swarm of autonomous vehicles equipped with sensors that can take point measurements of the signal. Vehicles are not able to measure their current position or to communicate with each other. Our approach induces the vehicles to perform a biased random walk inspired by bacterial chemotaxis and controlled by a stochastic hybrid automaton. With such a controller, it is shown that the positions of the vehicles evolve towards a probability density that is a specified function of the spatial profile of the measured signal, granting higher vehicle densities near the signal maxima.

This material is based upon work supported by the Inst. for Collaborative Biotechnologies through grant DAAD19-03-D-0004 from the U.S. Army Research Office. The first author was partially funded by CAPES (Brazil) grant BEX 2316/05-6.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Berg, H., Brown, D.: Chemotaxis in Escherichia coli analysed by three-dimensional tracking. Nature 239(5374), 500–504 (1972)

    Article  Google Scholar 

  2. Alt, W.: Biased random walk models for chemotaxis and related diffusion approximations. J. Math. Biol. 9(2), 147–177 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  3. Burian, E., Yoerger, D., Bradley, A., Singh, H.: Gradient search with autonomous underwater vehicles using scalar measurements. In: Proceedings of the 1996 Symposium on Autonomous Underwater Vehicle Technology, 1996. AUV 1996, June 1996, pp. 86–98 (1996)

    Google Scholar 

  4. Sousa, J., Johansson, K., Silva, J., Speranzon, A.: A verified hierarchical control architecture for co-ordinated multi-vehicle operations. International Journal of Adaptive Control and Signal Processing 21(2-3), 159–188 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  5. Mayhew, C., Sanfelice, R., Teel, A.: Robust source-seeking hybrid controllers for autonomous vehicles. In: Proceedings of the 2007 American Control Conference. ACC 2007, July 2007, pp. 1185–1190 (2007)

    Google Scholar 

  6. Hoskins, D.A.: Least action approach to collective behavior. In: Parker, L.E. (ed.) Proc. SPIE, vol. 2593, pp. 108–120; Microrobotics and Micromechanical Systems. In: Parker, L.E. (ed.) The Society of Photo-Optical Instrumentation Engineers (SPIE) Conference. vol. 2593, pp. 108–120 (December 1995)

    Google Scholar 

  7. Bachmayer, R., Leonard, N.: Vehicle networks for gradient descent in a sampled environment. In: Proceedings of the 41st IEEE Conference on Decision and Control, pp. 112–117 (December 2002)

    Google Scholar 

  8. Zhang, C., Arnold, D., Ghods, N., Siranosian, A., Krstic, M.: Source seeking with non-holonomic unicycle without position measurement and with tuning of forward velocity. Systems & Control Letters 56(3), 245–252 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Pang, S., Farrell, J.: Chemical plume source localization. IEEE Transactions on Systems, Man and Cybernetics, Part B 36(5), 1068–1080 (2006)

    Article  Google Scholar 

  10. Vergassola, M., Villermaux, E., Shraiman, B.: ’infotaxis’ as a strategy for searching without gradients. Nature 445(7126), 406–409 (2007)

    Article  Google Scholar 

  11. Dorigo, M., Gambardella, L.M.: Ant colony system: A cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation 1(1), 53–66 (1997)

    Article  Google Scholar 

  12. Ferrée, T., Lockery, S.: Computational rules for chemotaxis in the nematode C. Elegans. Journal of Computational Neuroscience 6, 263–277 (1999)

    Article  MATH  Google Scholar 

  13. Dhariwal, A., Sukhatme, G.S., Requicha, A.A.: Bacterium-inspired robots for environmental monitoring. In: IEEE International Conference on Robotics and Automation, New Orleans, Louisiana, April 2004, pp. 1436–1443. IEEE, Los Alamitos (2004)

    Google Scholar 

  14. Aluffipentini, F., Parisi, V., Zirilli, F.: Global optimization and stochastic differential-equations. Journal of Optimization Theory and Applications 47(1), 1–16 (1985)

    Article  MathSciNet  Google Scholar 

  15. Dekkers, A., Aarts, E.: Global optimization and simulated annealing. Math. Program. 50(3), 367–393 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  16. Stroock, D.: Some stochastic processes which arise from a model of the motion of a bacterium. Probability Theory and Related Fields 28(4), 305–315 (1974)

    MATH  Google Scholar 

  17. Papanicolaou, G.: Asymptotic analysis of transport processes. Bulletin of the American Mathematical Society 81(2), 330–392 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  18. Davis, M.H.A.: Markov models and optimization. In: Monographs on statistics and applied probability, Chapman & Hall, London, UK (1993)

    Google Scholar 

  19. Hespanha, J.P.: Modeling and analysis of stochastic hybrid systems. IEE Proc — Control Theory & Applications, Special Issue on Hybrid Systems 153(5), 520–535 (2007)

    Article  MathSciNet  Google Scholar 

  20. Hu, J., Lygeros, J., Sastry, S.: Towards a theory of stochastic hybrid systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 160–173. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  21. Kaper, H.G., Lekkerkerker, C.G., Hejtmanek, J.: Spectral Methods in Linear Transport Theory. Birkhäuser Verlag, Basel (1982)

    Google Scholar 

  22. Mokhtar-Kharroubi, M.: Mathematical Topics in Neutron Transport Theory. World Scientific, Singapore (1997)

    MATH  Google Scholar 

  23. Risken, H.: The Fokker-Planck Equation - Methods of Solution and Applications. Springer Series in Synergetics. Springer, Berlin (1984)

    MATH  Google Scholar 

  24. Pazy, A.: Semigroup of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983)

    Google Scholar 

  25. Dunford, N., Schwartz, J.: Linear Operators. In: Pure and Applied Mathematics, vol. VII, Interscience Publishers, New York (1957)

    Google Scholar 

  26. Derriennic, Y., Lin, M.: Uniform ergodic convergence and averaging along markov chain trajectories. Journal of Theoretical Probability 7(3), 483–497 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  27. Mesquita, A., Hespanha, J., Åstrom, K.: Optimotaxis: A stochastic multi-agent optimization procedure with point measurements: Extended version. Technical report, University of California, Santa Barbara (October 2007), http://www.ece.ucsb.edu/~hespanha/techreps.html

  28. Lasota, A., Mackey, M.: Chaos, Fractals, and Noise. Stochastic Aspects of Dynamics. In: Applied Mathematical Sciences, vol. 97, Springer, New York (1994)

    Google Scholar 

  29. Krengel, U.: Ergodic Theorems. de Gruyer Studies in Mathematics. vol. 6, Walter de Gruyter, Berlin, New York (1985)

    Google Scholar 

  30. Pichór, K., Rudnicki, R.: Continuous markov semigroups and stability of transport equations. Journal of Mathematical Analysis and Applications 249, 668–685 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  31. Mokhtar-Kharroubi, M., Sbihi, M.: Spectral mapping theorems for neutron transport, l 1-theory. Semigroup Forum 72, 249–282 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  32. Lin, J.: Divergence measures based on shannon entropy. IEEE Transactions on Information Theory 37(1), 145–151 (1991)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Control, Dynamical Systems and Computation, University of California, Santa Barbara, CA 93106,  

    Alexandre R. Mesquita, João P. Hespanha & Karl Åström

Authors
  1. Alexandre R. Mesquita
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. João P. Hespanha
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Karl Åström
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Magnus Egerstedt Bud Mishra

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Mesquita, A.R., Hespanha, J.P., Åström, K. (2008). Optimotaxis: A Stochastic Multi-agent Optimization Procedure with Point Measurements. In: Egerstedt, M., Mishra, B. (eds) Hybrid Systems: Computation and Control. HSCC 2008. Lecture Notes in Computer Science, vol 4981. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78929-1_26

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-78929-1_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-78928-4

  • Online ISBN: 978-3-540-78929-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics