The basic unit for the exocomp was a common industrial servo mechanism that had been used for years by the Tyrans.
Farallon began working on an exocomp prototype a few years prior to 2369 when she had three working units in operation aboard the Tyrus VIIA station for maintenance purposes, during the development of Farallon's particle fountain technology. The exocomp was not intended to be sentient, but due to the adaptive nature of its design it evolved, gaining sentience. (TNG: "The Quality of Life")
The basis of the exocomp was an industrial servo mechanism which had been in common use on Tyrus VIIA for many years. This basic design was extended by Dr. Farallon who named them 'exocomps'. The main design goal was to make the exocomp a problem-solver. (TNG: "The Quality of Life")
The exocomp consisted of a micro-replication system, a boridium power converter and axionic chip network. This axionic network gave the exocomp formidable computational power. The micro-replicator not only created tools which the exocomp could use to solve problems but also created new circuit pathways in the exocomps memory when it performed new tasks. This mechanism gave the exocomp the ability to learn. The more tasks it had to perform, the more pathways were formed in its memory.
Recognition of sentience
Lieutenant Commander Data was testing an exocomp on the particle fountain and had completed nineteen separate tests when the device was sent into an access tunnel to seal a plasma conduit. The exocomp returned without finishing its task. When Dr. Farallon tried to send it back into the access tunnel by overriding the exocomp's commands, her control pad overloaded. A few seconds later the plasma conduit exploded. If the exocomp had returned to the access tunnel, it would have been destroyed. (TNG: "The Quality of Life")
When Data brought the exocomp back to the USS Enterprise-D for analysis, it was found that the exocomp had shut down and that the interface circuitry which connected the exocomp to the control pad was completely burned out. Further investigation revealed that the number of new circuit pathways had increased by 632 percent. Dr. Farallon explained that sometimes an exocomp randomly generated large numbers of new pathways, which ultimately led to a total shutdown. When this happened the exocomp became totally useless and had to be erased and reprogrammed all over again. Data mentioned that the new pathways did not appear to interfere with the original circuitry. This led Lieutenant Commander La Forge to comment that somehow the exocomp knew that the conduit would explode and therefore it had to leave the access tunnel. Because this remark would imply some form of self-preservation, Data took it upon himself to perform a level one diagnostic on the exocomp. (TNG: "The Quality of Life")
The diagnostic Data performed revealed that the command module was working normally. When checking the exocomp's sensor logs it turned out that the exocomp had burned out its own command interface circuitry, and then ran a self-repair program on the same circuitry two hours later. In a short briefing it was decided to test whether the exocomp possessed a survival instinct or not. (TNG: "The Quality of Life")
A test was created where an exocomp had to repair a small conduit breach in a Jefferies tube in which a plasma cascade failure was simulated by means of a transient overload signal. The exocomp performed the repair and was returned after the plasma overload simulation would have destroyed it. Data performed thirty-four additional tests and all tests had the same outcome. Every single time the exocomp would complete the repairs. Because Doctor Crusher distracted Data from his latest test, the exocomp returned automatically and Data noticed it had a different tool than when it entered the tube. In the previous tests the exocomp was recalled when the simulated plasma overload would have occurred. When Data checked the sensor logs he discovered that the exocomp had deactivated the overload signal. It had not failed the test; it had seen right through it. (TNG: "The Quality of Life")
When the situation on the particle fountain went critical the decision was made to reconfigure the exocomps so their power cells would explode when beamed into the particle matter stream, but because of their survival instincts their command pathways would have to be disconnected. Data locked out the transporter controls preventing the exocomps from being transported because he did not believe that it was justified to sacrifice one lifeform for another. Commander Riker proposed to ask the exocomps if they were willing to perform this mission. When their command pathways were reconnected they reprogrammed the commands Data had entered and altered the transporter coordinates to send them inside the station core, instead of into the matter stream. They solved the problem by distorting the particle stream frequency. Unfortunately, one of the exocomps did not survive, as it had to stay behind to disrupt the particle stream so the other two could safely be beamed back to the Enterprise.
By 2380, exocomps were recognized as sentient lifeforms by the Federation, had developed a family structure amongst themselves (or other lifeforms), and had developed the capacity to engage in linguistic communication with humanoids. At least one exocomp chose a name using an algorithm designed to determine the "perfect name": Peanut Hamper. (LD: "No Small Parts")
That year, Peanut Hamper had been granted a commission as a Starfleet officer and reported for duty aboard the USS Cerritos. Ensign Peanut Hamper was initially excited to serve aboard the Cerritos, and excelled in the ship's medical division. Unfortunately, when asked to undertake a risky mission to save her ship and fellow crew members from a hostile Pakled ship, Peanut Hamper became fearful, declared that she had only joined Starfleet to anger her father, and went AWOL by beaming herself off the Cerritos. She was subsequently stranded in the vacuum of space. (LD: "No Small Parts")
List of exocomps
In early drafts of "The Quality of Life", exocomps were known as "metacomps", but the name was changed when the staff discovered that a company with the same name existed. (Star Trek: The Next Generation Companion (3rd ed., p. 227))
The exocomps were originally intended to be simple wall terminals and household appliances. Writer Naren Shankar envisioned them as a modular device that would be added to existing tools, "like a high-tech Transformer toy," and above all, that would be alien in appearance and easily overlooked. In addition, he hoped that the eventual look of the exocomps would not be the "cute R2-D2 type," referencing the Star Wars films. He further commented, "As long as they're cute and fuzzy people respond, but if it's a nasty, ugly-looking thing they won't save it." (Star Trek: The Next Generation Companion (3rd ed., p. 227))
Senior illustrator and technical consultant Rick Sternbach designed the exocomps, but the episode budget allowed only two to be built. In "The Quality of Life", three exocomps can be seen; the third was digitally inserted in post-production. Their motion was supplied with control rods by puppeteer Kevin D. Carlson, who was also "painted out" later. (Star Trek: The Next Generation Companion (3rd ed., p. 227)) Sternbach loosely based their design on the character Nanmo from the animated series The Dirty Pair. (Star Trek Encyclopedia (4th ed., vol. 1, p. 255)) The first edition of the Star Trek Encyclopedia (p. 96) mistakenly referred to the character of "Mugi".
In the Star Trek: Enterprise second season episode "Dead Stop", the exocomp casing was used as a medical prop to heal Malcolm Reed's leg. One of the tools of the exocomp later re-appeared as the hand-held tool of the Sikarian atmospheric sensor in the Star Trek: Voyager first season episode "Prime Factors". It was later sold off on the Profiles in History auction. 
Star Trek: Lower Decks executive producer Mike McMahan said, "I love the Exocomps. I think the actual model of the Exocomp, the physical model, is somehow both ludicrous and insanely adorable at the same time. Because you can tell in the original episode they’re being held up with fishing line, I had the artists design the way the Exocomp moves, to sway a little bit when she’s on fishing line. The idea of painting a Starfleet uniform onto a little Exocomp just really tickled me." 
In Star Trek Online, exocomps appear to have become at least partially affiliated with Starfleet, where they have become sentient and are a member of the Federation. They can be found as player-owned "pets" (deployable in combat and non-combat versions), or in the game's Duty Officer system as members of the player's crew.