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Report a translation problem
input = output/s
pitch = rotor pitch
yaw = differential rotor pitch / differential collective
roll = differential collective / differential rotor pitch
To switch from vertical flight to horizontal flight you need to switch yaw and roll in your logic.
The nicest way is to multiply the roll and yaw inputs by your rotor tilt.
differentialCollective = yaw*rotorTilt + roll*(1-rotorTilt)
differentialRotorPitch = roll*rotorTilt + yaw*(1-rotorTilt)