Newton-Euler Approach Research Articles

An innovative fuzzy backstepping sliding mode controller for a Tri-Rotor Unmanned Aerial Vehicle

The dynamical model of a Tri-Rotor Unmanned Aerial Vehicle (UAV) is presented in this paper. The Tri-Rotor has three rotors with two fixed-pitch propellers and a tiltable propeller to control the yaw displacement. The model is obtained via the Newton–Euler approach and a nonlinear control strategy called fuzzy backstepping sliding mode control is proposed for the attitude stabilization and altitude tracking of the vehicle. The designed controller consists of a backstepping sliding mode controller and a fuzzy logic controller. For the problem of determining the backstepping sliding mode control coefficients, an optimization method of gradient descent algorithm has been used. However, the control precision of the backstepping sliding mode is intimately dependent on the precision of coefficients. Besides, the uncertain unmodeled coefficients as well as the characteristics of the complex electromechanical system could cause the coefficients not be invariable. Therefore, a fuzzy logic controller is proposed to compensate the coefficients uncertainty to improve the robustness. The effectiveness of the proposed control algorithm is demonstrated via certain simulation results based on the actual parameters of UAV, and its advantages are indicated in comparison with the backstepping sliding mode control without fuzzy logic control.

Embedded Super Twisting Control for the Attitude of a Quadrotor

This paper focuses on the embedded super twisting control for the orientation dynamics of a quadrotor. The Newton-Euler approach is applied to obtain the dynamic model of the quadrotor and a functional description of the experimental platform is described. In order to implement the control algorithm and perform real-time flights, a commercial flight computer is used. Experimental results are obtained in real-time during the autonomous flight.

Modeling and Adaptive Backstepping Control for Quadrotor Robots with Blade Flapping

Dynamics modeling and control for quadrotor aerial robots are considered in this paper. The threedimensional dynamics model of the quadrotor is first derived using the Newton-Euler approach. When the propelling rotor rotating with respect to the moving robot, the rotating blades could be deflected with an effect on the aerial vehicles known as flapping. The modeling with blade flapping is considered. Then a nonlinear stable adaptive control with flapping parameters estimation is proposed using the backstepping technique for the position and yaw angle trajectory tracking. Finally, computer simulation is used to validate the performance of the proposed control strategy. In the simulation study, the desired trajectory is constructed using the cubic spline interpolation.

Dynamic Modeling of a Six Degree-of-Freedom Flight Simulator Motion Base

This paper presents a closed-form solution for the direct dynamic model of a flight simulator motion base. The motion base consists of a six degree-of-freedom (6DOF) Stewart platform robotic manipulator driven by electromechanical actuators. The dynamic model is derived using the Newton–Euler method. Our derivation is closed to that of Dasgupta and Mruthyunjaya (1998, “Closed Form Dynamic Equations of the General Stewart Platform Through the Newton–Euler Approach,” Mech. Mach. Theory, 33(7), pp. 993–1012), however, we give some insights into the structure and properties of those equations, i.e., a kinematic model of the universal joint, inclusion of electromechanical actuator dynamics and the full dynamic equations in matrix form in terms of Euler angles and platform position vector. These expressions are interesting for control, simulation, and design of flight simulators motion bases. Development of a inverse dynamic control law by using coefficients matrices of dynamic equation and real aircraft trajectories are implemented and simulation results are also presented.

Simulation of 5DOF Model for Arial Grasping

This study presents dynamic modeling and simulation of an air vehicle consisting of a body, gripper and a claw. This model is inspired from birds’ aerial hunting, while considering the extra degree of freedom associated with the claw. For a manipulator like a gripper, additional degree of freedom creates more flexibility for grasping. The main contribution of this paper focuses on the development of a model that is suitable for trajectory optimization in grasping phase. Mathematical representation of the system is developed based on the Newton-Euler approach in MATLAB-Simulink environment, considering the motion in vertical plane. The dynamic behavior of the system is evaluated by simulation in variety situations and sensitivity analysis is carried out to determine and characterize the parameters having the most and least effects on grasping. It is shown that the initial position of the gripper and the claw as well as the additional mass that is added to the system in grasping phase make considerable changes in the dynamics that necessitates the use of the control system. In addition, smooth trajectories and controls are obtained by adding friction to the system in order to avoid dynamic divergence.

Multibody Modeling and Simulation of Monocopter Micro Air Vehicle

In the current paper, seven degrees of freedom multibody model of a monocopter air vehicle is developed based on the Newton-Euler approach along with nonlinear simulation in different flight phases. Aerodynamic forces and moments are modeled using blade element momentum theory. The sole control surface is modeled like a conventional flap on a wing. Free flight simulation is performed in MATLAB Simulink environment to evaluate the behavior of the system and to demonstrate the effectiveness and applicability of the proposed model. Simulation results show harmonic oscillations in Euler angles, linear and angular velocities that are consistent with the physics and mathematical foundations. Static stability of the vehicle is evident in free flight by careful choice of initial conditions. The presented multibody model is useful for comparative study and design purposes.

Development and Analysis of Linear Model Representations of the Quad-Rotor System

A Quad-rotor, which is an airplane with four rotors, is considered a complex and challenging control problem. Analysis and design of its control systems is usually started by careful consideration of its mathematical models description. This paper presents a detailed mathematical model for a Vertical Takeoff and Landing (VTOL) type Unmanned Aerial Vehicle (UAV) known as the quad rotor. The presented paper focus on the nonlinear modeling of an experimental type quad-rotor. The first objective of this paper aims to develop a nonlinear dynamical model based on Newton-Euler approach. Then, a linear model is obtained around an optimized hovering point. The state space, transfer function matrix and matrix fraction description models are derived. Finally, a linear controller is designed to achieve a stable compensated system around a hovering point. The methodology applied in this paper takes the ST-450 experimental quad-rotor as a case study.

Modeling and robust H-infinite control of a novel non-contact ultra-quiet Stewart spacecraft

This paper presents the modeling and robust H∞ control of a novel ultra-quiet spacecraft which employs the non-contact Stewart platform to actively control its support module (SM) and payload module (PM). The SM and PM are mechanically separated such that the disturbances and vibrations from the SM can be perfectly suppressed. However, this novel spacecraft has internal instability. To overcome the instability, this paper derives the dynamics model of the non-contact Stewart spacecraft using Newton–Euler approach at first. Then, the mixed sensitivity robust H∞ control is developed to guarantee both the attitude stability and precision pointing. Finally, simulation studies are provided to validate the effectiveness of the proposed approach.

Dynamic Modeling of a High-Dynamic Flight Simulator

High-dynamic flight simulator (HDFS), using a centrifuge as its motion base, is a machine utilized for simulating the acceleration environment associated with modern advanced tactical aircrafts. This paper models the HDFS as a robotic system with three rotational degrees of freedom. The forward and inverse dynamic formulations are carried out by the recursive Newton-Euler approach. The driving torques acting on the joints are determined on the basis of the inverse dynamic formulation. The formulation has been implemented in two numerical simulation examples, which are used for calculating the maximum torques of actuators and simulating the time-histories of kinematic and dynamic parameters of pure trapezoid Gz-load command profiles, respectively. The simulation results can be applied to the design of the control system. The dynamic modeling approach presented in this paper can also be generalized to some similar devices.

MATHEMATICAL MODELING AND EXPERIMENTAL STUDY ON SIT-TO-STAND PROCESS BASED ON ASSISTIVE STANDING-UP ROBOT

The new assistive standing-up robot followed the rule of sit-to-stand movement was developed. Mathematical model during standing-up motion was built by using Newton-Euler approach for kinetics analysis. Force and moment equilibrium equations were obtained and simulation model was built in Simulink by standing up with robot-aided, robot and arms supported and robot, arm and lower limbs of weakness of muscle strength. By means of assistive standing-up robot and sensors, force and moment were measured and analyzed. The results show that standing-up robot can be efficiently used to assist the rising, especially in initial stage, in spite of sit-to-stand aided-method. Arm-supported standing-up maneuver can keep the posture balance and stable, and has compensation ability of necessary force and moment of lower extremity, particularly close to upright standing posture,and force and moment can be predicted accurately by the standing posture simulation model. Lower limbs of deficient muscle strength play limited role to assist the rising.

Disturbance characteristics analysis of CMG due to imbalances and installation errors

The control moment gyroscope (CMG) is used as the actuator of attitude control for modern satellites. Because of static and dynamic rotor imbalances and installation errors, it becomes one of the main vibration sources on a satellite. To provide a quiet environment for optical payloads, CMG disturbance characteristics due to imbalances and installation errors are analyzed, and the application of the CMG on remote sensing satellites is discussed. In the first step, we construct the dynamic CMG model according to the Newton-Euler approach, taking the static and dynamic imbalances and installation errors of the rotor into consideration. This dynamic model is analyzed in detail, and the axial dynamic equation of the gimbal and that of the rotor are derived. The validity of this model is analyzed and tested by numerical simulation. A cluster of CMGs is adopted, and the integrated satellite dynamic model is derived. In the third part, we analyze the influences of disturbances caused by CMGs on attitude precision and stabilization of satellites. To meet the requirements of attitude precision and attitude stabilization for remote sensing satellites, the constraint conditions of the CMG performance indexes are obtained.

The imaging stability enhancement of optical payload using multiple vibration isolation platforms

To reduce high frequency vibration propagated into the optical payload on spacecraft, multiple vibration isolation platforms are employed. This means that the vibration isolation platform can not only be used to isolate the disturbances caused by the actuators such as control moment gyros or the reaction wheels (RWs), but it can also be placed between the spacecraft bus and optical payload. The dynamic modeling of the spacecraft with multiple vibration isolation platforms and its applications are discussed. Firstly, the spacecraft dynamic model with only one vibration isolation platform is derived using the Newton-Euler approach. Then the integrated spacecraft dynamic formulation is obtained based on the above dynamic model with only one vibration isolation platform. Multiple vibration isolation platforms are used to interface the disturbance source with the spacecraft bus. For example, each RW could have a vibration isolation platform to reduce the vibration. The frequency domain characteristics and the safety reliability of the spacecraft with multiple vibration isolation systems are discussed based on the above dynamic model. Finally, the validity of the dynamic model of the integrated spacecraft with multiple vibration isolation platforms can be proved by numerical simulation. Other than that, the simulation results illustrate the ameliorative effect of multiple vibration isolation platforms on the optical payload attitude stabilization.

The Vibration Modeling and Analysis of Stewart Platform-Based Machine Tool

In this paper, the vibration modeling and analysis of Stewart platform-based machine tool is presented. The vibration modeling includes the derivation of the vibration equation and the detailed processes to deal with that. Each of the kinematic chains is considered as a flexible chain and simplified into a spring-damper submodel. Vibration modeling of the machine tool is established by Newton-Euler approach. Then, the natural frequencies of the moving platform are obtained based on the vibration equation by the aid of MATLAB. The vibration characteristics of the machine tool are analyzed and discussed by means of the numerical examples considering the different poses of the moving platform. The conclusion can be drawn that the natural frequencies of the platform are influenced by the poses of the platform.

Design and Analysis of a Novel 5 Dimensional Active Vibration Isolator with Parallel Mechanism

A novel 5-DOF parallel mechanism applied to active vibration isolation is proposed in this paper. And by using Newton-Euler approach we set up models of the kinematics and dynamics of the isolator. Besides, a wide-range giant magnetostrictive actuator (GMA) composed of a GMA and a micro-displacement amplification mechanism is designed for the actuation of the isolator. Finally modal analysis of this isolator is carried out in ANSYS software to testify that the parallel mechanism is suitable for active vibration isolation.

Vision-based autonomous hovering for a miniature quad-rotor

SUMMARYIn this paper, a vision-based scheme for the autonomous hovering of a miniature quad-rotor is developed. Cameras are used to estimate the position and the translational velocity of the vehicle. The dynamic model of the miniature quad-rotor is developed using the Newton–Euler approach. A nonlinear controller based on a separated saturation control strategy for a miniature quad-rotor is presented. To validate the theoretical results, an embedded control system for the miniature quad-rotor has been developed. Thus, the analytic results are supported by experimental tests. Experimental results have validated the proposed control strategy.

Inverse Kinematics and Dynamics of a 3-DOF Spatial Parallel Manipulator

Recently the parallel manipulator with less DOFs has attracted industry and academia, but the research on its dynamics is still an open problem. In this paper, the inverse dynamic of a spatial parallel manipulator with two translational degrees of freedom and one rotational degree of freedom is studied based on the Newton-Euler approach. The kinematics analysis is firstly performed in a closed form. The inverse dynamic equation of this manipulator is formulated by using the Lagrange multiplier approach and choosing the Cartesian position and orientation as the generalized coordinates. Finally a numerical example is given for the kinematic and dynamic simulation of this manipulator. The model will be useful to improve the design of the mechanical components and the control algorithm.

Full model of a buoyancy-driven airship and its control in the vertical plane

A new concept of airship without thrust, elevator or rudder is considered in this paper. It is actuated by a moving mass and an internal air bladder with adjustable mass. This results into the motion of the center of gravity and the change of the net lift. The development of this concept of airship is motivated by energy saving. The moving mass and the airshipʼs rigid body are viewed independently, which renders the modeling easy and displays clearly the interconnection of the two subsystems. An eight degrees-of-freedom (DOF) complete nonlinear mathematical model of this airship is derived through the Newton–Euler approach. The dynamics in the vertical plane are analyzed and controlled, using maximal feedback linearization. The modeling, analysis, and control are solved for special cases of the airship which become gradually complex. The most constrained case reduces to a two-DOF system. It is shown that the basic properties of this two-DOF mechanical system remain instrumental for the analysis and synthesis of advanced airships. These properties are far from being obvious when the most complex model is considered.

Improved dynamic equations for the generally configured Stewart platform manipulator

In this paper, a Newton-Euler approach is utilized to generate the improved dynamic equations of the generally configured Stewart platform. Using the kinematic model of the universal joint, the rotational degree of freedom of the pods around the axial direction is taken into account in the formulation. The justifiable direction of the reaction moment on each pod is specified and considered in deriving the dynamic equations. Considering the theorem of parallel axes, the inertia tensors for different elements of the manipulator are obtained in this study. From a theoretical point, the improved formulation is more accurate in comparison with previous ones, and the necessity of the improvement is clear evident from significant differences in the simulation results for the improved model and the model without improvement. In addition to more feasibility of the structure and higher accuracy, the model is highly compatible with computer arithmetic and suitable for online applications for loop control problems in hardware.

Test method for empirically determining inertial properties of manual wheelchairs

The iMachine is a spring-loaded turntable used to measure inertial properties of irregularly shaped rigid bodies, specifically manual wheelchairs. We used a Newton-Euler approach to calculate wheelchair mass and center of mass (CM) location from static force measurements using load cells. We determined the moment of inertia about the vertical axis from the natural frequency of the system in simple harmonic motion. The device was calibrated to eliminate the effects of platform components on measurement error. For objects with known inertial properties, the average relative error of the mass and the CM coordinates (x and y) were 0.76%, 0.89%, and 1.99%, respectively. The resolution of the moment of inertia calculation depends on the ratio of test piece inertia to system inertia, such that the higher the ratio, the more accurate the measurements. We conducted a Gage Repeatability and Reproducibility (Gage R&R) test using three manual wheelchairs measured three times by three operators; the results showed that over 90% of the variance in inertia was caused by differences in the wheelchairs being measured. Gage R&R analysis indicated that measurement system operation was acceptable using criteria from the Automobile Industry Action Group for both inertia and mass measurements.

Modelling dynamics of certain class of discrete multi-body systems based on direct method of the dynamics of relative motion

The paper presents the author’s method of numerical modelling multi-body systems of a rail vehicle class. The method exploits dynamics of relative motion, which describes perturbations in general motion of the vehicle. Quite a few original elements are included in the author’s approach. This approach is compared to other possibilities of describing dynamics of multi-body systems in relative motion. The author’s method makes use of Kane’s equations that are opposed in the paper to the Newton-Euler approach that is used most often in the analogous applications. Numerical implementation of the theoretical results is also presented and a sample of the corresponding numerical analysis. Both these show the particular way to model dynamics of such systems efficiently and what consequences might be of the simplification in the description of relative motion. This appears to be more important than it is usually believed, particularly when accelerating or breaking the vehicle.