Best Path for PhD in Engineering - which Undergrad Major at which Colleges?

You should think about which aspect of R&D in robotics you want to do in the future. You probably need to explore more in college to find out. It is also common to cross/change discipline in grad school. You should not overplan it for now. UMich would be a great school for you, not only for the strength in all engineering fields but also an in state school that you have the advantages financially and academically. The in state CoA is $28-$30k at UMich and they meet the need of in state student. It may still be cheaper than other OOS schools after NMS scholarships. My D did not even apply to any schools that give NMS. If your actual score is higher than the NMS cut off (Michigan is not that high anyway), you may get merit aids from other schools as well. The Scholarship of Honors at CoE is $8000/yr for in state students. You should check out the NPC to estimate your cost too.