From a related video: the reaction wheels spin up while keeping total angular momentum at zero, then apply a rapid (magnetic) brake to transfer the momentum to the body (from the wheels). I'm assuming if you do that precisely enough (and in three dimensions), you can generate linear movement.
I'm not positive, but I'm pretty sure wherever you put the wheels, you aren't going to get the drone to rotate about any point other than its center of mass.
Makes sense, when thinking of it like a force - any where you push at the exterior (or interior) that's not directly at the center, would cause rotation around the center. I gather internal forces would add up/cancel out and never end up in a vector that pushes on the center of mass.
The system in the (cool) video is in contact with a table.
The table exerts a "normal" force on the cube, allowing a change in vertical momentum. If the system in question is the cube alone, this is an external force.
This method could be used if the drone were cubic and near a wall of the space-station, by kicking off of the wall. That could get it moving, but until it hit the opposite wall, there's nothing it could do to stop.
how does conservation of linear momentum apply?
edit: this question was asked when the parent comment claimed that this machine could "generate linear momentum" from the wheels.
Imagine holding up a bicycle in the air from the midpoint. Now spin both wheels in opposite directions. No movement. Now apply one brake. Now you have movement. Now do that in three dimensions with precision and you have this thing.
Conservation of momentum applies when there are "no external forces", which wouldn't be the case here when you apply the brake.
EDIT: Yeah, my apologies. I didn't mean to write "momentum".
The brake is an internal force though (the force and its reaction both act on the bicycle). The whole unit's only external forces are from the fans so that's all it can use to translate. That and bumping into things.
Come to think of it - in air you're constantly bumping into things - air molecules. I think it could technically be possible to steer in zero-g within an atmosphere by pure rotation (e.g. consider that a fast-spinning object is kind of a (crappy) fan).
Can it face you with one of its fans and run it at the same high speed as the opposite fan, to keep you cool, and take photos of you with your hair blowing in the wind?
well, momentum is defined as the product of mass and velocity. movement implies velocity, and we are not talking about massless things here, so yes, movement implies momentum.
EDIT: I'm probably very wrong about the movement.
EDIT: The video: https://youtu.be/n_6p-1J551Y