A process for marking the real position and real orientation of a tool in relation to the manipulator arm of a robot. The process utilizes the amplitude measurements of acoustic signals and the flight time measurement of the acoustic waves emitted by an acoustic probe of the tool and reflected by the fixed reference elements. The position of the center of reference of the probe relative to the end of the manipulator arm is determined. The axes X and Y defining the plane of the probe along reference axes X′ and Y′ of known orientations are oriented so that the modification of the position and of the orientation of the probe in the reference frame can be defined. The displacements of the manipulator arm are managed by the controller based on the position of the probe in relation to the manipulator arm and the reference orientation of the probe.