Optimal control of slender microswimmers

Marta Zoppello (1) , Antonio Desimone (2) , François Alouges (3) , Laetitia Giraldi (4) , Pierre Martinon (5)

1 UNITN - Università degli Studi di Trento = University of Trento
2 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 McTAO - Mathematics for Control, Transport and Applications
5 Commands - Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems

We discuss a reduced model to compute the motion of slender swimmers which propel themselves by changing the curvature of their body. Our approach is based on the use of Resistive Force Theory for the evaluation of the viscous forces and torques exerted by the surrounding fluid, and on discretizing the kinematics of the swimmer by representing its body through an articulated chain of N rigid links capable of planar deformations. The resulting system of ODEs governing the motion of the swimmer is easy to assemble and to solve, making our reduced model a valuable tool in the design and optimization of bio-inspired artificial microdevices. We prove that the swimmer is controllable in the whole plane for N is greater of equal to 3 and for almost every set of stick lengths. As a direct result, there exists an optimal swimming strategy to reach a desired configuration in minimum time. Numerical experiments for N = 3 (Purcell swimmer) suggest that the optimal strategy is periodic, namely a sequence of identical strokes. Our results indicate that this candidate for an optimal stroke indeed gives a better displacement speed than the classical Purcell stroke.

Domaines: Mathématiques [math]; Optimisation et contrôle [math.OC]

Marta Zoppello, Antonio Desimone, François Alouges, Laetitia Giraldi, Pierre Martinon. Optimal control of slender microswimmers. Gerisch, Alf and Penta, Raimondo and Lang, Jens. Multiscale Models in Mechano and Tumor Biology, Springer International Publishing, pp.21, 2017, 978-3-319-73371-5. ⟨10.1007/978-3-319-73371-5_8⟩. ⟨hal-01393327⟩