Optimized high-performance robots for washing dishes, adapted to the consumer environment, have been available for almost a century. They're called, quite aptly, dishwashers.
Get two dishwashers and put your clean dishes in one of them.
Put a sticker on it marked "clean". Need a plate? Take it out of the "clean" dishwasher. Got a dirty plate? Put it into the other dishwasher. Other dishwasher full? Turn it on and move the "clean" sticker to that one.
Double buffering with dishwashers turns them into magic cupboards. I don't know why most kitchens only come with one.
What works is maintaining the invariant "if the door is locked, the dishes inside are clean". If you open a locked door, you either empty the dishwasher or relock the door.
It sounds good but I wonder how it would work in practice? What if you have a lot of guests over and use more dishes than usual?
What about items that you don't use fast enough? They'd stay left in the clean machine and you'd have to manually put them away before it turns into a "dirty" machine.
It would be great for consumers if these came with an app store where you could buy programs to do different tasks around the house (wash dishes, cook a specific meal, etc). If it was useful enough, it's not crazy to think that a family would spend 20k on one (same cost as a car).