  The aim of this paper is to describe the self-propulsion of a micro-robot (or
micro-swimmer) consisting of $N$ spheres moving along a fixed line. The spheres
are linked to each other by arms with the lengths changing periodically. For
the derivation, we use the asymptotic procedure containing the two-timing
method and a distinguished limit. We show that in the main approximation, the
self-propulsion velocity appears as a linear combination of velocities of all
possible triplets of spheres. Velocities and efficiencies of three-, four-, and
five-swimmers are calculated.
  The paper is devoted to H.K.Moffatt, who initiated the author's interests in
low-Reynolds-number fluid dynamics.
