The Automatons have a special building called "Orbital Platforms". Be aware that they have two kinds of those. One increases the population (not the one for this achievement), the other is the one we want.
The one you need is unlocked through the technology "Symbiotic Satellites" in the Trading and Diplomacy tree.
Once you have that, build it in 10 of your systems and have a fleet of at least 15 ships in every one of them. IMPORTANT NOTE: You have to have 15 ships there, not 15 Command points. 4 Capital ships are not enough.