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Generally, it's a good idea to have a look at the corresponding source code if the documentation is not sufficient. Have a look at the file goal_functions.cpp in base_local_planner/src, method isGoalReached (defined right at the end of the file). To me it seems like it is using the euclidean distance and the yaw of the robot orientation to check if the current pose is within the tolerances of the goal.

As you can see in the source code, the last point of the global plan is used as goal pose. I guess that all poses in the global plan are discretized with respect to the size of your global costmap which could explain the small errors you get.