  We study the energetic efficiency of navigating microswimmers by explicitly
taking into account the geometry of their body. We show that, as their shape
transitions from prolate to oblate, non-steering microswimmers rotated by flow
gradients naturally follow increasingly time-optimal trajectories. At the same
time, they also require larger dissipation to swim. The coupling between body
geometry and hydrodynamics thus leads to a generic trade-off between the
energetic costs associated with propulsion and navigation, which is accompanied
by the selection of a finite optimal aspect ratio. We derive from optimal
control theory the steering policy ensuring overall minimum energy dissipation,
and characterize how navigation performances vary with the swimmer shape. Our
results highlight the important role of the swimmer geometry in realistic
navigation problems.
