The White Robots are servants to the Master of the Land of Fiction.
The White Robots are fictional characters which the Master created. They were in the nowhere place where they saw Jamie and Zoe. Afterwards when the Doctor, Jamie and Zoe landed in the Land of Fiction the White Robots would search for the Doctor and his companions.
The White Robots traced Jamie in Rapunzel's tower along with the Doctor and Zoe later on. The White Robots guard the Master and took the Doctor and his friends to him. They trapped Jamie and Zoe in a book and turned them into fiction. But the Doctor managed to get them out of the book. The White Robots traced the Doctor and his companions where the Master Brain was. Unfortuantly the White Robots aimed at the Master Brain instead of the Doctor. The White Robots destroyed the Master Brain and every character and thing in the Land of Fiction.
The White Robots appeared in:
Season 6: The Mind Robber