@article {2010,
title = {Optimally swimming Stokesian Robots},
number = {SISSA;54/2010/M},
year = {2010},
abstract = {We study self propelled stokesian robots composed of assemblies of balls, in dimen-\\nsions 2 and 3, and prove that they are able to control their position and orientation. This is a result of controllability, and its proof relies on applying Chow\\\'s theorem in an analytic framework, similarly to what has been done in [3] for an axisymmetric system swimming along the axis of symmetry. However, we simplify drastically\\nthe analyticity result given in [3] and apply it to a situation where more complex swimmers move either in a plane or in three-dimensional space, hence experiencing also rotations. We then focus our attention on energetically optimal strokes, which we are able to compute numerically. Some examples of computed optimal strokes are discussed in detail.},
url = {http://hdl.handle.net/1963/3929},
author = {Fran{\c c}ois Alouges and Antonio DeSimone and Luca Heltai and Aline Lefebvre and Benoit Merlet}
}
@article {2008,
title = {Optimal Strokes for Low Reynolds Number Swimmers: An Example},
journal = {J. Nonlinear Sci. 18 (2008) 277-302},
year = {2008},
publisher = {Springer},
abstract = {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).},
doi = {10.1007/s00332-007-9013-7},
url = {http://hdl.handle.net/1963/4006},
author = {Fran{\c c}ois Alouges and Antonio DeSimone and Aline Lefebvre}
}