Multi-agent reinforcement learning methods are one of the newest and actively developing areas of machine learning. Among the methods of multi-agent reinforcement learning, one of the most promising is the MADDPG method, the advantage of which is the high convergence of the learning process. The disadvantage of the MADDPG method is the need to ensure the equality of the number of agents N at the training stage and the number of agents K at the functioning stage. At the same time, target multi-agent systems (MAS), such as groups of UAVs or mobile ground robots, are systems with a variable number of agents, which does not allow the use of the MADDPG method in them. To solve this problem, the article proposes an improved MADDPG method for multi-agent reinforcement learning in systems with a variable number of agents. The improved MADDPG method is based on the hypothesis that to perform its functions, an agent needs information about the state of not all other MAS agents, but only a few nearest neighbors. Based on this hypothesis, a method of hybrid joint / independent learning of MAS with a variable number of agents is proposed, which involves training a small number of agents N to ensure the functioning of an arbitrary number of agents K, K> N. The experiments have shown that the improved MADDPG method provides an efficiency of MAS functioning com-parable to the original method with varying the number of K agents at the stage of functioning within wide limits.

The paper deals with a problem of position and orientation errors of mobile platform of large-sized parallel cabledriven robots. The advantages of parallel cable-driven robots are simplicity of structure and scalability. At the same time, parallel cable-driven robots are difficult to design due to the specific problems such as collision of cables, geometric and structural nonlinearity in the mathematical models of the main elements of the robot. In this paper, we consider the problem of eliminating the uncertainty associated with deformations of the elements of the robot structure. Such a configuration of the cable system is selected, in which the proximal anchor points of some cables can be considered without errors relatively to given positions. The cable system of a large-sized robot is mounted on the towers. The errors in the proximal anchor points relatively to given positions become significant due to the significant deformations of upper sections of the towers. The deformations of the towers in lower sections can be considered insignificant, and the proximal anchor points have to be located no higher than the middle of the tower to be considered corresponding to a given position. The aim is to compensate the position and orientation errors of the mobile platform of large-sized parallel cable-driven robot due to deformations of the cables and towers. The task suppose uncertainty about the coordinates of the proximal anchor points of the upper cables. Cable deformations are determined from Hooke’s law using tensile forces measurement in cables. The problem of compensations is solved in two stages. At the first stage, the approximate bias of the center of mass of the mobile platform along the vertical coordinate is found. It is defined as the height of the truncated pyramid, the edges of which are formed by stretched lower cables. At the second stage, rotation angles of the mobile platform are determined. Using the rotation matrix, biases in the heights of each distal anchor points are found in the tool coordinate system. In the studied cases PID regulation is used, however, more advanced techniques of automatic regulation, for example, optimal control, can provide better results. The tasks are applied to the model of large-sized symmetric parallel eight-cable-driven robot.

The aim of the work is to find a mechanical analogue of cyclotron motion and to determine the scheme of the corresponding device, which is appropriate to call a stabilized rotator. From the key circumstance that determines the possibility of generalizing cyclotron motion to mechanics, which consists in the fact that the Lagrangian of an electron is twice as large as its kinetic energy, which, as applied to a stabilized rotator, should be interpreted as the equality of kinetic and potential energies, it follows that the composition of a stabilized rotator should include elements, which are able to store both of these types of energy, namely, the load and the spring. The natural frequency of rotation of a stabilized rotator is strictly fixed (it does not depend on either the moment of inertia or the moment of momentum) and remarkably coincides with the natural frequency of oscillations of a pendulum with identical parameters. When the angular momentum changes, the radius and tangential velocity change (the rotation frequency does not change and is equal to its own). The position of the load, in which its center of mass coincides with the axis of rotation, corresponds to a state of indefinite equilibrium. During rotation, the load can deviate with equal probability in any of the two directions and, accordingly, both compression and extension of the spring can develop. The state of indefinite equilibrium can be eliminated by providing the initial (static) displacement of the load and the initial deformation of the spring equal to it. Just as the frequency does not coincide with the natural frequency during forced oscillations of the pendulum, the rotation frequency of a stabilized rotator under loading does not coincide with the natural rotation frequency. At zero torque in the stationary mode, the rotational speed of the stabilized rotator cannot be arbitrary and takes on a single value. A stabilized rotator can be used to control the natural frequency of a radial oscillator, although in this capacity it may have strong competition from mechatronic systems. On the contrary, as a rotation stabilizer, its competitive capabilities are undeniable and are determined by the extreme simplicity of the design.

The research problem of a surface’s profile with an extended precision detail of irregular shape with a given accuracy is considered by the contactless scanning profilometer. The contact of the measuring block with a controlled surface needs to be excluded because of a possibility of damage of a product and, at the same time, to provide the necessary accuracy of assessment of its profile. For the solution of this task in work the double-circuit system containing two sensors is used: the distance converter on the basis of optical tunneling for the “exact” channel and the converter on the basis of a chromatic aberration for “rough” channel of scanning. It is shown that based on these measurements of the “rough” channel providing the guaranteed exception of contact of “rough” channel’s contact with a surface of the studied product. It is possible to predict situation and traverse speed of the sensor of the “exact” channel for the purpose of an exception of contact with the studied surface and ensuring necessary accuracy of measurements. The mathematical model of a dynamic system of scanning based on a prior information about entering it elements and blocks is developed. The analysis of the main dynamic properties of a system of scanning is carried out and the law of its management providing the required quality of transition processes based on mathematical modeling is constructed. The algorithm of the forecast of the subsequent position of the sensor of the “exact” channel based on these measurements of “rough” channel, which provides the required speed and accuracy of scanning depending on the predicted object’s surface profile height is developed. The flowchart of the algorithm determining the value of movement of the sensor of the “exact” channel in the vertical direction depending on the received assessment of measurements of “rough” channel is developed. The conducted researches allowed developing the block diagram of a double-circuit measuring system. Modeling of this system in the environment of MATLAB/SIMULINK, which allowed evaluating efficiency of its functioning for the different studied profiles was carried out. Results of modeling showed efficiency of the offered scheme of a profilometer’s control system.

The article solves a problem aimed at creating a control system for the planning of a rocket projectile. The existing method of calculating the missile range does not provide the necessary accuracy. The use of computer simulation methods is the most promising approach for the development of a rocket planning control system based on laws. The proposed control system is based on the use of a reference trajectory of the rocket flight calculated for the predicted average values of the velocity of the longitudinal component of the wind. An algorithm for controlling the planning of a rocket by changing the angle of rotation of a horizontal support is proposed, based on the dependence of vertical and horizontal coordinates and on the pitch angle. The computer system of visual programming Simulink was used as a platform for the development of the algorithm. As a result, a block diagram of the rocket planning control was obtained, including a model of the rocket flight path as a control object and an on-board control system organized on the basis of a dual-core ESP-32 microcontroller. The technique of wireless recording of the control program into the memory of the microcontroller in the field is proposed. Based on the Simulink Desktop software package, a half-scale rocket flight model was developed in real time, including an ESP-32 microcontroller, a PCI-1710HG board and a Simulink rocket flight trajectory model with a variable mass in the vertical plane. A series of experiments were conducted that showed a high degree of accuracy of the missile hitting the target because of the projectile planning control system.

Various simulators with motion cueing simulation stands, which make it possible to create an acceleration environment for the pilot that is close to a real flight, are used for training aircraft pilots. The article considers the formulation of the motion cueing simulation on a stand based on an industrial manipulator. Motion cueing simulation algorithms include two phases: motion cueing simulation phase and phase of return to the working area center. During simulation phase the stand must implement such a movement that the angular accelerations acting on the person and the overload vector acting on the center of mass of the operator completely coincide with the real ones. If it is not possible then just the directions of these vectors should coincide. During the second phase the stand end point must return to the working area center with acceleration values below the threshold, but in the fastest way. This task can be presented as a generalization of the brachistochrone problem. The article considers the problem of the material point motion in a uniform gravity field along a curve located in a vertical plane, in the presence of restrictions on the trajectory curvature. It is necessary to choose the curve shape in such a way that the descent time is minimal. The problem solution is obtained by optimal control methods, the cases of regular and singular control realization are considered, the question of its conjugation. Also, the switching number between sections of regular and singular control is studied.

In this work, a rendezvous of two satellites is considered. The active satellite approaches the passive satellite for a remote partial recharge of the passive spacecraft’s dead battery. In the first case, the active and passive spacecraft are in geocentric circular orbits, having an altitude of 499.9 km and 500 km, respectively. It is assumed that the rendezvous is unperturbed and the rendezvous plane coincides with the plane of the passive satellite’s orbit. Close-range guidance starts as soon as the sensor on the active spacecraft recognizes the passive spacecraft. A method implementing the line of sight is used for the close-range guidance process. A mathematical model of the relative motion is formed and numerically solved to investigate the rendezvous parameters against time. For solving the model, different values of 499.9, 499.8, 499.7 km are considered as the initial orbit altitude of the active spacecraft, assuming that the angle between state vectors of the spacecraft has a small value of 0.01 degrees. The results show that the active spacecraft with an initial altitude of 499.7 km approaches the passive spacecraft to a distance of 80 meters in less than 50 seconds, where a final velocity impulse is needed to maintain this distance.