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Mission Design Strategies for Rendezvous and Servicing of Sun-Earth Libration Point Missions

With the launch of the James Webb Space Telescope (JWST) and future launches of the Roman Space Telescope (RST) and larger telescopes such as the proposed Habitable Worlds Observatory (HWO), the questions of where and how to rendezvous to enable servicing of these telescope missions arise. To aid in determining the allowable locations to rendezvous for servicing from a trajectory design approach, our previous research and analysis has shown feasible transfer trajectories between the Sun-Earth Libration L2 region (Quasi-Halo orbit) and the Earth Moon vicinity (Distant Retrograde Orbit (DRO), Quasi-Halo Orbit, Halo Orbit, and Near Rectilinear Halo Orbit (NRHO)), along with the related transfer constraints and the corresponding total fuel mass costs. We now focus on operational-like optimal scenarios for these transfers to complete a rendezvous to permit servicing at various Libration orbit locations. In this paper, we address how operational navigation and maneuver execution uncertainties impact the rendezvous timing and fuel mass (via ΔV). While optimization techniques are applied to ensure minimal ΔVs, we also analyze various transfer trajectory durations and rendezvous arrival geometries. The analysis presented includes dynamical system approaches and applies optimization through several tools including the Adaptive Trajectory Design (ATD) module as an initial guess, numerical computation using the General Mission Analysis Tool (GMAT) and Systems Tool Kit (STK) with higher fidelity perturbation modeling, and recently developed optimization tools that incorporate dynamical systems directly into the optimization process. Transfer trajectory options examined include a direct transfer from Earth versus departures from the previously examined Earth-Moon regime orbits, e.g. NRHOs and DROs. A return from Sun-Earth to lunar vicinity for a complete servicing after a rendezvous in Sun-Earth orbit is also considered. The resultant ΔV’s for each scenario is provided with discussions on various transfer trades, rendezvous considerations, and orbital limitations from the dynamical systems. A Poincare-like mapping of trajectory and rendezvous conditions categorize feasible and optimum transfer approaches, dependent on Sun-Earth orbit mission parameters. The focus of this research addresses questions for upcoming trades regarding servicing options for current and future Sun-Earth L1 and L2 missions. By doing a comprehensive analysis approach (dynamical systems + high fidelity optimization with true operational constraints), this paper will serve as a guide for mission architecture and operational trade considerations.

Maneuver Design↗

NASA NTRS1972

Control of linear uncertain systems utilizing mismatched state observers

The control of linear continuous dynamical systems is investigated as a problem of limited state feedback control. The equations which describe the structure of an observer are developed constrained to time-invarient systems. The optimal control problem is formulated, accounting for the uncertainty in the design parameters. Expressions for bounds on closed loop stability are also developed. The results indicate that very little uncertainty may be tolerated before divergence occurs in the recursive computation algorithms, and the derived stability bound yields extremely conservative estimates of regions of allowable parameter variations.

Goldstein, B.↗

NASA NTRS1993

Space Shuttle Main Engine performance analysis

For a number of years, NASA has relied primarily upon periodically updated versions of Rocketdyne's power balance model (PBM) to provide space shuttle main engine (SSME) steady-state performance prediction. A recent computational study indicated that PBM predictions do not satisfy fundamental energy conservation principles. More recently, SSME test results provided by the Technology Test Bed (TTB) program have indicated significant discrepancies between PBM flow and temperature predictions and TTB observations. Results of these investigations have diminished confidence in the predictions provided by PBM, and motivated the development of new computational tools for supporting SSME performance analysis. A multivariate least squares regression algorithm was developed and implemented during this effort in order to efficiently characterize TTB data. This procedure, called the 'gains model,' was used to approximate the variation of SSME performance parameters such as flow rate, pressure, temperature, speed, and assorted hardware characteristics in terms of six assumed independent influences. These six influences were engine power level, mixture ratio, fuel inlet pressure and temperature, and oxidizer inlet pressure and temperature. A BFGS optimization algorithm provided the base procedure for determining regression coefficients for both linear and full quadratic approximations of parameter variation. Statistical information relative to data deviation from regression derived relations was also computed. A new strategy for integrating test data with theoretical performance prediction was also investigated. The current integration procedure employed by PBM treats test data as pristine and adjusts hardware characteristics in a heuristic manner to achieve engine balance. Within PBM, this integration procedure is called 'data reduction.' By contrast, the new data integration procedure, termed 'reconciliation,' uses mathematical optimization techniques, and requires both measurement and balance uncertainty estimates. The reconciler attempts to select operational parameters that minimize the difference between theoretical prediction and observation. Selected values are further constrained to fall within measurement uncertainty limits and to satisfy fundamental physical relations (mass conservation, energy conservation, pressure drop relations, etc.) within uncertainty estimates for all SSME subsystems. The parameter selection problem described above is a traditional nonlinear programming problem. The reconciler employs a mixed penalty method to determine optimum values of SSME operating parameters associated with this problem formulation.

Santi, L. Michael↗

NASA NTRS2004

Advanced Applications of Adifor 3.0 for Efficient Calculation of First-and Second-Order CFD Sensitivity Derivatives

This final report will document the accomplishments of the work of this project. 1) The incremental-iterative (II) form of the reverse-mode (adjoint) method for computing first-order (FO) aerodynamic sensitivity derivatives (SDs) has been successfully implemented and tested in a 2D CFD code (called ANSERS) using the reverse-mode capability of ADIFOR 3.0. These preceding results compared very well with similar SDS computed via a black-box (BB) application of the reverse-mode capability of ADIFOR 3.0, and also with similar SDs calculated via the method of finite differences. 2) Second-order (SO) SDs have been implemented in the 2D ASNWERS code using the very efficient strategy that was originally proposed (but not previously tested) of Reference 3, Appendix A. Furthermore, these SO SOs have been validated for accuracy and computational efficiency. 3) Studies were conducted in Quasi-1D and 2D concerning the smoothness (or lack of smoothness) of the FO and SO SD's for flows with shock waves. The phenomenon is documented in the publications of this study (listed subsequently), however, the specific numerical mechanism which is responsible for this unsmoothness phenomenon was not discovered. 4) The FO and SO derivatives for Quasi-1D and 2D flows were applied to predict aerodynamic design uncertainties, and were also applied in robust design optimization studies.

Taylor, Arthur C., III↗

NASA NTRS2018

Assessment and Verification of SLS Block 1-B Exploration Upper Stage State and Stage Disposal Performance

One of the SLS Navigation System's key performance requirements is a constraint on the payload system's delta-v allocation to correct for insertion errors due to vehicle state uncertainty at payload separation. The SLS navigation team has developed a Delta-Delta-V analysis approach to assess the effect on trajectory correction maneuver (TCM) design needed to correct for navigation errors. This approach differs from traditional covariance analysis based methods and makes no assumptions with regard to the propagation of the state dynamics. This allows for consideration of non-linearity in the propagation of state uncertainties. The Delta-Delta-V analysis approach re-optimizes perturbed SLS mission trajectories by varying key mission states in accordance with an assumed state error. The state error is developed from detailed vehicle 6-DOF Monte Carlo analysis or generated using covariance analysis. These perturbed trajectories are compared to a nominal trajectory to determine necessary TCM design. To implement this analysis approach, a tool set was developed which combines the functionality of a 3-DOF trajectory optimization tool, Copernicus, and a detailed 6-DOF vehicle simulation tool, Marshall Aerospace Vehicle Representation in C (MAVERIC). In addition to delta-v allocation constraints on SLS navigation performance, SLS mission requirement dictate successful upper stage disposal. Due to engine and propellant constraints, the SLS Exploration Upper Stage (EUS) must dispose into heliocentric space by means of a lunar fly-by maneuver. As with payload delta-v allocation, upper stage disposal maneuvers must place the EUS on a trajectory that maximizes the probability of achieving a heliocentric orbit post Lunar fly-by considering all sources of vehicle state uncertainty prior to the maneuver. To ensure disposal, the SLS navigation team has developed an analysis approach to derive optimal disposal guidance targets. This approach maximizes the state error covariance prior to the maneuver to develop and re-optimize a nominal disposal maneuver (DM) target that, if achieved, would maximize the potential for successful upper stage disposal. For EUS disposal analysis, a set of two tools was developed. The first considers only the nominal pre-disposal maneuver state, vehicle constraints, and an a priori estimate of the state error covariance. In the analysis, the optimal nominal disposal target is determined. This is performed by re-formulating the trajectory optimization to consider constraints on the eigenvectors of the error ellipse applied to the nominal trajectory. A bisection search methodology is implemented in the tool to refine these dispersions resulting in the maximum dispersion feasible for successful disposal via lunar fly-by. Success is defined based on the probability that the vehicle will not impact the lunar surface and will achieve a characteristic energy (C3) relative to the Earth such that it is no longer in the Earth-Moon system. The second tool propagates post-disposal maneuver states to determine the success of disposal for provided trajectory achieved states. This is performed using the optimized nominal target within the 6-DOF vehicle simulation. This paper will discuss the application of the Delta-Delta-V analysis approach for performance evaluation as well as trajectory re-optimization so as to demonstrate the system's capability in meeting performance constraints. Additionally, further discussion of the implementation of assessing disposal analysis will be provided.

Patrick, Sean↗

NASA NTRS1989

Uncertainty modelling for the control of an active structure

Two approaches to uncertainty modeling of a precision active truss structure for control design are presented. The first approach is based on the H(infinity) optimal control theory, which is used for robust control design with an additive uncertainty model. It is designed to provide vibration suppression to selected modes of the structure at the accelerometer locations. The uncertainty model can be used as an adjustable design parameter which will enable a study of the trade-offs between performance and robust stability. The second approach is based on mu-synthesis. Although the structured singular value can be used to analyze the robustness of any type of uncertainty, there exist difficulties in synthesis if the uncertainty block contains both real and complex variations. Mu-synthesis techniques do not allow for real-parameter variations in the synthesis procedure. The use of a complex variation description enclosing the real variation is suggested.

Blackwood, G. H.↗

NASA NTRS2004

Aerodynamic Optimization of Rocket Control Surface Geometry Using Cartesian Methods and CAD Geometry

Aerodynamic design is an iterative process involving geometry manipulation and complex computational analysis subject to physical constraints and aerodynamic objectives. A design cycle consists of first establishing the performance of a baseline design, which is usually created with low-fidelity engineering tools, and then progressively optimizing the design to maximize its performance. Optimization techniques have evolved from relying exclusively on designer intuition and insight in traditional trial and error methods, to sophisticated local and global search methods. Recent attempts at automating the search through a large design space with formal optimization methods include both database driven and direct evaluation schemes. Databases are being used in conjunction with surrogate and neural network models as a basis on which to run optimization algorithms. Optimization algorithms are also being driven by the direct evaluation of objectives and constraints using high-fidelity simulations. Surrogate methods use data points obtained from simulations, and possibly gradients evaluated at the data points, to create mathematical approximations of a database. Neural network models work in a similar fashion, using a number of high-fidelity database calculations as training iterations to create a database model. Optimal designs are obtained by coupling an optimization algorithm to the database model. Evaluation of the current best design then gives either a new local optima and/or increases the fidelity of the approximation model for the next iteration. Surrogate methods have also been developed that iterate on the selection of data points to decrease the uncertainty of the approximation model prior to searching for an optimal design. The database approximation models for each of these cases, however, become computationally expensive with increase in dimensionality. Thus the method of using optimization algorithms to search a database model becomes problematic as the number of design variables is increased.

Nelson, Andrea↗

NASA NTRS2009

Robust Optimal Adaptive Control Method with Large Adaptive Gain

In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly. However, a large adaptive gain can lead to high-frequency oscillations which can adversely affect robustness of an adaptive control law. A new adaptive control modification is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. The modification is based on the minimization of the Y2 norm of the tracking error, which is formulated as an optimal control problem. The optimality condition is used to derive the modification using the gradient method. The optimal control modification results in a stable adaptation and allows a large adaptive gain to be used for better tracking while providing sufficient stability robustness. Simulations were conducted for a damaged generic transport aircraft with both standard adaptive control and the adaptive optimal control modification technique. The results demonstrate the effectiveness of the proposed modification in tracking a reference model while maintaining a sufficient time delay margin.

Nguyen, Nhan T.↗

NASA NTRS1975

Computation of output feedback gains for linear stochastic systems using the Zangnill-Powell Method

Because conventional optimal linear regulator theory results in a controller which requires the capability of measuring and/or estimating the entire state vector, it is of interest to consider procedures for computing controls which are restricted to be linear feedback functions of a lower dimensional output vector and which take into account the presence of measurement noise and process uncertainty. To this effect a stochastic linear model has been developed that accounts for process parameter and initial uncertainty, measurement noise, and a restricted number of measurable outputs. Optimization with respect to the corresponding output feedback gains was then performed for both finite and infinite time performance indices without gradient computation by using Zangwill's modification of a procedure originally proposed by Powell. Results using a seventh order process show the proposed procedures to be very effective.

Kaufman, H.↗

NASA NTRS1977

Computation of output feedback gains for linear stochastic systems using the Zangwill-Powell method

Kaufman, H.↗

NASA NTRS2003

Reducing Design Risk Using Robust Design Methods: A Dual Response Surface Approach

Space transportation system conceptual design is a multidisciplinary process containing considerable element of risk. Risk here is defined as the variability in the estimated (output) performance characteristic of interest resulting from the uncertainties in the values of several disciplinary design and/or operational parameters. Uncertainties from one discipline (and/or subsystem) may propagate to another, through linking parameters and the final system output may have a significant accumulation of risk. This variability can result in significant deviations from the expected performance. Therefore, an estimate of variability (which is called design risk in this study) together with the expected performance characteristic value (e.g. mean empty weight) is necessary for multidisciplinary optimization for a robust design. Robust design in this study is defined as a solution that minimizes variability subject to a constraint on mean performance characteristics. Even though multidisciplinary design optimization has gained wide attention and applications, the treatment of uncertainties to quantify and analyze design risk has received little attention. This research effort explores the dual response surface approach to quantify variability (risk) in critical performance characteristics (such as weight) during conceptual design.

Unal, Resit↗

NASA NTRS2022

Analyzing the Efficacy of Flexible Execution, Replanning, and Plan Optimization for a Planetary Lander

Plan execution in unknown environments poses a number of challenges: uncertainty in domain modeling, stochasticity at execution time, and the presence of exogenous events. These challenges motivate an integrated approach to planning and execution that is able to respond intelligently to variation. We examine this problem in the context of the Europa Lander mission concept, and evaluate a planning and execution framework that responds to feedback and task failure using two techniques: flexible execution and replanning with plan optimization. We develop a theoretical framework to estimate gains from these techniques, and we compare these predictions to empirical results generated in simulation. These results indicate that an integrated approach to planning and execution leveraging flexible execution, replanning, and utility maximization shows significant promise for future tightly-constrained space missions that must address significant uncertainty.

Chien, Steve↗

NASA NTRS2008

Climate Model Evaluation using New Datasets from the Clouds and the Earth's Radiant Energy System (CERES)

There are some in the science community who believe that the response of the climate system to anthropogenic radiative forcing is unpredictable and we should therefore call off the quest . The key limitation in climate predictability is associated with cloud feedback. Narrowing the uncertainty in cloud feedback (and therefore climate sensitivity) requires optimal use of the best available observations to evaluate and improve climate model processes and constrain climate model simulations over longer time scales. The Clouds and the Earth s Radiant Energy System (CERES) is a satellite-based program that provides global cloud, aerosol and radiative flux observations for improving our understanding of cloud-aerosol-radiation feedbacks in the Earth s climate system. CERES is the successor to the Earth Radiation Budget Experiment (ERBE), which has widely been used to evaluate climate models both at short time scales (e.g., process studies) and at decadal time scales. A CERES instrument flew on the TRMM satellite and captured the dramatic 1998 El Nino, and four other CERES instruments are currently flying aboard the Terra and Aqua platforms. Plans are underway to fly the remaining copy of CERES on the upcoming NPP spacecraft (mid-2010 launch date). Every aspect of CERES represents a significant improvement over ERBE. While both CERES and ERBE measure broadband radiation, CERES calibration is a factor of 2 better than ERBE. In order to improve the characterization of clouds and aerosols within a CERES footprint, we use coincident higher-resolution imager observations (VIRS, MODIS or VIIRS) to provide a consistent cloud-aerosol-radiation dataset at climate accuracy. Improved radiative fluxes are obtained by using new CERES-derived Angular Distribution Models (ADMs) for converting measured radiances to fluxes. CERES radiative fluxes are a factor of 2 more accurate than ERBE overall, but the improvement by cloud type and at high latitudes can be as high as a factor of 5. Diurnal cycles are explicitly resolved by merging geostationary satellite observations with CERES and MODIS. Atmospheric state data are provided from a frozen version of the Global Modeling and Assimilation Office- Data Assimilation System at the NASA Goddard Space Flight Center. In addition to improving the accuracy of top-of-atmosphere (TOA) radiative fluxes, CERES also produces radiative fluxes at the surface and at several levels in the atmosphere using radiative transfer modeling, constrained at the TOA by CERES (ERBE was limited to the TOA). In all, CERES uses 11 instruments on 7 spacecraft all integrated to obtain climate accuracy in TOA to surface fluxes. This presentation will provide an overview of several new CERES datasets of interest to the climate community (including a new adjusted TOA flux dataset constrained by estimates of heat storage in the Earth system), show direct comparisons between CERES ad ERBE, and provide a detailed error analysis of CERES fluxes at various time and space scales. We discuss how observations can be used to reduce uncertainties in cloud feedback and climate sensitivity and strongly argue why we should NOT "call off the quest".

Loeb, Norman G.↗

NASA NTRS2011

Base Flow Investigation of the Apollo AS-202 Command Module

In recent years, both Europe and the US are developing hypersonic research and operational vehicles. These include (re)entry capsules (both ballistic and lifting) and lifting bodies such as ExoMars, EXPERT, ARV, CEV and IXV. The research programs are meant to enable technology and engineering capabilities to support during the next decade the development of affordable (possibly reusable) space transportation systems as well as hypersonic weapons systems for time critical targets. These programs have a broad range of goals, ranging from the qualification of thermal protection systems, the assessment of RCS performances, the development of GNC algorithms, to the full demonstration of the performance and operability of the integrated vehicles. Since the aerothermodynamic characteristics influence nearly all elements of the vehicle design, the accurate prediction of the aerothermal environment is a prerequisite for the design of efficient hypersonic systems. Significant uncertainties in the prediction of the hypersonic aerodynamic and the aerothermal loads can lead to conservative margins in the design of the vehicle including its Outer Mould Line (OML), thermal protection system, structure, and required control system robustness. The current level of aerothermal prediction uncertainties results therefore in reduced vehicle performances (e.g., sub-optimal payload to mass ratio, increased operational constraints). On the other hand, present computational capabilities enable the simulation of three dimensional flow fields with complex thermo-chemical models over complete trajectories and ease the validation of these tools by, e.g., reconstruction of detailed wind tunnel tests performed under identified and controlled conditions (flow properties and vehicle attitude in particular). These controlled conditions are typically difficult to achieve when performing in flight measurements which in turn results in large associated measurement uncertainties. Similar problems arise when attempting to rebuild measurements performed in "hot" ground facilities, where the difficulty level is increased by the addition of the free-flow characterization itself. The implementation of ever more sophisticated thermochemical models is no obvious cure to the aforementioned problems since their effect is often overwhelmed by the large measurement uncertainties incurred in both flight and ground high enthalpy facilities. Concurrent to the previous considerations, a major contributor to the overall vehicle mass of re-entry vehicles is the afterbody thermal protection system. This is due to the large acreage (equal or bigger than that of the forebody) to be protected. The present predictive capabilities for base flows are comparatively lower than those for windward flowfields and offer therefore a substantial potential for improving the design of future re-entry vehicles. To that end, it is essential to address the accuracy of high fidelity CFD tools exercised in the US and EU, which motivates a thorough investigation of the present status of hypersonic flight afterbody heating. This paper addresses the predictive capabilities of after body flow fields of re-entry vehicles investigated in the frame of the NATO/RTO - RTG-043 Task Group and is structured as follows: First, the verification of base flow topologies on the basis of available wind-tunnel results performed under controlled supersonic conditions (i.e., cold flows devoid of reactive effects) is performed. Such tests address the detailed characterization of the base flow with particular emphasis on separation/reattachment and their relation to Mach number effects. The tests have been performed on an Apollo-like re-entry capsule configuration. Second, the tools validated in the frame of the previous effort are exercised and appraised against flight-test data collected during the Apollo AS-202 re-entry.

Walpot, Louis M. G.↗

NASA NTRS1974

Hot and cold body reference noise generators from 0 to 40 GHz

This article describes the design, development, and analysis of exceptionally accurate radiometric noise generators from 0-40 GHz to serve as standard references. Size, weight, power, and reliability are optimized to meet the requirements of NASA air- and space-borne radiometers. The radiometric noise temperature of these noise generators is, unavoidably, calculated from measured values rather than measured directly. The absolute accuracy and stability are equal to or better than those of reliable standards available for comparison. A noise generator has been developed whose measurable properties (VSWR, line loss, thermometric temperatures) have been optimized in order to minimize the effects of the uncertainty in the calculated radiometric noise temperatures. Each measurable property is evaluated and analyzed to determine the effects of the uncertainty of the measured value. Unmeasurable properties (primarily temperature gradients) are analyzed, and reasonable precautions are designed into the noise generator to guarantee that the uncertainty of the value remains within tolerable limits.

Hornbostel, D. H.↗

NASA NTRS1979

Improvement of scanning radiometer performance by digital reference averaging

Most radiometers utilize a calibration technique in which measurements of a known reference are subtracted from measurements of an unknown source so that common-mode bias errors are cancelled. When a radiometer is scanned over a varying scene, it produces a sequence of outputs, each being proportional to the difference between the reference and the corresponding input. A reference averaging technique is presented that employs a simple digital algorithm which exploits the asymmetry between the time-variable scene inputs and the nominally constant reference input by averaging many reference measurements to decrease the statistical uncertainty in the reference value. This algorithm is, therefore, optimized by an asymmetric chopping sequence in which the scene is viewed for more than one-half of the duty cycle (unlike the analog Dicke technique). Reference averaging algorithms are well within the capabilities of small microprocessors. Although this paper develops the technique for microwave radiometry, it may be beneficial for any system which measures a large number of unknowns relative to a known reference in the presence of slowly varying common-mode errors.

Bremer, J. C.↗

NASA NTRS1984

Redundancy relations and robust failure detection

All failure detection methods are based on the use of redundancy, that is on (possible dynamic) relations among the measured variables. Consequently the robustness of the failure detection process depends to a great degree on the reliability of the redundancy relations given the inevitable presence of model uncertainties. The problem of determining redundancy relations which are optimally robust in a sense which includes the major issues of importance in practical failure detection is addressed. A significant amount of intuition concerning the geometry of robust failure detection is provided.

Chow, E. Y.↗

NASA NTRS1994

Metrology: Calibration and measurement processes guidelines

The guide is intended as a resource to aid engineers and systems contracts in the design, implementation, and operation of metrology, calibration, and measurement systems, and to assist NASA personnel in the uniform evaluation of such systems supplied or operated by contractors. Methodologies and techniques acceptable in fulfilling metrology quality requirements for NASA programs are outlined. The measurement process is covered from a high level through more detailed discussions of key elements within the process, Emphasis is given to the flowdown of project requirements to measurement system requirements, then through the activities that will provide measurements with defined quality. In addition, innovations and techniques for error analysis, development of statistical measurement process control, optimization of calibration recall systems, and evaluation of measurement uncertainty are presented.

Castrup, Howard T.↗