The article studies the problem of the eXactfeedback linearization of the nonlinear control systems. This is a problem how to use the feedback controls in order to modify the original internal dynamics of a controlled system in such a way as to obtain to same behavior of certain prescribed autonomous linear systems. It presents possibilities of a successful selection of the linearizing feedback from the structure form of the initial nonlinear control system, as well as from the considered domain of the phase state. In this article the authors present a specific feature of construction of a linearizing feedback, when the initial nonlinear control system has the first integral and the control process takes start from the initial state where this first integral equals to zero. As an eXample a problem of three-aXis reorientation of a rigid spacecraft was considered. Three reaction wheels were employed to produce the necessary torque in the aXes of the initial. The controlling moments, applied to the flywheels, were offered to be generated by means of a feedback in the form of nonlinear functions of the phase variables of the considered nonlinear controlled system of differential equations, including dynamic Euler equations and kinematic equations in Rodrigues-Hamilton variables (in terms of the quaternion). As a result, the solution to the original nonlinear problem was narrowed down to the elementary linear control problems. The above-mentioned peculiarity in construction of the linearizing feedback takes place in this problem, when the initial angular velocities of the spacecraft and reaction wheels equal to zero.

A posteriori broadband input noise characteristics of the analog phase locked loop (PLL) system along the cycle slip trajectory were studied on the basis of Markov stochastic model. It was demonstrated that the cycle slips were caused by an unlikely event - existence of an extended period of time, in which a random process, which describes the noise, mainly preserves its sign. A mathematical model of the most probable cycle slip trajectory in the stochastic analog of PLL of the first and second orders in the form of the ordinary differential equations with respect to the coordinate system on the phase plane was presented. There was demonstrated equivalence ofthe approaches to search the most probable cycle slip trajectory: the search for the maximum of the probability density function of the points of coordinates along the trajectory and the solution of the variational problem. A model of abnormal noise associated with the cycle slips effect was presented. An approximated formula for description of the spectral power density of the abnormal noise was offered. The process of the cycle slips in the PLL with the non-linear element in the feedback loop was investigated. It was demonstrated that such systems have improved characteristics of the average time before a cycle sleep in comparison with the traditional ones. An explanation for an increase of time before a tracking failure, when using a non-linear element in the feedback loop, was presented. Approaches to selection of the type of nonlinearity were considered. Numerical values for the average time before a cycle sleep for various types of non-linearity and parameters of PLL on the basis of computer simulation were presented.

The considered problems of aggregation of the swarm robots are mainly connected with the simplest computing, sensors and built-in actuators, as well as limited resources of the homogeneous swarm robots. In the area of the swarm robotics the multi-agent technologies are used to simulate the interaction of big groups of simple homogeneous robots. The limited resources of the individual robots have a significant effect on the configuration and capabilities of the whole system, however, the distributed swarm intelligence based on the data obtained during the mass pair interactions of the robots ensures the existence of a swarm and, due to it, solving of the set tasks. A review of the main methods for solving of the problem of aggregation in a swarm of robots (the method of the virtual forces, the probabilistic and evolutionary methods) showed that the choice of the used method, first of all, depends on the sensor, computing and network resources ofthe robots. Examples of different aggregation algorithms for the robot swarms, as well as limitations on the design solutions during implementation of these algorithms are presented. For estimation of the effectiveness of the robot aggregation the spatial and temporal methods are mainly used. The specific choice ofthe metrics depends on the parameters ofthe form, which should be achieved, as well as the aggregation method which is technically possible to implement to ensure control of a given robot swarm. By the results of the analysis, a conclusion was made that the systems, which use the neural networks for the swarm control are the most promising in terms of the further improvement of the aggregation algorithms, however, their implementation requires large onboard computational resources. During the preliminary research concerning the swarm robotics the principles and conceptual model were developed for the process of reconfiguration of the spatial position of the group of robots. They take into account the restrictions on the geometrical dimensions of a set of homogeneous robots and the occupied area of the initial position of the robots, the spatial characteristics, density of the robots' locations, as well as the ways of defining of the target position coordinates of the robots in a new spatial configuration. The further research will be aimed to solve the tasks of interaction within the robot swarm during construction of more complex forms, taking into account a bigger number of the physical parameters.

In this paper we present the method of control of mobile robots moVing in the conVoy type formation. The problem of localization of robots, using relatiVe obserVations between the robots, is solVed. The relatiVe position and relatiVe orientation are estimated using an Extend Kalman Filter. Special attention is giVen to obtain a follower robot motion control law along the trajectory giVen by the leading robot. The simulation results are also presented.

This paper discusses the design of two human-like robotic hands. The kinematics of this design was introduced to offer a more generic, speedy, and precise solution for a wide range of robotic applications. This research is focused on integration of the control of both arms and hands as one entity. A solution involving several manipulators requires coordination between them. In order to arrange a stable grasp, the angle of inclination of the predefined hand orientation normal was used with the angle of inclination of the object's center of gravity vector. The center of the gravity vector was calculated using the image intensity of the object splines. The splines of the predefined hand contact points were adapted to the object 3D model splines. The maximal and minimal values of the joints' angle ranges were measured to define the fingers' workspace. Gestures were classified as prismatic and circular, regardless ofthe grasping power or precision, while the circular grasping implied a strong correlation among the finger joints. The human-like hands were intended for many applications involving a specific series of tasks like artificial limbs of the handicapped people, they were also meant for the fire fighters, production workers, surgeons, and for use as a research platform.

An operator's hand is a spatial mechanism, the configuration of which defines situation and orientation of a robot's hand in space. The biomechanical model of a hand represents a kinematic chain consisting of 18 links with 18 hinges. This design realizes 27 degrees of freedom for the links. Modeling the movements of an operator's hand to a target point is similar to the solution of the feedback problem of positioning in robotics. For complex kinematic structures with a big number of degrees of mobility a solution to this problem involves certain difficulties. At the same time, one of the main problems is the problem of an elbow joint position definition during setting of the final configuration of a person's hand in a target position. This problem can be reduced to the optimization problem with application of a criterion based on the principle of the "lower elbow" described by E. Nakano. Further application of this solution is quite difficult, if it is necessary to model the movement of the higher limb of the operator as a whole, including fingers. Therefore, we have to look for a method, which would allow us to expand the solution, if necessary. At the same time, the method should be simple, reliable and requiring little time and computational complexity. The analysis of the known solutions of the feedback problem of kinematics demonstrated a definite advantage of application of the Forward and Backward Reaching Inverse Kinematics (FABRIK) method. This method excludes the bulkiness and complexity connected with the use of matrices of rotation by direct definition of the situation on a straight line. After definition of new positions of the kinematic chain nodes it is possible without resorting to considerable efforts to calculate the vector of the generalized coordinates. Research of the accuracy of guiding of the operator's hand to the set target position was made in a SimMechanics package of MatLab for checking of the operability of the proposed method. As basic it chose several positions located in the operational space. Movement control of a hand was exercised by the controller, basing his work on FAB-RIK method. During research the following facts were revealed: the maximum error in position of a hand was 1,55 mm; the maximum size of discrepancy to the set orientation was 0,17. Accuracy of the received results confirmed the set re#uirements and the undoubted advantages of the considered method (little computing and time expenditure, simplicity of realization, visually natural pose received due to the solution and also a possibility of work with several final nodes) make it most expedient for application as the solution to the feedback problem of kinematics.

A new method for measuring of the geomagnetic field vector and magnetometer option for its implementation was proposed as a solution to the problems in the sphere of the geomagnetic fields' measurements during geophysical and cosmic investigations. Under consideration is a magnetometer option, which uses one flux-gate sensor, as a basic functional element, oriented on measurement of three orthogonal components of a weak magnetic field, rigidly connected with the platform axes, on which the magnetometer is installed. The vector parameters of the investigated field are defined by means of the magnetometer at the previously known orientation of the platform axes. Application of the additional effect of the useful signals modulation, which arises during rotation of the flux-gate sensor in the residual field and during its biasing by the test alternating magnetic field, allows us to minimize all the measurement errors of the field components: graduation errors and sensibility variations (multiplicative error); zero shift and fluctuation (additional error). In the work a new test measurement algorithm is substantiated; an option of magnetometer structural block-diagram is considered; peculiarities of the measuring procedures and magnetometer functioning modes are analyzed. The proposed option of the magnetometer in combination with separate types offlux-gate sensors has high reliability, resistance to interferences, insignificant power consumption, relatively small weight and dimensions. The use of such an option of magnetometer as a precision null-indicator will allow us to measure accurately the geomagnetic field components, to carry out the works, connected with different geophysical investigations; with determination of the magnetic deviation, created by different movable objects. With its sufficient sensitivity and high precision of transformation, as well as a sharp directivity graph, the magnetometer option under consideration may be used also in the tracking systems, allowing orientation of different objects on the geomagnetic field.

The article is devoted to the problems of development of the modern systems for control of the electric valve actuator of the rotary support device (RSD). It examines the tasks of modeling of real physical objects, including designing of the control systems, testing and development of the working prototypes. The most effective solution to the set tasks is the ModelBased Design - MBD. This method integrates into a single working process different stages of designing of the system, such as formulation of the technical requirements, modeling, development of the system, its debugging and testing. The most convenient instrument for realization of the model-oriented designing of the control system is MATLAB-Simulink environment. In this work on the example of two-coordinate RSD for the electric valve actuator of the azimuthal axis the first stages of MBD are considered in detail: - Development of the structural models based on a mathematical description and using the structural blocks of Simulink package and its Blocksets; - Development of the simulation models, using the masked blocks of SimScape package; - Development of the executable code by means of MATLAB-Simulink for comptrollers of STM32F103 series. Kits of program resources - MATLAB-Simulink, CubeMX, and Keil, the set of library modules - Target Support Package - STM32 Adapter, etc., offered to the developer, provide an opportunity for realization of the algorithm for operation of the systems of any complexity, which do not require engineers' deep knowledge in the area of programming. On the example of the developed system for control of the electric valve actuator of the azimuthal axis of RSD the algorithm for development of the executable code was presented, consisting of the following steps: - Initialization of the comptroller (indication of the peripheral modules involved in the control system with their tuning) in CubeMX program; - Programming of the algorithm for operation of the comptroller in MATLAB-Simulink environment with the use of different library modules, including the embedded and the pluggable ones; - Generation of the executable code with its subsequent recording in the microcontroller.

This paper presents a novel architecture of the executive-level control system for management of the discrete machinery productions. It combines the use of a supervisory control and a data acquisition system, and the tasks of the execution system based on the use of virtual Forth-machine. The widely used solutions for modern manufacturing are based on interaction of the manufacturing execution system directly with the supervisory control and data acquisition system, but this is not suitable for a discrete machinery manufacture, because of complexity of its production process. In the proposed architecture the supervisory control and data acquisition system are used for the online state monitoring of the CNC-machines hardware, signal logging and fault prediction. The task execution system downloads the manufacturing task, designed as the Forth program, from the manufacturing execution system and uploads it into the virtual machine, which controls the sequence of operations during one manufacturing task. Besides, the task execution system includes information exchange module, which ensures a software abstraction layer between the virtual machine and the hardware. The proposed architecture allows us to combine in one manufacturing process operations with a different degree of automation, and ensures replacement ofthe manual processes with automated ones without changing the manufacturing tasks documentation. The experimental results show that the proposed architecture is implementable, which determines the relevance of the further development in this direction.