Rigid-flexible Multibody System Research Articles

Attitude Stabilization of Tug–Towed Space Target by Thrust Regulation in Orbital Transfer

This paper studies the stability control of a target towed by a space-tug via a tether in orbital transfer. The attitude of the towed target is controlled by thrust regulation at the tug with the consideration of the coupling effect between the attitudes of the tug and towed target and the motion of the flexible and elastic tether. A model-based control scheme is proposed, where the tug and towed target are assumed as rigid bodies and the tether is approximated as a series of extensible but incompressible rods connected by spherical hinges. The governing equations of motion of the coupled rigid–flexible multibody system are derived based on the recursive dynamics algorithm. The attitude motion of the tug with the presence of tether tension disturbance is controlled by a simple proportional–derivative torque controller. The attitude motion of the towed target and the elongation oscillation of the tether are stabilized simultaneously via the tether tension by regulating the thrust at the tug. The thrust control is achieved by first designing an optimal trajectory considering the system constraints based on a reference model, and then the trajectory is tracked by a robust global terminal sliding-mode controller with the consideration of thrust saturation and tether slackness avoidance. Finally, numerical simulation is carried out to demonstrate the effectiveness of the proposed attitude control law based on the thrust regulation.

Dynamics modeling and attitude control of spacecraft flexible solar array considering the structure of the hinge rolling

It is well known that the rolling of the hinge mechanism is the most fragile part on the fully-deployed solar array system when the spacecraft involves a rapid maneuver. In this investigation, a new accurate solar array model is proposed with introducing the hinge rolling in order to capture its inner deformation and stress. The structure of the hinge rolling is explicitly presented. Both the panel and the hinge rolling are modeled by a three-dimensional (3D) fully-parameterized beam using the Absolute Nodal Coordinate Formulation (ANCF). When assembling the panels and its hinge rolling, the concept of body coordinate system is first used to address slope discontinuity problem, and then a set of linear kinematic formulations of the rigid joint is derived that is used for them connection. The resulting equations of motion for the constrained rigid-flexible multibody system is solved by the implicit 4th Adams algorithm. The proposed model is validated using the FE part module of MSC.ADAMS commercial software. Four numerical examples are simulated to study the performance and advantages of the proposed solar array model. Furthermore, this proposed model is also used for the attitude control study of spacecraft main body. It is shown that this accurate model can be a good candidate for the engineering application and subsequent control usage.

Unmanned wave glider heading model identification and control by artificial fish swarm algorithm

We introduce the artificial fish swarm algorithm for heading motion model identification and control parameter optimization problems for the “Ocean Rambler” unmanned wave glider (UWG). First, under certain assumptions, the rigid-flexible multi-body system of the UWG was simplified as a rigid system composed of “thruster + float body”, based on which a planar motion model of the UWG was established. Second, we obtained the model parameters using an empirical method combined with parameter identification, which means that some parameters were estimated by the empirical method. In view of the specificity and importance of the heading control, heading model parameters were identified through the artificial fish swarm algorithm based on tank test data, so that we could take full advantage of the limited trial data to factually describe the dynamic characteristics of the system. Based on the established heading motion model, parameters of the heading S-surface controller were optimized using the artificial fish swarm algorithm. Heading motion comparison and maritime control experiments of the “Ocean Rambler” UWG were completed. Tank test results show high precision of heading motion prediction including heading angle and yawing angular velocity. The UWG shows good control performance in tank tests and sea trials. The efficiency of the proposed method is verified.

Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid

As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics (SPH) method is used to model the compressible fluid, the natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit (GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.

Thermal shock induced dynamics of a spacecraft with a flexible deploying boom

The dynamics in the process of deployment of a flexible extendible boom as a deployable structure on the spacecraft is studied. For determining the thermally induced vibrations of the boom subjected to an incident solar heat flux, an axially moving thermal-dynamic beam element based on the absolute nodal coordinate formulation which is able to precisely describe the large displacement, rotation and deformation of flexible body is presented. For the elastic forces formulation of variable-length beam element, the enhanced continuum mechanics approach is adopted, which can eliminate the Poisson locking effect, and take into account the tension-bending-torsion coupling deformations. The main body of the spacecraft, modeled as a rigid body, is described using the natural coordinates method. In the derived nonlinear thermal-dynamic equations of rigid-flexible multibody system, the mass matrix is time-variant, and a pseudo damping matrix which is without actual energy dissipation, and a heat conduction matrix which is relative to the moving speed and the number of beam element are arisen. Numerical results give the dynamic and thermal responses of the nonrotating and spinning spacecraft, respectively, and show that thermal shock has a significant influence on the dynamics of spacecraft.

Deployment dynamics simulation and ground test of a large space hoop truss antenna reflector

In recent years, the space community has paid much attention to the development of the hoop truss antenna of satellite so as to improve the quality of telecommunication of high frequency. The antenna reflector is mainly composed of a mesh net and a deployable ring truss, which can be considered as a rigid-flexible multibody system. During the research process of the hoop truss antenna of satellite, an accurate and effective dynamics model has to be built. In order to describe the flexible components in this system accurately, the Absolute-Coordinate-Based (ACB) method combining the Absolute Nodal Coordinate Formulation (ANCF) and Natural Coordinate Formulation (NCF) is used to predict the deployment dynamics of the reflector antenna. Furthermore, the parallel computation methodology based on the multilevel decomposition method and the Schur Complement method is used to improve the computational efficiency. Using the parallel computation methodology, the dynamic simulation of a rigid-flexible multibody system is efficiently completed based on the Message Passing Interface. To analyze the asynchronous deployment phenomenon in the ground test, the decrease of the driving force is applied to the antenna reflector model. Finally, based on the above method, a computational program is developed via the Fortran language to analyze the deployment dynamics of the hoop truss mesh antennas. Using the program, the second phase of the deployment process of the hoop truss mesh antennas is simulated, and the computational results are verified by a deployment experiment on the 4 m aperture antenna reflector.

Absolute Nodal Coordinate Formulation in a Pre-Stressed Large-Displacements Dynamical System

The design process for dynamical models has to consider all the properties of a mechanical system that have an effect on its dynamical response. In multi-body dynamics, flexible bodies are frequently modeled as rigid, resulting in non-valid modeling of the pre-stress effect. In this research a focus on the pre-stress effect for a flexible body assembled in a rigid-flexible multibody system is presented. In a rigid-flexible assembly a flexible body is modeled with an absolute nodal coordinate formulation (ANCF) of finite elements. The geometrical properties of the flexible body are evaluated based on the frequency response and compared with the experimental values. An experiment including the pre-stress effect and large displacements is designed and the measured values of the displacement are compared to the numerical results in order to validate the dynamical model. The pre-stress was found to be significant for proper numerical modeling. The partially validated numerical model was used to research the effect of different parameters on the dynamical response of a pre-stressed, rigid-flexible assembly.

Fuzzy tuning control approach to perform cooperative object manipulation by a rigid–flexible multibody robot

We study cooperative object manipulation control of rigid–flexible multibody systems in space. During such tasks, flexible members like solar panels may get vibrated. Which in turn may lead to some oscillatory disturbing forces on other subsystems and consequently produce errors in the motion of the end-effectors of the cooperative manipulating arms. Therefore, to design and develop capable model-based controllers for such complicated systems, deriving a dynamics model is required. However, due to practical limitations and real-time implementation, the system dynamics model should require low computations. So, first, to obtain a precise compact dynamics model, the rigid–flexible interactive dynamics modeling (RFIM) approach is briefly introduced. Using this approach, the system is virtually partitioned into two rigid and flexible portions, and a convenient model for control purposes is developed. Next, a fuzzy tuning manipulation control (FTMC) algorithm is developed for a simple conceptual model for cooperative object manipulation. In fact, a suitable setup is designed for practical implementation of this controller. After that, a wheeled mobile robot (WMR) system with flexible appendages is considered as a practical case that necessitates delicate force exertion by several end-effectors to move an object along a desired path. The WMR system contains two cooperative manipulators, appended with two flexible solar panels. To reveal the merits of the developed model-based controller, the maneuver is deliberately planned such that flexible modes of solar panels get stimulated due to arms motion. The obtained results show an effective performance of the proposed approach as will be discussed.

Quasi-time-optimal controller design for a rigid-flexible multibody system via absolute coordinate-based formulation

Previous studies have shown that the absolute coordinate-based formulation is an accurate modeling approach for the rigid-flexible multibody system subject to both large rotation and large deformation. However, it is almost impossible to design the complex controller for a rigid-flexible multibody system via the absolute coordinate-based formulation because of its high dimensions. The primary aim of this study is to design a quasi-optimal controller for a rigid-flexible multibody system via the absolute coordinate-based formulation. The design procedure includes two steps. As the first step, the simplified model for a rigid-flexible multibody system is established via the floating frame of reference formulation first, and then, a time-optimal controller is designed for the simplified model by using the Gauss pseudo-spectral method. In the second step, a quasi-time-optimal closed-loop tracking controller is achieved for the absolute coordinate-based formulation of the rigid-flexible multibody system by superposing a PD controller to track the pre-designed optimal trajectory. The paper presents two case studies for a hub-beam system, where only the motion of the rigid part is observable and driven. The numerical results of the two case studies well verify the effectiveness of the proposed controller.

Compliant dynamics of a rectilinear rear-independent system

The rectilinear rear-independent suspension investigated in this paper could remain the wheel alignment parameters invariable in theory. However, its dynamics is much more complex than that of the existing suspensions because of its redundant constraints in structure. Considering the elasticity of the rectilinear rear-independent suspension, a rigid-flexible half-car dynamic model is established for the first time based on the discrete time transfer matrix method. At the same time, a rigid half-car dynamic model is established as a comparison. The natural frequency characteristics and dynamic response of the rectilinear rear-independent suspension under random road excitations are analyzed and compared with those of rigid half-car dynamic model. The results reveal that the suspension system has apparent influence to the dynamics of vehicle. The wheel alignment parameters will fluctuate within a narrow range which is mainly determined by the rolling vibration of vehicle. And the suspension system could reduce and filter the road excitations with high frequency and small amplitude. This provides a good effect on the ride comfort of vehicle. Dynamics analysis of the rectilinear rear independent suspension reveals that the proposed modeling approach could deal with the dynamics of rigid-flexible multibody systems with redundant constraints effectively.

A new elastohydrodynamic lubricated spherical joint model for rigid-flexible multibody dynamics

In a unified global coordinate system frame, a new elastohydrodynamic (EHD) lubricated spherical joint model for flexible multibody dynamics is proposed. The proposed joint can be further used to model the human gait artificial hip joints. To mesh the flexible spherical socket of the joint, an isoparametric fifteen-node pentahedron finite element with global nodal position coordinates is introduced. The element elastic forces and their Jacobians are derived using a continuum mechanics approach. The ball within the spherical joint is assumed to be rigid, and it is described using the absolute nodal coordinate formulation reference node (ANCF-RN). The spherical joint lubricant pressure is obtained by solving the Reynolds’ equation using the successive over relaxation (SOR) algorithm. To address the lubrication interface non-conformance problem that exists between the lubricant grid and the socket inner surface node grid, a novel lubricant finite-difference grid rotation scheme is introduced. The assembled equations of motion for the constrained rigid-flexible multibody system with a large number of degrees of freedom are solved using the generalized-alpha algorithm. Finally, four numerical examples are studied to validate the proposed EHD lubricated spherical joint model. Some numerical results are also verified using the commercial software ADINA.

Uncertain dynamic analysis for rigid-flexible mechanisms with random geometry and material properties

This paper proposes an uncertain modelling and computational method to analyze dynamic responses of rigid-flexible multibody systems (or mechanisms) with random geometry and material properties. Firstly, the deterministic model for the rigid-flexible multibody system is built with the absolute node coordinate formula (ANCF), in which the flexible parts are modeled by using ANCF elements, while the rigid parts are described by ANCF reference nodes (ANCF-RNs). Secondly, uncertainty for the geometry of rigid parts is expressed as uniform random variables, while the uncertainty for the material properties of flexible parts is modeled as a continuous random field, which is further discretized to Gaussian random variables using a series expansion method. Finally, a non-intrusive numerical method is developed to solve the dynamic equations of systems involving both types of random variables, which systematically integrates the deterministic generalized-α solver with Latin Hypercube sampling (LHS) and Polynomial Chaos (PC) expansion. The benchmark slider-crank mechanism is used as a numerical example to demonstrate the characteristics of the proposed method.

Dynamics modeling and attitude control of a flexible space system with active stabilizers

Attitude control of rigid-flexible multi-body systems by active stabilizers is studied in this paper. During slewing maneuvers, flexible members like solar panels may be excited to vibrate. These vibrations, in turn, produce oscillatory disturbing forces on other subsystems and consequently produce error in the spacecraft motion. Also, to develop a proper model-based controller for such complicated system, the system dynamic model is derived. However, due to practical limitations and real-time control implementation, the system dynamic model should be structured such that low computations burden will be imposed on the model-based controller. In this paper, in contrast to many accumulating dynamic modeling approach, a precise compact dynamic model for an active stabilized spacecraft (ASS) system with flexible members is derived. Toward this goal, the total system is virtually partitioned into two rigid and flexible portions. Moreover, the obtained model of these complicated systems is vigorously verified using ANSYS and ADAMS programs. Finally, based on the derived dynamics and a proper virtual damping parameter, an attitude control algorithm is then developed. The suggested controller structure takes the advantage of utilizing the piezoelectric smart materials to dissipate the vibration of solar panels. The obtained results reveal the merits and effectiveness of the proposed suggested modeling and control methods for reliable attitude maneuvering of the system. In addition, it will be shown that the undesired vibrations of the flexible solar panels result in disturbing forces on the ASS system which can be significantly eliminated by the proposed attitude control algorithm.

Investigation of the dynamic behaviour of an automobile wiper system

A rigid-flexible multi-body system dynamic model of a passenger vehicle windscreen wiper system is established in this study to investigate the systems dynamic behaviour. To simulate the impact forces applied by the blades on the windshield and the pressure force distributions along the wiper blades, the blades are modelled as flexible bodies in consideration of their bend and twist deformations. On the basis of the dynamic analysis results, structure improvement measures, including changing the torsional stiffness of the neck of the blade segment and modifying the positions of the pivot points on the blades, are implemented to reduce the reversal impact and improve the wiping uniformity.

Dynamics of spatial rigid–flexible multibody systems with uncertain interval parameters

A non-intrusive computation methodology is proposed to study the dynamics of rigid–flexible multibody systems with a large number of uncertain interval parameters. The rigid–flexible multibody system is meshed by using a unified mesh of the absolute nodal coordinate formulation (ANCF). That is, the flexible parts are meshed by using the finite elements of the ANCF, while the rigid parts are described via the ANCF reference nodes (ANCF-RNs). Firstly, the interval differential-algebraic equations are directly transformed into the nonlinear interval algebraic equations by using the generalized-alpha algorithm. Then, the Chebyshev sampling methods, including Chebyshev tensor product sampling method and Chebyshev collocation method, are used to transform the nonlinear interval algebraic equations into sets of nonlinear algebraic equations with deterministic sampling parameters. The proposed computation methodology is non-intrusive because the original generalized-alpha algorithm is not amended. OpenMP directives are also used to parallelize the solving process of these deterministic nonlinear algebraic equations. To circumvent the interval explosion problem and maintain computation efficiency, the scanning method is used to determine the upper and lower bounds of the deducted Chebyshev surrogate models. Finally, two numerical examples are studied to validate the proposed methodology. The first example is used to check the effectiveness of the proposed methodology. And the second one of a complex rigid–flexible robot with uncertain interval parameters shows the effectiveness of the proposed computation methodology in the dynamics analysis of complicated spatial rigid–flexible multibody systems with a large number of uncertain interval parameters.

Adaptive hybrid suppression control of space free-flying robots with flexible appendages

SUMMARYControl of rigid–flexible multi-body systems in space, during cooperative manipulation tasks, is studied in this paper. During such tasks, flexible members such as solar panels may vibrate. These vibrations in turn can lead to oscillatory disturbing forces on other subsystems, and consequently may produce significant errors in the position of operating end-effectors of cooperative arms. Therefore, to design and implement efficient model-based controllers for such complicated nonlinear systems, deriving an accurate dynamics model is required. On the other hand, due to practical limitations and real-time implementation, such models should demand fairly low computational complexity. In this paper, a precise dynamics model is derived by virtually partitioning the system into two rigid and flexible portions. These two portions will be assembled together to generate a proper model for controller design. Then, an adaptive hybrid suppression control (AHSC) algorithm is developed based on an appropriate variation rule of a virtual damping parameter. Finally, as a practical case study a space free-flying robot (SFFR) with flexible appendages is considered to move an object along a desired path through accurate force exertion by several cooperative end-effectors. This system includes a main rigid body equipped with thrusters, two solar panels, and two cooperative manipulators. The system also includes a third and fourth arm that act as a communication antenna and a photo capturing camera, respectively. The maneuver is deliberately planned such that flexible modes of solar panels get stimulated due to arms motion, while obtained results reveal the merits of proposed controller as will be discussed.

A Simplified Flexible Multibody Dynamics for a Main Landing Gear with Flexible Leaf Spring

The dynamics of multibody systems with deformable components has been a subject of interest in many different fields such as machine design and aerospace. Traditional rigid-flexible systems often take a lot of computer resources to get accurate results. Accuracy and efficiency of computation have been the focus of this research in satisfying the coupling of rigid body and flex body. The method is based on modal analysis and linear theory of elastodynamics: reduced modal datum was used to describe the elastic deformation which was a linear approximate of the flexible part. Then rigid-flexible multibody system was built and the highly nonlinearity of the mass matrix caused by the limited rotation of the deformation part was approximated using the linear theory of elastodynamics. The above methods were used to establish the drop system of the leaf spring type landing gear of a small UAV. Comparisons of the drop test and simulation were applied. Results show that the errors caused by the linear approximation are acceptable, and the simulation process is fast and stable.

Kinematics analysis and numerical simulation of a manipulator based on virtual prototyping

Manipulator kinematics refers the analytical study of the motion of manipulator, such as positions, velocities, and accelerations of the links of a manipulator. As formulating the suitable kinematics models for a manipulator is very crucial for analyzing the behavior of manipulators and light weight design of manipulators, many researches have been focused on it in recent decades with a result of many valuable contributions. However, current researches always focus on rigid manipulator, while the manipulator is always a rigid-flexible coupling multibody system, which can affect the accuracy of kinematics analysis and numerical simulation. This paper proposed a model of kinematics analysis of manipulator based on rigid-flexible coupling virtual prototyping. After a model of manipulator kinematics based on the D-H method was proposed, rigid-flexible coupling virtual prototyping-based kinematics simulation and numerical simulation was then put forward. The kinematical experiment is carried out based on manipulator physical prototyping, which demonstrates that the accuracy of the kinematics calculation and the rationality of design based on rigid-flexible coupling virtual prototyping. The design of a five-degrees-of-freedom manipulator is given as an example, which demonstrates that the methodology is obviously helpful to manipulator design.

Dynamic simulation and tension compensation research on subsea umbilical cable laying system

For studying the dynamic performance of subsea umbilical cable laying system and achieving the goal of cable tension and laying speed control, the rigid finite element method is used to discrete and transform the system into a rigid-flexible coupling multi-body system which consists of rigid elements and spring-damping elements. The mathematical model of subsea umbilical cable laying system kinematic chain is presented with the second order Lagrange equation in the joint coordinate system, and dynamic modeling and simulation is performed with ADAMS. The dynamic analysis is conducted assuming the following three statuses: ideal laying, practical laying under wave disturbance, and practical laying with tension compensation. Results show that motion disturbances of the laying budge under sea waves, especially with heaving and pitching, will cause relatively serious fluctuations in cable tension and laying speed. Tension compensation, i.e., active back tension torque control can restrict continuous tension increasing or decreasing effectively and rapidly, thus avoiding cable breach or buckling.

Cooperative Object Manipulation by a Space Robot with Flexible Appendages

Modelling and control of rigid-flexible multibody systems is studied in this paper. As a specified application, a space robotic system with flexible appendages during a cooperative object manipulation task is considered. This robotic system necessitates delicate force exertion by several end-effectors to move an object along a desired path. During such maneuvers, flexible appendages like solar panels may get stimulated and vibrate. This vibrating motion will cause some oscillatory disturbing forces on the spacecraft, which in turn produces error in the motion of the end-effectors of the cooperative manipulating arms. In addition, vibration control of these flexible members to protect them from fracture is another challenging problem in an object manipulation task for the stated systems. Therefore, the multiple impedance control algorithm is extended to perform an object manipulation task by such complicated rigid-flexible multibody systems. This extension in the control algorithm considers the modification term which compensates the disturbing forces due to vibrating motion of flexible appendages. Finally, a space free-flying robotic system which contains two 2-DOF planar cooperative manipulators, appended with two highly flexible solar panels, is simulated. Obtained results reveal the merits of the developed model-based controller which will be discussed.