EDIT: if you have gravity available, the video on that site illustrates a clever way to use those reaction wheels to move around by tumbling.
EDIT2: "for maneuvering around in space there are twelve electric micro-fans or μFans"[1]. The SE thread has a screenshot of a video which shows the placement of those fans.
EDIT3: Full video about the Int-Ball[2].
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[0] - http://www.kenkai.jaxa.jp/eng/research/electrical/triaxial.h...
[1] - https://space.stackexchange.com/questions/22324/how-does-jax...
[2] - https://www.youtube.com/watch?v=ZtIARUS7Lqc&feature=youtu.be...
EDIT: I'm probably very wrong about the movement.
EDIT: The video: https://youtu.be/n_6p-1J551Y
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".
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).
It uses an array of 12 small rotating fans placed around its surface to push jets of air and move itself from place to place.
My point was that in principle, you could abuse reaction wheels to give you translation capability if you're moving through air.
In the person + bike system, the brake action would result in internal forces. I don't see how this system could translate.
Thinking about it, the bicycle would only rotate about the center unless it had something to react against, as was pointed out by others.
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.
You can rotate it. You wouldn't be able push it around that way though.. if you manged that it would be a reactionless drive..
..a...b..
Rotate ~180 degrees around a, then b?
[ed: from other comments I see I may be too used to thinking in a gravity constrained environment..?]
Maybe they could make a version with ionic thrusters, that stays outside all of the time. It could have a 'nest' where it parks and refuels when not in use.
Easier to start inside, where you can pick it up if it runs out of batteries or glitches out. Less chance of poking a hole in something critical, as well.
Maybe make it magnetic and roll it on the exterior hull.
They also don't say, but they link to this article: http://www.kenkai.jaxa.jp/eng/research/electrical/triaxial.h... which has a lot more technical detail. Unfortunately I don't have time to dig deeper, but hopefully it will help you search a bit better.
Energy efficiency or fan reliability perhaps?
Note, space telescopes effectively use both approaches.
Okay, just saw EDIT2 of TeMPOraL: https://news.ycombinator.com/item?id=14795857, it appears to move around using micro fans.