The Robot Doctor was created by the Daleks to “infiltrate and kill” the First Doctor and his companions.
Vicki happened to stow away onboard the Dalek time machine when the Robot Doctor was created. She alerted the real Doctor, Ian and Barbara to its existence. By that point, the robot had already duped Barbara into believing it was the real Doctor, and nearly killed her. When the whole party met the Robot Doctor, the timing of the meeting was such that Ian, Barbara and Vicki couldn’t tell which was the real Doctor and which was the robot. In the confusion, Ian attacked the real Doctor. The robot kept up the pretence and tried to persuade Ian to kill the real Doctor by smashing his head with a rock. Before Ian could do so, the robot made a fatal mistake and revealed that its knowledge of The Doctor’s travelling was outdated by calling Vicki “Susan.” Barbara immediately realised that it was in fact the robot, and prevented Ian from killing the real Doctor. The robot was subsequently destroyed in the fight with The Doctor and his companions. (The Chase)
Many years after she left the TARDIS, Vicki met the Eighth Doctor and mistakenly suspected him of being another robot duplicate of her friend. (PApocrypha Bipedium)
BEHIND THE SCENES
Edmund Warwick, previously employed upon occasion as William Hartnell’s double, did not make for a very convincing “exact duplicate”, although Hartnell did dub all the robot’s lines (barring one instance of the robot saying “No,” which was accidentally left undubbed).
During the era of Doctor Who in which The Chase took place, The Doctor was referred to as “Dr. Who” in the ending credits, though not in dialogue. The episode of The Chase in which the Daleks’ impersonator of The Doctor appears has the title “The Death of Doctor Who”, which presumably (and misleadingly) refers to the destruction of the robot.
The Robot Doctor was listed as “Robot Dr Who” in the episode credits.