Newton-Euler Formulation Research Articles

A Google map-based traffic accident reconstruction system

Both traffic accident reconstruction and responsibility confirmation of traffic accident depend on crash scene diagramming and crash simulation. However, mistakenly recorded road geometry of the crash scene usually causes misunderstandings in the crash scene diagramming and thus the result of accident reconstruction is untrustworthy. Research has thus been continuously done to solve the problem. This study proposed a Google Map-based accident reconstruction system integrating functions of crash scene diagrammingand crash simulation. The modulus of crash scene diagramming includes positioning of accident location, Google satellite map and Google Sketch Up to accurately present road geometry and accident vehicle position information. The modulus of crash simulation refers to the vehicle dynamic differential equations generated using the Newton-Euler formulation, and enhances with the calculation of momentum conservation in the collision to predict the vehicle dynamics after collision. The system developed in this study was validated using a real case. The results showed that a crash scene diagramming correctly drawn on the Google satellite map was an ideal platform to present the crush simulation, and help people understand or make a judgment for accident authentication. Key words: Accident reconstruction, Google map, crash scene diagramming, crash simulation.

Modeling and Control of a Quadrotor Helicopter System under Impact of Wind Field

Aiming at the hovering problem of a quadrotor helicopter system under impact of wind field, in this study, a nonlinear integral backtepping controller was designed. The quadrotor helicopter is a nonlinear system which is underactuated and strongly coupled. The wind field would lead to the nonlinear change of aerodynamic force and moment and make the flight condition worse. For the highly nonlinear characteristic of the system, first we establish the dynamic model that considers the effect of wind field via Newton-Euler formalism; and then we develop a controller based on integral backstepping algorithm and validate the stability of the system by Lyapunov theory. Simulation results demonstrate that the model can accurately reflects dynamic performance of the system and the controller presents good robustness in the effect of wind field.

상하동요 감쇠장치 적용을 통한 새로운 다물체동역학 프로그램의 적용성 검토

In this paper, dynamic response analysis of a heave compensation system is performed for offshore drilling operations based on multibody dynamics. With this simulation, the efficiency of the heave compensation system can be virtually confirmed before it is applied to drilling operations. The heave compensation system installed on a semi-submersible platform consists of a passive and an active heave compensator. The passive and active heave compensator are composed of several bodies that are connected to each other with various types of joints. Therefore, to carry out the dynamic response analysis, the dynamics kernel was developed based on mutibody dynamics. To construct the equations of motion of the multibody system and to determine the unknown accelerations and constraint forces, the recursive Newton-Euler formulation was adapted. Functions of the developed dynamics kernel were verified by comparing them with other commercial dynamics kernels. The hydrostatic force with nonlinear effects, the linearized hydrodynamic force, and the pneumatic and hydraulic control forces were considered as the external forces that act on the platform of the semi-submersible rig and the heave compensation system. The dynamic simulation of the heave compensation system of the semi-submersible rig, which is available for drilling operations with a 3,600m water depth, was carried out. From the results of the simulation, the efficiency of the heave compensation system were evaluated before they were applied to the offshore drilling operations. Moreover, the calculated constraint forces could serve as reference data for the design of the mechanical system.

Dynamics of serial kinematic chains with large number of degrees-of-freedom

This paper investigates the dynamic behaviour of serial chains with degrees-of-freedom (DOF) as large as 100,000. A recursive solver called Recursive Dynamic Simulator (ReDySim), based on the Newton–Euler formulation and the Decoupled Natural Orthogonal Complement (DeNOC) matrices, was used to simulate the dynamics of these systems. Planar, as well as spatial motions of chains with moderate- (DOF≤1,000), large- (1,000 10,000) DOF were simulated. The results were validated by several means, such as comparisons with reported results wherever available, results obtained from commercial software, energy checks, etc. The study shows that ReDySim is capable of analysing serial chains of huge-DOF with acceptable numerical accuracy. The scheme is found to be numerically stable as well as computationally efficient, owing to the linear-time computation of the joint accelerations. Numerical studies were conducted to establish the theoretical basis for better performance of the proposed ReDySim solver. With the demonstrated capabilities of ReDySim, it may be found suitable for a large number of applications involving serial systems with huge-DOF.

Reduced-order forward dynamics of multiclosed-loop systems

In this work, a reduced-order forward dynamics of multiclosed-loop systems is proposed by exploiting the associated inherent kinematic constraints at acceleration level. First, a closed-loop system is divided into an equivalent open architecture consisting of several serial and tree-type subsystems by introducing cuts at appropriate joints. The resulting cut joints are replaced by appropriate constraint forces also referred to as Lagrange multipliers. Next, for each subsystem, the governing equations of motion are derived in terms of the Lagrange multipliers, which are based on the Newton–Euler formulation coupled with the concept of Decoupled Natural Orthogonal Complement (DeNOC) matrices, introduced elsewhere. In the proposed forward dynamics formulation, Lagrange multipliers are calculated sequentially at the subsystem level, and later treated as external forces to the resulting serial or tree-type systems of the original closed-loop system, for the recursive computation of joint accelerations. Note that such subsystem-level treatment allows one to use already existing algorithms for serial and tree-type systems. Hence, one can perform the dynamic analyses relatively quickly without rewriting the complete model of the closed-loop system at hand. The proposed methodology is in contrast to the conventional approaches, where the Lagrange multipliers are calculated together at the system level or simultaneously along with the joint accelerations, both of which incur higher order computational complexities, and thereby a greater number of arithmetic operations. Due to the smaller size of matrices involved in evaluating Lagrange multipliers in the proposed methodology, and the recursive computation of the joint accelerations, the overall numerical performances like computational efficiency, etc., are likely to improve. The proposed reduced-order forward dynamics formulation is illustrated with two multiclosed-loop systems, namely, a 7-bar carpet scrapping mechanism and a 3-RRR parallel manipulator.

UAV Mathematical Modeling, Analysis and Fuzzy Controller Design

The objective of this work is to introduce the design, simulation and control of a quad rotor, equipped with Inertial Sensors, as an example of unmanned aerial vehicle. To fulfill this objective a mathematical model of the quad rotor has been developed, using Newton-Euler Formulation. The simulation of the model and controller design is developed in MATLAB/Simulink environment. It is intended to make the model flexible and easily modified to be used with any similar model. In order to evaluate the real model mass and mass moment of inertia, a solid model had been built using Autodesk Inventor software package. To validate the proposed model output results, a comparison with published research has been carried out which showed a good agreement. Finally, a fuzzy controller is designed to control the quad rotor altitude and the three Euler angles of roll, pitch and yaw. The controller showed a good controllability within a certain range of the controlled parameter.

Design of Auto-Stabilization Control Technique for a Quadrotor System

This paper presents the design of auto-stabilization control technique for a quadrotor system. Aquadrotor is a highly nonlinear and has to be stabilized by a suitable control technique. Therefore, the main focus of this research is to design an appropriate control algorithm that able to auto-stabilize the quadrotor at hover. The dynamic modeling of the quadrotor is described by sets of equations of motion that are derived based on the Newton-Euler formalism with the implementation of UKF for parameter identification and state estimation. The control strategy adopted includes feedback linearization coupled with Proportional-Derivative (PD) controller for the translational subsystem and backstepping based Proportional-Integral-Derivative (PID) controller for the rotational subsystem. It is developed in MATLAB/Simulink platform and is validated via real-time implementation. Both controllers give satisfactory simulation results, where acceptable peak of overshoot and small steady state errors are achieved. Experimentally, the throttle is controlled in manual mode while attitude angles are stabilized automatically. The simulation and experimental results show that the proposed controller is able to effectively stabillized the quadrotor.

Solving elastic deformation of some parallel manipulators with linear active legs using computer-aided design variation geometry

It has been a significant and challenging issue to determine the elastic deformation of parallel manipulators for their precision analysis and control. A new method is proposed and studied for solving the elastic deformation of some parallel manipulators with linear active legs using computer-aided design variation geometry. First, an original simulation mechanism of a parallel manipulator is constructed; each of the vectors in the force transformation matrix of the parallel manipulators is constructed by this simulation mechanism. The active/constrained wrench and their pose are determined based on the Newton–Euler formulation. Second, the elastic deformed dimensions of the active legs are determined based on the elastic deformation equation and the active/constrained wrench. Third, a new simulation mechanism of this parallel manipulator is constructed by replacing the original dimensions of active legs with the deformed dimensions of active legs and the elastic deformations of parallel manipulators are solved using the pose difference between the original and new simulation mechanisms. Finally, two parallel manipulators are illustrated and their elastic deformations are solved and verified by both analytic approach and finite element method.

A16 動力学モデル用いた油圧ショベルの掘削作業解析(M-OS9-1:ビークルの運動と制御I,M-OS9 ビークルの運動と制御,「海を越え,国を越え,世代を超えて!」)

In this research, the linkage mechanism of hydraulic excavator which contains the closed loops is modeled based on the Newton-Euler formulation, and the motion equation is derived. Moreover, we apply a soil model for simulation, based on the two dimensional distinct element method (DEM), in order to reproduce reaction force from grounds. These models are integrated and able to analyze detailed interaction between machine and ground. The hydraulics force is analyzed, when an excavator performs digging operations according to the preprogramed digging trajectory. We conduct inverse-dynamics analysis to estimate the influence of digging resistance force on generative cylinder forces. The simulation results show that cylinder generative forces, varying depending on digging reaction force, significantly influence the cylinder force during digging operations.

Control of a Quadrotor Using a Smart Self-Tuning Fuzzy PID Controller

This paper deals with the modelling, simulation-based controller design and path planning of a four rotor helicopter known as a quadrotor. All the drags, aerodynamic, coriolis and gyroscopic effect are neglected. A Newton-Euler formulation is used to derive the mathematical model. A smart self-tuning fuzzy PID controller based on an EKF algorithm is proposed for the attitude and position control of the quadrotor. The PID gains are tuned using a self-tuning fuzzy algorithm. The self-tuning of fuzzy parameters is achieved based on an EKF algorithm. A smart selection technique and exclusive tuning of active fuzzy parameters is proposed to reduce the computational time. Dijkstra's algorithm is used for path planning in a closed and known environment filled with obstacles and/or boundaries. The Dijkstra algorithm helps avoid obstacle and find the shortest route from a given initial position to the final position.

Modeling and Robust Trajectory Tracking Control for a Novel Six-Rotor Unmanned Aerial Vehicle

Modeling and trajectory tracking control of a novel six-rotor unmanned aerial vehicle (UAV) is concerned to solve problems such as smaller payload capacity and lack of both hardware redundancy and anticrosswind capability for quad-rotor. The mathematical modeling for the six-rotor UAV is developed on the basis of the Newton-Euler formalism, and a second-order sliding-mode disturbance observer (SOSMDO) is proposed to reconstruct the disturbances of the rotational dynamics. In consideration of the under-actuated and strong coupling properties of the six-rotor UAV, a nested double loops trajectory tracking control strategy is adopted. In the outer loop, a position error PID controller is designed, of which the task is to compare the desired trajectory with real position of the six-rotor UAV and export the desired attitude angles to the inner loop. In the inner loop, a rapid-convergent nonlinear differentiator (RCND) is proposed to calculate the derivatives of the virtual control signal, instead of using the analytical differentiation, to avoid “differential expansion” in the procedure of the attitude controller design. Finally, the validity and effectiveness of the proposed technique are demonstrated by the simulation results.

Modeling Approach of a Near-Space Airship Using Newton-Euler and Lagrangian Formulation

This paper presents dynamics modeling approach of the near-space airship. First, reference frames and motion variables of the airship are defined, and dynamics model of an airship is derived from the Newton-Euler formulation. Second, the Lagrangian modeling approach in terms of quasi-coordinates is presented, and dynamics model is derived form the Lagrangian formulation, considering the airship and its ambient air as a “rigid body-fluid” system from an energy point of view. The added inertial, gravity, aerostatics, and dissipative forces are incorporated into the dynamics model, and are expressed as parameterized matrices in a common framework. Third, the validity of the proposed dynamics model is verified by comparing simulations with the dynamics model derived from Newton-Euler formulation.

Concept design, modeling and station-keeping attitude control of an earth observation platform

The stratosphere airship provides a unique and promising platform for earth observation. Researches on the project design and control scheme for earth observation platforms are still rarely documented. Nonlinear dynamics, model uncertainties, and external disturbances contribute to the difficulty in maneuvering the stratosphere airship. A key technical challenge for the earth observation platform is station keeping, or the ability to remain fixed over a geo-location. This paper investigates the conceptual design, modeling and station-keeping attitude control of the near-space earth observation platform. A conceptual design of the earth observation platform is presented. The dynamics model of the platform is derived from the Newton-Euler formulation, and the station-keeping control system of the platform is formulated. The station-keeping attitude control approach for the platform is proposed. The multi-input multi-output nonlinear control system is decoupled into three single-input single-output linear subsystems via feedback linearization, the attitude controller design is carried out on the new linear systems using terminal sliding mode control, and the global stability of the closed-loop system is proven by using the Lyapunov theorem. The performance of the designed control system is simulated by using the variable step Runge-Kutta integrator. Simulation results show that the control system tracks the commanded attitude with an error of zero, which verify the effectiveness and robustness of the designed control system in the presence of parametric uncertainties. The near-space earth observation platform has several advantages over satellites, such as high resolution, fast to deploy, and convenient to retrieve, and the proposed control scheme provides an effective approach for station-keeping attitude control of the earth observation platform.

Dynamics analysis of a 3-RRP spherical parallel manipulator using the natural orthogonal complement

In the present research, application of the Natural Orthogonal Complement (NOC) for the dynamic analysis of a spherical parallel manipulator, referred to as SST, is presented. Both inverse and direct dynamics are considered. The NOC and the SST fully parallel robot are explained. To drive the NOC for the SST manipulator, constraints between joint variables are written using the transformation matrices obtained from three different branches of the robot. The Newton–Euler formulation is used to model the dynamics of each individual body, including moving platform and legs of the manipulator. D’Alembert’s principle is applied and Newton–Euler dynamical equations free from non-working generalized constraint forces are obtained. Finally two examples, one for direct and one for inverse dynamics are presented. The correctness and accuracy of the obtained solution are verified by comparing with the solution of the virtual work method as well as commercial multi-body dynamics software.

Design, modeling and control for a stratospheric telecommunication platform

The stratospheric airship provides a unique and promising platform for broad band telecommunication relay missions, which combine the advantages of both terrestrial and satellite communication. In this paper, the conceptual design, dynamics modeling and attitude control of the stratospheric telecommunication platform are presented. First, the stratospheric telecommunication platform is introduced, including conceptual design, configuration, energy sources, propeller and payload. Second, dynamics model of the platform is derived form the Newton–Euler formulation and the station-keeping attitude control problem is formulated. Then, the adaptive fuzzy sliding mode control scheme is proposed to develop the attitude-tracking control system, with a particular focus on parametric uncertainties and external disturbances. Finally, simulation results verify the effectiveness and robustness of the proposed control scheme. The proposed conceptual design and control scheme provide a promising approach for telecommunication relay missions using the stratospheric station-keeping airship.

Constraint-wrench analysis of robotic manipulators

The constraint-wrench analysis of mechanisms, with focus on parallel robots, is the subject of this paper. Although the method proposed here can be generalized for parallel robots with multiple-loop kinematic chains, here, single-loop chains are targeted. To this end, a novel representation of the constraints imposed by the kinematic pairs is introduced. With this representation, the constraint matrix of a mechanism is readily derived. For the calculation of the constraint wrenches, by means of the constraint matrix and based on the Newton–Euler formulation, a new procedure is introduced. As a case study, the constraint wrench analysis of the McGill Schonflies Motion Generator (SMG), while undergoing a test cycle adopted by the industry, is conducted.

Design and construction of a novel quad tilt-wing UAV

This paper presents aerodynamic and mechanical design, prototyping and flight control system design of a new unmanned aerial vehicle SUAVI (Sabanci University Unmanned Aerial VehIcle). SUAVI is an electric powered quad tilt-wing UAV that is capable of vertical takeoff and landing (VTOL) like a helicopter and long duration horizontal flight like an airplane. Aerodynamic and mechanical designs are optimized to enhance the operational performance of the aerial vehicle. Both of them have great importance for increasing efficiency, reaching the flight duration goals and achieving the desired tasks. A full dynamical model is derived by utilizing Newton–Euler formulation for the development of the flight control system. The prototype is constructed from carbon composite material. A hierarchical control system is designed where a high level controller (supervisor) is responsible for task decision, monitoring states of the vehicle, generating references for low level controllers, etc. and several low level controllers are responsible for attitude and altitude stabilization. Results of several simulations and real flight tests are provided along with flight data to show performance of the developed UAV.

Effect of Terrain Traction, Suspension Stiffness and Grasp Posture on the Tip-Over Stability of Wheeled Robots with Multiple Arms

In this paper, dynamics, postural stability and control of suspended wheeled mobile manipulators for cooperative heavy object manipulation are elaborated considering the effect of grasping posture. The presented model considers a system equipped with multiple manipulators with flexible suspension, which also contains an accurate nonlinear behavior of the tires. Moreover, it includes the vibratory response of the tires as unsprung masses. Therefore, this is one of the most complete models that have been presented for wheeled mobile manipulators to date. First, based on the Newton–Euler formulation for a chain of rigid bodies, the dynamics model of such complicated systems in three-dimensional maneuvers is developed without considering a nonlinear frictional model of tires, which was verified using the ADAMS multibody simulator. Then, a proper nonlinear friction model is added to the developed dynamics to provide a more complete one. Considering pneumatic tires, the Dugoff tire friction model is adopted to describe the longitudinal and lateral forces produced at the contact patch of the wheels. Using the obtained dynamics along with the moment-height stability measure the effect of frictional effects as well as suspension attributes on the postural stability of such systems are accurately investigated for maneuvers over flat and rough terrains. Finally, the effect of grasping posture and relevant configuration of the robot on the stability of the system is examined during a heavy object manipulation task.

ATTITUDE CONTROL OF SMALL UNMANNED FOUR-ROTOR HELICOPTER BASED ON ADAPTIVE INVERSE CONTROL THEORY

A dynamic model of small unmanned four-rotor built according to Newton-Euler formalism was proposed in this paper. Base on this model, Adaptive Inverse Control (AIC) Theory was used in the control of the small unmanned four-rotor for the first time and the attitude stabilization control was also realized on the experimental platform. The attitude control experiment indicates that AIC is robust in the attitude control of the small unmanned four-rotor. DOI: http://dx.doi.org/10.5755/j01.mech.18.1.1288

Mathematical modeling and vertical flight control of a tilt-wing UAV

This paper presents a mathematical model and vertical flight control algorithms for a new tilt-wing unmanned aerial vehicle (UAV). The vehicle is capable of vertical take-off and landing (VTOL). Due to its tilt-wing structure, it can also fly horizontally. The mathematical model of the vehicle is obtained using Newton-Euler formulation. A gravity compensated PID controller is designed for altitude control, and three PID controllers are designed for attitude stabilization of the vehicle. Performances of these controllers are found to be quite satisfactory as demonstrated by indoor and outdoor flight experiments.