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# Vol. 18, no. 5, 2022 Conference NIR-2022

 Abstract Citation: Introductory Note, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 753-753
 Marchuk E. A.,  Kalinin Y. V.,  Sidorova A. V.,  Maloletov A. V. Abstract This paper deals with the application of force sensors to estimate position errors of the center of mass of the mobile platform of a cable-driven parallel robot. Conditions of deformations of cables and towers of the robot are included in the numerical model and external disturbance is included too. The method for estimating the error in positioning via force sensors is sensitive to the magnitude of spatial oscillations of the mobile platform. To reduce torsional vibrations of the mobile platform around the vertical axis, a dynamic damper has been included into the system. Keywords: cable, robot, additive, printing, position, orientation, errors, force sensors Citation: Marchuk E. A.,  Kalinin Y. V.,  Sidorova A. V.,  Maloletov A. V., On the Problem of Position and Orientation Errors of a Large-Sized Cable-Driven Parallel Robot, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 755-770 DOI:10.20537/nd221209
 Shaker W. K.,  Klimchik A. S. Abstract This paper deals with the stiffness modeling of the double pantograph transmission system. The main focus is on the comparison analysis of different stiffness modeling approaches: virtual joint modeling (VJM) and matrix structural analysis (MSA). The aim of this work is to investigate the limitations of the considered approaches. To address this issue, corresponding MSA-based and VJM-based stiffness models were derived. To evaluate the deflections of the end effector, the external loads were applied in different directions at multiple points in the robot workspace. The computational cost and the difference in end-effector deflections were studied and compared. MSA was found to be 2 times faster than VJM for this structure. The results obtained showed that the MSA approach is more appropriate for the double pantograph mechanism. Keywords: stiffness modeling, parallel robot, double pantograph, virtual joint modeling, matrix structural analysis Citation: Shaker W. K.,  Klimchik A. S., Stiffness Modeling of a Double Pantograph Transmission System: Comparison of VJM and MSA Approaches, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 771-785 DOI:10.20537/nd221208
 Ali Deeb A.,  Shahhoud F. Abstract This paper investigates the problem of object detection for real-time agents’ navigation using embedded systems. In real-world problems, a compromise between accuracy and speed must be found. In this paper, we consider a description of the architecture of different object detection algorithms, such as R-CNN and YOLO, to compare them on different variants of embedded systems using different datasets. As a result, we provide a trade-off study based on accuracy and speed for different object detection algorithms to choose the appropriate one depending on the specific application task. Keywords: robot navigation, object detection, embedded systems, YOLO algorithms, R-CNN algorithms, object semantics Citation: Ali Deeb A.,  Shahhoud F., Image-Based Object Detection Approaches to be Used in Embedded Systems for Robots Navigation, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 787-802 DOI:10.20537/nd221218
 Saypulaev G. R.,  Adamov B. I.,  Kobrin A. I. Abstract The subject of this paper is a spherical robot with an internal platform with four classictype omniwheels. The motion of the spherical robot on a horizontal surface is considered and its kinematics is described. The aim of the research is to study the dynamics of the spherical robot with different levels of detailing of the contact friction model. Nonholonomic models of the dynamics of the robot with different levels of detailing of the contact friction model are constructed. The programmed control of the motion of the spherical robot using elementary maneuvers is proposed. A simulation of motion is carried out and the efficiency of the proposed control is confirmed. It is shown that, at low speeds of motion of the spherical robot, it is allowed to use a model obtained under the assumption of no slipping between the sphere and the floor. The influence of the contact friction model at high-speed motions of the spherical robot on its dynamics under programmed control is demonstrated. This influence leads to the need to develop more accurate models of the motion of a spherical robot and its contact interaction with the supporting surface in order to increase the accuracy of motion control based on these models. Keywords: spherical robot, dynamics model, kinematics model, omniwheel, omniplatform, multicomponent friction Citation: Saypulaev G. R.,  Adamov B. I.,  Kobrin A. I., Comparative Analysis of the Dynamics of a Spherical Robot with a Balanced Internal Platform Taking into Account Different Models of Contact Friction, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 803-815 DOI:10.20537/nd221219
 Demian A. A.,  Klimchik A. S. Abstract This paper is devoted to the design of gravity compensators for prismatic joints. The proposed compensator depends on the suspension of linear springs together with mechanical transmission mechanisms to achieve the constant application of force along the sliding span of the joint. The use of self-locking worm gears ensures the isolation of spring forces. A constantforce mechanism is proposed to generate counterbalance force along the motion span of the prismatic joint. The constant-force mechanism is coupled with a pin-slot mechanism to transform to adjust the spring tension to counterbalance the effect of rotation of the revolute joint. Two springs were used to counterbalance the gravity torque of the revolute joint. One of the springs has a moving pin-point that is passively adjusted in proportion with the moving mass of the prismatic joint. To derive the model of the compensator, a 2-DoF system which consists of a revolute and a prismatic joint is investigated. In contrast to previous work, the proposed compensator considers the combined motion of rotation and translation. The obtained results were tested in simulation based on the dynamic model of the derived system. The simulation shows the effectiveness of the proposed compensator as it significantly reduces the effort required by the actuators to support the manipulator against gravity. The derived compensator model provides the necessary constraints on the design parameters. Keywords: prismatic joints, static balancing, gravity compensation, manipulator design Citation: Demian A. A.,  Klimchik A. S., Gravity Compensation for Mechanisms with Prismatic Joints, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 817-829 DOI:10.20537/nd221212
 Shamraev A. D.,  Kolyubin S. A. Abstract Animal running has been studied for a long time, but until now robots cannot repeat the same movements with energy efficiency close to animals. There are many controllers for controlling the movement of four-legged robots. One of the most popular is the convex MPC. This paper presents a bioinspirational approach to increasing the energy efficiency of the state-of-theart convex MPC controller. This approach is to set a reference trajectory for the convex MPC in the form of an SLIP model, which describes the movements of animals when running. Adding an SLIP trajectory increases the energy efficiency of the Pronk gait by 15 percent over a range of speed from 0.75 m/s to 1.75 m/s. Keywords: quadruped, model predictive control, spring-loaded inverted pendulum, bioinspiration, energy efficiency Citation: Shamraev A. D.,  Kolyubin S. A., Bioinspired and Energy-Efficient Convex Model Predictive Control for a Quadruped Robot, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 831-841 DOI:10.20537/nd221214
 Almaghout K.,  Klimchik A. S. Abstract Although deformable linear objects (DLOs), such as cables, are widely used in the majority of life fields and activities, the robotic manipulation of these objects is considerably more complex compared to the rigid-body manipulation and still an open challenge. In this paper, we introduce a new framework using two robotic arms cooperatively manipulating a DLO from an initial shape to a desired one. Based on visual servoing and computer vision techniques, a perception approach is proposed to detect and sample the DLO as a set of virtual feature points. Then a manipulation planning approach is introduced to map between the motion of the manipulators end effectors and the DLO points by a Jacobian matrix. To avoid excessive stretching of the DLO, the planning approach generates a path for each DLO point forming profiles between the initial and desired shapes. It is guaranteed that all these intershape profiles are reachable and maintain the cable length constraint. The framework and the aforementioned approaches are validated in real-life experiments. Keywords: robotic comanipulation, deformable linear objects, shape control, visual servoing Citation: Almaghout K.,  Klimchik A. S., Vision-Based Robotic Comanipulation for Deforming Cables, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 843-858 DOI:10.20537/nd221213
 Ali W.,  Kolyubin S. A. Abstract In this study, we discuss a new machine learning architecture, the multilayer preceptronrandom forest regressors pipeline (MLP-RF model), which stacks two ML regressors of different kinds to estimate the generated gripping forces from recorded surface electromyographic activity signals (EMG) during a gripping task. We evaluate our proposed approach on a publicly available dataset, putEMG-Force, which represents a sEMG-Force data profile. The sEMG signals were then filtered and preprocessed to get the features-target data frame that will be used to train the proposed ML model. The proposed ML model is a pipeline of stacking 2 different natural ML models; a random forest regressor model (RF regressor) and a multiple layer perceptron artificial neural network (MLP regressor). The models were stacked together, and the outputs were penalized by a Ridge regressor to get the best estimation of both models. The model was evaluated by different metrics; mean squared error and coefficient of determination, or $r^2$ score, to improve the model prediction performance. We tuned the most significant hyperparameters of each of the MLP-RF model components using a random search algorithm followed by a grid search algorithm. Finally, we evaluated our MLP-RF model performance on the data by training a recurrent neural network consisting of 2 LSTM layers, 2 dropouts, and one dense layer on the same data (as it is the common approach for problems with sequential datasets) and comparing the prediction results with our proposed model. The results show that the MLP-RF outperforms the RNN model. Keywords: sEMG signals, multilayer perceptron regressor (MLP), random forest regressor (RF), recurrent neural network (RNN), robot grasping forces, skill transfer learning Citation: Ali W.,  Kolyubin S. A., EMG-Based Grasping Force Estimation for Robot Skill Transfer Learning, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 859-872 DOI:10.20537/nd221221
 Kazakov Y.,  Kornaev A.,  Shutin D.,  Kornaeva E.,  Savin L. Abstract Despite the fact that the hydrodynamic lubrication is a self-controlled process, the rotor dynamics and energy efficiency in fluid film bearing are often the subject to be improved. We have designed control systems with adaptive PI and DQN-agent based controllers to minimize the rotor oscillations amplitude in a conical fluid film bearing. The design of the bearing allows its axial displacement and thus adjustment of its average clearance. The tests were performed using a simulation model in MATLAB software. The simulation model includes modules of a rigid shaft, a conical bearing, and a control system. The bearing module is based on numerical solution of the generalized Reynolds equation and its nonlinear approximation with fully connected neural networks. The results obtained demonstrate that both the adaptive PI controller and the DQNbased controller reduce the rotor vibrations even when imbalance in the system grows. However, the DQN-based approach provides some additional advantages in the controller designing process as well as in the system performance. Keywords: active fluid film bearing, conical bearing, simulation modeling, DQN-agent, adaptive PI controller Citation: Kazakov Y.,  Kornaev A.,  Shutin D.,  Kornaeva E.,  Savin L., Reducing Rotor Vibrations in Active Conical Fluid Film Bearings with Controllable Gap, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 873-883 DOI:10.20537/nd221226
 Savin S. I.,  Khusainov R. R. Abstract In this work, a nonminimal coordinate representation of tensegrity structures with explicit constraints is introduced. A method is proposed for representation of results on tensegrity structures in sparse models of generalized forces, providing advantages for code generation for symbolic or autodifferentiation derivation tasks, and giving diagonal linear models with constant inertia matrices, allowing one not only to simplify computations and matrix inversions, but also to lower the number of elements that need to be stored when the linear model is evaluated along a trajectory. Keywords: tensegrity, dynamic model, nonminimal representation, linearized model Citation: Savin S. I.,  Khusainov R. R., Sparse Node-Distance Coordinate Representation for Tensegrity Structures, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 885-898 DOI:10.20537/nd221225
 Mikishanina E. A. Abstract The problem of controlling the rolling of a spherical robot with a pendulum actuator pursuing a moving target by the pursuit method, but with a minimal control, is considered. The mathematical model assumes the presence of a number of holonomic and nonholonomic constraints, as well as the presence of two servo-constraints containing a control function. The control function is defined in accordance with the features of the simulated scenario. Servo-constraints set the motion program. To implement the motion program, the pendulum actuator generates a control torque which is obtained from the joint solution of the equations of motion and derivatives of servo-constraints. The first and second components of the control torque vector are determined in a unique way, and the third component is determined from the condition of minimizing the square of the control torque. The system of equations of motion after reduction for a given control function is reduced to a nonautonomous system of six equations. A rigorous proof of the boundedness of the distance function between a spherical robot and a target moving at a bounded velocity is given. The cases where objects move in a straight line and along a curved trajectory are considered. Based on numerical integration, solutions are obtained, graphs of the desired mechanical parameters are plotted, and the trajectory of the target and the trajectory of the spherical robot are constructed. Keywords: spherical robot, pendulum actuator, control, equations of motion, nonholonomic constraint, servo-constraint, pursuit, target Citation: Mikishanina E. A., Motion Control of a Spherical Robot with a Pendulum Actuator for Pursuing a Target, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 899-913 DOI:10.20537/nd221223
 Kurakin L. G.,  Ostrovskaya I. V. Abstract The stability problem of a moving circular cylinder of radius $R$ and a system of $n$ identical point vortices uniformly distributed on a circle of radius $R_0^{}$, with $n\geqslant 2$, is considered. The center of the vortex polygon coincides with the center of the cylinder. The circulation around the cylinder is zero. There are three parameters in the problem: the number of point vortices $n$, the added mass of the cylinder $a$ and the parameter $q=\frac{R^2}{R_0^2}$. The linearization matrix and the quadratic part of the Hamiltonian of the problem are studied. As a result, the parameter space of the problem is divided into the instability area and the area of linear stability where nonlinear analysis is required. In the case $n=2,\,3$ two domains of linear stability are found. In the case $n=4,\,5,\,6$ there is just one domain. In the case $n\geqslant 7$ the studied solution is unstable for any value of the problem parameters. The obtained results in the limiting case as $a\to\infty$ agree with the known results for the model of point vortices outside the circular domain. Keywords: point vortices, Hamiltonian equation, Thomson’s polygon, stability Citation: Kurakin L. G.,  Ostrovskaya I. V., On the Stability of the System of Thomson’s Vortex $n$-Gon and a Moving Circular Cylinder, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 915-926 DOI:10.20537/nd221217
 Astafyeva P. Y.,  Kiselev O. M. Abstract The article is devoted to a comprehensive study of linear equations of the second order with an almost periodic coefficient. Using an asymptotic approach, the system of equations for parametric subresonant growth of the amplitude of oscillations is obtained. Moreover, the time of a turning point from the growth of the amplitude to the bounded oscillations in the slow variable is found. Also, a comparison between the asymptotic approximation for the turning time and the numerical one is shown. Keywords: classical analysis and ODEs, subresonant, almost periodic function,small denominator Citation: Astafyeva P. Y.,  Kiselev O. M., Formal Asymptotics of Parametric Subresonance, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 5, pp. 927-937 DOI:10.20537/nd221220

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