Mecanim Rigidbody character slope limit issue

I'm pretty sure it does work. All my characters have a controller, and use mecanim w/ root motion.

What's the problem that happens when you do have a controller on the character?

Well of course $$anonymous$$ecanim works with Character Controller. But Character Controller doesn't work with characters that have a Rigidbody attached.

Or it does? If so, then how exactly? When I try this Rigidbody+Character Controller combo, my player character sinks to infinity defying any colliders.