I was thinking the same thing.
In addition, I was thinking that if you're going to use a robot to do the laundry, then it would make more sense to make a laundry system condusive the abilities of the robot. Also, I was thinking that a robot doesn't have to have human limitations such as two arms. Instead, it can have more limbs which can assist in the process.
1) Opening and closing the door.. I would imagine that this would be done by the machine, not by the robot.
2) Sorting the laundry. While it's certainly optimal if we could use specialized tags to identify the clothing, it can be tricky. Mens' clothing would be easy since sticking an RFid on a tag could be done easily enough, but women's garments which tend to be much closer to the skin can be problematic. So the robot would in fact have to be able to sort using vision. This is acceptable. If the robot were to lay the garments on a table and properly lay them out, then patterns can be recognized. In addition, choosing which mode to use should be pretty simple as the weight of the garment relative to its size should be an effective means of doing this.
3) Operating the machine... like the door, it's a matter of having a machine that the robot can speak with.
4) folding the laundry. This is difficult for one particular reason. It's because clothing is often left in an unknown state. My daughter for example has never once in her life actually put her pants in the hamper without them being inside-out. The robot would need to lay out the article and then appropriately invert the garment. I as a human have trouble at times identifying with certain garments which way is which. I'm pretty sure a routine of "Place the garments unable to be properly identified in a pile. Wait for the user to assist in teaching the robot what should be done with it next time. To be fair, this is not a robot problem, my wife and I do this with each other as well. Women's clothing can be a major problem as well. H&M for example recently sold a kind of "over dress" which is kind of like a fishnet garment. I tried folding this once.. my fingers kept getting stuck in the holes. This would kill a robot haha
5) Choosing how to fold each garment.... When in doubt, ask Sheldon Cooper. He has a nifty device which can apparently fold anything. A robot should manage quite ok with that. For hanging garments, I assume it would take effort, but it can be done.
I think the article wasn't bad. It points out the obvious problem that when operating with fabric, there is so much entropy involved that a laundry robot can be amazingly difficult to make. That said, difficult is not impossible and therefore, I would say that while it might take a massive investment to produce a robot of such intelligence, it would also be a huge step towards revolutionizing the garment production industry. So I'm sure it would be worth while to a company like Foxconn to invest heavily in such a machine.