How to calculate ship position and rotation in a pipeline with raycasts

I'm developing a little game in which a spaceship navigate in a pipeline, and I need to push the ship down (with a little release and a floating effect) and let it turn and go forward in any direction. (the pipelines extends in all the three dimenctions X, Y and Z). If someone has some code snippet or at least a list of things to do to obtain this result please post it! I whink that it could be done even with barycventricCoordinates...