Multibody Framework Research Articles

System identification and force estimation of robotic manipulator using semirecursive multibody formulation

AbstractForce estimation in multibody dynamics relies heavily on knowing the system model with a high level of accuracy. However, in complex mechatronic systems, such as robots or mobile machinery, the values of model parameters may be only roughly estimated based on design information, such as CAD data. The errors in model parameters consequently have a direct effect on force estimation accuracy because the estimator compensates the erroneous inertia, friction, and applied forces by changing the value of estimated external force. The objective of this study is to present the workflow of system identification and state/force estimation of an open-loop multibody structure. The system identification utilizes a linear regression identification method used in robotics adapted to the multibody framework. The semirecursive multibody formulation, in particular, is studied as a formulation for both system identification and force estimation. The multibody state/force estimator is constructed using extended Kalman filter. The specific aim of this paper is to demonstrate the utilization of these per se known modeling, identification, and estimation tools to address their current lack of integration as a complete toolchain in virtual sensing of multibody systems. The methodology of the study is tested with both artificial and experimental data of Stäubli TX40 robotic manipulator. In the experimental analysis, an openly available benchmark data set was used. Artificial data were created by running an inverse dynamics analysis with inertia and friction parameters taken from literature. The results show that the multibody inertia and friction parameters can be accurately identified and the identified model can be used to produce decent estimates of external forces. The proposed multibody system identification method itself opens new opportunities in tuning the multibody models used in product development. Moreover, effective use of system identification together with state estimation helps to build more accurate estimators. When the system model is accurately identified, the capability of state estimator to observe unknown inputs, such as external forces, is significantly enhanced.

A peridynamics approach to flexible multibody dynamics for fracture analysis of mechanical systems

The classical theory of continuum mechanics is formulated using partial differential equations (PDEs) that fail to describe structural discontinuities, such as cracks. This limitation motivated the development of peridynamics, reformulating the classical PDEs into integral-differential equations. In this theory, each material point interacts with its neighbours inside a characteristic length-scale through bond-interaction forces. However, while peridynamics can simulate complex multi-physics phenomena, its integration in the study of mechanical systems is still limited. This work presents a methodology that incorporates a peridynamics formulation into a planar multibody dynamics (MBD) formulation to allow the integration of flexible structures described by peridynamics into mechanical systems. A flexible body is described by a collection of point masses, in analogy with the meshless collocation scheme commonly used for peridynamics discretisations. Each point mass interacts with other point masses through nonlinear forces governed by a bond-based peridynamics (BBPD) formulation. The virtual bodies methodology enables the definition of kinematic joints connecting the flexible body with the neighbouring bodies. The implementation of the methodology proposed is illustrated using various mechanisms with different levels of complexity. Notched plates subjected to different loading conditions are compared with the results presented in the literature of the peridynamics field. The deformations of a flexible slider-crank mechanism compare well with the results obtained using a classical flexible MBD formulation. Additionally, three scenarios involving a rotating pendulum illustrate how the methodology proposed allows simulating impact scenarios. The results demonstrate how this methodology is capable to successfully simulate highly nonlinear phenomena, including crack propagation, in a multibody framework.

Nonlinear dynamic optimization of marine riser system anti-recoil under a flexible multibody framework

Anti-recoil safety of marine risers is critical for deep water offshore drilling. The challenges of riser anti-recoil optimization stem primarily from two factors: (a) nonlinearities of the violent transient response with various system stages and types of design variables and (b) discontinuities of the objective and constraint functions expressed by max–min over the time domain. In this paper, a nonlinear dynamic optimization model and solution method of marine riser system anti-recoil under a flexible multibody framework is proposed. The objective and constraint functions are elaborately designed to protect the system from dynamic buckling and wellhead and riser collision. Corresponding treatments to system state changes and time step sampling are proposed for numerical sensitivity smoothing. In addition, an extra acceleration constraint is imposed to trim and regularize the feasible domain defined by the discontinuous clearance constraint. Following that, the global convergent method of moving asymptotes (GCMMA) is applied. The presented continuous optimization formulation is numerically tested on a real marine riser platform from the X oil field in the South China Sea with a water depth of 1547 m. The numerical results are compared with those computed using a genetic algorithm (GA), surrogate method and interior point method, and the effectiveness and efficiency of the proposed method is demonstrated.

Advances in fine line-of-sight control for large space flexible structures

The increased need in pointing performance for Earth observation and science Space missions together with the use of lighter and flexible structures directly come with the need of a robust pointing performance budget from the very beginning of the mission design. An extensive understanding of the system physics and its uncertainties is then necessary in order to push control design to the limits of performance and constrains the choice of the set of sensors and actuators. A multi-body framework, the Two Input Two Output Ports approach, is used to build all the elementary flexible bodies and mechanisms involved in a fine pointing mission. This framework allows the authors to easily include all system dynamics with an analytical dependency on varying and uncertain mechanical parameters in a unique Linear Fractional Transformation (LFT) model. This approach opens the doors to modern robust control techniques that robustly guarantee the expected fine pointing requirements. In particular, a novel control architecture is proposed to reduce the microvibrations induced both by reaction wheel imbalances and Solar Array Drive Mechanism driving signal, by letting them work during the imaging phase. Thanks to a set of accelerometers placed at the isolated base of the payload and in correspondence of the mirrors with the largest size in a Space telescope (typically the primary and secondary ones), it is possible to estimate the line-of-sight error at the payload level by hybridizing them with the low-frequency measurements of the camera. While a classical Fast Steering Mirror in front of the camera can compensate for a large amount of microvibration, an innovative architecture with a set of six Proof-Mass Actuators installed at the payload isolator level can further improve the pointing performance. In particular, it is shown how the proposed architecture is able to robustly guarantee an absolute performance error of 10 arcsec in face of system parametric uncertainties at low frequency (≈ 1rad/s) with a progressive reduction of the jitter down to 40 marcsec for higher frequencies where micro-vibration sources act.

Open Simulation Environment for Learning and Practice of Robot-Assisted Surgical Suturing

Automation has the potential to improve the standard of care but is difficult to realize due to perceptual challenges, especially in soft-tissue surgery. Machine learning can provide solutions, but typically requires large amounts of training data, which is time-consuming to collect. Even with shared platforms, hardware differences can prevent effective sharing of data between institutions. This letter proposes a standardized simulation platform for training and testing algorithms to control surgical robotic systems, which is built upon an open-source simulator, the Asynchronous Multi-Body Framework (AMBF), to enable quick prototyping of different scenes. An illustrative example of a suturing task on a phantom is presented and has formed the basis of a challenge, released to the community. The top-level contribution is the open-source release of a dynamic simulation environment that enables realistic suturing on a phantom, but supporting contributions include its extendable architectural design and a series of algorithmic optimizations to achieve real-time control and collision detection, realistic behavior of the needle and suture, and generation of multi-modal ground-truth data, including labeled depth data. These capabilities enable simulation-based surgical training and support research in machine learning for surgical scene perception and autonomous action.

Virtual reality for synergistic surgical training and data generation

ABSTRACT Surgical simulators not only allow planning and training of complex procedures, but also offer the ability to generate structured data for algorithm development, which may be applied in image-guided computer assisted interventions. While there have been efforts on either developing training platforms for surgeons or data generation engines, these two features, to our knowledge, have not been offered together. We present our developments of a cost-effective and synergistic framework, named Asynchronous Multibody Framework Plus (AMBF+), which generates data for downstream algorithm development simultaneously with users practicing their surgical skills. AMBF+ offers stereoscopic display on a virtual reality (VR) device and haptic feedback for immersive surgical simulation. It can also generate diverse data such as object poses and segmentation maps. AMBF+ is designed with a flexible plugin setup that allows for unobtrusive extension for simulation of different surgical procedures. We show one use case of AMBF+ as a virtual drilling simulator for lateral skull-base surgery, where users can actively modify the patient anatomy using a virtual surgical drill. We further demonstrate how the data generated can be used for validating and training downstream computer vision algorithms.

A Track Geometry Measuring System Based on Multibody Kinematics, Inertial Sensors and Computer Vision.

This paper describes the kinematics used for the calculation of track geometric irregularities of a new Track Geometry Measuring System (TGMS) to be installed in railway vehicles. The TGMS includes a computer for data acquisition and process, a set of sensors including an inertial measuring unit (IMU, 3D gyroscope and 3D accelerometer), two video cameras and an encoder. The kinematic description, that is borrowed from the multibody dynamics analysis of railway vehicles used in computer simulation codes, is used to calculate the relative motion between the vehicle and the track, and also for the computer vision system and its calibration. The multibody framework is thus used to find the formulas that are needed to calculate the track irregularities (gauge, cross-level, alignment and vertical profile) as a function of sensor data. The TGMS has been experimentally tested in a 1:10 scaled vehicle and track specifically designed for this investigation. The geometric irregularities of a 90 m-scale track have been measured with an alternative and accurate method and the results are compared with the results of the TGMS. Results show a good agreement between both methods of calculation of the geometric irregularities.

Investigation for Failure Response of Suspension Spring of Railway Vehicle: A Categorical Literature Review

Helical spring is used as primary suspension to absorb shock and vibration in rail vehicle system which calls for investigation under failure response because of different loading conditions. This paper is based on the categorical literature review on case study of failure response of suspension spring of railroad vehicle. Here, the investigation of a multibody framework approach is introduced that can be utilized to create complex model of railroad vehicle suspension system. The literature presented encounters results in various domains of analysis including static and dynamic analytical analysis, experimental investigation, dynamic model and finite element analysis for its failure study and examination. It has been observed that the stress may initiate at the inside diameter of spring due to curvature effect during manufacturing occurs residual stress. Also, it induces due to lateral and longitudinal load due to curving and tracking of the rail vehicle system.

Geometrically exact static 3D Cosserat rods problem solved using a shooting method

This paper aims to solve the equations of geometrically exact 3D nonlinear Cosserat static rods under large displacements with a mesh free alternative method to finite elements: the shooting method. One of the main goal of the work presented is to introduce a new multiple shooting method to handle geometrical discontinuities as well as beams assembled through mechanical linkages in a multi-body framework. An additional purpose is to propose a new shooting method algorithm in which the dual set of Modified Rodrigues Parameters (MRP) and Shadow Modified Rodrigues Parameters (SMRP) are used for rotations parameterization along the length of the beam in order to model extremely large rotations. Several numerical examples demonstrate the validity, the performance and accuracy of the proposed approach.

Impact Dynamics of Single-Layered Graphene Sheets in Multibody Framework Using Nonlocal-Based-ANCF Modeling

A new nonlinear model based on the absolute nodal coordinate formulation (ANCF) and the nonlocal elasticity theory is proposed to investigate the single-layered graphene sheets (SLGSs) impacted by nanoparticles. The geometrical definition of SLGSs is described by using the ANCF thin plate element, and the strain energy is expressed by using the nonlocal theory. The Lennard–Jones pair potential is adopted to model the van der Waals (vdW) force between SLGSs and nanoparticles. The impact dynamics of the system is simulated in multibody framework by using the generalized-alpha numerical integration method. The impact response of the gold atom–SLGSs system is simulated to validate the performance of the proposed model. Three impact dynamic simulations are conducted to investigate the influence of nanoparticles on the impact dynamics of SLGSs. The results show that the coupling of SLGSs vibration and vdW force led to the amplitude inconsistence of [Formula: see text]-position for nanoparticles.

An electromechanically coupled intrinsic, mixed variational formulation for geometrically nonlinear smart composite beam

• Geometrically exact formulation for smart slender structures. • Non-linear analysis of piezoelectric laminated composite beam. • Excellent agreement of results with the literature as well as the finite element software, ABAQUS. • Development of a platform for faster analysis while maintaining the accuracy. The work presented in this article is the outcome of a combined strategy of a mathematical tool for 2D cross-sectional analysis, i.e., Variational Asymptotic Method (VAM) as well as the 1D exact beam analyzer, i.e., the intrinsic mixed variational formulation for modeling and analysis of Piezoelectric-laminated composite beams. This work talks about a novel approach of mixed variational formulation to analyze a two-way electromechanically coupled piezoelectric composite beam. In a classical intrinsic mixed variational approach for a passive structure, the 1D exact beam model deals only with mechanical degrees of freedom. In the present case, an extra 1D electrical degree of freedom has been incorporated. A computational code is developed based on the present theory to solve the two-way coupled electromechanical beam problem. In the present case, we have validated the static results for sensor application. Both linear and nonlinear results have been discussed. Results obtained are very promising and are helpful in building a platform where design, optimization and nonlinear analysis of composite ‘smart’ beams in a multibody framework can be done faster while maintaining acceptable accuracy.

Stochastic response reduction on offshore wind turbines due to flaps including soil effects

This work attempts to investigate the load mitigation effects on foundations of NREL 5-MW offshore wind turbine (OWT) supported on fixed structures using blade trailing edge flaps. The analysis is subjected to turbulent wind and irregular wave loads. The offshore wind turbine is simulated for five met-ocean conditions for Indian scenario, covering operational to the parked region of turbine. Sea states being stochastic, the responses are obtained using average of Monte Carlo simulations. The blade element momentum theory is used to obtain the aerodynamic loads by modelling in a multi-body framework while the hydrodynamic and geotechnical analysis are performed in a finite element framework. Soil-structure interaction is modelled using nonlinear Winkler spring model along the length of the pile. The trailing edge flaps are numerically implemented through a dynamic link library into the aerodynamic program. Loose sandy soils with uniform density is considered for analysis. The results bring out the importance of including blade trailing edge flaps in OWT studies with significant response reduction (2.1–16.0%) for designing pile foundations.

Multi-body engine simulation including elastohydrodynamic lubrication for non-conformal conjunctions

The evaluation of lubricated contacts is an essential step in modern internal combustion engine simulation to estimate run-time behaviour. A thorough investigation of the occurring thin oil films is critical to estimate friction, wear, noise, vibration and harshness and the overall dynamic behaviour. The prediction of contact pressure and oil film height poses a complex task, especially in non-conformal conjunctions, such as between a cam and a follower. This paper introduces a generic algorithm to solve the elastohydrodynamic lubrication problem and integrates it into a multi-body simulation environment. A focus is put on the versatile integration of the elastohydrodynamic lubrication model into the multi-body framework to create a basis for a full engine simulation. The Reynolds equation and the film thickness equation are treated as modular decoupled systems and, therefore, allow a modular structure of the elastohydrodynamic lubrication algorithm. The method introduced here incorporates existing relaxation techniques and uses them in a decoupled elastohydrodynamic lubrication solver for flexible multi-body dynamics simulation. The contact between a cam and a follower of an internal combustion engine is used as an exemplary contact to test the derived elastohydrodynamic lubrication model. A four-cylinder full engine model with 16 valves and two flexible camshafts is investigated as an example to outline effects of an oil film lubricated cam follower conjunctions in valve train simulation.

Geometrically nonlinear analysis of composite beams using Wiener-Milenković parameters

This paper presents a geometrically nonlinear analysis of composite beams including static, dynamic, and eigenvalue analyses. With the increase in size and flexibility of engineering components such as wind turbine blades, geometric nonlinearity plays an increasingly significant role in structural analysis. The Geometric Exact Beam Theory (GEBT), pioneered by Reissner and extended by Hodges, is adopted as the foundation for this work. Special emphasis is placed on the vectorial parameterization of finite rotation, which is a fundamental aspect in the geometrically nonlinear formulation. This method is introduced based on Euler's rotation theorem and the property of rotation operation: the length preservation of the rotated vector. The GEBT is then implemented with the Wiener-Milenković parameters using a mixed formulation. Several numerical examples are studied based on the derived theory, and the results are compared with analytical solutions and those available in the literature. The analysis of a realistic composite wind turbine blade is provided to show the capability of the present model for generalized composite slender structures. It concludes that the proposed model can be used as a beam tool in a multibody framework whose valid range of rotation is up to 2π.

Prediction of elbow joint contact mechanics in the multibody framework

Computational multibody musculoskeletal models of the elbow joint that are capable of simultaneous and accurate predictions of muscle and ligament forces, along with cartilage contact mechanics can be immensely useful in clinical practice. As a step towards producing a musculoskeletal model that includes the interaction between cartilage and muscle loading, the goal of this study was to develop subject-specific multibody models of the elbow joint with discretized humerus cartilage representation interacting with the radius and ulna cartilages through deformable contacts. The contact parameters for the compliant contact law were derived using simplified elastic foundation contact theory. The models were then validated by placing the model in a virtual mechanical tester for flexion-extension motion similar to a cadaver experiment, and the resulting kinematics were compared. Two cadaveric upper limbs were used in this study. The humeral heads were subjected to axial motion in a mechanical tester and the resulting kinematics from three bones were recorded for model validation. The maximum RMS error between the predicted and measured kinematics during the complete testing cycle was 2.7mm medial-lateral translation and 9.7° varus–valgus rotation of radius relative to humerus (for elbow 2). After model validation, a lateral ulnar collateral ligament (LUCL) deficient condition was simulated and, contact pressures and kinematics were compared to the intact elbow model. A noticeable difference in kinematics, contact area, and contact pressure were observed for LUCL deficient condition. LUCL deficiency induced higher internal rotations for both the radius and ulna during flexion and an associated medial shift of the articular contact area.

A Study on the Flexible Multibody Dynamic Modeling of an Axial Piston Pump Considering Housing Flexibility

Axial piston type hydraulic pump is an important source of fluid power in hydraulic systems. In the present work, a methodology for modeling the dynamics of the pump in multibody framework considering component flexibility is studied. A multibody dynamic model of the pump is developed considering housing flexibility and pressure forces acting on the pistons. The flexibility of the housing is modeled using the relative nodal coordinate formulation (RNCF) with a floating frame of reference. The bearing forces, control piston force, swashplate motion and torque ripple are studied. The bearing and control piston force results are compared with the case of a rigid housing assembly. The experiments are conducted to measure the end cover vibration levels during operation of the pump. The vibration levels are also obtained from the simulation and compared with experiments. Numerical studies are conducted to better understand the influence of housing flexibility on the dynamics of the pump.

Flight Loads Prediction of High Aspect Ratio Wing Aircraft Using Multibody Dynamics

A framework based on multibody dynamics has been developed for the static and dynamic aeroelastic analyses of flexible high aspect ratio wing aircraft subject to structural geometric nonlinearities. Multibody dynamics allows kinematic nonlinearities and nonlinear relationships in the forces definition and is an efficient and promising methodology to model high aspect ratio wings, which are known to be prone to structural nonlinear effects because of the high deflections in flight. The multibody dynamics framework developed employs quasi-steady aerodynamics strip theory and discretizes the wing as a series of rigid bodies interconnected by beam elements, representative of the stiffness distribution, which can undergo arbitrarily large displacements and rotations. The method is applied to a flexible high aspect ratio wing commercial aircraft and both trim and gust response analyses are performed in order to calculate flight loads. These results are then compared to those obtained with the standard linear aeroelastic approach provided by the Finite Element Solver Nastran. Nonlinear effects come into play mainly because of the need of taking into account the large deflections of the wing for flight loads computation and of considering the aerodynamic forces as follower forces.

Assessment of Gearbox Operational Loads and Reliability under High Mean Wind Speeds

This paper investigates the dynamic loads occurring in the drivetrain of wind turbines with a focus on offshore applications. Herein a model of the gearbox of the 5 MW wind turbine is presented. The model is developed in a multi-body framework using commercial software MSC ADAMS. Validation of the model was based on the experimental data provided by NREL for 750kW prototype gearbox. Failures of gearboxes caused by high dynamic loads have a significant influence on the cost of operation of wind farms. For these reasons in the study, the probability of failure of the gearbox working in an offshore wind turbine that operates in storm conditions with mean wind speeds less than 30 m/s is presented. In the study, normal shut-downs of a wind turbine in storm conditions were investigated. The analysis were conducted for two storm control strategies and different wind conditions from an extreme operating gust, normal turbulence model and extreme turbulence model. In the paper, loads in the planetary gear are quantified as well as the torsional moments in the main shaft. On the basis of simulation results the annual probability of failure of the gearbox in a wind turbine with soft storm controller is calculated, and compared with the one had the gearbox working in a wind turbine operating with hard storm controller. In the study, it was found that normal shut-downs do not have a significant influence on the ultimate loads in the gearbox, since they are related mostly to the gusts occurring during turbulence. Application of the storm controller with reduction of the wind turbine power allowed the decrease of the probability of failure for ultimate stresses.

Evaluation of a musculoskeletal model with prosthetic knee through six experimental gait trials

Knowledge of the forces acting on musculoskeletal joint tissues during movement benefits tissue engineering, artificial joint replacement, and our understanding of ligament and cartilage injury. Computational models can be used to predict these internal forces, but musculoskeletal models that simultaneously calculate muscle force and the resulting loading on joint structures are rare. This study used publicly available gait, skeletal geometry, and instrumented prosthetic knee loading data [1] to evaluate muscle driven forward dynamics simulations of walking. Inputs to the simulation were measured kinematics and outputs included muscle, ground reaction, ligament, and joint contact forces. A full body musculoskeletal model with subject specific lower extremity geometries was developed in the multibody framework. A compliant contact was defined between the prosthetic femoral component and tibia insert geometries. Ligament structures were modeled with a nonlinear force–strain relationship. The model included 45 muscles on the right lower leg. During forward dynamics simulations a feedback control scheme calculated muscle forces using the error signal between the current muscle lengths and the lengths recorded during inverse kinematics simulations. Predicted tibio-femoral contact force, ground reaction forces, and muscle forces were compared to experimental measurements for six different gait trials using three different gait types (normal, trunk sway, and medial thrust). The mean average deviation (MAD) and root mean square deviation (RMSD) over one gait cycle are reported. The muscle driven forward dynamics simulations were computationally efficient and consistently reproduced the inverse kinematics motion. The forward simulations also predicted total knee contact forces (166N<MAD<404N, 212N<RMSD<448N) and vertical ground reaction forces (66N<MAD<90N, 97N<RMSD<128N) well within 28% and 16% of experimental loads, respectively. However the simplified muscle length feedback control scheme did not realistically represent physiological motor control patterns during gait. Consequently, the simulations did not accurately predict medial/lateral tibio-femoral force distribution and muscle activation timing.

Multibody Muscle Driven Model of an Instrumented Prosthetic Knee During Squat and Toe Rise Motions

Detailed knowledge of knee joint kinematics and dynamic loading is essential for improving the design and outcomes of surgical procedures, tissue engineering applications, prosthetics design, and rehabilitation. The need for dynamic computational models that link kinematics, muscle and ligament forces, and joint contacts has long been recognized but such body-level forward dynamic models do not exist in recent literature. A main barrier in using computational models in the clinic is the validation of the in vivo contact, muscle, and ligament loads. The purpose of this study was to develop a full body, muscle driven dynamic model with subject specific leg geometries and validate it during squat and toe-rise motions. The model predicted loads were compared to in vivo measurements acquired with an instrumented knee implant. Data for this study were provided by the "Grand Challenge Competition to Predict In-Vivo Knee Loads" for the 2012 American Society of Mechanical Engineers Summer Bioengineering Conference. Data included implant and bone geometries, ground reaction forces, EMG, and the instrumented knee implant measurements. The subject specific model was developed in the multibody framework. The knee model included three ligament bundles for the lateral collateral ligament (LCL) and the medial collateral ligament (MCL), and one bundle for the posterior cruciate ligament (PCL). The implanted tibia tray was segmented into 326 hexahedral elements and deformable contacts were defined between the elements and the femoral component. The model also included 45 muscles on each leg. Muscle forces were computed for the muscle driven simulation by a feedback controller that used the error between the current muscle length in the forward simulation and the muscle length recorded during a kinematics driven inverse simulation. The predicted tibia forces and torques, ground reaction forces, electromyography (EMG) patterns, and kinematics were compared to the experimentally measured values to validate the model. Comparisons were done graphically and by calculating the mean average deviation (MAD) and root mean squared deviation (RMSD) for all outcomes. The MAD value for the tibia vertical force was 279 N for the squat motion and 325 N for the toe-rise motion, 45 N and 53 N for left and right foot ground reaction forces during the squat and 94 N and 82 N for toe-rise motion. The maximum MAD value for any of the kinematic outcomes was 7.5 deg for knee flexion-extension during the toe-rise motion.