Hi,
I believe that the answer that you are looking for is in this code:
https://github.com/yujinrobot/kobuki_core
A Turtlebot2 has a base called Kobuki. Such base is where the controller is located.
I did not really check it properly, but I am pretty sure that the specific code that you can use as a reference is there. Check the following files: include/kobuki_driver/modules/diff_drive.hpp and src/driver/diff_drive.cpp
If you have problems with the controller, send me a private message ;)
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