Biblical marching formation

Not sure if this is the right place to ask this, but…

In the Torah’s description of Bnei Yisrael’s marching formation, does the nation remain fixed to the compass points, so that, for example, Yehuda is always pointing east, or do they rotate so that Yehuda always marches in the front?

I ask because, if the shevatim remain fixed, then, for the most part, Yehuda isn’t marching on the leading edge, as most mefarshim say, except at a few places, such as the immediate departure from Sinai (which is where the marching order is first commanded, hence the Torah’s usage of the cardinal directions).

Bonus points for commentators and sources.