In some cases the repeats of a "perpetuum mobile" piece are at a different pitch (while a modulation or a chord progression occurs during the repeatable part): some of the riddle canons of Bach's Das Musikalische Opfer are examples of this particular kind of Perpetuum Mobile/Canon Perpetuus.
Perpetuum mobile as a genre of separate musical compositions was at the height of its popularity by the end of the 19th century.