FPS Character Controller stick to mesh.

Hello everyone,

I'm fairly new to Unity and I'm trying to make a Mario Galaxy-esque level where the player essentially sticks to the mesh as he traverses across. The character will be roaming around miniature planets (spheres) as well as running up the walls and ceilings of pipes (inverted cylinders). So yeah, if anyone could point me in the right direction as to how I can make this a possibility, I would be forever in your debt.