The regeneration unit (also referred to as the regeneration tank and regen disc by Thorne and Starkey respectively) was a maintenance device implanted in robots such as K9 Mark I.
History
When K9 was infected by the Swarm, he went into "self-regeneration" to recover. (TV: The Invisible Enemy) The Fourth Doctor and Romana I also concurred that K9's only chance of survival after he'd been badly hurt by the Ogri was a "complete circuit regeneration". (TV: The Stones of Blood) It is not known whether this ability was related to the regeneration circuit.
After K9 self-destructed to defeat four Jixen warriors, Starkey retrieved the unit and K9 regenerated; lightning and flashes of bright light erupted around the hovering regeneration unit, and ghostly schematics of K9's new casing flew around it before solidifying into a new body. Following regeneration, K9 remembered his name but couldn't recall additional details of his past; memories of his adventures with the Doctor and Leela, his two former masters, appeared to be at least temporarily lost. He did, however, appear remember the circumstances immediately leading up to his regeneration, including the identity of Starkey. (TV: Regeneration)
Thorne and Lomax knew of the regeneration unit and decided to acquire it starting with Thorne's failed plot to cause K9 to regenerate with the use of a suicide bomber. (TV: Robot Gladiators) They eventually succeeded, Thorne coming to Darius Pike with a proposal, not giving the requested component's name and calling it "the cybernetic equivalent of an appendix". He had him try to convince K9 to agree into surrendering the device in return for his missing memory chip, promising Darius his father would be released from his imprisonment if he complied. K9 thought it a trick, although he couldn't resist the opportunity to discover his lost memories and accepted; it turned out to be a trick. Thorne gave the unit to an unknown force. (TV: Hound of the Korven)
The unit was contained inside the Trojan, a behemoth created by mixing together DNA from aliens encountered by K9. After K9 depleted his energy banks to defeat the Trojan, the absence of his regeneration unit signalled his demise. However it returned to him just in time, recharging his powercore and giving him a new lease on life, reconstituting him completely. (TV: The Eclipse of the Korven)
Behind the scenes
In the wreckage of K9, writing on his regeneration unit resembles Old High Gallifreyan. (TV: Regeneration)
The regeneration unit prop had writing on it which resembled the Greek-and-mathematics text used to represent Old High Gallifreyan in the classic series of Doctor Who. Specifically, it contained the phrase "∂³Σx²", which was used to represent the Doctor's name in the first edition of the 1972 behind-the-scenes book The Making of Doctor Who by Terrance Dicks and Malcolm Hulke. This would seem to suggest that K9's regeneration unit was installed by the Doctor, or otherwise connected to him.
Bob Baker, K-9's co-creator and executive producer of the K9 TV series, said that the regeneration unit was "put there presumably by the Time Lords, but of course we're not allowed to mention that."[1]
