Plasmodium of Physarum polycephalum is a single huge (visible by naked eye) cell with a myriad of nuclei. The plasmodium is a promising substrate for non-classical, nature-inspired computing devices. It is capable of approximation of the shortest path in a maze, computation of planar proximity graphs and plane tessellations, primitive memory and decision making. The unique properties of the plasmodium make it an ideal candidate for a role of amorphous biological robots with massive parallel information processing and distributed inputs and outputs. We show that when adhered to a lightweight object resting on a water surface the plasmodium can propel the object by oscillating its protoplasmic pseudopodia. In experimental laboratory conditions and computational experiments we study phenomenology of the plasmodium-floater system, and possible mechanisms of controlling motion of objects propelled by on-board plasmodium.