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Gait controllability of length-changing slender microswimmers

Paolo Gidoni, Marco Morandotti and Marta Zoppello
Vol. 12 (2024), No. 4, 471–505
DOI: 10.2140/memocs.2024.12.471
Abstract

Controllability results of four models of two-link microscale swimmers that are able to change the length of their links are obtained. The problems are formulated in the framework of geometric control theory, within which the notions of fiber, total, and gait controllability are presented, together with sufficient conditions for the latter two. The dynamics of a general two-link swimmer is described by resorting to resistive force theory and different mechanisms to produce a length-change in the links, namely, active deformation, a sliding hinge, growth at the tip, and telescopic links. Total controllability is proved via gait controllability in all four cases, and illustrated with the aid of numerical simulations.

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Keywords
motion in viscous fluids, fluid-solid interaction, microswimmers, resistive force theory, controllability
Mathematical Subject Classification
Primary: 76Z10
Secondary: 70Q05, 93B05
Milestones
Received: 20 May 2024
Revised: 23 September 2024
Accepted: 24 October 2024
Published: 29 December 2024

Communicated by Roberto Natalini
Authors
Paolo Gidoni
Dipartimento Politecnico di Ingegneria e Architettura
Università degli Studi di Udine
33100 Udine
Italy
Marco Morandotti
Dipartimento di Scienze Matematiche “G. L. Lagrange”
Politecnico di Torino
10129 Torino
Italy
Marta Zoppello
Dipartimento di Scienze Matematiche “G. L. Lagrange”
Politecnico di Torino
10129 Torino
Italy
© 2024 MSP (Mathematical Sciences Publishers).