US robot maker Nilanjan Sarkar and psychologist Craig Smith are building just such a machine.
They want it to be as sensitive to our moods and emotions as humans are themselves.
No emotions of its own
It won't have emotions of its own.
But it should be able to respond to its owner's mood.
So, if you're a bit down the robot will move forward and ask if it can help you.
Apparently it's not an easy job because everyone shows emotions in quite different ways.