| Summary: | There are numerous ways to control objects in the Stokes regime, with microscale
examples ranging from the use of optical tweezers to the application of external
magnetic fields. In contrast, there are relatively few explorations of theoretical
controllability, which investigate whether or not refined and precise control is
indeed possible in a given system. In this work, seeking to highlight the utility
and broad applicability of such rigorous analysis, we recount and illustrate key
concepts of geometric control theory in the context of multiple particles in
Stokesian fluids interacting with each other, such that they may be readily and
widely applied in this largely unexplored fluid-dynamical setting. Motivated both
by experimental and abstract questions of control, we exemplify these techniques
by explicit and detailed application to multiple problems concerning the control
of two particles, such as the motion of tracers in flow and the guidance of one
sphere by another. Further, we showcase how this analysis of controllability
can directly lead to the construction of schemes for control, in addition to
facilitating explorations of mechanical efficiency and contributing to our overall
understanding of non-local hydrodynamic interactions in the Stokes limit.
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