DiGORO is a learning robot developed at UEC (University of Electro-Communications); it can learn by watching humans. The robot learns about objects when presented by its helpers. After watching people manipulate the objects, DiGORO can imitate the actions.
DiGORO can also perform accurate face recognition and move around safely in open spaces on its Segway platform.
Take a look at this DiGORO video.
(DiGORO robot learning video)
I was trying to think of a better example of science fictional robots that learn by watching people, but the best robots I could come up are the "wheelies" from Stephen Barr's excellent 1960 short story Callahan and the Wheelies. As I recall, they learned to recharge themselves at standard wall sockets by watching people.
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