Stability Analysis of Bio-Inspired Source Seeking with Noisy Sensors

Inaki Rano, Mehdi Khamassi, KongFatt Wong-Lin

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Braitenberg vehicles have been used for decades to implement source seeking and avoidance behaviours in bio-inspired robotics. Recently, new theoretical results have derived convergence conditions of these bio-inspired controllers under the assumption of noiseless sensors. Although Braitenberg vehicles have been experimentally shown to work in outdoor scenarios, there is no theoretical evidence that shows they also can work in perceptually harsh environments. In this paper we mathematically analyse the source seeking behaviour of Braitenberg vehicle 3a with noisy sensors, when noise cannot be ignored. We approximate the stimulus the vehicle is seeking close to a source and derive the evolution equations for the average and covariance of the trajectory realisations. The analysis of the resulting non-linear differential equations shows that, under some conditions, the average trajectory is convergent and the dispersion around this trajectory is bounded.We illustrate these theoretical results through simulations, but also show that our results extend to general source seeking situations where the approximations do not hold.
Original languageEnglish
Number of pages6
Publication statusPublished (in print/issue) - 3 Jan 2022
Event2021 European Control Conference (ECC): ECC 2021 - Virtual Conference, Rotterdam, Netherlands
Duration: 29 Jun 20212 Jul 2021


Conference2021 European Control Conference (ECC)
Internet address

Bibliographical note

Funding Information:
ACKNOWLEDGEMENTS This work was supported by the Royal Society International Exchange Scheme under grant IE151293.

Publisher Copyright:
© 2021 EUCA.


  • Stability analysis
  • Braitenberg vehicles
  • noisy sensors
  • evolution equations
  • analytical trajectories
  • bio-inspired robotics


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