What major is beneficial for a long-term career goal in medical robotics/ robotics/ artificial intelligence?
Robotics in itself is an inter-disciplinary field, which I assume is why you are asking the question and have no just found it online.  There are some programs specializing in robotics, but the main question is what part of robotics you want to work on.  Control, Design, Theory, etc..  Humanoid robotics is different than nano robotics.    

If your end goal is Nano electronics, look into schools that specialize in... Nano electronics.  In that field as well, you should figure out what aspect you are interested in.  Department of Physics will sometimes have these majors, or some inter-discipline schools may have a special Nano program.

Purdue has a Nanoelectronics field inside engineering: https://engineering.purdue.edu/NRL/Students/index.html

Carnegie Mellon Univ. has a Nanorobotics lab inside mechanical Engineering:
http://nanolab.me.cmu.edu/

Utah State has a bionanoelectronis lab in its Biological Engineering lab:
http://be.usu.edu/htm/research/research-labs

As you can see, "nano" is a hot topic, and can be approached by different fields.  First figure out what aspect your intersted in, and if you do not want to go directly to PHD, you can major is a more generalized aspect, either Mechanical engineering, Physics, Chemistry, or Electrical Engineering.

If your interested in Artificial Intelligence, then you may want to go into Computer Science. 

If you want build medical robotics, it may be useful to have some medical training ontop of your EE background, which may make you attractive to interdisciplinary labs.  Or you can do Mechanical Engineering.

Saying your interested in Robotics, is a bit like saying you want to "Build Things".  You want to build Sculpture, Houses, Sky Scrappers, Bridges, Circuit Boards. Etc..