United States v. Miller, 307 U.S. 174 (1939) - The Court stated in part:
In the absence of any evidence tending to show that possession or use of a "shotgun having a barrel of less than eighteen inches in length" at this time has some reasonable relationship to the preservation or efficiency of a well regulated militia, we cannot say that the Second Amendment guarantees the right to keep and bear such an instrument. Certainly it is not within judicial notice that this weapon is any part of the ordinary military equipment, or that its use could contribute to the common defense. Aymette v. State, 2 Humphreys (Tenn.) 154, 158. The signification attributed to the term Militia appears from the debates in the Convention, the history and legislation of Colonies and States, and the writings of approved commentators. These show plainly enough that the Militia comprised all males physically capable of acting in concert for the common defense. 'A body of citizens enrolled for military discipline.' And further, that ordinarily when called for service these men were expected to appear bearing arms supplied by themselves and of the kind in common use at the time.
This ruling was about whether sawn off shotguns were covered under the 2nd Amendment - it was ruled that they were not. However, the ruling also brings up that the second amendment was intended to allow the "militia" which "compromised all males physically capable of acting in concert for the common defense" to appear bearing arms "supplied by themselves and of the kind in common use at the time." Assault weapons ARE of the kind in common use as of today, and are a part of ordinary military equipment.
And as to the usual argument people like you bring up about the militia..
10 U.S. Code § 246.Militia: composition and classes
(a)The militia of the United States consists of all able-bodied males at least 17 years of age and, except as provided in section 313 of title 32, under 45 years of age who are, or who have made a declaration of intention to become, citizens of the United States and of female citizens of the United States who are members of the National Guard.
(b)The classes of the militia are—
(1)the organized militia, which consists of the National Guard and the Naval Militia; and
(2)the unorganized militia, which consists of the members of the militia who are not members of the National Guard or the Naval Militia.