It is known that mobility of future robotic construction plants, which is their main function, is ensured by the possibility of high-precision positioning and by the orientation capability of a movable robot in reference to a stable (engineering type) system of coordinates related to the parameters of the site. We think that in the conditions of a construction site, modules for measuring the position of the construction plant should comprise cheap and reliable systems adapted, as much as possible, to geodetic beacons and the features of construction methods. This article describes a unique system of positioning the mobile general-purpose construction plant relative to navigation beacons placed on the site in accordance with the construction design. The system comprises a laser transmitter which is placed on the plant at a fixed point and has a built-in photo detector, and a plant-borne computer with a console connected to it for initial geometric data input. The transmitter forms two sectoral laser planes crossing each other at a specified angle, and ensures their synchronous rotation about their longitudinal axes. At least three beacons i.e. corner reflectors, are placed on the site. They return laser radiation to the transmitters photo detector whereby their angles or view can be measured. From the data obtained, the computer will determine the position of the plant and its angular orientation in space. The article deals with the basic principle of building the system and with the experimental developments. Some examples of its practical applications are also described.