A rifle using a Intermediate sized round: larger than a pistol, smaller than a rifle. Designed in WWII by the Nazi for close quarters, rapid fire, and to allow large amounts of ammo to be carried into battle.
High muzzle velocity 1000m/sec.
Adolph Hitler called the MP43 the Sturmgewehr (literally "storm rifle", "storm" as in "military attack"), translates into Assault Rifle.
We should regulate back to muzzle velocities and rates of fire the way Scalia likes it: when the Amendment was written. That would be 3 rounds per minute, no more than 1500fps.
While you're at it, how about banning assault weapons use by non-law enforcement agencies. There's no reason the Dept of Education, FEMA, or even the IRS needs assault rifles and riot shotguns. If they run into situations that need that kind of firepower, either they are overstepping their charter, or they can call the police or US Marshalls who at least have some judicial oversight.
Two words contradict you: Citizens United. The doctrine of separate corporate personality came a century later. When the founders wrote the Bill of Rights, the owners spoke for the joint-stock company.