Hello, I plan to implement character controller for my physics engine. I seek advice from you, what it does, what are the common features. And what to do when, say the character is laying on the floor (what to do with the bounding volume?)
IMO the biggest decision you have to make when thinking about designing a character controller is whether you make you characters actual rigid bodies or not. Whether you can do this will depend on the game type - in LBP, sackboy was a rigid body which wasn't allowed to rotate (inv inertia tensor of zero).
Having the character be a real rigid body rather than a proxy has advantages and disadvantages. It was great in LBP because sackboy has a lot of very close interaction with his environment; he pushes on things, pulls them and gets squashed by them - to facilitate this sackboy actually had his own character constraint which allowed him to be an integral part of the constraint solver