PostgreSQL database: Get rid of redundant transitive relation (maybe 3NF is failed)

I'm creating a hybrid between "X-Com Enemy Unknown" and "The Sims". I maintain game state in a database--PostgreSQL--but my question is structural, not engine-specific.

1. As in X-Com, there are some bases in different locations, so I create a table named Base with ID autoincrement identity as primary key.
2. Every base has some facilities in its territory, so I create a table named Facility with a foreign key Facility.Base_ID, referring to Base.ID.
3. Every base has some landing crafts in its hangars, so I create a table named Craft with a foreign key Craft.Base_ID, referring to Base.ID.
4. Every base has some troopers in its barracks, so I create a table named Trooper with a foreign key Trooper.Base_ID, referring to Base.ID. Just to this point, everything seems to be ok, doesn't it? However...
5. I want to have some sort of staff instruction. Like in the X-Com game, every trooper can be assigned to some craft for offense action, or can be unassigned. In addition, every trooper can be assigned to some facility (or can be unassigned) for defense action. So, I have to add nullable foreign keys Trooper.Craft_ID and Trooper.Facility_ID, referring to Craft.ID and Facility.ID respectively.

That database has a redundancy. If some trooper is assigned to a craft or to a facility (or both), it has two (or even three) relations to the base--one direct relation through its Base_ID and some indirect relations as Facility(Trooper.Facility_ID).Base_ID and Craft(Trooper.Craft_ID).Base_ID. Even if I get rid of Trooper.Base_ID (e.g. I can make both assignment mandatory and create a mock craft and a mock facility in every base), I can't get rid of both trooper-facility-base and trooper-craft-base relations.

In addition to this redundancy, there is a worse problem--in case of a mistake, some trooper can be assigned to a craft from one base and to a facility from another base, that's a really nasty situation. I can prohibit it in the application business logic tier, but it's still allowed by the database.

There can be some constraints to apply, but is there any structural modification to the schema that can get rid of the redundancy and potential inconsistency as a result of a good structure, not as a result of constraints?

CREATE TABLE base (
  id int PRIMARY KEY
);

CREATE TABLE facility (
  id int PRIMARY KEY,
  base_id int REFERENCES base
);

CREATE TABLE craft (
  id int PRIMARY KEY,
  base_id int REFERENCES base
);

CREATE TABLE trooper (
  id int PRIMARY KEY,
  assigned_facility_id int REFERENCES facility,
  assigned_craft_id int REFERENCES craft,
  base_id int REFERENCES base
);

Now I want to get some sort of constraints on a trooper t so that

facilities.get(t.assigned_facility_id).base_id IS NULL OR EQUAL TO t.base_id
crafts.get(t.assigned_craft_id).base_id IS NULL OR EQUAL TO t.base_id

This hypothetical constraint has to be applied to table trooper, because it applies in boundaries of each trooper row separately. Constraints on one table have to check equality between fields of two other tables.

I would like to create a database schema where there is exactly one way, having a trooper.id, to find its referenced base.id. How do I normalise my schema?