"Swimming" in flat spacetime Is it possible for a machine with a velocity of zero to translate its position in a perfectly flat region of spacetime? This is possible in curved spacetime https://groups.csail.mit.edu/mac/users/wisdom/swimming.pdf, but I have not seen anything other than the almost-fictional Alcubierre Drive capable of replicating this effect in flat spacetime. Are there any realistic ways of doing this?
 A: That paper is a bit silly. To say that spacetime is curved in some region is essentially to say that the gravitational acceleration isn't constant there. In that situation, you can deform your body to put different parts of it in regions with different accelerations, such that the integrated acceleration over your whole body changes. This is true in general relativity for essentially the same reason that it's true in Newtonian gravity, and the fact that the field can be pictured as curved spacetime in GR isn't really relevant to the result. I'm not convinced that it's reasonable to call it swimming, and the paper's conclusion that "Translation in space can be accomplished [...] without thrust or external forces" makes little sense in a relativistic (even Galilean-relativistic) theory.
If the gravitational field is constant (and in particular if there's no gravity) then you have no control over your overall acceleration. Your center of gravity will follow a geodesic no matter what you do.
You can change your orientation/attitude, though, using a reaction wheel for example. The reason angular position can be changed and not linear position is that rotating objects eventually return to their starting points. If you could throw a ball, wait for it to return to you from the opposite direction, and catch it again, you would be in your original state but at a new position. That doesn't happen with linear motion, but it does happen with angular motion. (It could also happen in a non-Euclidean space, but that's different from the "swimming" in local curvature that was discussed in the paper.)
