Abstract: The invention relates to the determination of the position of a self-contained operating apparatus movable along any line of displacement over any immersed structure.A follower apparatus is associated with the operating apparatus, and the position of this follower apparatus, along a line of displacement chosen as the reference line, is determined at any instant. The follower apparatus is displaced by the operating apparatus by servo-control means, and at any instant the transverse distance between the operating apparatus and the follower apparatus is monitored.