Addendum to "Local Controllability of the Two-Link Magneto-Elastic Micro-Swimmer"
Laetitia Giraldi (1), Pierre Lissy (2), Cl\'ement Moreau (3),, Jean-Baptiste Pomet (1) ((1) McTAO, CNRS (2) CEREMADE (3) McTAO, ENS Cachan)
TL;DR
This paper clarifies the controllability properties of a class of magneto-elastic micro-swimmers, demonstrating that they cannot achieve small-time local controllability, thus resolving an open question from previous work.
Contribution
It proves that the magneto-elastic micro-swimmers previously studied are not small-time locally controllable, completing the analysis of their controllability characteristics.
Findings
The systems cannot be small-time locally controllable.
The previous weaker controllability result is confirmed.
The open question about STLC is definitively answered.
Abstract
In the above mentioned note (<hal-01145537>, <arXiv:1506.05918>, published in IEEE Trans. Autom. Cont., 2017), the first and fourth authors proved a local controllability result around the straight configuration for a class of magneto-elastic micro-swimmers.That result is weaker than the usual small-time local controllability (STLC), and the authors left the STLC question open. The present addendum closes it by showing that these systems cannot be STLC.
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