Electronics will serve you well in robotics, but mechanical engineering is needed, too.  The most interesting work that I have seen in robotics had to do with the mechanics of the machines and the electronics control.  The software is non-trivial, but if you don't have the fundamentals of mechanics and electronics, you won't even get started in robotics.

All three are needed, but I recommend a focus in mechanical engineering and electrical engineering.  Robotics is really all three (adding in software).

I have a friend with a PhD in robotics and he can make a wide variety of devices.  While his work is in manufacturing automation, his hobby takes his to much broader areas.  His strong card if mechanical, second in electronics, and he is taking night classes to catch up in software, both for design and control.  But, if he didn't have that strong foundation in mechanical and electrical engineering, he would not be able to make the things he does.

The number of students who are now taking up electrical engineering degree online has increased. Whatever you decide on, make sure that you are happy with it.