If the Karas always stay to the right, they will not collide in the wide sections of the corridor. Problems arise only in the narrow sections. To make sure that there is only one Kara in a narrow section at any given time, the world fields of these sections are marked as monitor fields. Note that not only the fields in between mushrooms must be marked, but also the two fields before and after a narrow section.
The program of this solution is straight-forward and makes the Karas follow the wall of trees and mushrooms.
Attention: Because the monitor fields are section of the solution, the worlds have to be adjusted (i.e. the monitor fields have to be added) before the program can be started!