We already have robots that do our laundry. We call them "washing machines." They save us from having to carry our clothes down to the river, soaking them in the current, rubbing them in the rocks, then drying them in the sun.
My washing machine senses how much I have loaded into it, adds water, meters in the soap I have placed in the soap container, then goes through an elaborate ritual of swishing my clothes around in various ways with various combinations of hot and cold water until my clothes are clean, then it signals me to move them to the dryer. In the dryer a simpler program tumbles my clothes around, adding heat as necessary, and monitoring moisture content until the clothes have reached my preset level of "doneness."
Improving upon our current level of automation seems possible. Wanting to instantly reach the end state of a magic machine that does it all without going through the design evolutions to get there might where the problem lies. For example, many people have suggested that RFID tags in clothing could carry the same information as the tags that are on many articles of clothing now; these might even be an improvement for humans, let alone machines. Older eyes trying to read tiny writing on laundry tags don't do so well (I find this as I slowly grow older). If our clothing had such tags, its easy to see how a washing machine could set itself to the right program for the load of clothes it contains. It might need some logic to achieve the best cleaning at the lowest level of risk if the clothing is of mixed types, and it might need an alarm to signal if truly incompatible clothing has been loaded, but it can be done. From there we can imagine an improvement where in we put all of our clothes into some kind of container, and the container has the ability to sort the clothing into compatible sets, then load them into a washing compartment. Since we have manipulators in our machine now, we can use them to move the sorted/washed sets of compatible clothes from the washing compartment to the drying compartment (or design a compartment that can do both washing and drying). There - robotic laundry.
But wait one might say - we still have to put the clothes into a box - why doesn't the machine go around and pick up the clothes for us? My answer would be that isn't a robotic laundry, that is a robotic butler. Which we could also develop, especially since our clothes now already have RFID tags in them. The robotic butler can even keep track of what clothing ends up where/when, deducing whether we have actually worn it, then making assumptions about whether it needs to be washed or not. It might not be able to sense the amount of dirt or wrinkles at first, but those problems can be solved as well.
All designs go through evolution. To the extent that you can simulate evolutionary forces in a lab environment, you may be able to leapfrog your competitors and bring out a device that consumers "must have" that they haven't foreseen, but you run the risk of evolving faster than your consumers tastes or ability to understand the value of your product. Look at the evolution of portable music players from the Sony Walkman cassette player and the little Sony FM radios, now combined with portable telephones (remember bag phones?) and with Personal Digital Assistants. Now we have smart phones like the various Android phones and the iPhone. We didn't get there instantly. We got there through an evolutionary process of designs that were tested in the marketplace, where consumer consumption provided the natural selection.
Robotic laundry could go the same way, if the evolutionary pressures are present, and a little design mutation is introduced by the appliance manufacturers.