Maybe. The Constitution protects the right of "people" to "keep and bear" (i.e. keep and carry) "arms." There is at least a textual basis for interpreting "arms" to exclude weapons (like nukes and attack aircraft) that are not ordinarily carried by individuals.

But note, at the time of the founding, it was perfectly legal for private citizens to own armed warships. These ships had dozens of cannons that could fire over a mile (thus sieging a city). Canons moreover could fire grapeshot, causing massive casualties to groups of people. These weapons were far more destructive than an AR-15.