Japan has a bit of a head start on this, recognizing early that it will soon have a lot of old people and not enough young people to both take care of them and keep the economy running. Honda's ASIMO is explicitly a mobility assistance robot. Osaka U. Actroids mimic human appearance. Mitsubishi's Wakamaru approaches the function of a receptionist.
So far, no robot seems even close to taking on the everyday tasks performed by low-wage nursing home employees in the US. But take a look at "Babyloid" and "Pepper". They are robots designed to socially engage with people, so they don't get lonely and depressed.
Japan's elderly may soon be conversing with chatbots more often than living people. Baby Boomers in the US had better take note.