Inertial Parameters Research Articles

Orbit-attitude coupled dynamics modeling and adaptive sliding mode control for detumbling large space debris

For non-cooperative large tumbling space debris, the use of detumbling techniques to reduce its angular velocity facilitates capturing and deorbiting operations. In our recent work, a new detumbling device combining three harpoons and a nanosatellite was designed. The device is released from the servicing satellite and attaches to the surface of the target. Then, the device's thrusters are actuated to reduce the target's angular velocity. In this paper, the dynamics and control issues involved in this strategy are further investigated. The collision model between the detumbling device and the target in the process of attachment is built based on the principle of momentum conservation. A high-precision orbit-attitude coupled dynamics model of the combined system during the detumbling mission is established, in which major external disturbances as well as inertial parameter variations due to the fuel consumption of the nanosatellite are taken into account. In addition, an adaptive sliding mode control scheme incorporating pulse-width pulse-frequency (PWPF) modulation is proposed for debris targets with parametric uncertainties and external disturbances. Finally, the effectiveness and robustness of the detumbling control scheme are demonstrated by numerical simulations. The results show that the detumbling device is capable of detumbling a large tumbling rocket upper stage within 4000s.

Robust Geometric Control for a Quadrotor UAV with Extended Kalman Filter Estimation

This study proposes a robust geometric controller tailored for quadrotor unmanned aerial vehicles (UAVs). The original geometric controller exhibits excellent performance in quadrotor UAV maneuvers. However, as a model-based nonlinear control method, it is sensitive to system model parameters. By integrating a novel extended Kalman filter (EKF)-based estimator for real-time, online estimation of the quadrotor’s inertia parameters, the controller adeptly handles internal uncertainties and external perturbations during flight maneuvers. This approach significantly improves the robustness of the control system against model inaccuracies. Empirical evidence is provided through both simulation and extensive real-world flight tests, demonstrating the controller’s effectiveness and its practical applicability in dynamic environments. The results confirm that this integration substantially enhances system reliability and performance under varied operational conditions.

On synchronization of third-order power systems governed by second-order networked Kuramoto oscillators incorporating first-order magnitude dynamics

This study explores the sufficient conditions for achieving synchronization in the third-order one-axis generator models in modern power systems, characterized by the second-order networked Kuramoto oscillators integrating the first-order amplitude dynamics. First, we provide detailed descriptions of dynamic models for this particular class of third-order power systems, which are governed by second-order networked Kuramoto oscillators incorporating first-order voltage magnitude dynamics. Then, we show that if the phase difference of oscillators is less than π2 and the initial amplitudes are positive, then the amplitudes are bounded and possess a positive lower bound. Furthermore, under specific conditions on the coupling strength, inertia, and oscillator parameters, we prove that the third-order model exhibits a frequency synchronization and the derivatives of amplitudes converge to zero. Numerical simulations are performed to support our main results.

Real-time estimation of vehicle inertia parameters based on Kalman-bucy filter

Vehicle inertial parameters such as mass and moments of inertia are required for most vehicle dynamic control systems. Due to the wide range variation of these parameters during vehicle operation, accurate estimation of their values in real-time plays an important role in improving the efficiency of vehicle control systems. In this article, the vehicle sprung mass and moments of inertia are estimated in real-time based on a Kalman-Bucy filter algorithm designed for a spatial vibration model of a two-axle truck. This proposed method requires measuring only the vertical, roll, and pitch velocity of the sprung mass and, therefore can reduce the sensor cost significantly. The simulation results for a random roughness road profile according to ISO 8608 class C with step variations in sprung mass and moments of inertia showed that the designed estimator rejected the process and measurement noises and tracked the real vehicle parameters effectively with acceptable errors

Parameters online identification‐based data‐driven backstepping control of hypersonic vehicles

SummaryThe control problem of the hypersonic vehicles is studied in this article. A new control approach is presented. This approach consists of a data‐driven dynamic model established by multiple neural networks, an online identification method for system parameters, and a basic backstepping controller. The implementation of this approach requires a dynamic model and system parameters including the moment of inertia and aerodynamic parameters of the hypersonic vehicles. The parameter identification problem is regarded as a dynamic optimization process. The loss function is designed by the Lagrange criterion, and its constraints are determined by the physical and the numerical values. In the case of model mutation, the system parameters identified online are used as the nominal values of the output of the neural network in the data‐driven model to adjust the controller through its gradient descent. Simulation comparisons are given to show the effectiveness of the proposed data‐driven approach.

A robust model predictive control unified framework for autonomous rendezvous and docking with a tumbling target

During autonomous rendezvous and docking (AR&D) with a tumbling target, multiple unfavorable engineering constraints exist, such as constraints on the control, velocity, or collision avoidance. Meanwhile, many sources of uncertainty exist, including incomplete and inaccurate measurements, control deviation, dynamic uncertainty, and inertial parameter uncertainty of the tumbling target, which significantly complicate the design of the guidance and control algorithm. Considering these challenges, this paper proposes a robust identification, planning, and control unified framework for AR&D with a tumbling target, which incorporates an extended Kalman filter (EKF) with a robust tube-based model predictive control for tracking (TMPT) controller. First, the EKF is designed to estimate the system state and inertial parameters of the target and then predict the future behavior of the tumbling target. Additionally, the prediction information of the target is transmitted to the designed TMPT controller as a reference signal. This TMPT controller unites trajectory planning and control in a single layer that can ensure the stability and recursive feasibility of the algorithm with a short prediction horizon. Moreover, it can guarantee that the closed-loop system is robustly and asymptotically convergent to the reachable set whose center is the optimal reachable periodic trajectory concerning the docking port of the tumbling target. The unified framework represents a robustness-to-optimality control strategy that can accomplish the AR&D mission efficiently while considering multiple engineering constraints and uncertainties. Finally, the efficiency of the proposed control framework is verified through a numerical simulation.

Human–robot mechanics model using hip torque identification with a dual-arm nursing-care transfer robot

In response to the growing demand for robotic interventions to mitigate the profound physical strain experienced by caregivers during transfers, dual-arm robotic systems have emerged as a focal point of interest in the caregiving community due to their adaptability and versatility. However, the accuracy of existing human–robot mechanics model is insufficient, impacting the execution of transfer tasks. To enhance the model’s precision, an improved model is proposed, integrating hip torque identification. This proposed methodology involves the simplification of the human structure based on the kinematic attributes associated with the embrace of individuals by robotic arms and the subsequent computation of its inertial parameters. Accordingly, the application of D’Alembert’s principle is employed to analyze the impact of embracing motion, human posture, and the position of human–robot contact on the forces exerted on the human. This culminates in the establishment of a model. Considering the static indeterminacy predicament inherent in the model, a biomechanical data set is curated for the dual-arm transfer scenario. Leveraging this data set, a deep neural network utilizing multilayer perceptron is trained to accurately identify hip torque, thereby improving the model. Accordingly, a robotic transfer platform featuring dual arms is developed and trailed on six subjects with varying anatomical profiles. The results show that the constructed model has high accuracy. This study provides critical mechanics insights for dual-arm transfer tasks, offering potential application value in the field of nursing and rehabilitation.

ФОРМАЛИЗМ РЕШЕНИЯ ПЕРВОЙ ЗАДАЧИ ДИНАМИКИ ШАГАЮЩИХ И КОЛЕСНО-ШАГАЮЩИХ МАШИН

The aim is to solve the first problem of the dynamics of machines moving their bodies with the help of legs, i.e., to calculate the control actions of the leg actuators that provide the given dynamics of the absolute motion of the body and satisfy the constraints, when fulfilled, there is no sliding of the supporting legs relative to the supporting surface. The research methods are related to system analysis, mechanics of body systems and robotics. We consider walking and wheel-walking machines with legs suspended from the body, in which the last kinematic pair is translational, there is no controlled foot, and the foot and the supporting surface interact at a single point. The resultsof the study contain analytical formulas for calculating dynamic reactions at the points of contact between the legs and the supporting surface, as well as driving forces and moments of forces in the drives of the supporting and carrying legs, providing a given motion of the body relative to the supporting surface, as well as its corresponding relative motion of the bodies of the supporting legs. A formalism for solving such problems is described, based on inverse vector recurrence formulas for calculating forces and moments of forces of dynamic reactions in kinematic pairs of tree-like systems of bodies with closure of the last body of the branch on the supporting surface. This formalism is extended to wheeled, wheel-walking and walking machines, which is demonstrated by appropriate examples. Analytical conditions for realizing a step without slipping of the support legs relative to the support surface are written down. Two simple wheel-walking machines, consisting of a linear electric drive and a driven (passive) wheelset, are proposed for the experimental determination of sliding and rolling friction coefficient values. In analytical forms of deduced calculation formulas (equations and inequalities) the structural, geometric, inertial and kinematic parameters of the investigated machines are explicitly expressed. The proposed formalism is demonstrated on the solutions of four problems from simple to complex through the reuse of formulas. Conclusion. The obtained mathematical models can be used in the processes of calculation and design of similar machines and their layouts.

Research on icing scaling technology for large civil aircraft icing wind tunnel test

This article explores the icing scaling technology for large civil aircraft icing wind tunnel tests. Based on the typical critical icing conditions of large civil aircraft and the calibration of icing wind tunnel, and through the similarity analysis of water droplet trajectories, water collection, and energy balance, four similar parameters, namely modified inertia parameter, drop energy transfer parameter, stagnation freezing coefficient, and accumulation parameter, were selected as similarity criteria for icing scaling. Based on this criteria, icing scaling was conducted on the critical icing conditions of large civil aircraft, and the scaling results were evaluated by icing code. The results show that the water droplet collection and the ice shape before and after the scaling are in good agreement, and the similarity criteria used are appropriate. Finally, icing wind tunnel test was conducted in 3m × 2m test section using scaled icing conditions. The test results show that the main characteristics of the experimental ice shape are in good agreement with the calculated ice shape, and the calculated ice shape is more critical. The calculated ice shape can be used as a critical ice for aerodynamic wind tunnel tests and flight tests with simulated ice.

Relaxed Inertial Projective Forward-backward Splitting Algorithms for Regularized Least Square Problems

This study presents flexible conditions of the inertial extrapolation parameter for easy implementation that is added to the algorithm in faster convergence. Modified inertial forward-backward splitting algorithms for solving variational inclusion problems are introduced to apply to solve the LASSO problem for image restoration and signal recovery, and the elastic net model for classification problem. Projection methods are used in the final step for narrowing down the search field, resulting in a better solution.

Chelyshkov wavelet-based numerical technique for the solution of Darcy–Forchheimer flow of Erying–Powell radiated dusty fluid over a stretching sheet with Cattaneo–Christov heat flux

This article presents the Chelyshkov wavelet-based numerical technique (CWBNT) for the solution of the system of non-linear differential equations arising in the study of Darcy–Forchheimer flow of Erying–Powell radiated dusty fluid over a stretching sheet with Cattaneo–Christov heat flux. Initially, the proposed technique is implemented on the test problem having exact solution. The obtained results are highly accurate in comparison with the solutions obtained by shooting technique based Runge–Kutta Fehlberg 4th–5th order method. The proposed technique is applied to the governing equations of the considered dusty fluid problem. The results obtained for some fixed values of parameters resemble the previously published results. The comparisons validate the method. The flow behavior of dusty fluid is analyzed and the effect of various factors on the velocity and thermal attribute of the dust and fluid phase are studied. It is inferred that the Erying–Powell fluid parameters ε and α have entirely different effects on temperature, velocity profiles, and skin-friction coefficient. The local inertia parameter decreases the velocity and thermal relaxation parameter decreases the temperature. Enhancement in temperature ratio and radiation parameters escalates the temperature and Nusselt number. The proposed technique is simple, reliable, efficient tool to solve the differential equations arising in dusty fluid flow problems.

Development and Analysis of Novel Integrable Nonlinear Dynamical Systems on Quasi-One-Dimensional Lattices. Two-Component Nonlinear System with the On-Site and Spatially Distributed Inertial Mass Parameters

The main principles of developing the evolutionary nonlinear integrable systems on quasi-onedimensional lattices are formulated in clear mathematical and physical terms discarding the whimsical mathematical formulations and computer-addicted presentations. These basic principles are substantiated by the actual development of novel semi-discrete integrable nonlinear system, whose auxiliary spectral and evolutionary operators are given by 4 × 4 square matrices. The procedure of reduction from the prototype nonlinear integrable system with twelve field functions to the physically meaningful nonlinear integrable system with four field functions is described in details prompted by our previous cumulative experience. The obtained ultimate semi-discrete nonlinear integrable system comprises the two subsystems of essentially distinct physical origins. Thus, the first subsystem is the subsystem of the Toda type. It is characterized by the on-site (spatially local) mass parameter and the positively defined elasticity coefficient. In contrast, the second subsystem is characterized by the spatially distributed mass parameters and the negatively defined elasticity coefficient responsible for the low-amplitude instability. We believe our scrupulous consideration of all main steps in developing the semidiscrete nonlinear integrable systems will be useful for the researchers unfamiliar with the numerous stumbling blocks inevitable in such an interesting and prospective scientific field as the theory of semi-discrete nonlinear integrable systems.

A hybrid particle swarm optimization algorithm for solving engineering problem

To overcome the disadvantages of premature convergence and easy trapping into local optimum solutions, this paper proposes an improved particle swarm optimization algorithm (named NDWPSO algorithm) based on multiple hybrid strategies. Firstly, the elite opposition-based learning method is utilized to initialize the particle position matrix. Secondly, the dynamic inertial weight parameters are given to improve the global search speed in the early iterative phase. Thirdly, a new local optimal jump-out strategy is proposed to overcome the "premature" problem. Finally, the algorithm applies the spiral shrinkage search strategy from the whale optimization algorithm (WOA) and the Differential Evolution (DE) mutation strategy in the later iteration to accelerate the convergence speed. The NDWPSO is further compared with other 8 well-known nature-inspired algorithms (3 PSO variants and 5 other intelligent algorithms) on 23 benchmark test functions and three practical engineering problems. Simulation results prove that the NDWPSO algorithm obtains better results for all 49 sets of data than the other 3 PSO variants. Compared with 5 other intelligent algorithms, the NDWPSO obtains 69.2%, 84.6%, and 84.6% of the best results for the benchmark function (f1-f13\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${f}_{1}-{f}_{13}$$\\end{document}) with 3 kinds of dimensional spaces (Dim = 30,50,100) and 80% of the best optimal solutions for 10 fixed-multimodal benchmark functions. Also, the best design solutions are obtained by NDWPSO for all 3 classical practical engineering problems.

Rotary inverted pendulum control using neuro-adaptive robust generalized dynamic inversion

The objective of this research is to design a robust control system for trajectory tracking of the under-actuated Rotary Inverted Pendulum (RIP). The focus is on achieving semi-global asymptotic stability in the absence of knowledge about the RIP geometric and inertia parameters. The control design commences by formulating differential servo constraint dynamics (VCD) that encapsulates the control objectives for the RIP. The baseline generalized dynamic inversion (GDI) control law is derived by inverting the VCD for the control voltage input using the Moore–Penrose generalized inverse. To enhance robustness against modeling uncertainties and exogenous disturbances, a sliding mode control (SMC) element is integrated within the GDI control system, resulting in the robust GDI (RGDI) control system. Furthermore, an adaptive estimator that is based on Radial Basis Function Neural Networks (RBF-NN) is adopted to eliminate the dependency of the RGDI control system on the RIP mathematical model. The weighting matrices of the RBF-NN are updated with the aid of a Lyapunov control function. The proposed control system offers robust solution and guarantees semi-global asymptotic stability to the unstable equilibria of the RIP dynamics in the absence of a mathematical model. The proposed control system’s performance is evaluated through computer simulations and experimental tests on a real RIP system. Comparative analyses with traditional SMC and linear quadratic control methodologies are conducted to show the effectiveness of the proposed approach.

Computation of hydromagnetic tangent hyperbolic non-Newtonian flow from a rotating non-isothermal cone to a non-Darcy porous medium with thermal radiative flux

A theoretical and numerical study is conducted on nonlinear, steady-state thermal convection boundary layer flow of a magnetized incompressible Tangent Hyperbolic non-Newtonian fluid from a rotating cone to a non-Darcy porous medium. Power-law variation in temperature on the cone surface is considered and thermal radiation heat transfer is also present. The Brinkman-Darcy-Forchheimer model is deployed for the porous medium. The study is motivated by rotational (spin) coating with new emerging magnetic rheological polymers, a process which often utilizes filtration media and high temperatures. The transformed non-dimensional conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. Extensive visualization of axial, tangential velocity components and temperature distributions with variation in key parameters including Rosseland radiative number, Darcy number, Forchheimer number (non-Darcy inertial parameter), magnetic interaction parameter, tangent-hyperbolic non-Newtonian power-law index and Weissenberg (non-Newtonian) number is included. Additionally, axial and tangential (circumferential) skin friction and Nusselt number values are tabulated for variation in key control parameters. With increasing Weissenberg number, axial velocity is depleted near the cone surface, tangential velocity is suppressed throughout the boundary layer regime and temperature is strongly enhanced. Axial flow is strongly decelerated further from the cone surface with increasing tangent-hyperbolic power-law index and there is also a significant depletion in tangential (swirl) velocity. Temperature is however boosted throughout the boundary layer transverse to the cone surface with a rise in tangent-hyperbolic power-law index. Both tangential and axial velocity are suppressed with increment in magnetic interaction parameter whereas temperature and thermal boundary layer thickness are enhanced. With larger Darcy number (i.e. greater permeability), axial velocity is strongly increased near the cone surface with no tangible modification further from the cone; However tangential velocity is consistently elevated throughout the boundary layer with greater Darcy number whereas temperature is depleted. An increase in Forchheimer number substantially damps both axial and tangential velocity whereas it elevates temperature. Increasing radiative flux strongly energizes the magnetic polymer and elevates temperature but suppresses the axial and tangential velocities. With elevation in non-isothermal wall exponent, axial skin friction is suppressed whereas Nusselt number are elevated at the cone vertex. Further along the cone surface a similar response is observed but there is also a reduction in magnitudes of tangential skin friction.

Anti-unwinding adaptive robust backstepping attitude maneuver control for rigid spacecraft

In this paper, an anti-unwinding adaptive robust backstepping control law is proposed to solve the attitude control problem of rigid spacecraft with external disturbances and inertia uncertainties. A new variable based on hyperbolic sine functions is designed to prevent the unwinding phenomenon, and then a novel robust backstepping controller is developed. Initially, a nonlinear tracking law is designed to obtain the desired angular velocity and to ensure that the attitude maneuvering system could have two equilibrium points. Subsequently, an adaptive robust control law is devised, which incorporates the adaptive estimation method to update the inertial parameters in real-time. Moreover, the bounded external disturbances are taken into account in the design of the control law, and thus the robustness of the attitude control system is improved. Furthermore, the global asymptotic stability of the attitude control system is verified by the Lyapunov-Krasovskii theorem. Finally, numerical simulations are carried out to demonstrate the effectiveness and robustness of the proposed control law, as well as the anti-unwinding characteristics are perfectly validated during the attitude maneuver of rigid spacecraft.

A Novel Methodology for Inertial Parameter Identification of Lightweight Electric Vehicle via Adaptive Dual Unscented Kalman Filter

A Novel Methodology for Inertial Parameter Identification of Lightweight Electric Vehicle via Adaptive Dual Unscented Kalman Filter

Automatic calculation of step size and inertia parameter for convolutional dictionary learning

The convergent methods available for convolutional dictionary learning (CDL) are the proximal gradient method (PGM) and the inertial proximal gradient method (IPGM). However, it is not trivial and heuristic for IPGM to set the step size and inertia parameter, and IPGM produces local minima and oscillating solutions. To address these issues, in this paper, we introduce a dry friction, which has an oscillation-alleviating property. Specifically, the proposed IPGM with dry friction (IPGM-DF) generates the composite proximal mappings, whose construction and optimization solver are two challenges. An auxiliary function is designed to construct the composite proximal mappings, whose optimization problem is solved by the alternating direction method of multipliers. Fortunately, IPGM-DF obtains the formulas of the step size and inertia parameter. The finite convergence of IPGM-DF is proved. Experimental results of image reconstruction, separation, and fusion demonstrate the superiority of IPGM-DF over IPGM and the state-of-the-art methods. For image reconstruction, the objective function value of IPGM-DF is reduced by about 38.708% than that of IPGM. Throughout alleviating oscillations, IPGM-DF obtains a much lower value of the objective function than IPGM, which indicates that IPGM-DF jumps out of the local minima of IPGM. In addition, the average PSNR of IPGM-DF is about 3.5 dB larger than that of IPGM and the state-of-the-art methods. The code is available.

Extragradient methods with dual inertial steps for solving equilibrium problems

ABSTRACT The primary focus of this study is how to expedite the convergence rate of the extragradient method by tactfully choosing inertial parameters and building up the step-size rule. To achieve this goal, we introduce three improvements to Korpelevich's extragradient method. These improvements include the use of dual inertial steps as well as a self-adaptive step-size rule. The proposed iterative techniques are employed for solving equilibrium problems in real Hilbert spaces. Initially, we establish the results for weak convergence of the proposed methods, assuming the involved bifunction to be both pseudomonotone and Lipschitz-type continuous. Subsequently, we demonstrate linear convergence in scenarios where the bifunction is strongly pseudomonotone and Lipschitz-type continuous. Finally, we present multiple numerical experiments to illustrate the practical effectiveness of the proposed methods.

Trajectory Tracking Control of an Aerial Manipulator in the Presence of Disturbances and Model Uncertainties

The precise control of an aerial manipulator presents a formidable challenge due to the inherent mobility of its base, which is subject to both external disturbances and dynamic disturbances due to manipulator motions. In this paper, we introduce two Closed-Loop Inverse Kinematics (CLIK) control algorithms tailored to aerial manipulators. The first algorithm operates at the velocity level and uses the Generalized Jacobian for inverse kinematics, while the second one operates at the acceleration level. We evaluate their performance in a simulated environment, replicating real-world challenges such as the wind effect, sensors noise, uncertainty of the system inertial parameters, and impulsive forces at the end-effector. Trajectory tracking simulated experiments are carried out for a two- and three-degree-of-freedom (DOF) aerial manipulator tracking a circular trajectory with its end-effector. Both algorithms demonstrate promising results in coping with external disturbances and variations in the inertial parameters, enhancing the precision of the trajectory tracking control. The acceleration-level algorithm shows overall better performance compared to the velocity-level one in the face of greater implementation complexity and computational burden.