Driving motored vehicles on public roads is a privilege retained by the states under the Tenth Amendment. You can drive a tank on private property, if you can legally acquire one (Commerce Clause).

Unclear on explosives.

As far as "arms," the line is drawn at being able to be operated by a single person. So it would appear unconstitutional to prohibit keeping and bearing cannons and tactical nukes, though Congress can prohibit sale and interstate transfer.