The four possibilities are:
Both these walls are present when the robot is making a wide left turn. It will manage to rotate 90 degrees to the left, but it cannot move:
In the case where there's one wall adjacent to the origin:
This robot is making a wide right turn. It will move north some, but its eastward progress is stopped. It ends up here:
(If there had been another robot in the square ahead of Daniel, it would have been pushed north without rotating. If that robot could not move, the robot would act like a wall, and the situation would default to the example above.)
Similarly, if the wall had been directly in front of Daniel, the robot would have turned to face east and moved one square. (A robot in that square would have been pushed east if possible, and if not, the situation would default to the first example.)
The last case is when there are no walls adjacent to the origin.
If there are walls adjacent to the target square, then the robot hits the corner and can't move:
This robot, making a wide right turn, only rotates:
The same is true even if only one of the two depicted walls is present.
Of course, if there are no walls in the way, the robot simply moves to its target square.
Neither of these obstacles gets in the way of the wide left turn; the robot simply squeezes through:
If there had been another robot in the target square, it would have been pushed in the direction the moving robot eventually faces, which in this case was east. If the stationary robot could not move, it would act like walls around the target square, and the situation would default to the previous example.