Grid rotation for fps view

Hello everyone,
It’s been 6 days that I block on something …
I built a dungeon crawler (Master dungeon, grimrock) and I got to do the movements with vectors …
Not knowing how to apply these same movements to an AI, I left on a grid saying that it would be more simple…
I did 3/4 tutorial and it seems to me the most conclusive …

However, I can not make the displacements and the rotation for a view to the first person because of the directions which are fixed …
The camera is not the problem … The problem is rotation to direction (up , down, etc) who am not the forward of my pawn …
Here is a link to the desired result, which I already have in vectors but not in grid:

Otherwise, I’m interested in how to apply the same movements in vectors to AI …
Thanks in advance … or not;)