R2-D2 was not a puppet. He was operated from the inside by Kenny Baker - a highly talented actor who stood all of 3 feet, 8 inches tall.
Best known for bring R2-D2 to amazing life, Kenny was also one of the Ewoks. He was Dufflepud in the Prince Caspian TV series, was one of the little people in Willow (like, I suspect, every size challenged actor in Hollywood), and appeared in a lot of places. He was supposed to play R2-D2 in The Force Awakens, but the 81 year old actor was credited only as a consultant - perhaps because of his failing health. (R2-D2 appeared only briefly in The Force Awakens and will be played in Episode VIII by Jimmy Vee, who Baker trained to take over from him). Oh, and he did, surprise surprise, briefly run away to join the circus and also appeared in ice shows - which might explain some of the ways R2-D2 moved.
He had a good life and he did some amazing work. (I don't envy Vee having to replace him).