I applaud the idea because I am all for the rube-goldberg type devices, which are much more complicated than their final purpose, though a robotic arm that is able to distinguish between socks based on barcode would create a very expansive dryer.

The do have rings, which you place around the socks when they go into the washer that hold the pair of socks together until you remove the rings. Perhaps this is a case where a low-tech solution, however boring and uncomplicatedly uncool, beats the hi-tech super-cool solution.

I buy them by the dozen. Black, all looking alike. Sometimes low-tech works.

your overcomplicating things. That would break, be to expensive, look odd, and not work. Barcodes need a direct line of sight to be read. Electronics don't get along to well with water or heat. Plus tracking socks would be an Orwiliean nightmare (tm). How about Velcro, tying them together, or a colored strip on the toe (which has already been implemented).