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A collection of papers presented at the Fourth NASA Workshop on Computational Control of Flexible Aerospace Systems is given. The papers address modeling, systems identification, and control of flexible aircraft, spacecraft and robotic systems.
The inverse and forward dynamics problems for flexible multibody systems were solved using the techniques of spatially recursive Kalman filtering and smoothing. These algorithms are easily developed using a set of identities associated with mass matrix factorization and inversion. These identities are easily derived using the spatial operator algebra developed by the author. Current work is aimed at computational experiments with the described algorithms and at modelling for control design of limber manipulator systems. It is also aimed at handling and manipulation of flexible objects.
Viewgraphs on cost averaging techniques for robust control of flexible structural systems are presented. Topics covered include: modeling of parameterized systems; average cost analysis; reduction of parameterized systems; and static and dynamic controller synthesis.
This paper presents a variational formulation of constrained dynamics of flexible multibody systems, using a vector-variational calculus approach. Body reference frames are used to define global position and orientation of individual bodies in the system, located and oriented by position of its origin and Euler parameters, respectively. Small strain linear elastic deformation of individual components, relative to their body references frames, is defined by linear combinations of deformation modes that are induced by constraint reaction forces and normal modes of vibration. A library of kinematic couplings between flexible and/or rigid bodies is defined and analyzed. Variational equations of motion for multibody systems are obtained and reduced to mixed differential-algebraic equations of motion. A space structure that must deform during deployment is analyzed, to illustrate use of the methods developed.
This paper uses spatial operators to develop new spatially recursive dynamics algorithms for flexible multibody systems. The operator description of the dynamics is identical to that for rigid multibody systems. Assumed-mode models are used for the deformation of each individual body. The algorithms are based on two spatial operator factorizations of the system mass matrix. The first (Newton-Euler) factorization of the mass matrix leads to recursive algorithms for the inverse dynamics, mass matrix evaluation, and composite-body forward dynamics for the systems. The second (innovations) factorization of the mass matrix, leads to an operator expression for the mass matrix inverse and to a recursive articulated-body forward dynamics algorithm. The primary focus is on serial chains, but extensions to general topologies are also described. A comparison of computational costs shows that the articulated-body, forward dynamics algorithm is much more efficient than the composite-body algorithm for most flexible multibody systems.
Flexible computer model developed for evaluating benefits and costs of placing large space systems into operational orbits. Model contains performance envelopes of three primary propulsion systems for orbit transfer based on three low-thrust engines. Allows for any mission model to be input into program. Model also allows user to easily vary program to examine effects of various ratings and weighting of benefit parameters for baseline engines. Program written in FORTRAN IV for use on IBM 370 computer.
Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.
A potential hardware organization for the Flexible Processor Array is presented. An algorithm that implements a contextual classifier for remote sensing data analysis is given, along with uniprocessor classification algorithms. The Flexible Processor algorithm is provided, as are simulated timings for contextual classifiers run on the Flexible Processor Array and another system. The timings are analyzed for context neighborhoods of sizes three and nine.
A 3-D, finite element based simulation tool for flexible multibody systems is presented. Hinge degrees-of-freedom is built into equations of motion to reduce geometric constraints. The approach avoids the difficulty in selecting deformation modes for flexible components by using assumed mode method. The tool is applied to simulate a practical space structure deployment problem. Results of examples demonstrate the capability of the code and approach.
Abstract. The article presents a symbolic framework (also called computer algebra program) that is used to obtain, in symbolic mathematical form, the linear and nonlinear equations of motion of a mid-fidelity multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The shape function approach does not represent the state of the art for flexible multibody dynamics but is an effective trade-off to obtain mid-fidelity models with few degrees of freedom, taking advantage of the separation of space and time. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitates the creation and manipulation of models with various levels of complexity by adding or removing degrees of freedom. The symbolic treatment allows for analytical gradients and linearized equations of motion. The linear and nonlinear equations can be exported to Python code or dedicated software. There are multiple applications, such as time domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, and digital twins. In this article, we describe the method we used to systematically generate the equations of motion of multibody systems and present the implementation of the framework using the Python package SymPy. We apply the framework to generate illustrative land-based and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. The Python implementation is provided as an open-source project.
A variational-vector calculus approach is employed to derive a recursive formulation for dynamic analysis of flexible multibody systems. Kinematic relationships for adjacent flexible bodies are derived in a companion paper, using a state vector notation that represents translational and rotational components simultaneously. Cartesian generalized coordinates are assigned for all body and joint reference frames, to explicitly formulate deformation kinematics under small deformation kinematics and an efficient flexible dynamics recursive algorithm is developed. Dynamic analysis of a closed loop robot is performed to illustrate efficiency of the algorithm.
Formulation combines certain advantages of discrete and distributed coordinates by using both simultaneously. In report summarizing method, theoretical development is extended as necessary for applications of practical interest. Explicit analyses are presented in sufficient detail to establish utility in flexible space vehicle control system of hybrid coordinate formulation.
The proceedings of the workshop are presented. Some areas of discussion are as follows: modeling, systems identification, and control of flexible aircraft, spacecraft, and robotic systems.
Present satellite communications systems normally use separate solar cells and antennas. Since solar cells generally account for the largest surface area of the spacecraft, co-locating the antenna and solar cells on the same substrate opens the possibility for a number of data-rate-enhancing communications link architecture that would have minimal impact on spacecraft weight and size. The idea of integrating printed planar antenna and solar array cells on the same surface has been reported in the literature. The early work merely attempted to demonstrate the feasibility by placing commercial solar cells besides a patch antenna. Recently, Integrating multiple antenna elements and solar cell arrays on the same surface was reported for both space and terrestrial applications. The application of photovoltaic solar cell in a planar antenna structure where the radiating patch antenna is replaced by a Si solar cell has been demonstrated in wireless communication systems (C. Bendel, J. Kirchhof and N. Henze, 3rd Would Photovotaic Congress, Osaka, Japan, May 2003). Based on a hybrid approach, a 6x1 slot array with circularly polarized crossdipole elements co-located on the same surface of the solar cells array has been demonstrated (S. Vaccaro, J. R. Mosig and P. de Maagt, IEEE Trans. Ant. and Propag., Vol. 5 1, No. 8, Aug. 2003). Amorphous silicon solar cells with about 5-10% efficiency were used in these demonstrations. This paper describes recent effort to integrate advanced solar cells with printed planar antennas. Compared to prior art, the proposed WSAC concept is unique in the following ways: 1) Active antenna element will be used to achieve dynamic beam steering; 2) High efficiency (30%) GaAs multi-junction solar cells will be used instead of Si, which has an efficiency of about 15%; 3) Antenna and solar cells are integrated on a common GaAs substrate; and 4) Higher data rate capability. The IA/SAC is designed to operate at X-band (8-12 GH) and higher frequencies Higher operating frequencies enable greater bandwidth and thus higher data transfer rates. The first phase of the effort involves the development of GaAs solar cell MIMs (Monolithically Integrated Module) with a single patch antenna on the opposite side of the substrate. Subsequent work will involve the integration of MIMs and antennas on the same side of the substrate. Results from the phase one efforts will be presented.
This presentation, part of the JISEA 10th Annual (Virtual) Meeting, discusses options for resilient and flexible power systems in South American economies.
Global asymptotic stability of a class of nonlinear multibody flexible space structures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore, for the second case, the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems, including flexible space structures with articulated flexible appendages.
Global asymptotic stability of a class of nonlinear multibody flexible space-stnuctures under dissipative compensation is established. Two cases are considered. The first case allows unlimited nonlinear motions of the entire system and uses quaternion feedback. The second case assumes that the central body motion is in the linear range although the other bodies can undergo unrestricted nonlinear motion. The stability is proved to be robust to the inherent modeling nonlinearities and uncertainties. Furthermore for the second case the stability is also shown to be robust to certain actuator and sensor nonlinearities. The stability proofs use the Lyapunov approach and exploit the inherent passivity of such systems. The results are applicable to a wide class of systems including flexible space-structures with articulated flexible appendages.
In this paper an experiment is designed for the modal parameter identification of a flexible arm system. This experiment uses a function generator to provide input signal and an oscilloscope to save input and output response data. For each vibrational mode, many sets of sine-wave inputs with frequencies close to the natural frequency of the arm system are used to excite the vibration of this mode. Then a least-squares technique is used to analyze the experimental input/output data to obtain the identified parameters for this mode. The identified results are compared with the analytical model obtained by applying finite element analysis.