A career in Robotics can be envisioned in the various key components where in robotics can be applied like automation, artificial intelligence, Robotics and Healthcare, complex management systems, computer aided robotic production plants etc.
One can choose B.Tech in automation and robotics or a B.Tech in Mechatronics. This would be offered in MIT, Manipal, SRM Unviersity, TamilNadu, APIIT under Kurukshetra University. Please consider this if useful to you.
Of the two options, most would suggest a B.Tech in Electronics and instrumentation engineering because it would give you access to further jobs is most of the major engineering fields be it language, instruments, technology etc and EIE gives you a better chance to further change or move on in a specif path for further education once you have learnt something about most key areas of Engineering.