This is what I consider the best build for Tenet Dogs. I didn't see the robot dogs on Overframe here, so I used a Moa instead.

Just like Moa's, the robodogs have very minor differences between the different parts, so just choose the parts that you like best cosmetically for a build investment. robodog powers are kinda meh. they're basically moas that use melee instead of sentinel weapons, and their prospectus, audit, and denial mods are also kinda meh, but there are better / more useful ones.

The three open spots are for Tenet Dog-specific mods. You'll need to acquire multiple dogs from liches etc to get them. Here they are:

Prospectus:

Arial - The dog does an aerial strike that's a lot weaker than Vauban's. This is the weakest one. Don't bother with it.
Focused - The dog shoots a laser from its face that does heat damage and knocks enemies backwards, just like when a kuva lich shoots at you with a [Nukor]. This one is cool. I have a dog named "Dogmeat Laserface" exactly for this. But as far as weapons go, it's slow, takes a long time on each target, and doesn't do much damage. Looks cool though.
Synergized - This one is the most useful, though that still doesn't say much. It's chain lightning. I recommend this one in an overall general build.

Audit:

Equilibrium - This is a series of radial shockwaves that knocks down opponents nearby, but it's extremely visually annoying and lasts a long time.
Null - This lets the dog steal Eximus auras for a little while. Cool in practice, but it doesn't happen much, and can have negative unintended consequences. Like, if your dog is suddenly running around with a Frost bubble from a cold Eximus enemy, that's a big wandering bubble that you can't shoot through.
Repo - The most useful. It's basically a [Loki] disarm that will permanently disarm enemies within a radius around the dog. I recommend this one in an overall general build.

Denial:

Evasive - The dog occasionally teleports away from enemies, which is not very useful and also, being as the AI sucks, isn't very effective for its survival anyway.
Diversified - The dog splits up into three tiny dogs that each do 85% of the dog's normal damage. Potentially 155% extra DPS. And they're super cute. I recommend this one in an overall general build.
Reflex - Making a magnetic shield that reflects damage taken as a DOT on enemies. Kinda pointless, since we kill so fast anyway.