ajust AI movement to aim player

Hi all, don't really know where to post this.
sorry if I make any language mistakes, my english isn't that good...

I've tried things by miself a bit, but couldn't manage to do it properly (there are still bugs, or not working at all)

Basically, i have a player fighting combat robots, and one of the robot's attack is to activate jet engines and rush the player. I've got most of it working, but I would like to allow the robot to sligthly correct it's trajectory towards the player, since it's way too easy to dodge for now.

The robot charge direction is stored in a Vector3, and i would like to redierect this vector by a max angle towards the vector difference between the player and the robot (so where the player is from the robot), didn't know is that was clear...

I would like to do this both in 2d and 3d if possible.

any ideas of a good way to do this ?

 

I think I've got something working, but don't know if the maths are correct, because i don't really understand multiplying vectors and questernions.

what I am doing :

get angle between aimDirection and currentDirection,
clamp that angle between min and max authorized angle,
get the rotation axis with vector.cross(aimDirection, currentDirection)

and this is the thing I don't understand :

newDirection = Quaternion.AngleAxis(angle, rotationAxis) * currentDIrection

Any explanations ?

Also this does not work so well, I'm getting weird things like my robot doing full 180