In Federalist 46, Madison says that the citizens should have the right to own anything as that of a standing army of the 'kingdoms of Europe'. In other words, the citizens should be able to defend themselves from any entity which threatens their life, liberty, or property, even against the most powerful aggressor.
Hamilton reiterated this in Federalist 29 regarding the citizens being equipped as the army so 'that army can never be formidable to the liberties of the people'.
So while the Constitution doesn't define what arms we can hold, the writers made it clear, the citizens should be free to arm themselves as any standing army so as to always be able to defend themselves from any army.