Avoiding collisions can also be achieved using critical section states.
Before Kara takes a step forward, he determines whether that field can also be entered by another Kara. If the field ahead is also part of another route, he only steps on it when holding the critical section. If the field ahead only belongs to his route he steps on it right away.
If a Kara holds the critical section, he has to detect when he steps on a field that is not critical (i.e. only belongs to his route). In this case, he releases the critical section.