The paper describes the moving approximation algorithms for the functions, which have continuous and bounded derivatives of the first or higher orders. Firstly, Lagrange mean theorem is generalized for the equal and not equal steps. Additionally, la-grange mean theorem is generalized for the reduced time approximation. Estimations of the residuals in the generalized Lagrange theorems are proposed. Secondly, we consider application of the generalized Lagrange theorems for the design moving approximation algorithms. It is demonstrated, that an error approximation depends on the appropriate residual in the generalized la-grange theorems. Thirdly, we obtain results which allow us to compensate for an error approximation with a given accuracy. This fact is achieved due to a feedback compensation for the error approximation by using the derivative observers. The values of the time approximation and estimates of the approximation errors are presented. Simulations demonstrate that an approximation of the smooth functions by using algorithms with a compensation for the approximation error is better than an approximation without a compensation for the approximation error. If an approximated function has discontinuities in derivatives, it is recommended to use the algorithms without approximation with an error compensation, since the value of the function at the output of the observer in the derivative points of the discontinuity can be quite large.

The article investigates different approaches to the problem of autonomous robots' self-learning. The knowledge, which a priori is introduced into the on-board control system of an intelligent autonomous robot for control of its expedient behavior in certain situations, should, in general, be supplemented with the results of the self-learning based on the analysis of the accumulated experience. A variety of the autonomous robots' applications in combination with the diversity of the environmental uncertainty types makes possible several options for augmentation of knowledge. The authors employ the construction methods of the classification trees and the decision forests to find the hidden patterns in the arrays of the sensory data, which accumulate the experience, gathered by the robots operating in a complex environment. The prospects of the decision forests construction method were demonstrated for organization of the self-learning processes in the multi-robot systems (MRS). A new approach to MRS self-learning was developed based on a combination of the decision forests and evolutionary computation methods. It was proved that the method of the evolutionary decision forests can serve as a constructive basis for development of the intelligent self-learning autonomous robots operating together within a multi-robot system. The authors demonstrated that the role of the robotic agents was not confined to accumulation of their own sensory data, but that they were also capable of a knowledge exchange and its incorporation into their personal experience. The results of the model simulation are presented, confirming the effectiveness of the proposed approach.

The paper presents the problem of clustering and leader selection in a group of robots, using a static swarm model - fixed network at some point in time, consisting of the robots connected to one another via the communication channels. Robots use only local interaction, the topology of the swarm and the number of the robots is not known beforehand. It is proposed to take into account the relative positions of the robots and their neighbors, i.e., their local topology, which is known to them, and allows them, in the long run, to choose their leader out of the robots located close enough to the topological center of the whole group. It is known that the group has peripheral robots - those which have not all the communication channels occupied. They initiate the leader selection procedure by transmitting its weight to the center of the group. This allows to create there a subgroup of robots, with the biggest weights, one of which becomes the leader. It is considered as an option, when the static topology of the swarm changes, i.e. some robots are eliminated in the process of voting. It is demonstrated that in all these cases the leader selection algorithm succeeds. In addition, a clustering algorithm is proposed to solve the problem of the functional differentiation of robots, which will quickly produce their integration into subgroups. The conducted computing experiments prove the efficiency of the algorithms.

A dynamic model of the motion in the sagittal plane of the lower limbs of the exoskeleton, integrated with a human operator, was created with account of its lean on rigid weightless crutches. This model describes a mockup of the exoskeleton, which is a 5-link system incorporating the knee and hip drives, as well as massless hand supports. The dynamic model is based on the Lagrange equations of the second kind, which, alongside with the kinematic parameters, also includes the reaction support forces of the point feet and weightless crutches. When the parameters of the mathematical model were set, the inertial mass of the body characteristics of the resulting statistical processing of the tomography slices of a certain number of subjects were taken into account. In the model, the crutches are considered as an extension of the human hands, so the force application points of the crutches are the shoulders of the operator. Human reaction in the shoulder joint to the torque of the crutches is considered irrelevant. The model also takes into account the dynamics of the DC electrical drives. The synthesis is based on the method of solving the inverse tasks of the dynamics. Synthesis of the control system was carried out on the example of a flat, single support for comfortable walking. Since it is assumed that an operator has a weakened musculoskeletal system, but workable hands, it is considered that the given influences on the control system of the exoskeleton are the required torques in the hip and knee joints, viewed as a time function, while a person is assigned the function of providing power to the crutches. As a result, an analytical law motion control exoskeleton was designed, which provided locomotion to the hip and knee joints in accordance with the selected desired mode. The synthesized algorithms were applied to the constructed mathematical models and a numerical study of them was conducted. The article presents the results of the numerical simulation and of the investigated precision control.

This paper presents an automated method for fault diagnostics in the mechatronic modules of the optical-location stations. Apart from the existing methods, the use of an object native control system for the diagnostics purpose is discussed. It allows us not to use an external hardware during the diagnosis process, because all the information concerning the state of a mechanical structure could be acquired from the control loop information (data from the feedback sensors, outputs of the equalized filters, etc.). This data is enough to detect even the smallest mechanical defects. In future automatization of the control loop data analysis will allow even a low-qualified staff to diagnose and eliminate complex failures, critical for the precise mechatronic modules during the serial production. This is extremely important, because even small mechanical defects can influence the tracking precision of a complete system. This method was successfully implemented for the serially produced modules for the optical-location stations. Realization of the described method requires construction of an adequate mathematical model of a mechatronic module. The authors describe development of an ideal system model, including a servo-drive, a control system and additional hardware, such as sensors and servo-controller parameters. A list of typical failures for these types of systems is presented. This list was obtained after experimental diagnostics of over 100 produced units. The authors also describe how these failures can be presented in a mathematical model. An experiment is required to prove the effectiveness of this method by comparison of the model data with the data acquired.

The paper deals with the process control plating in a bath with multi-section anodes. The analysis of existing methods of process control in the bath with multi-section anodes. The influence of current density, distance between electrodes and electrolyte mixing intensity on the uniformity of coating and performance of the deposition process thickness. Established extreme nature of dependence of the uniformity of the coating on the current density, distance between electrodes and electrolyte mixing intensity. In this paper, the process of plating is considered as a object of automated control. The block diagram of a system of extreme process control plating based on the principle of management on indignation with using a mathematical model. The function chart of the extreme control system plating process in a bath of multi-anodes. In a control system there are four contours of regulation: contour of regulation of tension; contour of management of an arrangement of anode sections and intere-lectrode distance; contour of management of intensity of hashing of electrolyte and contour of maintenance of temperature of electrolyte. In feedback of all contours of regulation settle down: the block of sensors including sensors of temperature, concentration of components of electrolyte, conductivity and level; block of mathematical model of process of putting electroplated coating; block of algorithm of search of an extremum. The control algorithm of process of putting electroplated coating by means of the developed automated system of management in a bathtub with multisection anodes is developed.

The paper presents an active system for isolation of vibration, which compensates for the dynamic forces on the ground arising from the fluctuations of the elastically suspended mass with a vibro-active element by using the inertial forces in the antiphase. As the dynamic forces' compensator an electrodynamic drive is used, in which the linear movement of the rotor with an additional weight is carried out according to the information coming from a force sensor or accelerometer. The principle of the dynamic inertial compensation for the vibratory force boils down to the following: an oscillating mass actuator (compensator) with a mass on a movable body is mounted on the main body and with the reciprocating movement of the mass in an antiphase together with the motion of the elastically suspended vibro-active mass an additional inertial power is created, compensating for the vibro-active force at a given frequency. A possibility of mounting of an electrodynamic compensator is considered in this paper. The compensator is mounted on the oscillating weight, or on the body near the elements of the passive vibration isolation system. The active vibration isolation system with an electrodynamic compensator considered in this work can ensure an effective reduction of the power transmission to the base of the oscillation of the elastically suspended mass by 20-50 dB in the low frequency range.

The article is devoted to research different approaches used to determine the natural frequencies of the MEMS-gyro sensing element at the design stage. In a general case, the MEMS-gyro sensing element can be presented as one or more proof masses, which are connected with each other and with the gyro base by means of springs. Well-known mathematical models for the dynamics of the sensitive element consider it as a discrete system, where the proof masses are substituted by its mass center and the springs are substituted by their stiffness. The finite element modeling (FEM) allows us to consider the sensitive element as a system of linked solid deformable bodies. However, the results of the finite element simulation of the sensing element dynamics depends on the theory of bending supported in the elements used for modeling. Currently, the classical theory of bending of the Euler-Bernoulli and Timoshenko theory are widely used for the finite element simulation of the sensing element. Each of the three approaches (the mathematical models, FEM with Euler-Bernoulli theory, FEM with Timoshenko theory) has its advantages and disadvantages. In the paper the problem of the difference of the simulation results using one of the three approaches by the example for determination of the micromechanical gyroscope natural frequencies was investigated. Specific recommendations for the study of the micromechanical sensors and determination of their natural frequencies were formulated.

The paper concerns the design automation for the marine underwater object route control using'Wanderer" software. Marine underwater object (MUO) model is presented as a complex system of the non-linear differential equations of a high order. MUO control is a network structure by its nature (performed from several control stations). It is multidimensional, multichannel and carried out with the constrained maneuvering phase coordinates using several control facilities of the hydrodynamic and hydrostatic nature. The former group includes the hydrodynamic planes (rudder and planes), which allow MUO maneuver in space. The hydrodynamic plane's control efficiency depends on MUO velocity and their steering angles, permissive and actual values. The hydrostatic control facilities (balloons) are used, when a vessel is stopped. During the considered control mode we use balloons to make the ballast compensate for the squeezing forces and forces resulting from hydrology. Development of MUO maneuvering control algorithms, which are able to work correctly for several control modes, should be performed during investigation of MUO maneuvers with constraints on the intensity and a set of control facilities using a full-scale model of the object under consideration. In the process of realization of the route we have to ensure a maneuvering mode, in which MUO will make as little noises (acoustic, e. g.) as possible. In order to accomplish this task a muted noise maneuvering mode is used. This mode minimizes the cav-itational noises based on an object's phase coordinates monitoring. 'Wanderer' allows us to perform an automated maneuvering of MUO along the route in space utilizing the muted noise maneuvering mode algorithm with the additional phase coordinates' and object control facilities' constraints. 'Wanderer' project gave an impulse to evolution and improvement of the facilities of the developed full-scale simulation system and allowed us to test many approaches and solve interesting problems. "Wanderer" has already been used as a part of a bigger project for solving of the set tasks and it produced good results.

The article is devoted to a numerical study of the contour - anomalous wave system and the quantitative estimates of its energy parameters. The author discovered that the profile of an anomalous wave undergoes the following stages: the initial profile, the profile with the first maximum height, the two-humped profile, the profile with a second maximum height, and the breaking profile. The problem is solved by CFD method in three stages. At the beginning the density maximum of the kinetic energy and its position on the anomalous wave profiles was calculated. It was discovered that the anomalous wave profile with the second maximum has the highest energy density and presents the greatest danger to the contour stability. Then, the numerical studies demonstrated that the kinetic energy increased as we approached the time of the anomalous wave collapse. It was discovered that the sum of the kinetic and potential energies is reduced due to the dissipation associated with the physical and turbulent viscosity. Eventually, we calculated the contour capsizing work. It was revealed that the anomalous wave energy loss corresponded to the contour capsizing work and increased with the vessel displacement. The relative value limit of the anomalous wave energy losses on bad moving contour reached 40 %. The received results can be used, firstly, for development of CFD based numerical studies. Secondly, the results can be used as the database for improvement of the design of the vessels, and also as a motive to search for causes of shipwrecks of vessels over 27000 tons, which did not capsize due to anomalous wave.