K9 Mark I, II, III, and IV addressed whoever was directing them as "Master" or "Mistress" depending upon gender, and used the formal "affirmative" and "negative" rather than "yes" and "no". They were programmed to be both loyal and logical, with a penchant for taking orders literally, almost to a fault. Their striped collars mirrored the Fourth Doctor's trademark scarf.
The original K9 model was designed by visual effects designer Tony Harding. One early concept was to have a small actor in a large Doberman-shaped costume; however, Graham Williams vetoed this, saying that the robot should not look like a person in a costume. The eventual design was closely based on Harding's third concept sketch. (DCOM: The Invisible Enemy)
The initial idea for realising K9 was to use a small actor inside a robotic Dobermann costume, but that was rejected in favour of a radio-controlled prop, designed by Tony Harding and made by the BBC Visual Effects Department. The Radio Control Model Centre in Harlington Middx owned by Derek Wales was commissioned to build the electronics into the first original basic shell and consequently the centre operated the dog on set for the BBC. The robot suffered from numerous technical problems during its time in the series, often malfunctioning because the radio controls interfered with the cameras and vice versa. On location, K9 also proved unable to traverse uneven terrain, and shots had to be conceived with this in mind. Workarounds included using a concealed piece of twine to pull the character along (this string can be clearly seen in a shot of K9 on Brighton Beach), or laying wooden planks on which it could roll.
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While caught up in a Time war between the past and the future on the planet Aoris, K9 was forced to spend a thousand years hidden on the planet, setting himself up as 'the great Machina' so that he could found a cult that would aid the Doctor and Romana in bringing the war to an end, hiding behind a fake computer with a version of the TARDIS until he could return to the Doctor and Romana once the war ended (AUDIO: The Paradox Planet, Legacy of Death).
K9 stayed with Leela on Gallifrey for many years. It was only after the disappearance of her Time Lord husband, Andred, that Leela and her K9 met Romana II and her K9. The two K9s did not get on well and competed. (AUDIO: Weapon of Choice) After Leela became Romana's bodyguard and after many important missions on her behalf, Leela's K9 was destroyed by an exploding bomb. Leela was heartbroken, but refused to have a duplicate unit built. (AUDIO: Imperiatrix)
With his great intelligence, he had a tendency to bore people with facts and did not stop immediately when asked, as he did to Leela on Pluto. When being told that he would have to stay behind in the TARDIS, K9 often argued, giving the Doctor reasons why he should go such as "he would be a good dog." K9 always wanted to assist the Doctor. He had great intelligence and skill at chess, claiming to be able to beat the Doctor in six moves (although this may only have been because he was programmed with all chess games since 1886). (TV: The Sun Makers, The Androids of Tara) K9 had an aggression mode. (TV: State of Decay)
K9 Mark III first appeared in "A Girl's Best Friend", the 1981 pilot for a series, K-9 and Company, which never materialized beyond the first episode. In this, the character is presented to the Doctor's former companion Sarah Jane Smith (Elisabeth Sladen); together, the two embark on what a number of adventures. Only the first of these is depicted on-screen; several are shown in comic book and audio play adaptations, and others are alluded to by the television series. Mark III made a brief appearance alongside Sarah Jane in the Doctor Who 20th anniversary ninety-minute special The Five Doctors (1983), before appearing properly and for the final time in the revived series' episode "School Reunion" in 2006. By the time of that story, Mark III has fallen into disrepair and eventually sacrifices himself to stop a plot by the alien Krillitane and defeat their leader, Lucas Finch (Anthony Head). In the episode's conclusion, the Doctor presents Sarah Jane with a new K9 to encourage her to continue investigating alien activity; the Doctor "rebuilt" him after the Mark III's sacrifice, implying that he had the same mind and memories as his predecessor while still being a "brand new model".