Remotely operated vehicles were demonstrated in the late 19th century in the form of several types of remotely controlled torpedoes. The early 1870s saw remotely controlled torpedoes by John Ericsson (pneumatic), John Louis Lay (electric wire guided), and Victor von Scheliha (electric wire guided).
The Brennan torpedo, invented by Louis Brennan in 1877 was powered by two contra-rotating propellers that were spun by rapidly pulling out wires from drums wound inside the torpedo. Differential speed on the wires connected to the shore station allowed the torpedo to be guided to its target, making it “the world’s first practical guided missile”. In 1898 Nikola Tesla publicly demonstrated a “wireless” radio-controlled torpedo that he hoped to sell to the U.S. Navy. Archibald Low was known as the “father of radio guidance systems” for his pioneering work on guided rockets and planes during the First World War. In 1917, he demonstrated a remote controlled aircraft to the Royal Flying Corps and in the same year built the first wire-guided rocket.
Strictly speaking, there is no singular robotics program at MIT. People typically do robotics from one of three departments – Mechanical Engineering (Course 2), Electrical Engineering and Computer Science (Course 6), or Aeronautics and Astronautics (Course 16). Ironically, despite being probably traditionally the closest to robotics of the three, it is not possible to do a robotics specialization (at least as far as the name of the degree) in Course 6 (the main specializations are in EE, CS, or a combination of the two).
However, within either mechanical or aerospace engineering, you have the option of “concentrating” in robotics, through the 2A-6 or 16-ENG Robotics tracks. I believe that is the only way to make an MIT diploma have the word “robotics” on it (not that it really matters). There are some differences between taking any of those approaches, of course, and advantages/disadvantages depending on what you want your focus to be on, but ultimately, any of those (including the “straight” 2 and 16 tracks that don’t specifically focus on robotics) can give you a good basis for robotics.