At present, robotization of assembly processes is achieved through the use of industrial robots with high positioning accuracy in conjunction with tactile means of adaptation to the conditions of assembly of precision parts. The cost of such robots is many times higher than the cost of simple robots with low positioning accuracy of the robot arm. The research in this article is aimed at reducing the cost of assembly processes for precision parts by applying the position correction of the connected parts not by the robot hand, but by an additional technological module that is installed on the manipulator of a simple robot and performs high-speed stochastic mismatch scan of assembly objects. The article presents the results of a full factorial experiment of the process of joining precision cylindrical parts with a gap of no more than 3...5 microns. A regression model of this process is proposed, a formula for calculating the quasi-optimal modes of precision assembly and graphanalytical dependences of the assembly time on the scanning modes of the misalignment of assembly objects are given. The proposed high-speed method for compensating for the positioning error of an industrial robot makes it possible to assemble precision parts in a very short time within 1...3(s). The main economic effect of the research results is that the device for scanning the misalignment of assembly objects, which is installed on the arm of an inexpensive robot with a low positioning accuracy, can significantly increase the assembly speed and reduce capital investments in robotic assembly of high-precision parts.