Newton-Euler Equations Research Articles

Kinematic and dynamic characteristics' analysis of a scissor multi-rod ring deployable mechanism

Abstract. In this paper, the authors developed a double-layer ring truss deployable antenna mechanism (RTDAM) based on a scissor unit, which can be used as the deployment and support mechanism in large-aperture satellite antenna. Firstly, three configuration state diagrams of the scissor multi-rod RTDAM were displayed: folded, half-deployed, and deployed. The mechanism was decomposed into a closed-ring deployable mechanism unit and several non-closed-ring deployable mechanism units. The screw constraint topological diagram of the closed-ring deployable mechanism unit was drawn, and the number of degrees of freedom (DOFs) was calculated via the screw theory method. Then, the expressions for screw velocity and screw acceleration of each component in the resultant mechanism were analyzed, calculated, and solved. The screw velocity and screw acceleration of each component were obtained, and the six-dimensional velocity and acceleration of each component were obtained through screw conversion and recursion. Finally, using the Newton–Euler equation and virtual work principle, the dynamic equation of the RTDAM with an integral scissor multi-rod ring truss mechanism was established, and the theoretical analysis was validated through numerical calculation and simulation results. The RTDAM of the scissor multi-rod ring truss proposed in this paper has a single DOF and can be well applied to the large-aperture satellite antenna.

Dynamics of a 3-UPS-UPU-S Parallel Mechanism

In this paper, a parallel mechanism with two rotational degrees of freedom is proposed. It could rotate freely and continuously around the two coordinate axes at the fixed origin of the coordinate frame. The structure of the mechanism is a second-order over constraint parallel structure and the moving platform and base platform are connected by five kinematic chains. The motion characteristics of this structure are analyzed by reciprocal screw equation. Then, the kinematics and dynamics modelling are carried out systematically in a unified way. The kinematics of the mechanism is established by means of screws, the displacements and accelerations of each joint and any point on a link could be calculated by the kinematic screw equation directly. The analysis of acceleration and its mathematical expression in screw form are given, and the acceleration matrix could be applied into the dynamic analysis based on the Newton–Euler equation. All the constraint forces and torques could be obtained by a single set of Newton–Euler equations.

Modeling and Control of Quadcopter Based on Sliding Mode Robust Control in the Wind Field

Due to the low flying height, quadrotors are easily affected by external wind disturbances. In this paper, the dynamic model of the quadrotor flying in the wind field is established according to the Newton-Euler equation. The model introduces a weight function due to the phenomenon that different rotors are affected differently by the wind field due to their different positions relative to the wind field, and a sliding mode robust controller based on inner and outer loops is designed. The verification of the control system is carried out by means of simulation in a Gazebo and actual flight experiments in the wind field. The dynamic of the system and the controller performance under the wind field are also tested. The results show that the designed controller has the performance of stable flight in the wind field environment.

Robust inverse dynamics by evaluating Newton–Euler equations with respect to a moving reference and measuring angular acceleration

Maintaining stability while walking on arbitrary surfaces or dealing with external perturbations is of great interest in humanoid robotics research. Increasing the system’s autonomous robustness to a variety of postural threats during locomotion is the key despite the need to evaluate noisy sensor signals. The equations of motion are the foundation of all published approaches. In contrast, we propose a more adequate evaluation of the equations of motion with respect to an arbitrary moving reference point in a non-inertial reference frame. Conceptual advantages are, e.g., getting independent of global position and velocity vectors estimated by sensor fusions or calculating the imaginary zero-moment point walking on different inclined ground surfaces. Further, we improve the calculation results by reducing noise-amplifying methods in our algorithm and using specific characteristics of physical robots. We use simulation results to compare our algorithm with established approaches and test it with experimental robot data.

Non-Linear Model Predictive Control Using CasADi Package for Trajectory Tracking of Quadrotor

In this paper, we present the development of a non-linear model predictive controller for the trajectory tracking of a quadrotor using the CasADi optimization framework. The non-linear dynamic model of the quadrotor was derived using Newton–Euler equations, and the control algorithm and drone dynamics were wrapped in Matlab. The proposed controller was tested by simulating the tracking of a 3D helical reference trajectory, and its efficiency was evaluated in terms of numerical performance and tracking accuracy. The results showed that the proposed controller leads to faster computational times, approximately 20 times faster than the Matlab toolbox (nlmpc), and provides better tracking accuracy than both the Matlab toolbox and classical PID controller. The robustness of the proposed control algorithm was also tested and verified under model uncertainties and external disturbances, demonstrating its ability to effectively eliminate tracking errors.

Intelligent PIV Fuzzy Navigation and Attitude Controller for an Octorotor Mini-UAV

In this research, a proportional plus integral plus velocity (PIV) fuzzy gain scheduling flight controller for an octorotor mini-unmanned aerial vehicle is developed. The designed flight controller scheme, with a PIV term, is combined with a fuzzy gain scheduling approach. The tracking controller PIV fuzzy gain scheduling is based on two controllers connected in cascade with a saturation approach. The Newton–Euler equations of motion are applied to obtain a mathematical model for the octorotor mini-unmanned aerial vehicle (mini-UAV). The flight controller approach is applied to obtain coupling moments and forces with interconnected attitude and navigation tracking trajectory. In the design of a flight navigation controller with two layers, the inner layer consists of a PIV fuzzy gain scheduling controller that is applied to the attitude dynamics, obtaining the references for the coupling outer layer PIV fuzzy gain scheduling controller, which manipulates the translational dynamics. The navigation PIV fuzzy gain scheduling controller is saturated for bounding in translational forces to avoid large deviations of commands to Euler angles pitch and roll, and another saturated controller is implemented for the bounded thrust rotor to avoid the excessive angular speed of these rotors. The octorotor mini-UAV flight navigation simulation is performed to validate the tracking control of a sequence of motions in each axis, which is presented as a validation for the proposed control scheme.

Dynamic modeling and vibration analysis of cracked rotor-bearing system based on rigid body element method

Rotor crack occurs frequently in rotating machinery. It is of great significance to study the vibration mechanisms of the cracked rotor-bearing system, which can provide proofs for crack online monitoring. In this paper, a new dynamic model of the cracked rotor-bearing system is developed using the rigid body element (RBE) method, and vibration response analysis is then carried out. The rotor is discretized as a set of RBEs, and each two adjacent RBEs is connected by an elastic joint (EJ). Each EJ is modeled with six imaginary springs (three translational springs and three rotational springs). The breathing crack is modeled through time-varying stiffnesses of imaginary springs, which are obtained using real-time parameters (area, cross-section moment of inertia, and polar moment of inertia) in four processes (crack fully closed, crack partially opened, crack fully opened, and crack partially closed) in a full rotation angle. The interactions of adjacent RBEs are then given based on the force and moment analysis, and the bearing forces are obtained based on two models (i.e., equivalent spring-damper model, and Gupta bearing model). The equations of motions of the cracked rotor-bearing system are developed through Newton-Euler equations and solved by the fourth-order Runge-Kutta-Fehlberg method with a step-changing criterion. The displacement responses are then obtained, and the frequency spectrums of displacement responses and their instantaneous frequencies (IFs) under different rotation speeds are analyzed. Simulation results of the cracked rotor-bearing system are in good agreement with previously published results and experiment results. What’s more, analysis results show that the frequency spectrum of IF can be an indicator for online monitoring of the rotor crack.

Design and experiment of a large-scale space micro-vibration simulator

To solve the problems of difficult vibration sources simulation in the ground test of the on-orbit optical load, a multi-dimensional micro-vibration simulator based on the improved Gough–Stewart platform was designed, which can effectively reproduce the characteristics of wide frequency distribution and small vibration magnitude of space micro-vibration. The analytical formula was derived by using the virtual frequent principle and the Newton–Euler equation for the natural frequency of the system, and the simulator’s configuration was optimized. The structure of legs was designed and optimized according to the optimal configuration parameters. Finally, the micro-vibration simulator was tested, and the test results showed that the output bandwidth of the simulator was 5–300 Hz and the maximum magnitude error was 8%, thus demonstrating the multi-dimensional micro-vibration simulation platform has the characteristics of large frequent bandwidth, high load carrying capacity, and small vibration magnitude.

Transient modes of high-speed rotor whit electric drive

The paper presents the results of the study of the transient modes of a high-speed rotor with formally six degree of freedom, driven by an electric motor-generator during transition trough the resonance. Based on the Newton-Euler equation, the differential equations of motion are derived, and the frequency spectrum of the considered electro-mechanical system is determined. The following cases are considered: - transition trough resonance with unlimited (ideal energy source) and limited excitation by the motor; unstable frequency zones; phase trajectories and the influence of the electro-magnetic constant of the motor on the stability. The analysis of the stationary and nonstationary processes was carried out using the asymptotic method of Bogoliybov-Mitropolski. The stability of vibrations are determined by numerical solution of the equations in variations of the equilibrium states. These transitions are of great importance for the recently widespread so-called uninterruptible power sources (UP), as well as the kinetic energy recovery system (KERS ) used as additional propulsion energy .

Fuzzy Neural Network Dynamic Inverse Control Strategy for Quadrotor UAV Based on Atmospheric Turbulence

Quadrotor UAV is vulnerable to external interference, which affects search and rescue. In this paper, a fuzzy neural network dynamic inverse controller (FNN-DIC) is designed to eliminate the instability of the attitude angle caused by atmospheric turbulence. Considering the complexity of atmospheric turbulence, the component model of atmospheric turbulence is obtained firstly based on the Dryden model, using Gaussian white noise as a random input signal and a designed shaping filter. Combined with the Newton-Euler equation, a nonlinear dynamic model for the quadrotor UAV with atmospheric disturbance is established. While the traditional nonlinear dynamic inverse cancels the nonlinearity of the controlled object, it relies on precise mathematical models. The fuzzy neural network can adaptively compensate for the inaccurate part of the model and the inverse error of the model caused by the external disturbance, and the stability of the control system is strictly proved by using the Lyapunov function. The experiments are carried out on the simulation platform, and the results show that the FNN method can ensure that the quadrotor UAV can still fly smoothly against strong disturbances, and that robustness of the system is significantly improved.

Benchmarking Tracking Autopilots for Quadrotor Aerial Robotic System Using Heuristic Nonlinear Controllers

This paper investigates and benchmarks quadrotor navigation and hold autopilots’ global control performance using heuristic optimization algorithms. The compared methods offer advantages in terms of computational effectiveness and efficiency to tune the optimum controller gains for highly nonlinear systems. A nonlinear dynamical model of the quadrotor using the Newton–Euler equations is modeled and validated. Using a modified particle swarm optimization (MPSO) and genetic algorithm (GA) from the heuristic paradigm, an offline optimization problem is formulated and solved for three different controllers: a proportional–derivative (PD) controller, a nonlinear sliding-mode controller (SMC), and a nonlinear backstepping controller (BSC). It is evident through the simulation case studies that the utilization of heuristic optimization techniques for nonlinear controllers considerably enhances the quadrotor system response. The performance of the conventional PD controller, SMC, and BSC is compared with heuristic approaches in terms of stability and influence of internal and external disturbance, and system response using the MATLAB/SIMULINK environment. The simulation results confirm the reliability of the proposed tuned GA and MPSO controllers. The PD controller gives the best performance when the quadrotor system operates at the equilibrium point, while SMC and BSC approaches give the best performance when the system does an aggressive maneuver outside the hovering condition. The overall final results show that the GA-tuned controllers can serve as a benchmark for comparing the global performance of aerial robotic control loops.

Design and Analysis of a Space Dynamic Test Platform

This paper describes a kind of laboratory simulation test platform. The dynamic coupling model of the simulation test platform has been obtained by using the Newton-Euler equation. According to the inverse-system, the equation can be decoupled, and the decoupling analysis and calculation of the system are performed through the decoupling theorem. As a result, the coupled nonlinear Multiple-Input Multiple-Output system is converted to two linear decoupled Single-Input Single-Output subsystems. The establishment of the mathematical model can provide reference for the design of the controller in the simulation test platform. In order to verify the error of the rotation accuracy of the simulated test platform developed, a reasonable experimental scheme was developed for testing.

Design of Combined Neural Network and Fuzzy Logic Controller for Marine Rescue Drone Trajectory-Tracking

In recent years, the research on drones has increased rapidly because of its high applicability in many fields and its great development potential. In the maritime sector too, especially marine rescue, a Drone with a compact size and fast flight speed is an effective solution in search and surveillance, giving quick results and being very convenient. When operating at sea, marine rescue drones are often affected by the environment, especially wind, which leads to turbulence that causes the drone to deviate from its predetermined flight trajectory. To overcome the above problem, the author has proposed the application of a Neural-Fuzzy controller for unmanned marine rescue aircraft presented in this paper introduces a controller that combines neural networks and fuzzy controllers that enhance the efficiency of the drone’s trajectory tracking. The paper presents the mathematics of a quadcopter described by the Newton-Euler equations. Presentation on stable flight control and trajectory control of marine rescue drones. In this paper, Matlab/Simulink is used to describe the operation of the Drone, and the characteristics obtained after using the simulation are used to compare, test, and analyze the system. The obtained results show that the Neural-Fuzzy controller is much more sensitive, more resistant to turbulence, and can be used on different sizes, weights, and configurations of drones without adjusting PID gain.

Decentralized adaptive control applied to two links of a five degrees of freedom robot, using the polynomial technique

The objective of this work is to design and implement decentralized adaptive controllers in order to perform the position control of two links of an electromechanical manipulator robot with five degrees of freedom (DOF 5). The manipulator robot is consisted of five rotational joints, four links and a claw. Five DC motors are used to drive the robot and the motion transmission from the motors to the joints is achieved by gear trains. Models of the manipulators robots are obtained using Newton-Euler or Lagrange equations; and are coupled and nonlinear. In this work, the model of the links of the manipulator robot is obtained in real time for each sampling period. The parameters of the links to be controlled are identified by recursive least squares (RLS) method, according to data from the links, and are used in the designs of adaptive controllers for the positions control of the joints of the links under analysis. In the end, the experimental results are presented, like the evaluation of the performance achieved by the manipulator robot links.

DP-Climb: A Hybrid Adhesion Climbing Robot Design and Analysis for Internal Transition

This paper proposes a double propeller wall-climbing robot (DP-Climb) with a hybrid adhesion system based on the biomimetic design principle to address the problems of single adhesion-powered wall climbing robots (WCRs). Such problems include poor maneuverability and adaptability to orthogonal working surfaces with different roughness and flatness, weak flexibility of ground-wall transition motion, and easy stand stilling of transition,. Based on the clinging characteristics of different creatures, the hybrid system combines the rotor units’ reverse thrust, the drive wheels’ driving torque, and the adhesion force offered by the coating material to power the robot through a coupled control strategy. Based on the Newton–Euler equations, the robot’s kinematic characteristics during the ground-wall internal transition motion were analyzed, the safe adhesion conditions were obtained, and a dynamics model of the robot’s ground-wall transition was established. This provided the basis for the coupling control between different power units. Finally, an internal transition PID control strategy based on DP-Climb was proposed. Through mechanical and aerodynamic characteristic experiments, it is verified that the robot’s actual output pulling force can meet the transition motion demand. The experimental results show that the proposed strategy can enable the DP-Climb to complete the ground-wall mutual transition motion smoothly with a speed of 0.12 m/s. The robot’s maximum wall motion speed can reach 0.45 m/s, which verifies that the hybrid adhesion system can flexibly and quickly reach the specified position in a target area flexibly and quickly. The robustness and adaptability of WCR to complex application environments are improved.

An immersed boundary projection method for solving the fluid-rigid body interaction problems

We develop an immersed boundary projection method for solving the Naiver-Stokes equations and Newton-Euler equations to simulate the fluid-rigid body interactions in two and three dimensions. A novel fractional step algorithm is introduced for which fast solvers can be applied by exploiting the algebraic structure of the underlying schemes. The Navier-Stokes equations are decoupled while the Newton-Euler equations are solved simultaneously with a constraint equation of the immersed boundary force density. In contrast to previous works, the present method preserves both the fluid incompressibility and the kinematic constraint of the rigid body dynamics at a discrete level simultaneously while maintaining numerical stability. We demonstrate the numerical results of the present method involving spherical and spheroidal rigid bodies with a moderate range of density ratios, which are congruent with the results in the literature.

Vectorized Formulation of Newton-Euler Dynamics for Efficiently Computing Three-Dimensional Folding Chains

Abstract Within the wide field of self-assembly, the self-folding chain has unique potential for reliable and repeatable assembly of three-dimensional structures as demonstrated by protein biosynthesis. This potential could be translated to self-reconfiguring robots by utilizing magnetic forces between the chain components as a driving force for the folding process. Due to the constraints introduced by the joints between the chain components, simulation of the dynamics of longer chains is computationally intensive and challenging. This article presents a novel analytical approach to formulate the Newton–Euler dynamics of a self-reconfiguring chain in a single vectorized differential equation. The vectorized differential equation allows for a convenient implementation of a parallel processing architecture using single instruction multiple data (SIMD) or graphical processing unit (GPU) computation and as a result can improve simulation time of rigid body chains. Properties of existing interpretations of the Newton–Euler and Euler–Lagrange algorithms are discussed in their efficiency to compute the dynamics of rigid body chains. Finally, GPU and SIMD-supported simulation, based on the vectorized Newton–Euler equations described in this article, are compared, showing a significant improvement in computation time using GPU architecture for long chains with certain chain geometry.

СТАБИЛИЗАЦИЯ ДВИЖЕНИЯ КВАДРОКОПТЕРА ВДОЛЬ ЗАДАННОЙ ТРАЕКТОРИИ С ПОМОЩЬЮ СУБОПТИМАЛЬНОГО ЗАКОНА УПРАВЛЕНИЯ С -КРИТЕРИЕМ

The aim of the study is to construct a suboptimal controller with the -criterion that stabilizesthe deviation of the dynamic system from the given program trajectory. It is assumed that an impulsedisturbance will be applied to one input of the system, and an -disturbance to the second one.The -norm is equal to the maximum value of the -output norm for all - and impulse disturbancesvectors for which the sum of the quadratic form of the impulse disturbance vector with a givenweight matrix and the squared -norm of the second disturbance never greater than one. In this paper,it is required to demonstrate the process of calculating the -norm in terms of linear matrix inequalitiesfor a dynamical system and a system with uncertainty. An important role in the process ofcombining the -norm and the -norm in the -norm is played by the weight matrix includedin the definition of this norm. It should be noted that, unlike the -norm, the -norm is achievedin the sense of the worst - and impulse disturbances, where the maximum value of the -output normis reached. It is necessary to obtain and linearize the mathematical model of the quadcopter, build aprogrammed trajectory, and stabilize the deviations using a suboptimal control law with the -criterion in the presence of noise in the system. Linear matrix inequalities are used for suboptimal controlsearching. The object of this study is a quadcopter, which is an unmanned aerial vehicle with fourengines with propellers that create thrust. The axes of the propellers and the angles of the blades arefixed and only the speed of rotation is regulated, which greatly simplifies the design. Using the Newton-Euler equation, a nonlinear mathematical model of a quadcopter is obtained, and this model is linearized.In the MATLAB environment, using the applied package for modeling and optimization YALMIP,Sedumi toolbox, numerical modeling, and construction of quadcopter motion trajectories are performed.After that, in the Simulink environment, a control block that stabilizes the movement of thequadcopter along a given trajectory in the presence of - and impulse disturbances in the system isconstructed. At the end, a demonstration of the process of virtual visualization of the flight is made.

An Electromyography-Based Constitutive Law for Force Generation in Skeletal Muscle-Part II: Model Validation on the Ankle Joint Complex.

Part II of this study evaluates the predictive ability of the skeletal muscle force model derived in Part I within the ankle joint complex. The model is founded in dimensional analysis and uses electromyography and the muscle force-length, force-velocity, and force-frequency curves as inputs. Seventeen subjects (eight males, nine females) performed five different exercises geared toward activating the primary muscles crossing the ankle joint. Motion capture, force plate, and electromyography data were collected during these exercises for use in the analysis. A constant, Km, was calculated for each muscle of each subject using four of the five exercises. The fifth exercise was then used to validate the results by treating the moments due to muscle forces as known and all other components in Euler's second law as unknown. While muscle forces cannot be directly validated in vivo, methods can be developed to test these values with reasonable confidence. This study compared moments about the ankle joint due to the calculated muscle forces to the sum of the moments due to all other sources and the kinematic terms in the second Newton-Euler equation of rigid body motion. Average percent errors for each subject ranged from 4.2% to 15.5% with a total average percent error across all subjects of 8.2%, while maximum percent errors for each subject ranged from 33.3% to 78.0% with an overall average maximum of 52.4%. Future work will examine sensitivity analyses to identify any potential simplifications to the model and solution process, as well as validate the model on a more complex joint system to ensure it still performs at a satisfactory level.

Study on Effects of Road Conditions on the Lateral Instability of Tractor Semitrailer Vehicle during Turning Maneuver

Instability of vehicle can be defined as an unexpected response maneuver that induces disturbance, occurring in the ground plane. This can include the longitudinal, lateral, pitch, yaw, roll direction, or their combinations. Many tractor semitrailer vehicle accidents can be caused by lateral instabilities which may be classified into two types: rollover and yaw instability. Rollover occurs when centrifugal forces imposed on the vehicle during a maneuver exceed the rollover threshold of the vehicle. Yaw instability often occurs in tractor semitrailer vehicles during turning maneuver on the road with low friction coefficient. The yaw instability is shown by the loss of motion trajectory or Jack-knife. This paper establishes a dynamic model of tractor semitrailer vehicle, based on Multi-Body System Method analysis and Newton-Euler equations with Burckhardt’s tire model. This model is applied to evaluate the effect of road conditions on lateral instability of the tractor semitrailer vehicle during turning maneuver. The results can serve as the basis for determining the early warning and controlling the lateral instability of tractor semitrailer vehicle with the dynamic model.