From my own experience, a Computer Engineering degree is probably what you are looking for. The mathematics, physics, and other natural science will support your endeavors in engineering. The CE degree at my school was more 33/33/33 of EE/CE/CS. It also depends on what upper-level classes you later choose during your jr. and sr. year at an undergrad.
CE degree was very flexible at my school. It gave me many options of what level/layer of the work you wanted to get into. It can range anywhere from device design/physics to operating system programming (kernel-level).
I was the type that liked everything, coming into the college with a background in programming but an interest with digital and analog circuit. Some of the things I learned that are engineering related were embedded, micro-controller based system design, analog, and high-speed digital design.
I think any degree, EE, CE, or CS will definitely help you understand the hobby of electronics and robotics better. As for your career, it’s really hard to say what you will end up doing. I came into the college wanting to learn the skills necessary to develop a video game system and programming of it. In fact, my senior project was a video game system (micro-controller based) with my home-brewed Tetris game (user-space middleware) that plays on TV (RF modulator).
I was really into micro-controller based system design, so I ended being a TA for a design course for about 2 1/2 years. My last quarter there, I chose this course in high-speed digital design, which led me to a career in RF Engineering.
Just remember that just because the major you choose only touches a proportion of your hobby, doesn’t mean that you’ll suddenly forget or suddenly stops you from your hobbies. My hobbies involved RC Cars and robotics, and even though I do RF as a career, you can still develop the skills you need after-hours.
For me, I came to the realization that there’s nothing wrong with working in a field that’s far from your hobby, since that paycheck pays for my hobby… I would say check out the course curriculum for each type of major and see if there are any upper-level courses that will satisfy your craving…