Newton-Euler Method Research Articles

Quadrotor control in complex manoeuvres using a hybrid backstepping and feedback linearisation control strategy

In this article, a novel control algorithm called the combined backstepping and feedback linearisation method, along with an uncertainty estimator, is presented for quadrotors. The objective is to develop a robust control algorithm capable of handling various flight conditions, compensating for uncertainties and disturbances, and effectively controlling high-speed manoeuvres. To accomplish this, the quadrotor dynamics model is first derived using the Newton–Euler method. Subsequently, a backstepping control algorithm is designed for the quadrotor's internal control layer, followed by the application of the feedback linearisation method to the external control layer. An estimator is also designed to mitigate the effects of disturbances and uncertainties. A comparison is made between the proposed combined backstepping and feedback linearisation algorithm and the backstepping method, revealing that the combined backstepping and feedback linearisation algorithm outperforms the backstepping method across different aspects. Notably, the combined backstepping and feedback linearisation algorithm achieves faster trajectory tracking and demonstrates fewer steady-state errors. Additionally, the integration of the uncertainty estimator into the combined backstepping and feedback linearisation algorithm effectively mitigates the detrimental effects of disturbances and uncertainties. Comparative results for tracking control are presented to evaluate the performance of the proposed algorithm across various scenarios and case studies.

Active Control of Quasi-Zero-Stiffness Vibration Isolator with Variable Load

Quasi-zero-stiffness (QZS) isolator has great application potential in the field of low-frequency vibration isolation due to its high-static and low-dynamic (HSLD) nonlinear stiffness characteristic, but it is precisely this characteristic that makes it very sensitive to load changes. Once the load changes, causing it to deviate from the equilibrium position, it no longer qualifies zero-stiffness characteristic, and the vibration isolation capacity will be significantly decrease. To make the QZS isolator possess variable load capacity and be more suitable for engineering practice, an active QZS vibration isolator based on electromagnetic actuator is designed in this paper, which eliminates the influence of load changes through the active force of the electromagnetic actuator. First, the dynamic equation of the isolator is established by Newton–Euler method, and the dynamic characteristic of the isolator under standard load and load variations are analyzed through improved incremental harmonic balance (IHB) method based on discrete Fourier transform (DFT). Next, the improved particle swarm optimization (PSO) algorithm are employed to optimize the Proportion Integration Differentiation (PID) controller parameters. Then, the vibration isolation performance of QZS isolator in controlled and uncontrolled and linear systems in the same control state are compared in frequency domain and time domain, respectively. Finally, the performance of active QZS isolator under load variation is discussed. The results indicate that the isolation performance of the QZS isolator under active control is significantly better than in uncontrolled conditions and the controlled linear system. When the load changes, real-time compensation through the actuator output control force can also enable the QZS isolator to achieve a better vibration isolation performance.

Path‐Tracking Control of Tilting Quadrotor UAV Based on Variable Structure Sliding Mode Control Method

Tilting quadcopter unmanned aerial vehicles have the ability to perform vertical takeoff and landing, hover in the air, and cruise at high speeds, They can complete various flight tasks. Due to the special flight mode of tilting quadcopter unmanned aerial vehicles, in transition mode, as the tilt angle changes, the control process of the drone becomes more complex, and the difficulty of control also increases significantly. This article takes the tilting quadcopter drone as the research object and analyzes its overall layout and flight principles in various flight modes. Analyze using the Newton–Euler method and dynamically model three flight modes. The flight process is controlled using inner and outer loop control methods, and a sliding mode manifold control law for a tilting quadcopter unmanned aerial vehicle is designed using the hyperbolic tangent‐sliding mode control method. Finally, MATLAB/Simulink was used to simulate the path‐tracking process of the tilting quadcopter unmanned aerial vehicles, proving the stability of the controller.

Direct positional kinematics problem of the RRRRT manipulator in the maple software environment

This article presents the direct positional problem of the RRRRT manipulator created by the authors of the 3D model and its movement using the Maple software environment. In this paper, the positional kinematics problem of this manipulator is studied in detail. To find the kinematic characteristics of the manipulator, the Denavit-Hartenberg and Newton-Euler methods were rationally used. The results were obtained in the Maple software environment, which allows you to obtain the results of kinematic characteristics in the form of 3D graphs. Such graphs allow you to visually see how the modules and directions of the given parameters of the manipulator in the graphs change in space, depending on the position of the manipulator in space.

Trajectory tracking control of two-joint underwater manipulator in ocean-wave environment

In this study, a dynamic model of a two-joint manipulator used in underwater robots considering the influence of ocean waves was derived based on the Lagrange principle and Newton–Euler method. The Morison equation was employed to calculate the inertial force and water resistance of ocean waves acting on the manipulator. The ocean force terms in the new model vary with time, which makes trajectory tracking control more complicated than in models used in land and still-water environments. The ideal trajectory of the manipulator was tracked using proportional-derivative (PD) control and sliding mode control (SMC). The PD control proved weak in trajectory tracking, whereas the sliding mode control could quickly and accurately track the ideal trajectory. Three reaching laws were compared, and variable exponential reaching law 2 was the most suitable for trajectory tracking. To test the sliding mode control ability, an experiment was conducted in an ocean-wave environment with varying ocean wave heights, wave frequencies, and water depths. In addition, variations in input torque were observed. It was also found that the input torque required in an ocean-wave environment was higher than that required in land and still-water environments.

Dynamic Modeling and Performance Analysis of a Hip Rehabilitation Robot.

The dynamic performance of a 2-DOF hip joint rehabilitation robot configuration for patients with hip joint dyskinesia was analyzed. There were eight revolute pairs on one side of the hip joint rehabilitation robot configuration. The dynamics of the robot configuration were analyzed with the Newton-Euler method, and a dynamic model was developed. On the basis of the solved dynamic model, the dynamic performance index of the hip joint rehabilitation robot configuration is given, and the performance atlas under different parameters is drawn. The performance of the hip joint rehabilitation robot is theoretically verified. This study provides a theoretical basis for the research and development of exoskeleton rehabilitation robots.

Modelling and analysis for the dynamic behavior of 6-DOF motion platform used for simulating aerospace mechanical environment

As high carrying capacity, high frequency response and high precision control performance are presented, the 6 degree of freedom (DOF) motion platform is chosen as the aerospace device to implement mechanical environment simulation experiment on the ground. In this paper, a dynamic model of the 6 DOF motion platform is firstly developed based on the Newton-Euler method. Then the attitude determination and the driving force are analyzed by solving the dynamic equations. Furthermore, a parametric modelling method for the 6 DOF motion platform is proposed and applied to obtain the expansion amounts and the driving forces of the 6 hydraulic rods in the motion platform by adopting the Adams software. Results show a good agreement with the computation results of the theory dynamic model, which demonstratesthe validity of the proposed modelling method for analysis of the dynamic behavior of the 6-DOF motion platform.

Modeling and Disturbance Analysis of Spinning Satellites with Inflatable Protective Structures

The escalating proliferation of space debris poses an increasing risk to spinning satellites, elevating the probability of hazardous collisions that can result in severe damage or total loss of functionality. To address this concern, a pioneering inflatable protective structure is employed to ensure the optimal functionality of spinning satellites. Additionally, a multi-body dynamic modeling method based on spring hinge unfolding/spring expansion is proposed to tackle the complex dynamics of spinning satellites with inflatable protective structures during flight. This method enables analysis of the motion parameters of spinning satellites. First, the structural composition of a spinning satellite with inflatable protective structures is introduced and its flight process is analyzed. Then, an articulated spring hinge unfolding model or a spring expansion model using the Newton–Euler method is established to describe the unfolding or expansion of the spinning satellite with inflatable protective structures during flight. Finally, the effects on the motion parameters of a spinning satellite are analyzed through simulation under various working conditions.

Coordinated Control of Quadrotor Suspension Systems Based on Consistency Theory

This paper designs a cooperative control method for the multi-quadrotor suspension system based on consistency theory and realizes the cooperative formation trajectory tracking control of the multi-quadrotor suspension system by designing a consistent formation cooperative algorithm of virtual piloting and a nonlinear controller. First, a new quadrotor suspension system model is established based on the traditional quadrotor model using the Newton–Euler method. This model can accurately reflect the influence of the load on the quadrotor while obtaining the swing of the load. Then, the vertical and horizontal positions are designed separately based on the quadrotor motion characteristics, and the formation algorithm based on the virtual pilot consistency theory ensures that the final convergence of each position is consistent. An integral backstepping controller and an integral backstepping sliding mode controller are designed for quadrotor position, attitude, and load swing control to achieve accurate and fast quadrotor trajectory tracking control while reducing load swing. The stability of all the controllers is demonstrated using Lyapunov functions. Finally, a multi-quadrotor suspension system formation cooperative simulation experiment is designed to verify the designed control method.

Motion Performance Study of 2UPR-1RPS/2R Hybrid Robot Based on Kinematics, Dynamics, and Stiffness Modeling

Abstract The unique structural characteristics of hybrid robots, such as few degrees-of-freedom (DOF) and redundant constraints, lead to a series of challenges in the establishment of theoretical models. However, these theoretical models are indispensable parts of motion control. Therefore, this paper focuses on establishing the kinematics, dynamics, and stiffness models for an Exechon-like hybrid robot, which are then used for error compensation and velocity planning to improve the robot’s motion performance. First, the kinematic model is derived through intermediate parameters and the kinematics equivalent chains. By analyzing the parasitic motion due to few DOF, the redundant equations in the model are eliminated to obtain the solution of inverse kinematics. Second, based on the beam element, the optimal equivalent configuration of the moving platform which connects the parallel part and serial part is determined, and then an entire equivalent structure of the robot is formed. It helps establish the stiffness model by using the matrix structure analysis method. Next, the dynamic model is established by combining the Newton–Euler method with co-deformation theory to solve the underdetermined dynamic equations caused by redundant constraints. Finally, the compensation method is designed based on the stiffness model and kinematic model to improve the end positioning accuracy of the robot; the velocity planning algorithm is designed based on the dynamic model and kinematic model to enhance the smoothness of the robot motion. The methods proposed in this paper are also of referential significance to other Exechon-like hybrid robots.

Automatic vibration control method for grasping end of flexible joint robot

Because flexible robots have flexible components such as reducers, there are problems of accuracy deviation and end vibration in the process of external interference and trajectory tracking. This leads to the proposal of a Sliding Mode Control Approach Based on RBF Neural Network (SMC-RBF) parameter optimization. This method is mainly applied to reduce the end vibration and running position error of flexible robot. Firstly, the Newton-Euler method is used to establish the dynamic model of robot considering joint flexibility. At the same time, the experiment optimizes the Sliding Mode Control (SMC) method through RBF neural network. The experiments verify the control methods of the two-joint flexible robot and the six-joint flexible robot respectively. In the control of two-joint robot, the maximum tracking curve error of SMC is only about 0.25 rad under the interference of pulse signal; And the recovery time is only about 1 s. In the control of 6-joint robot, the maximum error of RBF-sliding mode control method on XYZ axis is 0.7 mm, 0.25 mm and 1.25 mm respectively; The error on three axes is smaller than that of traditional PD control method. The results demonstrate that the tracking error of the improved mode control is small, the chattering phenomenon of the robot system is weakened as well.

Gait planning and optimization of an 18 DOF quadruped robot with compliant shanks

Legged robots made of rigid links have disadvantages like poor energy efficiency and large impact forces during foot/terrain contact while walking on 3D uneven terrain. This paper proposes a unique design of an 18 DOF quadruped robot with compliant shanks. Compliance has been added to the quadruped by introducing a “c-section“ in the shank of each leg. The robot dynamics has been modeled using the projected Newton-Euler method, while the “Craig-Bampton Method” has been utilized to model the compliant shanks. Optimal body trajectory and foot placements while maintaining dynamic stability is obtained using an NLP based optimization strategy. A torque-based inverse dynamics control technique ensures that the quadruped follows the desired trajectory. The robot was simulated using Simscape Multibody, which utilizes the robot model’s “.stl,”“.step,” and “.xml” files to follow the optimized joint trajectories. The total energy consumed and joint torques are compared between the complaint and rigid link quadruped robots for walk on different types of terrain with different gaits and C-sections of 3, 4, 6, and 8 mm thickness. The simulation results show a significant reduction in joint torque spikes (more than 70% for all cases) due to the addition of compliance in each leg. This also leads to a reduction in total energy consumption during the walk especially over an uneven terrain. Hence, the results verify that the proposed design of quadruped is functionally more efficient than its rigid counterpart for walking on uneven terrain.

Screw Dynamics of a Multibody System by a Schoenflies Manipulator

This paper presents a screw dynamics method for multi-rigid-body systems. It establishes the relationship between velocity screw (twist) and force screw (wrench) in the theorem of momentum screw. Then, the structure of a 2UPS + 2UPU parallel manipulator is introduced as an example of application. By analyzing the constraint wrench of each limb and the twist of the moving platform in the theorem of momentum screw, the dynamics equation for solving the driving force makes the method very convenient for computer programming. The dynamics equation can be reorganized into a non-homogeneous linear equation and establishes the relationship between the constraint wrench of each limb and the twist of the moving platform in screw coordinate. The outstanding advantage of the algorithm proposed in this paper is that the average calculation time is only 83.21% of that of the Newton–Euler method for the 2UPS + 2UPU parallel manipulator on the same computer. This methodology provides a convenient canonical form for the dynamics analysis of multi-rigid-body systems.

Design and Experimental Study on the Torque Balancing Mechanism of a Satellite-Borne Two-Axis Rotary Table

With the rapid development of science and technology, high-resolution remote sensing cameras are now widely used in various fields. At the beginning of camera attitude adjustment, residual torque due to state changes can affect platform stability and lead to the degradation of imaging quality. This paper analyzes the effect of external disturbances on the attitude of the satellite platform according to the Newton–Euler method. In order to effectively realize the self-balancing of the torque of the remote sensing camera rotary table and eliminate the influence of the residual torque on the stability of the satellite platform, this study designs a torque balancing mechanism for the two-axis rotary table of a remote sensing camera based on the first-generation balancing mechanism. Firstly, this paper provides a detailed analysis of the mechanism equilibrium principle from the theoretical point of view based on the theories related to momentum moment theorem and momentum moment conservation law. Then, the dynamics model of the torque balancing mechanism is built, and the dynamics simulation analysis is carried out in this paper. The analysis results show that compared with the first-generation torque balancing mechanism, the residual torque of the second-generation torque balancing mechanism is reduced by 66.67%, the peak value of the residual torque is reduced by 57.55%, the mass of the balancing flywheel is reduced by 74.14%, and the torque balancing time is reduced by 42.86%. Finally, two torque balancing mechanism prototypes were fabricated at equal scale for test verification in this paper. The test results show that compared with the first-generation torque balancing mechanism, the residual torque of the second-generation test prototype is reduced by 40%, the peak of the residual torque is reduced by 25%, the mass of the balancing flywheel is reduced by 60.34%, and the torque balancing time is reduced by 51.06%. There are some differences between the simulation analysis and the experimental results, but the overall trend is consistent with the theory. Through theoretical derivation, simulation analysis and experimental verification, the correctness and feasibility of the proposed second-generation torque balancing mechanism are fully confirmed, which has certain reference significance and engineering application value for the torque self-balancing scheme of rotary tables.

Dynamic Analysis and Control of Redundant Manipulator for Agricultural Applications in a Virtual Environment

In the development of automated manipulators for fruit and vegetable picking technologies, the challenge of ensuring an efficient, stable, and loss-free picking process has been a complex problem. In such an environment, manipulators require the most efficient and robust control for effective operations. In this paper, a serial 9-DOF redundant manipulator (1P8R) is proposed with various controllers for trajectory tracking problems in agricultural applications. The dynamic analysis of redundant manipulator has been carried out using the Recursive Newton-Euler method. The joint configurations of the robot are determined using optimization techniques for specific Task Space Locations (TSLs) by avoiding obstacles. The process of generating joint trajectories has been implemented by considering the cubic polynomial function. For the task of controlling the robot trajectory tracking in the virtual agricultural environment, different combinations of Proportional (P), Integrative (I), Derivative (D), and Feed-Forward (FF) controllers are employed, and a comparative analysis has been performed among these controllers. To verify the performance of the manipulator, simulations are carried out in a virtual environment using Simulink software. Results show that the robot is able to reach specific TSL accurately with better control and it is found that the implementation of Feed-Forward and PID-CTC controllers has better performance in a complex environment.

Dynamic parameter identification and adaptive control with trajectory scaling for robot-environment interaction.

To improve the force/position control performance of robots in contact with the environment, this paper proposes a control scheme comprising dynamic parameter identification, trajectory scaling, and computed-torque control based on adaptive parameter estimation. Based on the Newton-Euler method, the dynamic equation and its regression matrix is obtained, which is helpful to reduce the order of the model. Subsequently, the least-square method is implemented to calculate the values of the basic parameters of the dynamics. The identified dynamic parameters are used as initial values in the adaptive parameter estimation to obtain the torque, and trajectory scaling is applied to control the contact force between the robot and the environment. Finally, the dynamic parameter identification method and control algorithm are verified by conducting a simulation. The results show that the comprehensive application can help improve the control performance of robots.

Simulation of aircraft multi-axis acceleration in a four-axis Human Centrifuge System

High G-accelerations produced during Aircraft Combat Manoeuvres (ACMs) can adversely affect the physiological and psychological conditions of aircrew and deteriorate their performance. Human Centrifuge Systems (HCSs) provide an effective G-acceleration training tool to prepare and increase the G-tolerance of aircrew. Though highly capable HCSs are available, they are yet to be fully optimised to accurately and reliably recreate the G-vectors produced by ACMs. Optimisation steps to achieve this improvement involve the configurational structure, motion capability, and motion control of HCSs. To improve the motion capability and control of HCSs, the relationship between aircraft G-vectors and HCS G-vectors should be profoundly investigated. This work analyses the G-vectors of common ACMs and the corresponding G-vectors as well as kinematics of an active four Degree-of-Freedom (DoF) HCS. The mathematical models of an aircraft and HCS kinematics are developed using rigid body equations of motion through Newton-Euler method. The relationship between aircraft G-vectors and HCS G-vectors is established using inverse kinematics with an optimal solver. The outcomes of this study show that an active four-DoF HCS with gondola roll, pitch, and yaw rotation can replicate the G-vectors of common ACMs with small discrepancies. The largest error between the reference and achieved G-vectors occurred along the local z-axis of the HCS gondola during the transition of roll, pitch, and yaw motions of the gondola to the required angle replicating the G-vectors of the ACMs. The tracing errors are not significant; hence they can be mitigated with an optimal control technique. The presented outcomes will provide an essential step in identifying the optimal design and refined requirements for an HCS to efficiently replicate aircraft G-vectors. The applied methodology is easily adaptable to HCS with different structures and DoFs.

Internal layout optimization of the blended-wing-body underwater glider based on a range target

The blended-wing-body underwater glider (BWBUG) has a high gliding efficiency because of its hydrodynamic shape and high lift-to-drag ratio. Because of the complex body shape of the BWBUG, designing the layout of the internal regulating devices is difficult, which can affect the motion performance. In this study, a dynamic model of the BWBUG was established using the Newton–Euler method. A mathematical model of the spatial constraints of the internal regulating devices was established based on the optimised shape obtained from the authors’ previous research. The stability determination condition equation of the BWBUG is established based on the BWBUG dynamic model and vertical surface evaluation model. An energy consumption model is established based on the BWBUG dynamic analysis and gliding performance evaluation index. The optimisation framework of the BWBUG internal regulating device layout is established with the total range as the target, based on the penalty function and genetic algorithm. Finally, an optimised design of the internal regulating devices is developed using a small BWBUG as an example, and the relationship between each variable and the total range is analysed. The optimisation results show that the maximum gliding range after optimization is 2084.3 km, which is 30.4% higher than the initial range, and the energy-carrying capacity is 23.0% higher than before.

Design and Analysis of a Bionic Gliding Robotic Dolphin

In this paper, we focus on the design and analysis of a bionic gliding robotic dolphin. Inspired by natural dolphins, a novel bionic gliding robotic dolphin is developed. Different from the existing ones, the gliding robotic dolphin developed in this work is specially introduced with a yaw joint to connect its three oscillating joints to improve maneuverability in both dolphin-like swimming and gliding motion. Consequently, the gliding robotic dolphin can realize several flexible motion patterns under the coordination of its flippers, yaw joint, oscillating joints, and buoyancy-driven modular. Thereafter, relying on the Newton-Euler method, a hybrid-driven dynamic model is constructed to further analyze the propulsive performance in both dolphin-like swimming and gliding motions. Finally, various simulations and experiments, including forward swimming, gliding, and turning in both dolphin-like swimming and gliding modes, are carried out to validate the effectiveness of the developed gliding robotic dolphin.

A Comparative Study for Control of Quadrotor UAVs

Modeling and controlling highly nonlinear, multivariable, unstable, coupled and underactuated systems are challenging problems to which a unique solution does not exist. Modeling and control of Unmanned Aerial Vehicles (UAVs) with four rotors fall into that category of problems. In this paper, a nonlinear quadrotor UAV dynamical model is developed with the Newton–Euler method, and a control architecture is proposed for 3D trajectory tracking. The controller design is decoupled into two parts: an inner loop for attitude stabilization and an outer loop for trajectory tracking. A few attitude stabilization methods are discussed, implemented and compared, considering the following control approaches: Proportional–Integral–Derivative (PID), Linear–Quadratic Regulator (LQR), Model Predictive Control (MPC), Feedback Linearization (FL) and Sliding Mode Control (SMC). This paper is intended to serve as a guideline work for selecting quadcopters’ control strategies, both in terms of quantitative and qualitative considerations. PID and LQR controllers are designed, exploiting the model linearized about the hovering condition, while MPC, FL and SMC directly exploit the nonlinear model, with minor simplifications. The fast dynamics ensured by the SMC-based controller together with its robustness and the limited estimated command effort of the controller make it the most promising controller for quadrotor attitude stabilization. The outer loop consists of three independent PID controllers: one for altitude control and the other two, together with a dynamics’ inversion, are entitled to the computation of the reference attitude for the inner loop. The capability of the controlled closed-loop system of executing complex trajectories is demonstrated by means of simulations in MATLAB/Simulink®.