I get that having more air decreases density and increases buoyancy. However, we can take the diver-BCD-oxygen-tank to be a single system. How can the pumping of air from the tank into a vest around him/her change the buoyancy of the tank-diver system? Maybe I just have a fundamental misunderstanding of the way BCDs work. It's unbelievably difficult to find anything on them beyond how to use them. To my understanding, they fill up a vest with air in order to make it (and therefore the system that consists of Yourself and the BCD) less dense, but if they are getting the air from Your tanks, they'll just be moving air around, which doesn't explain very much in terms of the overall buoyancy. Is the air collected from somewhere else? Is it a matter of the distribution of air?
(I am asking because I want to create a submarine robot and I am trying to understand how to use air to change the buoyancy)