I use a Logitech F310, which has the same button/stick layout, and this is what I have set:
Left stick up/down: pitch up/down
Left stick left/right: yaw left/right (I know, I know...)
Left stick push: Request docking clearance (Shift-L)
Right stick up/down: speed increase/decrease (W/S)
Right stick left/right: roll left/right
Right stick push: ECM (E)
4 way hat: views (F1/2/3/4)
A Button: Fire laser (A)
B Button: Fire missile (M)
X Button: Space compass next target (\)
Y Button: Missile target seek (T)
View Button (Back button on the F310): Fast activate second equipment (ie Tab key)
Menu Button (Start button on the F310): Begin hyperspace countdown (H)
LB: Engage torus (J)
RB: Injectors (I)
LT: Fast activate first equipment (ie 0 key)
RT: Activate ID recognition (R)
Hope this helps!
I've just gotten a "Horipad for Xbox One" working on Linux, and at least generally working in Oolite - I can use the left stick to turn the ship, and I've mapped some of the buttons. So that's all good.
However, the LT and RT buttons aren't actually buttons, they're "axis" triggers, which can be pulled partway down, which means Oolite isn't letting me map them to any button-only tasks. Anyone care to suggest whether there's anything useful for them to do in Oolite?
Also, in my version of Oolite, I can't seem to find entries for all of the above options - some are just renamed, but I can't seem to find an option to request docking clearance at all. Am I missing something obvious?
(Next up: figuring out what sort of splines I might want...)