Stochastic Source Seeking for Nonholonomic Vehicles

Part of the Communications and Control Engineering book series (CCE)


Steering mobile robots is the first application of extremum seeking in the book. Employing the approach developed for single-input systems, steering is conducted in concentration fields with an unknown spatial distribution, and without position (GPS) measurements available. The vehicle is driven to approach a small neighborhood of the source in a manner that seems partly random, but is provably convergent in a suitable probabilistic sense. The study presented in the chapter offers an interpretation for the chemotaxis motion of bacteria, which are stochastically driven and employ only local concentration measurements and no position measurements.


Small Neighborhood Convergence Speed Signal Field Deterministic Case Exponential Convergence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 6.
    Ariyur KB, Krstic M (2003) Real-time optimization by extremum seeking control. Wiley, Hoboken MATHCrossRefGoogle Scholar
  2. 18.
    Berg H (2003) E. coli in motion. Springer, New York Google Scholar
  3. 19.
    Berg H, Brown DA (1972) Chemotaxis in E. coli analyzed by three-dimensional tracking. Nature 239(5374):500–504 CrossRefGoogle Scholar
  4. 28.
    Cochran J, Krstic M (2009) Nonholonomic source seeking with tuning of angular velocity. IEEE Trans Autom Control 54(4):717–731 MathSciNetCrossRefGoogle Scholar
  5. 29.
    Cochran J, Ghods N, Siranosian A, Krstic M (2009) 3D source seeking for underactuated vehicles without position measurement. IEEE Trans Robot 25:117–129 CrossRefGoogle Scholar
  6. 30.
    Cochran J, Kanso E, Kelly SD, Xiong H, Krstic M (2009) Source seeking for two nonholonomic models of fish locomotion. IEEE Trans Robot 25:1166–1176 CrossRefGoogle Scholar
  7. 46.
    Ghods N, Krstic M (2010) Speed regulation in steering-based source seeking. Automatica 46:452–459 MathSciNetMATHCrossRefGoogle Scholar
  8. 100.
    Mesquita AR, Hespanha JP, Åström K (2008) Optimotaxis: a stochastic multi-agent optimization procedure with point measurements. In: Egerstedt M, Mishra B (eds) Hybrid systems: computation and control. Lecture notes in computer science, vol. 4981. Springer, Berlin, pp 358–371 CrossRefGoogle Scholar
  9. 146.
    Zhang C, Arnold D, Ghods N, Siranosian A, Krstic M (2007) Source seeking with nonholonomic unicycle without position measurement and with tuning of forward velocity. Syst Control Lett 56:245–252 MathSciNetMATHCrossRefGoogle Scholar
  10. 147.
    Zhang C, Siranosian A, Krstic M (2007) Extremum seeking for moderately unstable systems and for autonomous vehicle target tracking without position measurements. Automatica 43:1832–1839 MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  1. 1.Department of MathematicsSoutheast UniversityNanjingPeople’s Republic of China
  2. 2.Department Mechanical & Aerospace EngineeringUniversity of California, San DiegoLa JollaUSA

Personalised recommendations