I've seen this done using a pattern of positive and negative pads on one side, with a set of small brushes on the other, each designed so that they can't touch more than one pad and positioned so that the brushes will make contact with multiple pads. Pass the input from each brush into a rectifier, and you have a DC connection that will make itself as long as the two sides are more or less touching.
I think putting this on the floor might not be very safe, because anything conductive touching multiple pads while they were live would cause a short circuit. But it would be possible, if you really wanted to avoid having any on-board power source or storage.