Upgraded procedural moon system generator. Now it generates 3 types of moons:

Inner moons, small asteroid-like bodies orbiting close to the planet in its equatorial plane, near or inside its rings if they are present.

Regular moons, big spherical shapes satellites (or asteroidal with some small probability), orbiting planet in its equatorial plane with exponentially increasing semimajor axis (Dermott's law).

Outer moons, usually small asteroid-like bodies (or big spherical ones with some small probability), have irregular orbits.