I studied Manufacturing engineering and got a bachelors degree. This is very similar to ordinary Mechanical Engineering. I happened to be working on laundry products leading up to my time on the Dyson Robot. Its just a diverse enough company that they also operate in robotics. I now work for a medical devices company still working on motors.

My personal interests have been influenced by my father and elder brother who are both electronics engineers and I developed a keen interest in electronics and software from as far back as I remember and which I still have to this day. The ability for a mechanical engineer to fully understand the implications of the integration of mechanical systems, electronics and how they are prototyped and manufactured is key.

For instance when developing the wheels we were able to achieve minimal size by integrating the motors directly onto the PCB inside the gearbox and the PCB was an integeral part of the gearbox housing. This came about because all members of that part of the team understood each others domains to an extremely high degree.

Thank you for your detailed answer.

Electric Engineering is certainly a good option. Another is Mechanical Engineering, if you're more interested in the motion, industrial aspects and the construction of robots. And a bit of Computer Science is another option, if you're interested in software aspects, firmware development, machine learning to understand where the robot is, etc.