Journal of Nonlinear Science

, Volume 18, Issue 3, pp 277–302

Optimal Strokes for Low Reynolds Number Swimmers: An Example

  • François Alouges
  • Antonio DeSimone
  • Aline Lefebvre

DOI: 10.1007/s00332-007-9013-7

Cite this article as:
Alouges, F., DeSimone, A. & Lefebvre, A. J Nonlinear Sci (2008) 18: 277. doi:10.1007/s00332-007-9013-7


Swimming, i.e., being able to advance in the absence of external forces by performing cyclic shape changes, is particularly demanding at low Reynolds numbers. This is the regime of interest for micro-organisms and micro- or nano-robots. We focus in this paper on a simple yet representative example: the three-sphere swimmer of Najafi and Golestanian (Phys. Rev. E, 69, 062901–062904, 2004). For this system, we show how to cast the problem of swimming in the language of control theory, prove global controllability (which implies that the three-sphere swimmer can indeed swim), and propose a numerical algorithm to compute optimal strokes (which turn out to be suitably defined sub-Riemannian geodesics).


Biological and artificial micro-swimmersOptimal controlOptimal gaitPropulsion efficiencyMovement and locomotionLow-Reynolds-number (creeping) flow

AMS Subject Classifications


Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • François Alouges
    • 1
  • Antonio DeSimone
    • 2
  • Aline Lefebvre
    • 1
  1. 1.Laboratoire de MathématiquesUniversité Paris-SudOrsay cedexFrance
  2. 2.SISSA-International School for Advanced StudiesTriesteItaly