What should I study in high school to allow me to work with robots?
To prepare yourself for a college degree that will allow you to work with robots, you should study as much math as possible in high school. The best place for you to end up is calculus-ready when you enter college.
Most robot-related fields are highly technical, however you will also need to study other things that may surprise you. You will need good English skills so you will be able to communicate your ideas to others and an understanding of social studies is important so you will be able to understand how robots fit into society and how humans react to them.
In short, your best bet is to be as well rounded as possible in your studies.
Robotics is cross discipline. Electrical/Computer/Mechanical/AI/Material science/Physics/Industrial….
You really want to explore several areas and find your passion/niche.