This article discusses the features of the spatial processes of fast and accurate positioning of points on the external surface of the object using the manipulation robot when executing the sequence of technical operations. Considered, pregenerating digital models of the external surfaces of the object. The quality of obtaining the coordinates of the points of an object's surface, determines the accuracy of positioning the surface of an object in the working zone. Simulation of positioning the moving points on the surface of the body in the working zone of a robotic system to capture the object is determined relative to a fixed point of another object, with respect to which positioning is to perform technical operation. When it is not sufficiently accurate and fast positioning then it is required a new surface model of an object and positioning the technical points on the surface. The simulation in MATLAB making a conclusion about the possibility of application of fuzzy controller for fast and accurate correction values of a small deviations from the coordinates of selected technical points of the surface of an object in the given vectors in its orientation and approach to the fixed point of another object. © 2017 Univelt Inc. All rights reserved.