Start with a good math and physics base. Then either one of the degrees you mention or a combination would be appropriate. In most schools the first two years of any of those degrees have the same class requirements. So, if you can pick one then make the finial decision before the end of your second year.
Most Professional robotics development requires a team of people with mechanical, electrical, electronic, embedded systems and software experience.
Many of these fields do cross over. A BS is a minimum to get into the design aspect verse a Associate degree which would be minimum to work as a technician.
Just my take.
I have a BS in Physics but work as a electronic engineer. I do electronic and embedded system design, programming and managing of the projects and team members.