  We study two microswimmers consisting of a spherical rigid head and a passive
elastic tail. In the first one the tail is clamped to the head, and the system
oscillates under the action of an external torque. In the second one, head and
tail are connected by a joint allowing the angle between them to vary
periodically, as a result of an oscillating internal torque. Previous studies
on these models were restricted to sinusoidal actuations, showing that the
swimmers can propel while moving on average along a straight line, in the
direction given by the symmetry axis around which beating takes place. We
extend these results to motions produced by generic (non-sinusoidal) periodic
actuations within the regime of small compliance of the tail. We find that
modulation in the velocity of actuation can provide a mechanism to select
different directions of motion. With velocity modulated inputs the externally
actuated swimmer can translate laterally with respect to the symmetry axis of
beating, while the internally actuated one is able to move along curved
trajectories. The governing equations are analysed with an asymptotic
perturbation scheme, providing explicit formulas whose results are expressed
through motility maps. Asymptotic approximations are further validated by
numerical simulations.
