Newton-Euler Equations Research Articles

Static workspace analysis of a multi-robot collaborative towing system with floating base

The static workspace of the multi-robot collaborative towing system with floating base was analyzed. The spacial configuration of the system was built, and the system was divided into three types according to the actuation. The kinematic and dynamic models of the floating base and the towing system were established, respectively, by using the Newton-Euler equation. Then the static workspace of the system was analyzed, and the specific steps to solve the workspace with the improved Monte Carlo method were obtained. Finally, the static workspaces of three types of systems were solved though actual simulation calculation, the simulation results show that the improved Monte Carlo method can get a workspace with higher precision compare to the traditional Monte Carlo method. Results of this study lay a basis for the subsequent trajectory plan, stability analysis and configuration optimization of the system.

A New Recursive Composite Adaptive Controller for Robot Manipulators

In this paper, a new recursive implementation of composite adaptive control for robot manipulators is proposed. We investigate the recursive composite adaptive algorithm and prove the stability directly based on the Newton-Euler equations in matrix form, which, to our knowledge, is the first result on this point in the literature. The proposed algorithm has an amount of computation O n , which is less than any existing similar algorithms and can satisfy the computation need of the complicated multidegree manipulators. The manipulator of the Chinese Space Station is employed as a simulation example, and the results verify the effectiveness of this proposed recursive algorithm.

Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism.

The solution of the dynamic equations of the six-axis accelerometer is a prerequisite for sensor calibration, structural optimization, and practical application. However, the forward dynamic equations (FDEs) and inverse dynamic equations (IDEs) of this type of system have not been completely solved due to the strongly nonlinear coupling relationship between the inputs and outputs. This article presents a comprehensive study of the FDEs and IDEs of the six-axis accelerometer based on a parallel mechanism. Firstly, two sets of dynamic equations of the sensor are constructed based on the Newton–Euler method in the configuration space. Secondly, based on the analytical solution of the sensor branch chain length, the coordination equation between the output signals of the branch chain is constructed. The FDEs of the sensor are established by combining the coordination equations and two sets of dynamic equations. Furthermore, by introducing generalized momentum and Hamiltonian function and using Legendre transformation, the vibration differential equations (VDEs) of the sensor are derived. The VDEs and Newton–Euler equations constitute the IDEs of the system. Finally, the explicit recursive algorithm for solving the quaternion in the equation is given in the phase space. Then the IDEs are solved by substituting the quaternion into the dynamic equations in the configuration space. The predicted numerical results of the established FDEs and IDEs are verified by comparing with virtual and actual experimental data. The actual experiment shows that the relative errors of the FDEs and the IDEs constructed in this article are 2.21% and 7.65%, respectively. This research provides a new strategy for further improving the practicability of the six-axis accelerometer.

SECOND ORDER SLIDING MODE CONTROLLER DESIGN WITH OPTIMUM CHARACTERISTIC EQUATION FOR QUADROTORS

Nowadays, small structured micro unmanned aerial vehicles (UAV’s) with four-rotor appears in military and civilian applications. As the usage of these vehicles becomes widespread, the development of controller structures which allow the UAV’s to follow a specified trajectory precisely is a new area of interest for researchers. In this work, nonlinear mathematical model of a four-rotor UAV is obtained. In order to obtain the mathematical model of UAV Newton-Euler equations are used. In the trajectory tracking system of this vehicle, second order sliding mode controller (SOSMC) is designed. Inside of the controller, control process is divided into two subsystems in order to provide position and attitude control. SOSMC is applied to the fully actuated and under actuated subsystems individually. In the next step, coefficients of the SOSMC is determined with optimum characteristic equation. Based on the reference study, boundaries of the predefined characteristic equation is obtained. Later, appropriate values are observed. In final part, simulation results are obtained, and the results are compared with the reference study. As a result, Optimum Characteristic equation results proved its robustness according to the smaller steady state error and more precise flight performance in trajectory. In this study simulation results are obtained using Simulink/MATLAB environment.

Implementation of Translational Motion Dynamics for INS Data Fusion in DVL Outage in Underwater Navigation

Underwater navigation is generally accomplished through the data fusion of INS (Inertial Navigation System) and auxiliary sensors such as DVL (Doppler Velocity Logger) sensor. However, because of the possibility of DVL outage, alternative low-cost solutions are attractive. Among these, one is using vehicle kinetic model information extracted by the Newton-Euler equation to improve INS performance, which is called model-aided navigation. In this paper, only the vehicle translational motion dynamics are used to replace DVL in underwater navigation in DVL outage. The vehicle 3D translational dynamics has been obtained by using general Newton-Euler equations. Integrating these dynamics leads to the calculation of velocities in the body reference frame. Similar to DVL measurements, the calculated velocities (called “Pseudo-DVL” in this paper) are fused with INS. In this paper, a Kalman filter is used for INS/Pseudo-DVL data fusion. Field test data collected by an equipped research AUV called SUT-III is used to evaluate the proposed approach experimentally. Also, a comparison between the integrated navigation of INS-DVL and INS-Pseudo-DVL is performed and the results are provided. The results reveal that despite having low-cost MEMS IMUs, INS/Pseudo-DVL has effectively corrected standalone INS estimation. Finally it is concluded that despite slight degradation of navigation performance, an expensive DVL sensor can be replaced by using the proposed method in DVL outage.

INS-DVL Navigation Improvement Using Rotational Motion Dynamic Model of AUV

INS-DVL integration is a common method for underwater navigation. However, inherent errors of sensors, especially in MEMS IMUs, lead to inaccuracies in estimating the position and attitude. In this paper, dynamic motion model of AUV is used to improve MEMS INS-DVL navigation. In this method, which is called model-aided or model-based navigation, the information of the kinetic model of the vehicle (obtained from Newton-Euler equations) is used to improve the navigation performance. Previous model-aided navigation studies about AUVs have been focused on the translational dynamic model of vehicles. As the best of our knowledge, this paper is the first one which suggests using a rotational motion model of AUVs to improve the navigation performance and at the same time, reports successful implementation of method through field-testing. The utilized dynamic model, describes the rotational motion of AUV in a 3DOF form. Information extracted from the rotational dynamic model and the outputs of gyroscopes, will be fused in a secondary Kalman filter. So, before the fusion with auxiliary sensors in the main Kalman filter, the gyroscopes outputs have been improved by the rotational motion model. Therefore, the overall output will be better than the outputs of gyroscopes by itself. The main Kalman filter is a perturbation-based Kalman filter which is employed for data fusion. This algorithm is implemented on real data collected from field-test. The results show that this inexpensive method which requires no additional equipment was truly effective in improving navigation performance. Using this model, the accuracy of navigation was improved 5 to 10 times.

Dynamic Analysis of an Underwater Cable-Driven Manipulator with a Fluid-Power Buoyancy Regulation System.

This article presents an underwater cable-driven manipulator (UCDM) with a buoyancy regulation system (BRS), which is controlled by a fluid-power system. The manipulator consists of five sections, and each section is embedded with a buoyancy adjustment unit. By regulating buoyancy at each section, the static and dynamic states of the manipulator will be changed, promising a new operating mode of an underwater manipulator driven by buoyancy. In this article, a dynamic model of the manipulator is established by the Newton-Euler equation, considering cable tension, inter-joint force, buoyancy, water resistance and other variables. With a numerical method, the dynamic model is solved and the values of cable tension are obtained, which are used to evaluate the buoyancy-driven operating mode of underwater manipulator. This research will be useful for manipulator operating in fluid environments, such as underwater manipulator in the ocean, micro-manipulator in a blood vessel, and so on.

A Second-Order Sliding Mode Controller of Quad-Rotor UAV Based on PID Sliding Mode Surface with Unbalanced Load

Quad-rotor unmanned aerial vehicle (UAV) is a typical multiple-input-multiple-output underactuated system with couplings and nonlinearity. Usually, the flying environment is very complex, so that it is impossible for the UAV to avoid effects derived from disturbances and uncertainties. In order to improve the reliability of flight control, we established the dynamic model of quad-rotor UAV by Newton-Euler equation in unbalanced load conditions. Considering external disturbances in the attitude, a second-order sliding mode controller was designed with PID sliding mode surface and Extended State Observer (ESO). The simulation experiments have got good control performance, illustrating the effectiveness of our controller. Meanwhile, the controller was implemented in a quad-rotor UAV, which carried a pan-tilt camera for aerial photography. The actual flight experiments proved that this paper dealt with the high stabilization flight control problem for the quad-rotor UAV, which laid a good foundation for autonomous flight of the UAV.

Generic Adaptive Sliding Mode Control for a Quadrotor UAV System Subject to Severe Parametric Uncertainties and Fully Unknown External Disturbance

This paper aims to provide a generic robust controller that is able to manipulate all kinds of quadrotor unmanned aerial vehicle (UAV) systems automatically or adaptively in the presence of severe parametric uncertainties and fully unknown external disturbance. The dynamic model of the quadrotor is first obtained using Newton-Euler equations. Then, considering the underactuated and the strongly coupled characteristics of the quadrotor system, a nonlinear adaptive sliding mode control (ASMC) scheme is proposed. Meanwhile, additional adaptive laws are designed to estimate all the parameters of the quadrotor system, which in principle are difficult to be measured directly and accurately. Furthermore, to guarantee the asymptotic stability of the closed-loop system, the upper bound of the fully unknown external disturbance is estimated and adopted as the switching gain of the ASMC. Finally, simulations and experiments are carried out to illustrate the effectiveness and robustness of the proposed control scheme, where the superiority to linear quadratic control (LQR) and active disturbance rejection control (ADRC) has been demonstrated clearly.

On planar self-folding magnetic chains: Comparison of Newton–Euler dynamics and internal energy optimisation

Within the wide field of self-assembly, the self-folding chain has the unique capability to pass through narrow openings, too small for the assembled structure, yet consists in one connected body. This paper presents a novel analytical framework and corresponding experimental setup to quantify the results of a self-folding process using magnetic forces at the centimetre-scale, with the aim to put experimental results and prediction methods in the context of surgical anchoring and therapy. Two possibilities to predict the folding of a chain of magnetic components in 2D are compared and investigated in an experimental setup. Folding prediction by system Coulomb energy, neglecting folding dynamics, is compared with a simulation of the system dynamics using a novel approach for 2D folding chains, derived from the Newton–Euler equations. The presented algorithm is designed for the parallel computation architecture of modern computer systems to be easily applicable and to achieve an improved simulation speed. The experimental setup for the self-folding chain used to validate the simulation results consists of a chain of magnetic components where movement is limited to one plane and the chain is agitated by the magnetic forces between the chain components. The folding process of the experimental setup is validated for its stability and predictability under different deployment modes. Finally, the results are discussed in light of the folding prediction of longer chains. The implications of the presented findings for a 3D folding chain are discussed together with the challenges to apply the novel dynamics simulation algorithm to the 3D case. The work clearly demonstrates the potential for this novel approach for complex self-folding applications such as magnetic compression anastomosis and anchoring in minimally invasive surgery.

Multibody Dynamics Versus Fluid Dynamics: Two Perspectives on the Dynamics of Granular Flows

Abstract Considering that granular material is second only to water in how often it is handled in practical applications, characterizing its dynamics represents a ubiquitous problem. However, studying the motion of granular material poses stiff computational challenges. The underlying question in this contribution is whether a continuum representation of the granular material, established in the framework of the smoothed particle hydrodynamics (SPH) method, can provide a good proxy for the fully resolved granular dynamics solution. To this end, two approaches described herein were implemented to run on graphics processing unit (GPU) cards to solve the three-dimensional (3D) dynamics of the granular material via two solution methods: a discrete one, and a continuum one. The study concentrates on the case when the granular material is packed but shows fluid-like behavior under large strains. On the one hand, we solve the Newton–Euler equations of motion to fully resolve the motion of the granular system. On the other hand, we solve the Navier–Stokes equations to describe the evolution of the granular material when treated as a homogenized continuum. To demonstrate the similarities and differences between the multibody and fluid dynamics, we consider three representative problems: (i) a compressibility test (highlighting a static case); (ii) the classical dam break problem (highlighting high transients); and (iii) the dam break simulation with an obstacle (highlighting impact). These experiments provide insights into conditions under which one can expect similar macroscale behavior from multibody and fluid dynamics systems governed by manifestly different equations of motion and solved by vastly different numerical solution methods. The models and simulation platform used are publicly available and part of an open source code called Chrono. Timing results are reported to gauge the efficiency gains associated with treating the granular material as a continuum.

COMPARING METHODS FOR 3D INVERSE DYNAMICS ANALYSIS OF SQUAT LIFTING USING A FULL BODY LINKED SEGMENT MODEL

Objective: The main objective of this study was to assess the accuracy of bottom-up solution for three-dimensional (3D) inverse dynamics analysis of squat lifting using a 3D full body linked segment model. Least squares solution was used in this study as reference for assessment of the accuracy of bottom-up solution. Findings of this study may clarify how much the bottom-up solution can be reliable for calculating the joint kinetics in 3D inverse dynamics problems. Methods: Ten healthy males volunteered to perform squat lifting of a box with a load of one-tenth of their body weights. The joint moments were calculated using 110 reflective passive markers (46 anatomical markers and 64 tracking markers) and a 3D full body linked segment model. Ground reaction forces and kinematics data were recorded using a Vicon system with two parallel Kistler force plates. Three-dimensional Newton–Euler equations of motion with bottom-up and least squares solutions were applied to calculate joint moments. The peak and mean values of the joint moments were determined to check the quantitative differences as well as the time-to-peak value of the moment curves was determined to check the temporal differences between the two inverse dynamics solutions. Results: Significant differences (all [Formula: see text]-[Formula: see text]) between the two inverse dynamics solutions were detected for the peak values of the hip (right and left sides) and L5–S1 joint moments in the lateral anatomical direction as well significant differences (all [Formula: see text]-[Formula: see text]) were detected for the peak and mean values of the L5–S1 joint moment in all anatomical directions. Moreover, small differences (all [Formula: see text]) were detected between the two inverse dynamic solutions for the calculated lower body joint moments. Conclusions: The findings of this study clarified the disadvantages of the straightforward solutions and demonstrated that the bottom-up solution may not be accurate for more distal measures from the force plate (for hip and S1–L5) but it may be accurate for more proximal joints (ankle and knee) in 3D inverse dynamics analysis.

Parallel manipulator dynamics embedded in singularity free domains of functionality

Ordinary differential equations of motion for a broad spectrum of parallel manipulators are derived and implemented in manipulator input coordinates for system simulation and controller design. Equations of motion are systematically embedded in singularity free domains of manipulator configuration space, assuring controllability and existence of a unique solution of the equations of motion. The kinematic foundation for the formulation is a mechanics-based model of the underlying mechanism with forward and inverse kinematic mappings that are evaluated on singularity free domains of manipulator configuration space. The kinetic foundation is d’Alembert’s variational formulation of multibody dynamics that, with forward kinematic mappings, yields explicit ordinary differential equations of motion. No ad-hoc derivations of Lagrange’s equations, Newton–Euler equations, or Lagrange multiplier-based differential-algebraic equations are required. Differential equations of motion for a planar front-end loader and a spatial Stewart platform manipulator are implemented to illustrate the formulation.

Investigation of the Effect of Differential Morphing on Forward Flight by Using PID Algorithm in Quadrotors

In this study, modeling, control and differential morphing of a four-rotor unmanned aerial vehicle known as a quadrotor is discussed. With differential morphing, the forward flight performance and model of an autonomous quadrotor is presented. Due to the complex structure of the quadrotor, it is difficult to build the model. To get model parameters, a complete quadrotor model is drawn in the Solidworks program. In addition, Newton-Euler equations are used in the mathematical model. Simulation is done in Matlab / Simulink environment by using the parameters obtained from the model and the state-space model approach. PID (proportional, integral, derivative) is used as the quadrotor control algorithm. As a result of the study, the quadrotor forward flight is carried out using PID algorithm and differential morphing. The system characteristics of the situations with and without differential morphing are compared and the results are presented with graphs.

Saturated Adaptive Relative Motion Coordination of Docking Ports in Space Close-Range Rendezvous

An adaptive relative pose controller for docking ports of two uncertain spacecraft in autonomous rendezvous and docking is developed. A novel relative translational and rotational model represented in the chaser body-fixed frame is derived first based on the classical Newton–Euler equations. Based on the proposed model, a six-degrees-of-freedom adaptive control law is presented based on norm-wise estimations for the unknown parameters of two spacecraft to decrease the online computational burden. Meanwhile, an adaptive robust control input is designed by introducing an exponential function of states to improve the response performance with respect to the traditional adaptive robust control. Moreover, a linear antiwindup compensator is employed to ensure the bounded performance of the control inputs. The explicit tuning rules for designing parameters are derived based on the stability analysis of the closed-loop system. It is proved in Lyapunov framework that all closed-loop signals are always bounded and the pose tracking error ultimately converges to a small neighborhood of zero. Simulation results validate the performance of the proposed robust adaptive control strategy.

Analysis of ride comfort of a continuous tracked bogie system with variable configuration

In this study, the effect of change in height of a so-called variable configuration of a continuous tracked bogie system on ride comfort performance is investigated. To this end, constraint equations among different vehicle parts are derived recursively, and equations of motion are formulated according to the Newton–Euler equations using the embedding technique. Besides, to model the track as a closed-loop chain, the penalty method has been used instead of loop-closure equations. To mathematically model the contact between tracks, wheels, and the terrain, the continuous contact force model has been employed. To validate the mathematical model, the vehicle dynamic behavior is simulated by the Runge–Kutta method in MATLAB software and compared with those obtained from the identical model, built in RecurDyn software, and the results show good agreement. Moreover, the vibrational behavior of the tracked vehicle is investigated using two different vehicle configurations. This reveals that an increase in vehicle height does not change the vehicle vibrational frequencies. However, it increases the vehicle vibration amplitude and the energy absorbed by the vehicle components and decreases the ride comfort.

Predictive and sliding mode cascade control for cross-domain locomotion of a coaxial aerial underwater vehicle with disturbances

This paper presents the system design, dynamic model of a novel coaxial aerial underwater vehicle, and proposes an improved cascade control strategy to enable cross-domain locomotion of the vehicle in disturbance environments. The proposed aerial underwater vehicle merges the design of the coaxial rotor system and the foldable propeller for operating effectively in both mediums and transitioning between them. The vehicle’s continuous dynamics model is formulated based on the Newton-Euler equation considering time-varying environmental disturbances. Then, a predictive and sliding mode cascade control is developed and applied for motion control of the vehicle to perform cross-domain transitions, especially compensating for the effect of buoyancy variance with feedforward control. Finally, the feasibility and robustness of the proposed control scheme are verified by comparative simulation results with the PID controller.

Global Sensitivity Analysis for Modeling the Free-Flight Behavior of an Artillery Projectile

A vehicle’s in-flight behavior can be represented by the Newton–Euler equations of motion: usually, such a model has a nonlinear and continuous description based on ordinary differential equations. The model structure can be altered using analytic transformations (such as transformation into a quasi-LPV structure) and, when the model is supposed to reflect an existing physical system, some of its parameters might be uncertain. This paper’s objective is twofold: first, to investigate if a quasi-LPV model does accurately replicate the physical behavior of a large-caliber spin-stabilized projectile in free flight; second, to verify if the available embedded sensors data could be used to determine nonidentifiability of uncertain model parameters. To investigate these prospects, a permutation-based global sensitivity analysis is employed. The proposed study has highlighted the nonidentifiable parameters of the model, during either the whole flight or some periods of it. These results can help to enhance the preparation of free-flight experiments at the open-range test site of the French-German Research Institute of Saint Louis.

COMPARING METHODS FOR 3D INVERSE DYNAMICS ANALYSIS OF SQUAT LIFTING USING A FULL BODY LINKED SEGMENT MODEL

Objective: The main objective of this study was to assess the accuracy of bottom-up solution for three-dimensional (3D) inverse dynamics analysis of squat lifting using a 3D full body linked segment model. Least squares solution was used in this study as reference for assessment of the accuracy of bottom-up solution. Findings of this study may clarify how much the bottom-up solution can be reliable for calculating the joint kinetics in 3D inverse dynamics problems. Methods: Ten healthy males volunteered to perform squat lifting of a box with a load of one-tenth of their body weights. The joint moments were calculated using 110 reflective passive markers (46 anatomical markers and 64 tracking markers) and a 3D full body linked segment model. Ground reaction forces and kinematics data were recorded using a Vicon system with two parallel Kistler force plates. Three-dimensional Newton–Euler equations of motion with bottom-up and least squares solutions were applied to calculate joint moments. The peak and mean values of the joint moments were determined to check the quantitative differences as well as the time-to-peak value of the moment curves was determined to check the temporal differences between the two inverse dynamics solutions. Results: Significant differences (all [Formula: see text]-values [Formula: see text]) between the two inverse dynamics solutions were detected for the peak values of the hip (right and left sides) and L5–S1 joint moments in the lateral anatomical direction as well significant differences (all [Formula: see text]-values [Formula: see text]) were detected for the peak and mean values of the L5–S1 joint moment in all anatomical directions. Moreover, small differences (all RMSEs [Formula: see text]%) were detected between the two inverse dynamic solutions for the calculated lower body joint moments. Conclusions: The findings of this study clarified the disadvantages of the straightforward solutions and demonstrated that the bottom-up solution may not be accurate for more distal measures from the force plate (for hip and S1–L5) but it may be accurate for more proximal joints (ankle and knee) in 3D inverse dynamics analysis.

Formation of Generic UAVs-USVs System Under Distributed Model Predictive Control Scheme

This brief presents a distributed model predictive formation control algorithm of heterogeneous multi-agent systems with directed topology, which consists of unmanned surface vehicles (USVs) and generic unmanned aerial vehicles (UAVs). The dynamics of UAVs and USVs are modeled by the Newton-Euler equation and Euler-Lagrange equation, respectively. We design the distributed model predictive control scheme to coordinate the UAVs-USVs system, where both feasibility and stability analyses are presented to guarantee the satisfactory formation. Simulation results demonstrate the effectiveness of the proposed distributed predictive formation algorithm.