We report on the reptation of vertically vibrated droplets of fine particles lying on a solid incline. On the one hand, time-resolved measurements show that the gas pressure in the gap between the droplet bottom and the solid surface can be accounted for by a Darcy law. The cumulative effect of the viscous drag is responsible for the droplet formation. On the other hand, we show that the gap pressure is responsible for an effective horizontal acceleration whose cumulative effect is the upward reptation of the droplets. Using various geometries of the solid substrate, we manipulate the droplets and study the effects of the substrate geometry and of the experimental parameters on the droplet shape and dynamics. The experimental results are discussed in the light of theoretical arguments. This study demonstrates that, by the choice of a suitable geometry of the surface and characteristics of the vibration, one can develop tools for precise powder handling and control.