TY - RPRT T1 - Optimally swimming Stokesian Robots Y1 - 2010 A1 - François Alouges A1 - Antonio DeSimone A1 - Luca Heltai A1 - Aline Lefebvre A1 - Benoit Merlet AB - 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. UR - http://hdl.handle.net/1963/3929 U1 - 472 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - CHAP T1 - Biological Fluid Dynamics, Non-linear Partial Differential Equations T2 - Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 Y1 - 2009 A1 - Antonio DeSimone A1 - François Alouges A1 - Aline Lefebvre JF - Encyclopedia of Complexity and Systems Science / Robert A. Meyers (ed.). - Springer, 2009, 548-554 UR - http://hdl.handle.net/1963/2630 U1 - 1493 U2 - Mathematics U3 - Functional Analysis and Applications ER - TY - JOUR T1 - Optimal Strokes for Low Reynolds Number Swimmers: An Example JF - J. Nonlinear Sci. 18 (2008) 277-302 Y1 - 2008 A1 - François Alouges A1 - Antonio DeSimone A1 - Aline Lefebvre AB - 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). PB - Springer UR - http://hdl.handle.net/1963/4006 U1 - 396 U2 - Mathematics U3 - Functional Analysis and Applications ER -