Skip to main content
SpringerLink
Log in

Swarm Tracking

  • Chapter
Extremum-Seeking Control and Applications

Part of the book series: Advances in Industrial Control ((AIC))

  • 2424 Accesses

Abstract

In this chapter we study the swarm tracking problem, that is, the problem of finding a coordinated control scheme for a group of mobile agents that make them achieve and maintain a certain desired behavior; in particular, we concentrate on the problem of maintaining a given geometrical formation. At the same time, the agents need to seek a mobile source of a scalar signal or track a moving target. By using artificial potential functions to encode the agent-target, agent-agent, and/or agent-obstacle interaction, we are able to use extremum seeking techniques for controller design of each agent, which could be decentralized and in some instances does not require knowledge of target position and agent positions. The effectiveness of three different extremum seeking control designs is analytically established and compared via corresponding simulation results. Finally, an application of the swarming theory is presented, where localization of radar leakage points via a mobile sensor network is studied, and simulation results are provided.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Direct search is used here as a valid optimization method for NOESC because its behavior and properties are similar to those of derivative-free trust region methods. Moreover, since we rely on an asymptotic controller, all stability, convergence and robustness results from Chap. 5 directly apply here.

References

  1. Ariyur, K.B., Krstić, M.: Real-time Optimization by Extremum-seeking Control. Wiley-Interscience, Hoboken (2003)

    Book  MATH  Google Scholar 

  2. Barber, C., Gates, M., Selmic, R., Issa, H.A., Ordóñez, R., Mitra, A.: PADF RF localization experiments with multi-agent caged-MAV platforms. In: SPIE DSS (2011)

    Google Scholar 

  3. Biyik, E., Arcak, M.: Gradient climbing in formation via extremum seeking and passivity-based coordination rules. In: Proceedings of the Conference on Decision and Control, pp. 3133–3138 (2007)

    Google Scholar 

  4. Cochran, J., Kanso, E., Krstic, M.: Source seeking for a three-link model of fish locomotion. In: Proceedings of the American Control Conference, pp. 1808–1813 (2009)

    Google Scholar 

  5. Cochran, J., Krstić, M.: Source seeking with nonholonomic unicycle without position measurements and with tuning of angular velocity—part i: Stability analysis. In: Proceedings of the Conference on Decision and Control, pp. 6009–6016 (2007)

    Google Scholar 

  6. Cochran, J., Krstić, M.: Source seeking with nonholonomic unicycle without position measurements and with tuning of angular velocity—part ii: Applications. In: Proceedings of the Conference on Decision and Control, pp. 1951–1956 (2007)

    Google Scholar 

  7. Cochran, J., Krstić, M.: Extremum seeking for motion optimization: From bacteria to nonholonomic vehicles. In: Chinese Control and Decision Conference (2008)

    Google Scholar 

  8. Cochran, J., Krstić, M.: 3-d source seeking for underactuated vehicles without position measurement. IEEE Trans. Robot. 25(1), 117–129 (2009)

    Article  Google Scholar 

  9. Cochran, J., Krstić, M.: Nonholonomic source seeking with tuning of angular velocity. IEEE Trans. Autom. Control 54(4), 713–731 (2009)

    Article  Google Scholar 

  10. Cochran, J., Ghods, N., Siranosian, A., Krstić, M.: 3d source seeking for underactuated vehicles without position measurement. IEEE Trans. Robot. 25, 117–129 (2009)

    Article  Google Scholar 

  11. Cochran, J., Kanso, E., Kelly, S.D., Xiong, H., Krstić, M.: Source seeking for two nonholonomic models of fish locomotion. IEEE Trans. Robot. 25(5), 1166–1176 (2009)

    Article  Google Scholar 

  12. Desai, J.P., Ostrowski, J., Kumar, V.: Controlling formations of multiple mobile robots. In: Proc. 1998 IEEE Int. Conf. Robotics and Automation, Leuven, Belgium, pp. 2864–2869, May 1998

    Chapter  Google Scholar 

  13. Fu, L., Özgüner, Ü.: Extremum-seeking control in constrained source tracing with nonholonomic vehicles. IEEE Trans. Ind. Electron. 56(9), 3602–3608 (2009)

    Article  Google Scholar 

  14. Fu, L., Özgüner, Ü.: Sliding mode in constrained source tracking with non-holonomic vehicles. In: International Workshop on Variable Structure Systems (VSS’08), pp. 30–34 (2008)

    Chapter  Google Scholar 

  15. Gates, M., Barber, C., Selmic, R., Issa, H.A., Ordóñez, R., Mitra, A.: PADF RF localization criteria for multi-model scattering environments. In: SPIE DSS (2011)

    Google Scholar 

  16. Gazi, V., Ordóñez, R.: Target tracking using artificial potentials and sliding mode control. Int. J. Control 80(10), 1626–1635 (2007)

    Article  MATH  Google Scholar 

  17. Gazi, V., Passino, K.M.: A class of attraction/repulsion functions for stable swarm aggregations. Int. J. Control 77(18), 1567–1579 (2007)

    Article  MathSciNet  Google Scholar 

  18. Ghods, N., Krstic, M.: Multiagent deployment over a source. IEEE Trans. Control Syst. Technol. 1–10 (2011)

    Google Scholar 

  19. Ghods, N., Frihauf, P., Krstic, M.: Multi-agent deployment in the plane using stochastic extremum seeking. In: Proceedings of the Conference on Decision and Control (2010)

    Google Scholar 

  20. Ghods, N., Krstić, M.: Speed regulation in steering-based source seeking. Automatica 46, 452–459 (2010)

    Article  MATH  Google Scholar 

  21. Ghods, N., Krstić, M.: Source seeking with very slow or drifting sensors. J. Dyn. Syst. Meas. Control 133 (2011)

    Google Scholar 

  22. Jakobus, U.: Review of advanced EM modeling techniques in the computer code FEKO. Appl. Comput. Electromagn. Soc. Newsl. 18(2) (2003)

    Google Scholar 

  23. Kanchanavally, S., Ordóñez, R., Schumacher, C.J.: Path planning in three dimensional environment using feedback linearization. In: American Control Conference, Minneapolis, MN (2006)

    Google Scholar 

  24. Koksal, M.I., Gazi, V., Fidan, B., Ordóñez, R.: Tracking a maneuvering target with a non-holonomic agent using artificial potentials and sliding mode control. In: 16th Mediterranean Conference on Control and Automation (2008)

    Google Scholar 

  25. Krstić, M., Cochran, J.: Extremum seeking for motion optimization: from bacteria to nonholonomic vehicles. In: Proceedings of the Chinese Control and Decision Conference, pp. 18–27 (2008)

    Google Scholar 

  26. Lawton, J., Beard, R., Young, B.: A decentralized approach to formation maneuvers. IEEE Trans. Robot. Autom. 19(6), 933–941 (2003)

    Article  Google Scholar 

  27. Leonard, N.E., Fiorelli, E.: Virtual leaders, artificial potentials and coordinated control of groups. In: Proceedings of the IEEE Conf. Decision and Control, Orlando, FL, pp. 2968–2973 (2001)

    Google Scholar 

  28. Liu, S.-J., Krstić, M.: Stochastic source seeking for nonholonomic unicycle. IEEE Trans. Autom. Control 46, 1443–1453 (2010)

    MATH  Google Scholar 

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

    Google Scholar 

  30. Mesquita, A.R., Hespanha, J.P., Aström, K.: Optimotaxis: a stochastic multiagent optimization procedure with point measurements. In: Egerstedt, M., Mishra, B. (eds.) Hybrid Systems: Computation and Control. Lecture Notes in Computer Science, vol. 4981, pp. 358–371 (2008)

    Chapter  Google Scholar 

  31. Mitra, A.K., Gates, M., Barber, C., Goodwin, T., Selmic, R., Ordóñez, R., Sekman, A., Malkani, M.: Sensor agnostics for networked MAV applications. In: Evolutionary and Bio-Inspired Computation: Theory and Applications IV. Proc. of SPIE, vol. 7704, p. 77040R (2010)

    Google Scholar 

  32. Ordóñez, R., Gates, M., Moma, K., Mitra, A., Selmic, R., Detweiler, P., Cox, C., Parker, G., Goff, Z.: RF emitter localization with position-adaptive MAV platforms. In: IEEE NAECON (2010)

    Google Scholar 

  33. Raffard, R.L., Tomlin, C.J., Boyd, S.P.: Distributed optimization for cooperative agents: Application to formation flight. In: Proceedings of the IEEE Conference on Decision and Control, December 2004

    Google Scholar 

  34. Reif, J.H., Wang, H.: Social potential fields: a distributed behavioral control for autonomous robots. Robot. Auton. Syst. 27(3), 171–194 (1999)

    Article  Google Scholar 

  35. Rimon, E., Koditschek, D.E.: Exact robot navigation using artificial potential functions. IEEE Trans. Robot. Autom. 8(5), 501–518 (1992)

    Article  Google Scholar 

  36. Rotea, M.A.: Analysis of multivariable extremum seeking algorithms. In: Proceedings of the American Control Conference, vol. 1, pp. 433–437 (2000)

    Google Scholar 

  37. Selmic, R.R., Gates, M., Barber, C., Mitra, A., Ordóñez, R.: Position-adaptive direction finding of electromagnetic sources using wireless sensor networks. In: 19th Mediterranean Conference on Control and Automation, June 2011

    Google Scholar 

  38. Spooner, J.T., Maggiore, M., Ordóñez, R., Passino, K.M.: Stable Adaptive Control and Estimation for Nonlinear Systems, Neural and Fuzzy Approximator Techniques. Wiley, New York (2002)

    Book  Google Scholar 

  39. Stankovic, M.S., Stipanovic, D.M.: Discrete time extremum seeking by autonomous vehicles in a stochastic environment. In: Proceedings of the Conference on Decision and Control, pp. 4541–4546 (2009)

    Google Scholar 

  40. Stankovic, M.S., Stipanovic, D.M.: Stochastic extremum seeking with applications to mobile sensor networks. In: Proceedings of the American Control Conference, pp. 5622–5627 (2009)

    Google Scholar 

  41. Tan, Y., Nesic, D., Mareels, I., Astolfi, A.: On global extremum seeking in the presence of local extrema. Automatica 45, 245–251 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  42. Yamaguchi, H.: A cooperative hunting behavior by mobile-robot troops. Int. J. Robot. Res. 18(8), 931–940 (1999)

    Article  Google Scholar 

  43. Yao, J., Ordóñez, R., Gazi, V.: Swarm tracking using artificial potentials and sliding mode control. J. Dyn. Syst. Meas. Control 129(5), 749–754 (2007)

    Article  Google Scholar 

  44. Young, S., Mitra, A.K., Morton, T., Ordóñez, R.: Position-adaptive scatterer localization for radar imaging applications. In: Proc. SPIE, vol. 7308, Orlando, FL, April 2009

    Google Scholar 

  45. Zhang, C., Ordóñez, R.: Non-gradient extremum seeking control of feedback linearizable systems with application to ABS design. In: Proceedings of the Conference Decision and Control, pp. 6666–6671 (2006)

    Chapter  Google Scholar 

  46. Zhang, C., Ordóñez, R.: Numerical optimization-based extremum seeking control with application to ABS design. IEEE Trans. Autom. Control 52(3), 454–467 (2007)

    Article  Google Scholar 

  47. Zhang, C., Ordóñez, R.: Robust and adaptive design of numerical optimization-based extremum seeking control. Automatica 45, 634–646 (2009)

    Article  MATH  Google Scholar 

  48. Zhang, C., Siranosian, A., Krstić, M.: Extremum seeking for moderately unstable systems and for autonomous target tracking without position measurements. Automatica 43, 1832–1839 (2007)

    Article  MATH  Google Scholar 

  49. Zhang, C., Arnold, D., Ghods, N., Siranosian, A., Krstić, M.: Source seeking with nonholonomic unicycle without position measurement and with tuning of forward velocity. Syst. Control Lett. 56, 245–252 (2007)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Applied Materials, Inc., E. Arques Ave. 974, Sunnyvale, CA, 94085, USA

    Chunlei Zhang

  2. Dept. Electrical & Computer Engineering, University of Dayton, College Park 300, Dayton, OH, 45469-0232, USA

    Raúl Ordóñez

Authors
  1. Chunlei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raúl Ordóñez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chunlei Zhang .

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag London Limited

About this chapter

Cite this chapter

Zhang, C., Ordóñez, R. (2012). Swarm Tracking. In: Extremum-Seeking Control and Applications. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-2224-1_8

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-2224-1_8

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-2223-4

  • Online ISBN: 978-1-4471-2224-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation