You can target the pillars and shoot them away with the SRV's weapons too. (You can do it without targeting, but it's easy to hit the relic and knock it off). I guess it's worth seeing if anything happens if all 4 are 'freed'.
It didn't occur to me to clear the rocks around the base. They might be meaningful or might just be cosmetic.
As there is something spinning below the obeliscs (i think someone discovered this with the debug camera) i think it is possible that the obelisks can spin.
Maybe there are acustic hints if we do something right? Possible the the "machine" begins to roar if we find the first activation step. Quite sure there are several steps to complete until this thing works.
Ciao, Udo