No, robotics is very loosely linked to Physics or Math. If you want to build robots, learn to build robots in undergrads. It’s that simple. Don’t do math and physics in some vague hope that knowing quantum mechanics will give you skills to build (quantum?) robots :D.
Usually, robotics is a combination of many fields, experts from many fields combine their knowledge to build it. You want to be an expert for one of those, and more if you are a beast.
- computer vision (some math & CS & signal processing involved).
- Mechanical stuff (under-actuated control system, general mechE stuff).
- Planning & decision (Optimization & algorithms & math helps)
- Signal Processing (EE's do this a lot)
- Software (someone has to code up all the thinking of the robot)
So there you go, many fields from MechE, EE, applied math, CS are used in robotics, you just have to pick courses you like and be good at them.
My feel is that software & things that involve only math (algorithm/signal processing) etc… are more versatile because it is somewhat technology independent: doesn’t depend on what the current hardware looks like, all those ideas are transferable.