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We demonstrate a method by which domain walls (DWs) in planar magnetic ring-shaped nanowires can be propagated controllably at arbitrarily low velocities by confining them to geometrically defined energy minima. Using this technique, we propagate domain walls around a ring-shaped nanowire at velocities as small as 0.6 mm/s, low enough to allow ultra-cold atoms to be transported in magnetic “traps” formed by the domain wall’s stray field. We also show how the frequency of an external applied rotating field can be used to determine the domain walls’ velocity and that the thermally activated depinning of the walls from defects ultimately limits the precision to which their motion can be controlled.