Robotics Engineers design and maintain robots, develop new applications to utilize the potential of robots, and conduct research to expand the future potential of robotics. Also according to the Princeton Review, manufacturing engineering is currently the field of engineering most invested in robotic development.
Engineering, as a whole, is the study and application of the sciences, predominantly physics and mathematics, to develop and maintain a variety of processes most deem vital in everyday life. So for robotics engineering, depending on which concentration you would be most interested in, you would apply your learning to develop the physical beings used in robotics (mechanical, electrical, computer science, manufacturing, possibly civil), the software used in robotics (mostly computer science), or there are even possibilities within aerospace engineering to create airborne robotics. As you can see, there are many possibilities, and a defined field in specific robotic engineering is probably emerging as the search for new technology continues.