I’d add a few things to @KLSD’s great post.
One, inter-department flexibility is not the only way to get the breadth you need. This is highly dependent on how the school achieves the objective. At my son’s school (Cal Poly) for example, the first circuits course that all MEs take is an EE course, taught through the EE department. From there though, most everything else Electrical related is taught in the ME department. They have multiple mechatronics and robotics lab spaces and classes in the ME department. As an interesting side note, they don’t overlap in AE either. Both departments have multiple wind tunnels and separate fluids curricula. His department is giant (roughly 1000 ME undergrads) and is very well resourced. The point is, you need to be able to get the three areas (ME, EE and CS). How you arrive there can vary by school. You need to look at concentrations and/or minors available, and their curriculum charts.
Two, the program need not have the name “robotics” in it anywhere. As @KLSD alluded to, there are actually very few of them. You can’t even get a stand alone undergraduate degree in robotics at CMU. Nearly everyone working in robotics does not have a degree with robotics in its title. There just aren’t many of them out there.
Pull some job descriptions off of Indeed with a keyword search of “Robotics Engineer,” Amazon Robotics or Formlabs for example, and look for the qualifications they are looking for. They don’t typically ask for " robotics" experience, but rather things like “experience with controls systems,” or " experience with electro-mechanical systems. "
Third, you may or may not have all freshman year to explore. Not all schools use this style of curriculum. Some, like Oregon State use a very old style, 2 years of pre-engineering. Some, like Purdue, do one year together, and then compete to get the major of choice. Some, like my son’s school, have students compete for major at admissions and hit the ground running in major day one. Each has strengths and weaknesses. With the former, you might not get your major. The latter can be hard to switch.
Lastly, pay very careful attention to something @KLSD said… “Self Taught.” You can teach yourself many of the programming aspects you will need. My son is self taught in both C+ + and Python and uses both extensively.
Good luck!