Rules for Minions in 5.5e?

     I'm planning to play a necromancer character in my next campaign, and the main way to amass a horde of minions is with Animate Dead. However, I don't want to go spending an obscene amount of spell slots reasserting control over my summons each day, so I plan to strike deals with my summons to have them work for me on their own terms, as both Zombies and Skeletons have the ability to comprehend Common. But because I am not reasserting control, they are technically not under the effect of Animate Dead, so no using bonus action mental commands to control the summons. Does anyone know of any rules for controlling minions outside of these spell effects?

There are no rules for it. What you’re talking about is well into homebrew territory, so only your DM can answer the question of how, or if it would work. 

Personally, I wouldn’t allow it. Having an army of undead would definitely fill the class fantasy, and I get that. But it would be very unbalanced and really bog down combat. 
Of course, I’ll be the first to admit my opinion doesn’t matter in your game, so, yeah, ask your DM.

It's worth noting that the "on their own terms" bit is a fairly wholecloth invention- as written zombies are pretty explicitly running on feral animal behaviors and skeletons lack desires or agency of their own. Obviously every setting is different, but this would be contingent on either lore your DM has already established or that they're allowing you to insert into the setting.

If you aren't putting them under some form of magical or supernaturla control, you aren't controlling them -- they're allies or hirelings, and are under DM control like any other allies or hirelings (and neither zombies nor skeletons are really the kind of thing that you can make particularly useful deals with; zombies are way too stupid and skeletons, while not quite as stupid, also mostly lack meaningful desires).

Coming from a game design point of view, "spending an obscene amount of spell slots reasserting control over...summons each day" is part of the counterbalance of being able to "amass a horde of minions". 

Maybe you can ask your DM for a Night Caller. However, I'd be reluctant to let you do your deal straight. If I could be persuaded, I'd be attaching riders like you have to perform a skill check on each undead each day to keep them loyal. Fail the check, and they revert back to being feral. Sooner or later, you'll see the advantages of casting the spells instead.

Welcome to the sad reality of necromancer in 5/5.5E the good old days of the beloved skeleton template are gone and now them minions get uppity if you don't feed em spell slots. 

My suggestion is learn finger of death the undead made by that don't need reestablish control however building an undead army with level 6 spell slots may not be practical 

That and Finger of Death has to kill them to work. Being a 7th level spell, you only get four shots a day at it (if you're at level 20 and willing to blow all your 7, 8 and 9 slots on it). You get a maximum of 4 a day, and they're CR1/4.

D&D5e isn't kind to Necromancers.

I am going to go a step further than the “ask your DM” folks and give this piece of advice - drop this idea and do not even bother to ask your DM about it.  Your DM, everyone else at your table, and even yourself will thank you. 

While hoards of undead are a fun power fantasy in lots of contexts, in D&D they are an incredibly painful slog that leads to long, long, long turns of numerous often ineffective attacks.  There is likely nothing more painful in the entire game than watching a Necromancer Wizard try to command all their minions - the problem would only get worse if either you or the DM has to control a hoard that is not even limited by daily spell slot burning.

No one should ever play a Necromancer Wizard in the “I control a hoard of zombies way”; they certainly should not then change the rules to further erode limitations on how many minions the entire table has to slog though. 

That’s because necromancers doing the zombie army thing grind the table to a halt as they resolve all the turns, which isn’t particularly engaging for anyone else.