What begins? We have been sending "robotic" probes out for years.
The Robonaut was created by man.
There are many copies.
And it has a patent.
I'm thinking the term "robot" exaggerates the capabilities of many of these systems, especially the first two types.
The first two would definitely be considered "robots" IMO, especially since there's a certain amount of overlap in functionality in, say, commercial airliners where the aircraft can actually fly and even LAND itself without human intervention but otherwise can only move as the pilot tells it to. Later generations of Canadarm-style manipulators will probably be able to perform some simple operations automatically--like, say, unstowing equipment from cargo modules and so on--but will have a manual override for unscripted tasks. Teleoperated lunar probes are ALREADY being designed this way.
As for the third category, until you get something that can operate fully autonomously, you're really just talking about a very well-programmed robot. A machine that you can give a set of goals and let it decide how and when to accomplish those goals would be classified as an A.I. or possibly a "drone," in that they require almost no human intervention and can (reasonably) reliably complete their missions.