In the article an algorithm for finding linear equivalents (exact linearization) for noninvolutive distributions of control vector fields is considered. In contrast to the common approach to solving this problem — the use of dynamic linearization (the introduction of integrators), which leads to an expansion of the state space — an algorithm for obtaining involutive distributions and ensuring local controllability based on linearizing controls is proposed. The essence of the algorithm: choose such a control and find an explicit expression for it that a controlled vector field associated with this control, when attached to a drift vector field, will provide local controllability and involution of the corresponding distributions. To check the involution of distributions and find the decomposition functions of vector fields on the basis of the current distribution, and on them directly the conditions imposed on the linearization controls, the author has developed an algorithm and a program in the Maple package for finding these functions. For the convenience of presentation and maximum clarity of the proposed approach, in the article is using notation not generally accepted in applied differential geometry. This applies primarily to the representation of vector fields in coordinate form or in the form of differential operators, which is often not specified, but it is assumed that the shape of the vector field is determined from the context. In the article, these forms are clearly separated and their specific use is shown. An example is considered — a nonlinear affine control system of the fifth order with three controls, in which all stages of synthesis are reflected in detail.

The article is devoted to the development of algorithms for calculating the cross-correlation function and the correlation coefficient between the useful signal and the noise of a noisy signal. The authors analyze the factors influencing the adequacy of the results of solving the problems of monitoring, control, management, etc. It is noted that when processing noisy signals, algorithms and technologies for separate processing of the useful component and the noise should be used. It is shown that in the event of malfunctions, such an important condition as the absence of correlation between the useful signal and the noise is violated in monitoring and control systems. Therefore, the problem arises of calculating the crosscorrelation function and the correlation coefficient between the useful signal and the total noise as well. Algorithms are proposed for calculating the estimates of the correlation coefficient and the correlation function between the useful signal and the noise of noisy signals. It is pointed out that the moment of occurrence of the correlation between the useful signal and the noise can be monitored in real time in information systems. It is shown that the estimate of the variance of the total noise before the appearance of the correlation is a stable value. When a correlation appears, the value of the variance of the total noise changes. The difference in the variance estimates is taken as an analogue of the estimate of the cross-correlation function between the useful signal and the noise at zero time shift.A technology for conducting computational experiments is proposed. Discrete values of the useful signal, noise and noisy signal are generated. The correlation coefficient and the cross-correlation function between the useful signal and the noise are calculated by the developed and traditional algorithms. A comparative analysis is carried out. It is shown that the proposed technologies for calculating the estimates of the cross-correlation function and the correlation coefficient between the useful signal and the noise, as well as the variance of the total noise, make it possible to extract additional important information from noisy signals. This opens up the opportunity to increase the efficiency of the analysis of noisy signals.

The article discusses models and algorithms that allow quality control in welding by robotic technological complexes. The difference of this approach to solving the problem lies in the use of the calculus of variations and the definition of action plans that ensure the minimum deviation of the actual values of the actual values of the process quality indicators from the given values. The input data of the model are the target values of the quality indicators of the technological process, their actual values for a certain period and lists of measures to improve the quality of the process. As a measure of the deviation of quality indicators, objective functions were considered, which are minimized when solving the problem. An approach is considered on the example of arc welding of metal structures using Kawasaki robotic technological complexes with C40 controllers. The area of application of the developed software is the control systems of robotic complexes.

In situ bioprinting is an automated process of direct application of biomaterials to a defective area of living tissue during a medical operation. To perform such bioprinting, it is advisable to use robotic manipulators with five or more degrees of mobility, which can give the end effector the desired orientation. The actual task is to plan the trajectory of the robot for in situ bioprinting on a real curved surface. A brief analysis of solutions allowing to plan the trajectory of bioprinting is carried out. A mathematical description of the surface used as a defect model is given, which is necessary for constructing the trajectory. Additional restrictions were introduced in order to reduce the complexity of the scheduling algorithm. To localize a defect on a curved surface, information about a given contour covering this defect is used. An algorithm has been developed for forming a flat trajectory of the robot’s end effector to fill in the defect, followed by projecting it onto a real curved surface. The importance of preprocessing data on the scanned surface using the developed filtering algorithm based on the moving average method is noted. The trajectory of the robot’s end effector is formed by layers first in the plane. It is then projected onto a curved surface. For each point of the trajectory, such a homogeneous transformation matrix is calculated so that the robot’s end effector is perpendicular to the curved surface. The calculation of the orientation angles of the working body of the KUKA robot is presented on the basis of data obtained from a homogeneous transformation matrix. The operability of the proposed trajectory planning algorithm for in situ bioprinting is confirmed by the results of computer modeling using the software developed by the authors and the results of an experimental study of bioprinting performed by the KUKA LBR R820 collaborative robot on three samples with different surface curvature and defect contour

The article is devoted to the approach to the quantitative estimation of changes in the functional state of a person during an airplane flight based on the results of stabilometric and oculographic examinations of airplane passengers carried out before and after the flight. Fourteen volunteers of both sexes participated in the study. They performed 21 pairs of pre-flight and post-flight examinations. For the existing sample of volunteers, parameters were identified that had a consistent trend of change. These parameters include visual tracking quality and stabilometric characteristics. In 70 % probes a decrease in the slow phases of optokinetic nystagmus average speed was noted. In most volunteers, changes in the stabilometric parameters for the optokinetic test and the balance test on an unstable support in the form of foam plate are noticeable. The tracking speeds, the average velocity of the pressure center, and the quality index of the equilibrium function decreased after the flight in more than 70 % of all samples. It was noted that the Hurst index after the flight decreased compared to background sample, during get up on the polyurethane foam plate in the vast majority of volunteers. In test before the flight the change in this parameter was multidirectional. In a stabilometric test with a "stepped deviation", in which a volunteer on command made quick bends at a small angle due to a change in the angle in the ankle joint, 75 % of the subjects after the flights showed a decrease in the average speed.

The problem of uniaxial reorientation of an asymmetric rigid body is solved by means of external control moments. The given geometric restrictions are imposed on the control moments. External uncontrolled interference is taken into account, the statictical descriptions of which is not available. It is assumed that the control moments of external forces are "applied" to the main central axes of inertia connected with the body. The control process is modeled be a nonlinear conflict-controlled system of ordinary differential equations, including dynamic Euler equations and kinematic equations in Poisson variables. The control moments are formed according to the feedback principle as nonlinear functions (discontinuous) of the phase variables of the considered conflict-controlled system. The choise of such functions is determined by the following circumstances: 1) the solution of the original nonlinear reorientation problem can be reduced to the solution of linear antagonistic game problems (with an unfixed end time); 2) in the absence of interference, the control momets are time-suboptimal; 3) reorientation is achieved by one spatial turn without additional restrictions on the nature of the resulting movement (such as a flat turn, etc.). Solutions of the closed control system are understood in the Filippov sense. An estimate of admissible levels of external un controlled interference depending on the given restrictions on the control moments is indicated, the conclusion of which is based on the indicated interpretation of the solutions. This estimate is a sufficient condition under which a guaranteed solution of the reorientation problem is provided in finite time by means of proposed constructions of control moments. An iterative algorithm is given for finding the control moment parameters that determine the guaranteed reorientation time.