In reply to FesteringSore:
people bounce when they walk, try walking holding a cup of water and see how much it moves, even whe you are trying not to.
there's some things you could do to minimise it
... miniture steadicam stabilizer, but that will need to be handheld as the camera will tend to pan a little if not perfectly balanced
... stabilization software (basically repositions each frame slightly so that most of the image stays centralised but you'll need to crop the result as the edges jump about a bit
... record at 50/60fps and then slow the footage down, it'll take twice as long to play but the movement between each frame is half so it appears smoother (it's basically slow motion... you know the "power walk" scenes in movies, they are slight slowmotion to get that effect)
i'm sure there's others