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NASA NTRS2011

Constraint Embedding Technique for Multibody System Dynamics

Multibody dynamics play a critical role in simulation testbeds for space missions. There has been a considerable interest in the development of efficient computational algorithms for solving the dynamics of multibody systems. Mass matrix factorization and inversion techniques and the O(N) class of forward dynamics algorithms developed using a spatial operator algebra stand out as important breakthrough on this front. Techniques such as these provide the efficient algorithms and methods for the application and implementation of such multibody dynamics models. However, these methods are limited only to tree-topology multibody systems. Closed-chain topology systems require different techniques that are not as efficient or as broad as those for tree-topology systems. The closed-chain forward dynamics approach consists of treating the closed-chain topology as a tree-topology system subject to additional closure constraints. The resulting forward dynamics solution consists of: (a) ignoring the closure constraints and using the O(N) algorithm to solve for the free unconstrained accelerations for the system; (b) using the tree-topology solution to compute a correction force to enforce the closure constraints; and (c) correcting the unconstrained accelerations with correction accelerations resulting from the correction forces. This constraint-embedding technique shows how to use direct embedding to eliminate local closure-loops in the system and effectively convert the system back to a tree-topology system. At this point, standard tree-topology techniques can be brought to bear on the problem. The approach uses a spatial operator algebra approach to formulating the equations of motion. The operators are block-partitioned around the local body subgroups to convert them into aggregate bodies. Mass matrix operator factorization and inversion techniques are applied to the reformulated tree-topology system. Thus in essence, the new technique allows conversion of a system with closure-constraints into an equivalent tree-topology system, and thus allows one to take advantage of the host of techniques available to the latter class of systems. This technology is highly suitable for the class of multibody systems where the closure-constraints are local, i.e., where they are confined to small groupings of bodies within the system. Important examples of such local closure-constraints are constraints associated with four-bar linkages, geared motors, differential suspensions, etc. One can eliminate these closure-constraints and convert the system into a tree-topology system by embedding the constraints directly into the system dynamics and effectively replacing the body groupings with virtual aggregate bodies. Once eliminated, one can apply the well-known results and algorithms for tree-topology systems to solve the dynamics of such closed-chain system.

Woo, Simon S.↗

NASA NTRS1994

Modelling and simulation of Space Station Freedom berthing dynamics and control

A large-angle, flexible, multibody, dynamic modeling capability has been developed to help validate numerical simulations of the dynamic motion and control forces which occur during berthing of Space Station Freedom to the Shuttle Orbiter in the early assembly flights. This paper outlines the dynamics and control of the station, the attached Shuttle Remote Manipulator System, and the orbiter. The simulation tool developed for the analysis is described and the results of two simulations are presented. The first is a simulated maneuver from a gravity-gradient attitude to a torque equilibrium attitude using the station reaction control jets. The second simulation is the berthing of the station to the orbiter with the station control moment gyros actively maintaining an estimated torque equilibrium attitude. The influence of the elastic dynamic behavior of the station and of the Remote Manipulator System on the attitude control of the station/orbiter system during each maneuver was investigated. The flexibility of the station and the arm were found to have only a minor influence on the attitude control of the system during the maneuvers.

Cooper, Paul A.↗

DOE OSTI2025

Modeling and Verification of Lumped-Parameter, Multibody Structural Dynamics for Offshore Wind Turbines

This paper presents the modeling and verification of multibody structural dynamics for offshore wind turbines. The flexible tower and support structure of a monopile-based offshore wind turbine are modeled using an acausal, lumped-parameter, multibody approach that incorporates structural flexibility, soil-structure interaction, and hydrodynamic models. Simulation results are benchmarked against alternative modeling approaches, demonstrating the model's ability to accurately capture both static and dynamic behaviors under various wind and wave conditions while maintaining computational efficiency. This work provides a valuable tool for analyzing key structural characteristics of wind turbines, including eigenfrequencies, mode shapes, damping, and internal forces.

17 WIND ENERGY↗

NASA NTRS1991

A simulation of the instrument pointing system for the Astro-1 mission

NASA has recently completed a shuttle-borne stellar ultraviolet astronomy mission known as Astro-1. A three axis instrument pointing system (IPS) was employed to accurately point the science instruments. In order to analyze the pointing control system and verify pointing performance, a simulation of the IPS was developed using the multibody dynamics software TREETOPS. The TREETOPS IPS simulation is capable of accurately modeling the multibody IPS system undergoing large angle, nonlinear motion. The simulation is documented and example cases are presented demonstrating disturbance rejection, fine pointing operations, and multiple target pointing and slewing of the IPS.

Whorton, M.↗

NASA NTRS1989

Structural modeling for control design (articulated multibody component representation)

High gain, high frequency flexible responses in gimbaled multibody systems are discussed. Their origin and physical significance are described in terms of detailed mass and stiffness modeling at actuator/sensor interfaces. Guyan Reduction, Generalized Dynamic Reduction, inadequate mass modeling detail, as well as system mode truncation, are shown to suppress the high gain high frequency response and thereby lose system flexibility important for stability and performance predictions. Model validation by modal survey testing is shown to risk similar loss of accuracy. Difficulties caused by high frequency responses in component mode simulations, such as DISCOS, and also linearized system mode simulations, are described, and approaches for handling these difficulties are discussed.

Haugse, E. D.↗

NASA NTRS1980

Thermally induced response of flexible structures - A method for analysis

The phenomenon of a thermally induced spacecraft instability became apparent during the flight of the OGO-IV spacecraft in the late 1960s. The paper presents a generalized approach to the problem of obtaining a computationally practical simulation model for a thermally driven structure. The formulation is such that it can be utilized in a stand-along manner or be meshed into a general multibody simulation model such as that reported by Bodley et al. (1978). As presented, the formulation is restricted to the dynamic range for which linearized radiation is a valid assumption.

Frisch, H. P.↗

NASA NTRS2007

A Multibody Slosh Analysis for the Lunar Reconnaissance Orbiter

The Lunar Reconnaissance Orbiter (LRO) undergoes a series of thruster maneuvers to attain lunar orbit. The first of the series of lunar orbit insertion (LOI) maneuvers is crucial to the success of the mission. Therefore, it is important to characterize the disturbances acting on the spacecraft during this phase of the mission. This paper focuses on the internal disturbance force caused by fuel slosh and its impact on attitude control. During the first LOI maneuver (LOI-1), approximately 50% of the total fuel mass is used or roughly 25% of the spacecraft s wet mass, during the 38-minute burn. The forces imparted on the spacecraft from the fuel are dependent on the fill level of the two fuel tanks. During LOI-1, the fill level in both tanks varies greatly and thus so does the disturbance level caused by the fuel. It is therefore necessary to account for the time-varying mass properties of the spacecraft and the effects of the varying fuel levels during the entire 38-minute maneuver. Two simulations are developed in Mathworks s Simulink to analyze the fuel slosh effect. The first model, a baseline model, is a rigid body dynamics model where the fuel slosh is not modeled. The second is a multibody model, developed using a multibody dynamics toolbox, where each of the two fuel tanks and the remaining spacecraft body are treated as separate rigid bodies. The simulations are executed in a piece-wise fashion to account for the time-varying mass properties, and to accommodate the multibody toolbox. Disturbances caused by fuel slosh during both lunar and mission orbit insertions will be analyzed through simulation of different dynamics models. Results of the analysis will show the effects of the slosh disturbance on the spacecraft s attitude.

Shah, Neerav↗

NASA NTRS1989

Explicit modeling and computational load distribution for concurrent processing simulation of the space station

Two important aspects of concurrent processing under development at TRW are discussed. These are: (1) the derivation of explicit mathematical models of multibody dynamic systems, and (2) a balanced computational load distribution (BCLD) among loosely coupled computational units (processors) of a concurrent processing system. The developed methodologies are demonstrated by way of an application to the Phase 1 of the Space Station - a task being performed by TRW under NASA/JSC contract NAS9-17778. The mathematical model of the Space Station consists of three interconnected flexible bodies capable of undergoing large, rigid-body motion with respect to each other. Body 1 is the main central body and contains the pressurized modules inboard of the two Alpha gimbals. Bodies 2 and 3 are the starboard and port bodies connected to Body 1 at the Alpha gimbals and include all components on the transverse booms outboard of the Alpha gimbals (including the solar arrays). The control systems in the model maintain Body 1 in a prescribed 3-axis attitude control mode, while producing large-angle rotations of the flexible solar arrays to position them normal to the sun-line.

Gluck, R.↗

NASA NTRS1993

Reduced gravity multibody dynamics testing

The Final Report on reduced gravity multibody dynamics testing is presented. Tests were conducted on board the NASA KC-135 RGA in Houston, Texas. The objective was to analyze the effects of large angle rotations on flexible, multi-segmented structures. The flight experiment was conducted to provide data which will be compared to the data gathered from ground tests of the same configurations. The flight and ground tested data will be used to validate the TREETOPS software, software which models dynamic multibody systems, and other multibody codes. The flight experiment consisted of seven complete flights on board the KC-135 RGA during two one-week periods. The first period of testing was 4-9 Apr. 1993. The second period of testing was 13-18 Jun. 1993.

Sillanpaa, Meija↗

NASA NTRS2013

Estimated Probability of a Cervical Spine Injury During an ISS Mission

Introduction: The Integrated Medical Model (IMM) utilizes historical data, cohort data, and external simulations as input factors to provide estimates of crew health, resource utilization and mission outcomes. The Cervical Spine Injury Module (CSIM) is an external simulation designed to provide the IMM with parameter estimates for 1) a probability distribution function (PDF) of the incidence rate, 2) the mean incidence rate, and 3) the standard deviation associated with the mean resulting from injury/trauma of the neck. Methods: An injury mechanism based on an idealized low-velocity blunt impact to the superior posterior thorax of an ISS crewmember was used as the simulated mission environment. As a result of this impact, the cervical spine is inertially loaded from the mass of the head producing an extension-flexion motion deforming the soft tissues of the neck. A multibody biomechanical model was developed to estimate the kinematic and dynamic response of the head-neck system from a prescribed acceleration profile. Logistic regression was performed on a dataset containing AIS1 soft tissue neck injuries from rear-end automobile collisions with published Neck Injury Criterion values producing an injury transfer function (ITF). An injury event scenario (IES) was constructed such that crew 1 is moving through a primary or standard translation path transferring large volume equipment impacting stationary crew 2. The incidence rate for this IES was estimated from in-flight data and used to calculate the probability of occurrence. The uncertainty in the model input factors were estimated from representative datasets and expressed in terms of probability distributions. A Monte Carlo Method utilizing simple random sampling was employed to propagate both aleatory and epistemic uncertain factors. Scatterplots and partial correlation coefficients (PCC) were generated to determine input factor sensitivity. CSIM was developed in the SimMechanics/Simulink environment with a Monte Carlo wrapper (MATLAB) used to integrate the components of the module. Results: The probability of generating an AIS1 soft tissue neck injury from the extension/flexion motion induced by a low-velocity blunt impact to the superior posterior thorax was fitted with a lognormal PDF with mean 0.26409, standard deviation 0.11353, standard error of mean 0.00114, and 95% confidence interval [0.26186, 0.26631]. Combining the probability of an AIS1 injury with the probability of IES occurrence was fitted with a Johnson SI PDF with mean 0.02772, standard deviation 0.02012, standard error of mean 0.00020, and 95% confidence interval [0.02733, 0.02812]. The input factor sensitivity analysis in descending order was IES incidence rate, ITF regression coefficient 1, impactor initial velocity, ITF regression coefficient 2, and all others (equipment mass, crew 1 body mass, crew 2 body mass) insignificant. Verification and Validation (V&V): The IMM V&V, based upon NASA STD 7009, was implemented which included an assessment of the data sets used to build CSIM. The documentation maintained includes source code comments and a technical report. The software code and documentation is under Subversion configuration management. Kinematic validation was performed by comparing the biomechanical model output to established corridors.

Brooker, John E.↗

NASA NTRS1986

Attitude and articulation control concepts for the Earth Observing System

A study of pointing requirements and control approaches for the Earth Observing System, EOS, is presented. The proposed instrument set includes several massive instruments with varied articulation requirements, and pointing control requirements in several cases tighter than 0.01 degrees. Approaches to multipayload control and stability are explored, including: (a) the use of interconnected but dynamically isolated payload modules on a large platform, each with independent inertial control, and (b) precision basebody control of smaller platforms, with momentum compensated articulation and on-orbit dynamic balancing of spin-scan instruments. Results from multibody spacecraft models highlight potential payload dynamic interaction problems and suggest the need for dynamic isolation and disturbance rejection control techniques.

Bell, C. E.↗

NASA NTRS1989

Aspects of efficient and reliable multibody system simulation

Multibody system equations can be generated in various forms. All of these may be interpreted as results of two basic approaches, the augmentation- and the elimination-method. The former method yields the descriptor form of the system motion, a set of differential-algebraic equations (DAE), and the latter the state space representation, a minimal set of ordinary differential equations (ODE). Both of these methods are surveyed. Particular emphasis is on the discussion of recursive computational schemes, generating the equations of motion with a number of operations, which is proportional to the number N of system bodies (O(N)-formulations). For simulation purposes one would like to create that set of system equations, which can be generated most efficiently and for which the most efficient and reliable solution techniques are available. Numerical solution techniques for ODE have been studied in great detail and they are well-developed. By contrast, DAE have not been investigated for such a long time. In view of new developments in the latter field the generation of all the equations required for an efficient and reliable solution of DAE describing multibody system motion is discussed. These methods, i.e., an O(N)-formulation and new techniques for solving DAE, are implemented in the SIMPACK code. Its capabilities are illustrated by simulation of multibody robot models.

Schwertassek, R.↗

NASA NTRS2013

Basic Operational Robotics Instructional System

The Basic Operational Robotics Instructional System (BORIS) is a six-degree-of-freedom rotational robotic manipulator system simulation used for training of fundamental robotics concepts, with in-line shoulder, offset elbow, and offset wrist. BORIS is used to provide generic robotics training to aerospace professionals including flight crews, flight controllers, and robotics instructors. It uses forward kinematic and inverse kinematic algorithms to simulate joint and end-effector motion, combined with a multibody dynamics model, moving-object contact model, and X-Windows based graphical user interfaces, coordinated in the Trick Simulation modeling environment. The motivation for development of BORIS was the need for a generic system for basic robotics training. Before BORIS, introductory robotics training was done with either the SRMS (Shuttle Remote Manipulator System) or SSRMS (Space Station Remote Manipulator System) simulations. The unique construction of each of these systems required some specialized training that distracted students from the ideas and goals of the basic robotics instruction.

Todd, Brian Keith↗

NASA NTRSDate not supplied

Lunar Lander Landing Modeling and Simulation in Simscape

The landing gear is a critical subsystem of a lander for a successful landing on the moon or a planet. During a landing event, structural loading, energy absorption and toppling stability are important factors for the landing gear development. These aspects can be studied using simulations. The landing gear comprising the primary struct, secondary structs, footpad, and joints, is easily modeled using Simscape Multibody toolbox. The energy absorption mechanisms in the structs is readily modeled using Simulink and Multibody blocks based on the relative motions of the inner and outer cylinder of the structures. During touchdown, the footpads strike the lunar surface, and the contact forces can be modeled including the soil mechanical properties. Slosh dynamics are included using a mechanical pendulum model. Tip-over controllers are developed using Simulink blocks and toolboxes. This model was intensively tested manually then additionally with Monte Carlo simulation. It offers the opportunity for landing stability study, i.e. the max slope a lander can land without tipping over in 3D realistic landing situations.

Wei Wu↗

NASA NTRS1988

Obstacles to high fidelity multibody dynamics simulation

The authors take a wide ranging look at issues involved in the dynamic modeling of complex, multibodied orbiting space systems. The nature of the multibody problem is reviewed and capabilities and limitations of two major codes (DISCOS, TREETOPS) are assessed. Problem areas that limit accuracy or contribute to uncertainty in the modeling, simulation process are identified. As a specific case, the significance of including, or of not including, second-degree geometric nonlinearity in the elastic displacement field (foreshortening) is evaluated. Conclusions and recommendations are made concerning the direction future development should take to achieve higher-fidelity and more computationally efficient multibody software solutions.

Lips, K. W.↗

NASA NTRS1987

Dynamic and thermal response finite element models of multi-body space structural configurations

Presented is structural dynamics modeling of two multibody space structural configurations. The first configuration is a generic space station model of a cylindrical habitation module, two solar array panels, radiator panel, and central connecting tube. The second is a 15-m hoop-column antenna. Discussed is the special joint elimination sequence used for these large finite element models, so that eigenvalues could be extracted. The generic space station model aided test configuration design and analysis/test data correlation. The model consisted of six finite element models, one of each substructure and one of all substructures as a system. Static analysis and tests at the substructure level fine-tuned the finite element models. The 15-m hoop-column antenna is a truss column and structural ring interconnected with tension stabilizing cables. To the cables, pretensioned mesh membrane elements were attached to form four parabolic shaped antennae, one per quadrant. Imposing thermal preloads in the cables and mesh elements produced pretension in the finite element model. Thermal preload variation in the 96 control cables was adjusted to maintain antenna shape within the required tolerance and to give pointing accuracy.

Edighoffer, Harold H.↗

NASA NTRS1993

Hybrid equations of motion for flexible multibody systems using quasi-coordinates

A variety of engineering systems, such as automobiles, aircraft, rotorcraft, robots, spacecraft, etc., can be modeled as flexible multibody systems. The individual flexible bodies are in general characterized by distributed parameters. In most earlier investigations they were approximated by some spatial discretization procedure, such as the classical Rayleigh-Ritz method or the finite element method. This paper presents a mathematical formulation for distributed-parameter multibody systems consisting of a set of hybrid (ordinary and partial) differential equations of motion in terms of quasi-coordinates. Moreover, the equations for the elastic motions include rotatory inertia and shear deformation effects. The hybrid set is cast in state form, thus making it suitable for control design.

Meirovitch, L.↗

NASA NTRS1988

Explicit modeling and concurrent processing in the simulation of multibody dynamic systems

The objective is to present the activities at TRW in developing the capability to simulate the behavior of large flexible multibody space structures. The features of the simulation tools are: (1) to accommodate all rigid/flexible body degrees-of-freedom which incorporate the control system models and external forces, (2) to provide the flexibility to incorporate engineering-defined models and to retain parameters of significance to the engineer, (3) to reduce the computation cost by one order of magnitude (two orders of magnitude compared to a CRAY 1S), and (4) to keep it versatile so that radical variations in anticipated space structures can be accommodated. The current computer tools to simulate multibody systems appear not only to be very costly and time consuming, but also do not produce the desired fidelity of the mathematical models. In summary, a multibody simulation tool will be developed in the near future which will allow solution of the dynamics and controls of the deployment of the LDR backup structure, or the problem associated with the robotic assembly of the structure. The tools will allow the engineer to define the modeling technique and solve problems in less time and at reduced cost.

Gluck, R.↗