Imagine a carpet with a layer of "honey comb" below the surface (and pad) that could allow for a central system to suck dirt from below so the dust and dirt could be removed with out a vacuum. This may not totally remove the need for a top side vacuum to remove surface debris but it might reduce dust and dirt and thus reduce allergies.
An alternative idea would be to pump heat and air upward throught the same "honey comb" system so that heading and cooling would be distributed equally throughout the room (think radient heating systems).
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I certainly do not like the idea of pumping air through the carpet - all the dust and bacteria will be lifted into the breathable space.The other option reminds me of the clean rooms, which are very expensive to construct and maintain. I haven’t done any calculations but I think a vacuum cleaner will be more cost effective.
gtotev,
The idea would be to first suck out all the dirt for a few minutes in vacuum mode and then turn on the head or air to push back the environmental changes. Cleaning and cooling in the same system!!
-Voltmer
The carpet would act as a filter trapping all the dirt and dust deep in the carpet fibers. A conventional vacuum would not be able to remove the buried dirt, so the carpet would eventually need to be replaced. Just get a robot vac.