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This paper provides a survey of the use of modular multifunctional systems, called Flexible Transformers, to facilitate the exploration of extreme and previously inaccessible environments. A novel dynamics and control model of a modular algorithm for assembly, folding, and unfolding of these innovative structural systems is also described, together with the control model and the simulation results.
A flexible multibody dynamics approach is applied to the Space Launch System (SLS) liftoff Coupled Loads Analysis (CLA), enabling the inclusion of a large array of component nonlinearities with extreme computational efficiency. The nonlinearities include the cryogenic induced preloads due to the large rotations of the aft struts connecting the Core Stage (CS) to the boosters, the contact/separation and potential re-contact at the booster aft skirt to Mobile Launcher(ML) interface, contact/separation and potential re-contact at the ML/extensible columns interfaces, secondary disconnect of the CS umbilicals including the LOX and LH2 Tail Service Mast Umbilicals (TSMUs), and the disconnect of the upper stage umbilical, the Interim Cryogenic Propulsion Stage Umbilical (ICPSU). The ICPSU disconnect involves algorithms simulating the winch motors reeling lanyard ropes, the nonlinear modeling of ropes and hoses, the disconnect and capture of multiple umbilical ground plates by catch-nets (geometrically nonlinear models), and the large rotations of the ML gantry in order to track clearances between the lifting SLS vehicle and umbilicals rotating out of the way. The flexible multibody dynamics framework utilized for these simulations provided a systematic and efficient framework for adding complex nonlinearities at the system level which would have otherwise not been possible in standard CLAs or would have to be treated by separate local analyses thereby not accounting for the coupled system behavior.
For future in-space construction facility, one or more space cranes capable of manipulating and positioning large and massive spacecraft components will be needed. Inverse dynamics was extensively studied as a basis for trajectory generation and control of robot manipulators. The focus here is on trajectory generation in the gross-motion phase of space crane operation. Inverse dynamics of the flexible crane body is much more complex and intricate as compared with rigid robot link. To model and solve the space crane's inverse dynamics problem, LATDYN program which employs a three-dimensional finite element formulation for the multibody truss-type structures will be used. The formulation is oriented toward a joint dominated structure which is suitable for the proposed space crane concept. To track a planned trajectory, procedures will be developed to obtain the actuation profile and dynamics envelope which are pertinent to the design and performance requirements of the space crane concept.
The general rotorcraft aeromechanical stability program (GRASP) was developed to calculate aeroelastic stability for rotorcraft in hovering flight, vertical flight, and ground contact conditions. GRASP is described in terms of its capabilities and its philosophy of modeling. The equations of motion that govern the physical system are described, as well as the analytical approximations used to derive them. The equations include the kinematical equation, the element equations, and the constraint equations. In addition, the solution procedures used by GRASP are described. GRASP is capable of treating the nonlinear static and linearized dynamic behavior of structures represented by arbitrary collections of rigid-body and beam elements. These elements may be connected in an arbitrary fashion, and are permitted to have large relative motions. The main limitation of this analysis is that periodic coefficient effects are not treated, restricting rotorcraft flight conditions to hover, axial flight, and ground contact. Instead of following the methods employed in other rotorcraft programs. GRASP is designed to be a hybrid of the finite-element method and the multibody methods used in spacecraft analysis. GRASP differs from traditional finite-element programs by allowing multiple levels of substructure in which the substructures can move and/or rotate relative to others with no small-angle approximations. This capability facilitates the modeling of rotorcraft structures, including the rotating/nonrotating interface and the details of the blade/root kinematics for various types. GRASP differs from traditional multibody programs by considering aeroelastic effects, including inflow dynamics (simple unsteady aerodynamics) and nonlinear aerodynamic coefficients.
A computational procedure suitable for the solution of equations of motions for flexible multibody systems has been developed. A fully nonlinear continuum approach capable of accounting for both finite rotations and large deformations has been used to model a flexible beam component. The beam kinematics are referred directly to an inertial reference frame such that the degrees of freedom embody both the rigid and flexible deformation motions. As such, the beam inertia expression is identical to that of rigid body dynamics. The nonlinear coupling between gross body motion and elastic deformation is contained in the internal force expression. Numerical solution procedures for the integration of spatial kinematic systems can be directily applied to the generalized coordinates of both the rigid and flexible components. An accurate computation of the internal force term which is invariant to rigid motions is incorporated into the general solution procedure.
NASA’s science and exploration goals to return to the Moon and beyond will need to perform precision landings to place humans and cargo supplies near places of scientific interest, surface resources, or pre-established basecamps. With the maturation of new navigation technology, such as terrain relative navigation, precision landing is now feasible, enabling new exploration sites, such as the lunar poles. However, verification of precision landing performance becomes crucial since not reaching the designated landing site would have a high risk of loss of mission. Therefore, having a high-fidelity simulation platform to evaluate six degrees of freedom vehicle performance during high-risk phases of flight such landing is a fundamental part of the system verification and risk reduction. The NASA Marshall Space Flight Center has developed the GeneraLized Aerospace Simulation in Simulink® (GLASS) tool which incorporates guidance, navigation, and control algorithms, as well as vehicle and environmental models, such as gravity, vehicle mass properties, navigation sensors, propulsion, and terrain models. GLASS uses the MathWorks® Simulink® environment which provides a model-based design framework that allows the incorporation of vehicle models in a modular architecture. The Simulink® environment provides seamless integration with all the MathWorks® capabilities and toolboxes, such as control design toolboxes and Simscape™ Multibody™ dynamics toolbox. The MathWorks® environment also allows for guidance, navigation, and control algorithms to be auto coded in C language, enabling quick software and hardware in the loop testing. This paper provides an overview of GLASS capabilities for analyzing precision landing performance, including navigation trades applied to a NASA human lander reference design architecture.
A heuristic description is given for a simple harmonic oscillator as a basis for a model of anharmonicity. A formalism is applied in the process, which applies to complex excitation fields involving particle clusters and also facilitates a description of nonequilibrium multibody configurations by classical methods. The heuristic description is based on Streit's results (1965) and is free of linearization requirements in most physically interesting situations.
A nonlinear, multibody, six-degrees-of-freedom digital simulation has been developed to study generic Heavy Lift Airship (HLA) dynamics and control. The basic aerodynamic functions developed to model the hull, tail, and rotor loads continuously over all incidence ranges are reviewed and applied to a Quadrotor HLA with a low fineness ratio hull and a small vee-tail. Trim calculations for a test vehicle suggest control power deficiencies in crosswind stationkeeping for the unloaded vehicle. Gust responses show the importance of correctly calculating loads due to accelerated relative motion of air and hull. Numerically linearized dynamics for the test vehicle show the existence of a divergent yaw mode, and an oscillatory pitch mode whose stability characteristics are sensitive to flight speed. A considerable improvement in the vehicle's stability and response results from a simple multi-axis closed-loop control system operating on the rotors and propeller blades.
Some of the current and planned activities at the Air Force Systems Command in structures and controls for optical-type systems are summarized. Many of the activities are contracted to industry; one task is an in-house program which includes a hardware test program. The objective of the in-house program, referred to as the Aluminum Beam Expander Structure (ABES), is to address issues involved in on-orbit system identification. The structure, which appears similar to the LDR backup structure, is about 35 feet tall. The activity to date has been limited to acquisition of about 250 hours of test data. About 30 hours of data per excitation force is gathered in order to obtain sufficient data for a good statistical estimate of the structural parameters. The development of an Integrated Structural Modeling (ISM) computer program is being done by Boeing Aerospace Company. The objective of the contracted effort is to develop a combined optics, structures, thermal, controls, and multibody dynamics simulation code.
Th tiltrotor aircraft configuration has the potential to revolutionize air transportation by providing an economical combination of vertical take-off and landing capability with efficient, high-speed cruise flight. To achieve this potential it is necessary to have validated analytical tools that will support future tiltrotor aircraft development. These analytical tools must calculate tiltrotor aeromechanical behavior, including performance, structural loads, vibration, and aeroelastic stability, with an accuracy established by correlation with measured tiltrotor data. For many years such correlation has been performed for helicopter rotors (rotors designed for edgewise flight), but correlation activities for tiltrotors have been limited, in part by the absence of appropriate measured data. The recent test of the Tilt Rotor Aeroacoustic Model (TRAM) with a single, U4-scale V-22 rotor in the German-Dutch Wind Tunnel (DNW) now provides an extensive set of aeroacoustic, performance, and structural loads data. This paper will present calculations of airloads, wake geometry, and performance, including correlation with TRAM DNW measurements. The calculations were obtained using CAMRAD II, which is a modern rotorcraft comprehensive analysis, with advanced models intended for application to tiltrotor aircraft as well as helicopters. Comprehensive analyses have received extensive correlation with performance and loads measurements on helicopter rotors. The proposed paper is part of an initial effort to perform an equally extensive correlation with tiltrotor data. The correlation will establish the level of predictive capability achievable with current technology; identify the limitations of the current aerodynamic, wake, and structural models of tiltrotors; and lead to recommendations for research to extend tiltrotor aeromechanics analysis capability. The purpose of the Tilt Rotor Aeroacoustic Model (TRAM) experimental project is to provide data necessary to validate tiltrotor performance and aeroacoustic prediction methodologies and to investigate and demonstrate advanced civil tiltrotor technologies. The TRAM project is a key part of the NASA Short Haul Civil Tiltrotor (SHCT) project. The SHCT project is an element of the Aviation Systems Capacity Initiative within NASA. In April-May 1998 the TRAM was tested in the isolated rotor configuration at the Large Low-speed Facility of the German-Dutch Wind Tunnels (DNW). A preparatory test was conducted in December 1997. These tests were the first comprehensive aeroacoustic test for a tiltrotor, including not only noise and performance data, but airload and wake measurements as well. The TRAM can also be tested in a fill-span configuration, incorporating both rotors Lnd a fuselage model. The wind tunnel installation of the TRAM isolated rotor is shown. The rotor tested in the DNW was a 1/4-scale (9.5 ft diameter) model of the right-hand V-22 proprotor. The rotor and nacelle assembly was attached to an acoustically-treated, isolated rotor test stand through a mechanical pivot (the nacelle conversion axis). The TRAM was analyzed using the rotorcraft comprehensive analysis CAMRAD II. CAMRAD II is an aeromechanical analysis of helicopters and rotorcraft that incorporates a combination of advanced technologies, including multibody dynamics, nonlinear finite elements, and rotorcraft aerodynamics. The trim task finds the equilibrium solution (constant or periodic) for a steady state operating condition, in this case a rotor operating in a wind tunnel. For wind tunnel operation, the thrust and flapping are trimmed to target values. The aerodynamic model includes a wake analysis to calculate the rotor nonuniform induced-velocities, using a free wake geometry. The paper will present the results of CAMRAD II calculations compared to the TRAM DNW measurements for hover performance, helicopter mode performance, and helicopter mode airloads. An example of the hover performance results, comparing both mearements and calculations for the JVX (large scale) and TRAM (small scale) rotors, is shown. An example of the helicopter mode performance, showing the influence of the aerodynamic model (particularly the stall delay model) on the calculated power, induced power, and profile power is also shown. An example of the helicopter mode airloads, showing the influence of various wake and aerodynamic models on the calculations, is shown. Good correlation with measured airloads is obtained using the multiple-trailer wake model. The paper will present additional results, and describe and discuss the aerodynamic behavior in detail.
NASA is interested in designing a spacecraft capable of visiting a near-Earth object (NEO), performing experiments, and then returning safely. Certain periods of this mission would require the spacecraft to remain stationary relative to the NEO, in an environment characterized by very low gravity levels; such situations require an anchoring mechanism that is compact, easy to deploy, and upon mission completion, easy to remove. The design philosophy used in this task relies on the simulation capability of a high-performance multibody dynamics physics engine. On Earth, it is difficult to create low-gravity conditions, and testing in low-gravity environments, whether artificial or in space, can be costly and very difficult to achieve. Through simulation, the effect of gravity can be controlled with great accuracy, making it ideally suited to analyze the problem at hand. Using Chrono::Engine, a simulation pack age capable of utilizing massively parallel Graphic Processing Unit (GPU) hardware, several validation experiments were performed. Modeling of the regolith interaction has been carried out, after which the anchor penetration tests were performed and analyzed. The regolith was modeled by a granular medium composed of very large numbers of convex three-dimensional rigid bodies, subject to microgravity levels and interacting with each other with contact, friction, and cohesional forces. The multibody dynamics simulation approach used for simulating anchors penetrating a soil uses a differential variational inequality (DVI) methodology to solve the contact problem posed as a linear complementarity method (LCP). Implemented within a GPU processing environment, collision detection is greatly accelerated compared to traditional CPU (central processing unit)- based collision detection. Hence, systems of millions of particles interacting with complex dynamic systems can be efficiently analyzed, and design recommendations can be made in a much shorter time. The figure shows an example of this capability where the Brazil Nut problem is simulated: as the container full of granular material is vibrated, the large ball slowly moves upwards. This capability was expanded to account for anchors of different shapes and penetration velocities, interacting with granular soils.
The Magnetospheric MultiScale (MMS) mission employs a formation of spinning spacecraft with several flexible appendages and thruster-based control. To understand the complex dynamic interaction of thruster actuation, appendage motion, and spin dynamics, each spacecraft is modeled as a tree of rigid bodies connected by spherical or gimballed joints. The method presented facilitates assembling by inspection the exact, nonlinear dynamic equations of motion for a multibody spacecraft suitable for solution by numerical integration. The building block equations are derived by applying Newton's and Euler's equations of motion to an "element" consisting of two bodies and one joint (spherical and gimballed joints are considered separately). Patterns in the "mass" and L'force" matrices guide assembly by inspection of a general N-body tree-topology system. Straightforward linear algebra operations are employed to eliminate extraneous constraint equations, resulting in a minimum-dimension system of equations to solve. This method thus combines a straightforward, easily-extendable, easily-mechanized formulation with an efficient computer implementation.
A control strategy is presented for pointing particular modules of flexible multibody space structures while simultaneously attenuating structural vibrations. The application that is addressed is the planned Space Station Freedom in a growth configuration with Solar Dynamic (SD) module. A NASTRAN model of Freedom is used to demonstrate the control strategy. Two cases of SD concentrator fine-pointing controller bandwidths are studied with examples. The effect of limiting the controller motor torques to realistic baseline values is examined. SD pointing and station vibration control is accomplished during realistic disturbances due to aerodynamic drag, Shuttle docking, and Shuttle reaction control system plume impingement on SD. Gravity gradient induced torques on SD are relatively small and pseudo-steady.
TWOBODY implements improved version of Lagrange multiplier method. Program ultilizes programming technique eliminating computational instability in multibody simulations in which Lagrange multipliers used. In technique, one uses constraint equations, instead of integration, to determine coordinates that are not independent. To illustrate technique, it includes simple mathematical model of solid rocket booster and parachute connected by frictionless swivel. Written in FORTRAN 77.
Recent advances in computational fluid mechanics are discussed in reviews and reports. Sections are devoted to (1) the modeling of local phenomena and edge effects in solids, (2) stochastic modeling and simulation of fracture toughness, and (3) partitioning strategy and new finite elements. Particular attention is given to global and local finite-element/spectral-boundary-element techniques for failure analysis, simulations of microfracture in metal-matrix composites, fatigue analysis of cracked anisotropic plates under stochastic loading, mathematical modeling for the analysis of nonlinear aircraft dynamics, physical and mathematical modeling of wave propagation in the Ariane 5 VEB structure, partitioning based on symmetry transformations, an FEM approach to adaptive reliability assurance, and time-domain FEMs for the large rotational dynamics of multibody systems.
COFS 3 is the third project within the Control of Flexible Structures (COFS) program. It deals with developing multibody dynamics and control technology for large space structures. It differs from COFS 1 and 2 in two respects. First, it addresses a more complex class of structure, and second it is basically a scale model ground test and analysis program while COFS 1 and 2 feature Shuttle flight experiments. The specific technology thrusts within COFS 3 are model sensitivities, test methods, analysis validation, systems identification, and vibration suppression. The COFS 3 project will develop the methods for using dynamically scaled models and analysis to predict the structural dynamics of large space structures. The project uses the space station as a focus because it is typical of the structures of interest and provides the first opportunity to obtain full-scale on-orbit dynamics data.
A full three-dimensional finite element-multibody structural dynamic solver is coupled to a three-dimensional Reynolds-averaged Navier-Stokes solver for the prediction of integrated aeromechanical stresses and strains on a rotor blade in forward flight. The objective is to lay the foundations of all major pieces of an integrated three-dimensional rotor dynamic analysis - from model construction to aeromechanical solution to stress/strain calculation. The primary focus is on the aeromechanical solution. Two types of three-dimensional CFD/CSD interfaces are constructed for this purpose with an emphasis on resolving errors from geometry mis-match so that initial-stage approximate structural geometries can also be effectively analyzed. A three-dimensional structural model is constructed as an approximation to a UH-60A-like fully articulated rotor. The aerodynamic model is identical to the UH-60A rotor. For preliminary validation measurements from a UH-60A high speed flight is used where CFD coupling is essential to capture the advancing side tip transonic effects. The key conclusion is that an integrated aeromechanical analysis is indeed possible with three-dimensional structural dynamics but requires a careful description of its geometry and discretization of its parts.
Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.