Robotic apparatus for cleaning the surfaces of a train of rotating rollers for processing metal products, comprising: - abrasive means for removing dirt and/or surface irregularities from said rotating rollers; - first and second advancement means for advancement on said train of rotating rollers, and - a navigation device, included in a control unit, comprising absolute transducer means for detecting the position of said robotic apparatus with respect to a stationary external reference, and thus the position on said train of rotating rollers, said navigation device including a processing and driving module that, in function of said position signalled by said absolute transducer means and taking account of the rotation speed of the rotating rollers, consequently drives said first and second advancement means in a manner that is selective and differentiated from one another to generate a desired advancement of said robotic apparatus both in a transverse direction and in a longitudinal direction on said train of rotating rollers, so as to enable said abrasive means to treat the entire cylindrical surface of each said rotating rollers below and possible further rollers placed above said robotic apparatus, wherein said abrasive means comprises a plurality of abrasive elements distributed on one or more sides of said apparatus that are suitable for acting on zones below and above said robotic apparatus, said abrasive elements being connected in an articulated manner to enable the position of the abrasive elements to be adjusted with respect to said rollers and the force pressing on said rollers by said abrasive elements to be adjusted, wherein said abrasive means is of the rotating type and is chosen from a group comprising: abrasive brushes, abrasive discs, abrasive rollers, abrasive wheels, that are able to perform surface finishing operations. - abrasive means for removing dirt and/or surface irregularities from said rotating rollers; - first and second advancement means for advancement on said train of rotating rollers, and - a navigation device, included in a control unit, comprising absolute transducer means for detecting the position of said robotic apparatus with respect to a stationary external reference, and thus the position on said train of rotating rollers, said navigation device including a processing and driving module that, in function of said position signalled by said absolute transducer means and taking account of the rotation speed of the rotating rollers, consequently drives said first and second advancement means in a manner that is selective and differentiated from one another to generate a desired advancement of said robotic apparatus both in a transverse direction and in a longitudinal direction on said train of rotating rollers, so as to enable said abrasive means to treat the entire cylindrical surface of each said rotating rollers below and possible further rollers placed above said robotic apparatus, wherein said abrasive means comprises a plurality of abrasive elements distributed on one or more sides of said apparatus that are suitable for acting on zones below and above said robotic apparatus, said abrasive elements being connected in an articulated manner to enable the position of the abrasive elements to be adjusted with respect to said rollers and the force pressing on said rollers by said abrasive elements to be adjusted, wherein said abrasive means is of the rotating type and is chosen from a group comprising: abrasive brushes, abrasive discs, abrasive rollers, abrasive wheels, that are able to perform surface finishing operations.