  We study two mechanisms of locomotion of a body in an inviscid fluid, which
take place without the shedding of vorticity; we consider two simple examples
of robots which are able to move along a straight trajectory. The first one
consists of a sphere with an internal moving material point (actuator); this
illustrates \emph{the recoil locomotion}. The second robot represents a sphere
moving along a thin rigid rod, this is aimed at illustrating \emph{the
deformational locomotion}. The latter appears since this motion of a sphere can
be seen as a `soliton' deformation, moving along the rod. The equations of
motion for both robots are the same, while the intervals of variables are
different. The first robot was introduced by \cite{Saffman}, who also wrote
that he was unable to find any exact solution for the deformational locomotion:
our paper fills this gap. Some previous papers emphasize that, in the cases of
locomotion, the deformations must be not axisymmetric. We consider only
axisymmetric examples, which expands the range of the involved possibilities.
The simple construction of presented robots allows us to operate with the exact
solutions only, which can play a `reference' role. Our aim is to analyse the
main notions and terminology, used in this high-impact research area.
