Robot clowns were androids modelled on clowns.
Types of robot clown
Robot clowns assisted the chief clown in running the Psychic Circus. They were responsible for making people perform and entertain the Gods of Ragnarok. These clowns were not destroyed by them, but were used so that they would be entertained during the time when the humans and other species went to take part in the Talent Show. They were destroyed when the Seventh Doctor blew up the circus. (TV: The Greatest Show in the Galaxy)
Elijah Spellman also made a circus full of robot mannequins in the shape of clowns. He used them to attack Sarah Jane Smith and her friends, Clyde Langer, Luke Smith and Rani Chandra. She used her sonic lipstick to stop them from attacking the group. (TV: The Day of the Clown)
On Earth near the mid-21st century, advances in robot technology, thanks to Alistair Gryffen and his Thought Matrix, meant that robot clowns started appearing in circuses. (TV: Robot Gladiators) Darius Pike once had a nightmare in which he was trapped in his car, surrounded by three robot clowns along with Mr Floppy Fun Pants. (TV: Dream-Eaters)
Two robot clowns, Chuckles and Boris, were taken to be gladiators in Crashclub. K9 Mark 2 met and befriended them when he went undercover to take down the organisation. Boris was destroyed fighting the Pain-Maker, but he was rebuilt after Crashclub was shut down. Chuckles and Boris then returned to the circus. (TV: Robot Gladiators)
A type of toy robot clowns were used as children's therapy bots. Children could tell them stories that they were too afraid to tell adults, and the robot clowns would erase the bad memories, taking away the pain.
At some point after fighting in the Last Great Time War, the Ninth Doctor rode his TARDIS through a supernova to save one such robot clown, and then spent a week unsuccessfully trying to fully repair it. The robot clown then remained loose in the TARDIS. Much later, while still recovering from a recent regeneration, the Eleventh Doctor stumbled upon the robot clown while searching for a mirror in the TARDIS, and took a note to do something about it in the future.
Eventually, the Doctor and River Song took the robot clown to the TARDIS workshop and repaired it. Unbeknownst to the Doctor, River used the robot clown on him, erasing his memory of counting the children present on Gallifrey on the last day of the Time War. They then released the robot clown near a farming settlement.
The robot was eventually given to Cass Fermazzi when she was growing up. However, it did not work as intended and did not take away any of her memories, as it was already full of the Doctor's, which it kept "spewing out", leaving a profound effect on Cass and inspiring her to later in her life "fight for what's right" in the Last Great Time War and "never be cruel or cowardly." (PROSE: The Day of the Doctor)