Artillery was definitely considered a military weapon to be kept out of private hands. You wanted a distinction between sporting and military weapons.
Damn, I'm in a tight spot.
I think it is safe to assmume that the founding fathers were refering to small arms when the constitution was written. That being said, who knows what they might think about a private citizen owning a cannon. There are plenty of cannons and mortars in civilian circulation. Pay yer $200 tax and you can own practically anything.