Abstract: In order to displace a working tool at a constant speed over a surface having a random shape and orientation, particularly for cleaning, pumicing, painting or decorating the outer surface of an aircraft, an autonomous moving body with a special design is used. This moving body comprises two attachment assemblies (10,12) each equipped with attachment members (30,48) which can be moved towards and away from the surface, and a tool holder assembly (14), said three assemblies being able to move with respect to the surface in a given direction. Control means supported by the tool holder assembly (14) ensure both the advance at a constant speed of said assembly with respect to the attachment assembly (10,12) fixed to the surface and the advance in the same direction and at a higher speed of the other attachment assembly, the two attachment assemblies (10,12) being in turn fixed to the surface without stopping the tool holder assembly (14).