Although I do have a home robot that vacuums my floors...

I think home robots are a non-starter. They're seductive ideas because they duplicate things we already know (servants). But robots and automation don't work the way humans do, and there's no reason to assume that there will be a point where that stops being true. It used to be that if you were wealthy you had servants, or a service, who would clean your clothing by hand, wash your dishes, cook your meals, etc. Today automation has changed much of that. You have specialized devices which make washing clothes and dishes far less of a chore. You also have innovations in the kitchen which make cooking far less of a chore (everything from electric ovens to stand mixers to refrigeration to a wide variety of prepared or partially prepared foods and so forth) and you have a significant increase in the ability to acquire pre-made foods (at restaurants, fast food places, delivery, frozen foods, etc.)

By the same token I don't imagine that further automation in the home will necessarily take an anthropomorphic shape. It'll be things we haven't even thought of yet, tasks we don't appreciate are time sinks or perhaps don't consider to be automate-able. Look at the roomba, for example.

I beg to differ. We already have walking and object handling robots and their agility is rapidly increasing. In the future we will have to deal with the aging population. As the quality of life increases and more people get university education, the rate of birth declines. Then who will take care of all those old men and women? We need household robots and they will be invented in Japan if not in some other place. They will be a good expensive item to mass produce and sell.

Japanese are incredibly xenophobic, it makes more financial sense just to import housekeepers from the Philippines or Indonesia, but many don't like the idea of that so they'll develop household robots instead (lucky for us!). Also, the rise of China set manufacturing robots back by about 10 or 15 years; we are just now beginning to recover.

Sure, people like coming up with reasons why they aren't racist and xenophobic, and how it's perfectly logical, see?!

Hong Kong is much more dense than Tokyo, and they have imported an army of Philippine and Indonesian house keepers.

I think the real trend with aging is that more adults will be living with their parents.

The solution to the healthcare and aging issue is already happening: immigration.

I agree that home robots will be task specific and not anthropomorphic. Examples I would buy if they were cheap:

-robot to stack and unstack the dishwasher

-robot wheels to put the garbage bin out for weekly collection

-robot mower to cut the lawn

-robot laundry hamper to take clothes to washing machine when full

-robot to clean kitchen benches and stove-top nightly

Interestingly, the dishwasher is already a dish-washing robot.

Don't stack/unstack the dishwasher. Use two dishwashers instead. At any one time one has clean dishes and the other has the dirty ones.