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Daniel Guggenheim School of Aerospace Engineering

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https://hdl.handle.net/1853/70742

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College of Engineering

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Aerospace Design Group

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Aerospace Systems Design Laboratory (ASDL)

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Air Transportation Laboratory

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Cognitive Engineering Center

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Space Systems Design Laboratory (SSDL)

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Publication Search Results

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A Markovian State-Space Flexibility Framework Applied to Distributed-Payload Satellite Design Decisions

(Georgia Institute of Technology, 2011-09) Lafleur, Jarret M.

Over the past decade, the space industry has increasingly recognized the need for new systems to be designed for flexibility, or the capability to be easily modified in response to changes in future requirements or environments. Despite widespread interest, however, the state of the art in designing flexibility into space systems today remains limited. To address these limitations, this paper presents the basis of a quantitative, stochastic, multi-objective, and multi-period framework for integrating flexibility into space system design decisions. Central to the framework are five steps that (1) define configuration options and transition costs, (2) define a stochastic model for mission demand environment changes, (3) link configurations and demand environments via quantitative performance metrics, (4) identify Pareto-optimal configuration paths and decision policies, taking advantage of efficient multi objective Markov decision process techniques, and (5) utilize these path and policy results to inform initial system selection. The framework is applied to a realistic example in which design decisions are suggested for a hypothetical multi- or distributed-payload satellite system. The application illustrates how flexibility-informed trades can permit selection of a satellite system that most effectively responds to uncertain future demands.
The Conditional Equivalence of ΔV Minimization and Apoapsis Targeting in Numerical Predictor-Corrector Aerocapture Guidance

(Georgia Institute of Technology, 2011-08) Lafleur, Jarret M.

Interest in aerocapture, a maneuver in which a spacecraft dives into the atmosphere of a planet for nearly propellantless capture into planetary orbit, has grown steadily in recent years. One key element required to execute this maneuver is an appropriate guidance algorithm for the atmospheric phase of flight. A popular algorithm choice has been the numerical-predictor corrector (NPC), which typically iterates on a time-invariant bank angle to target apoapsis of the desired final orbit. This paper introduces the idea of using the NPC to select the bank angle that instead minimizes the sum of periapsis-raise ΔV and apoapsis-cleanup ΔV, and demonstrates the surprising finding that the two approaches are equivalent under a certain analytic condition. This condition is derived and then applied to correctly predict a scenario in which apoapsis targeting produces a suboptimal ΔV. This scenario is simulated, and the ΔV minimization algorithm is shown to reduce the required ΔV by 23%. Monte Carlo simulations confirm both the scenarios of equivalence and non-equivalence, and an automatable procedure is outlined that a user can execute prior to simulating or flying a trajectory to determine whether apoapsis targeting is ΔV optimal or whether a ΔV minimization algorithm is required.
Probabilistic AHP and TOPSIS for Multi-Attribute Decision-Making under Uncertainty

(Georgia Institute of Technology, 2011-03) Lafleur, Jarret M.

One challenging aspect in designing complex engineering systems is the task of making informed design decisions in the face of uncertainty.1,2 This paper presents a probabilistic methodology to facilitate such decision making, in particular under uncertainty in decision-maker preferences. This methodology builds on the frequently used multi-attribute decision-making techniques of the Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and it overcomes some typical limitations that exist in relying on these deterministic techniques. The methodology is divided into three segments, each of which consists of multiple steps. The first segment (steps 1-4) involves setting up the problem by defining objectives, priorities, uncertainties, design attributes, and candidate designs. The second segment (steps 5-8) involves applications of AHP and TOPSIS using AHP prioritization matrices generated from probability density functions. The third segment (steps 9- 10) involves visualization of results to assist in selecting a final design. A key characteristic measured in these final steps is the consistency with which a design ranks among the top several alternatives. An example satellite orbit and launch vehicle selection problem illustrates the methodology throughout the paper.
Extension of a Simple Mathematical Model for Orbital Debris Proliferation Mitigation

(Georgia Institute of Technology, 2011-02) Lafleur, Jarret M.

A significant threat to the future of space utilization is the proliferation of debris in low Earth orbit. To facilitate quantification of trends and the assessment of potential mitigation measures, this paper extends a previously proposed analytic debris proliferation model consisting of two coupled differential equations. Analyzed are the transient and equilibrium behavior of the parametric model, leading to assessment of the likely effectiveness of potential debris mitigation measures. Results suggest the current equilibrium capacity for intact satellites in low Earth orbit allows for only 25% of the satellites in orbit today and presents an average 2.8% per year risk of catastrophic collision for individual satellites. Results also suggest that direct removal of debris fragments has the potential to add decades or centuries of useful life to low Earth orbit. In addition to providing numerical results, this paper contributes a simple debris model particularly useful when more sophisticated models are unavailable or prohibitively time-consuming to utilize.
Regression Analysis of Launch Vehicle Payload Capability for Interplanetary Missions

(Georgia Institute of Technology, 2010-09) Wise, Marcie A. ; Lafleur, Jarret M. ; Saleh, Joseph H.

During the conceptual design of interplanetary space missions, it is common for engineers and mission planners to perform launch system trades. This paper provides an analytical means for facilitating these trades rapidly and efficiently using polynomial equations derived from payload planner’s guides. These equations model expendable launch vehicles’ maximum payload capability as a function of vis-viva energy (C3). This paper first presents the motivation and method for deriving these polynomial equations. Next, 34 polynomials are derived for vehicles among nine launch vehicle series: Atlas V, Delta IV, Falcon 9, and Taurus, as well as H-IIA, Long March, Proton, Soyuz, and Zenit. The quality of fit of these polynomials are assessed, and it is found that the maximum 95th percentile model fit error for all 34 vehicles analyzed is 4.43% with a mean of 1.44%, and the minimum coefficient of determination (R²) is 0.99967. As a result, the equations are suitable for launch vehicle trade studies in conceptual design and beyond. A realistic example of such a trade for the Mars Reconnaissance Orbiter mission is provided.
Sun and Earth Access Trades for Lunar South Pole Landing Site Selection

(Georgia Institute of Technology, 2010-08) Lafleur, Jarret M. ; Heeg, Casey

One of the leading candidate sites for future lunar exploration is Shackleton Crater, a 20- km-diameter, 4-km-deep depression offset 10 km from the south pole of the Moon. The perpetual darkness that exists at the floor of the crater, which makes it scientifically interesting and a potential supply of resources, is coupled with near-continuous sunlight atop the rim and some of the surrounding area. In order to leverage favorable Sun and Earth access conditions in the region, engineers designing future missions must be able to quantify these access conditions and effectively use this data to select an ideal landing or outpost site. This paper details work completed to develop this capability within Team X at the NASA Jet Propulsion Laboratory using a Satellite Tool Kit (STK) model coupled with a MATLAB site selection tool employing multi-attribute decision-making (MADM) techniques. Three scenarios are analyzed in terms of the fraction of the year for which Sun and Earth access exists, the maximum durations for which access is nonexistent, and access consistency. These multiple metrics are combined into an aggregate suitability score based on user weights and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and optimal sites are identified. In addition, weighting-independent Pareto-optimal points are identified and are shown to be clustered in four geographic regions. The most promising points have access to the Sun 89-93% of the year and to the Earth about 58% of the year. It is shown that access results are highly sensitive to a spacecraft's effective solar array or antenna altitude above the surface. Recommendations of future sites to consider are provided, and avenues for future expansion of this analysis and its tools are identified.
Exploring the F6 Fractionated Spacecraft Trade Space with GT-FAST

(Georgia Institute of Technology, 2009-11-12) Lafleur, Jarret M.

Released in July 2007, the Broad Agency Announcement for DARPA’s System F6 outlined goals for flight demonstration of an architecture in which the functionality of a traditional monolithic satellite is fulfilled with a fractionated cluster of free-flying, wirelessly interconnected modules. Given the large number of possible architectural options, two challenges facing systems analysis of F6 are (1) the ability to enumerate the many potential candidate fractionated architectures and (2) the ability to analyze and quantify the cost and benefits of each architecture. This paper applies the recently developed Georgia Tech F6 Architecture Synthesis Tool (GT-FAST) to the exploration of the System F6 trade space. GT-FAST is described in detail, after which a combinatorial analysis of the architectural trade space is presented to provide a theoretical contribution applicable to future analyses clearly showing the explosion of the trade space as the number of fractionatable components increases. Several output metrics of interest are defined, and Pareto fronts are used to visualize the trade space. The first set of these Pareto fronts allows direct visualization of one output against another, and the second set presents cost plotted against a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) score aggregating performance objectives. These techniques allow for the identification of a handful of Pareto-optimal designs from an original pool of over 3,000 potential designs. Conclusions are drawn on salient features of the resulting Pareto fronts, important competing objectives which have been captured, and the potential suitability of a particularly interesting design designated PF0248. A variety of potential avenues for future work are also identified.
Comparative Reliability of GEO, LEO, and MEO Satellites

(Georgia Institute of Technology, 2009-10) Hiriart, Thomas ; Castet, Jean-Francois ; Lafleur, Jarret M. ; Saleh, Joseph H.

Reliability has long been a major consideration in the design of space systems, and in recent years it has become an essential metric in spacecraft design trade-space exploration and optimization. The purpose of this paper is to statistically derive and compare reliability results of Earth-orbiting satellites as a function of orbit type, namely geosynchronous orbits (GEO), low Earth orbits (LEO) and medium Earth orbits (MEO). Using an extensive database of satellite launches and failures/anomalies, life data analyses are conducted over three samples of satellites within each orbit type and successfully launched between 1990 and 2008. Because the dataset is censored, the Kaplan-Meier estimator is used to estimate the reliability functions. Plots of satellite reliability as a function of orbit altitude are provided for each orbit type, as well as confidence bounds on these estimates. Using analytical techniques such as maximum likelihood estimation (MLE), parametric fits are conducted on the previous nonparametric reliability results using single Weibull and mixture distributions. Based on these parametric fits, a comparative reliability analysis is provided identifying similarities and differences in the reliability behaviors of satellites in these three types of orbits. Finally, beyond the statistical analysis, this work concludes with several hypotheses for structural/causal explanations of these trends and difference in on-orbit failure behavior.
Response Surface Equations for Expendable Launch Vehicle Payload Capability

(Georgia Institute of Technology, 2009-09) Fleming, Elizabeth S. ; Lafleur, Jarret M. ; Saleh, Joseph H.

Systems analysis and conceptual design for new spacecraft commonly require the capability to perform rapid, parametric assessments of launch vehicle options. Such assessments allow engineers to incorporate launch vehicle considerations in first-order cost, mass, and orbit performance trades early during conceptual design and development phases. This paper demonstrates an efficient approach to launch vehicle analysis and selection using response surface equations (RSEs) derived directly from launch vehicle payload planner's guides. These RSEs model payload capability as a function of circular orbit altitude and inclination. Following presentation of the RSE fitting method and statistical goodness of fit tests, the RSE and model fit error statistics for the Pegasus XL are derived and presented as an example. In total, 43 RSEs are derived for the following launch vehicles and their derivatives: Pegasus, Taurus, Minotaur, and Falcon series as well as the Delta IV, Atlas V, and the foreign Ariane and Soyuz vehicles. Ranges of validity and model fit error statistics with respect to the original planner's guide data are provided for each of the 43 fits. Across all launch vehicles fit, the resulting RSEs have a maximum 90th percentile model fit error of 4.39% and a mean 90th percentile model fit error of 0.97%. In addition, of the 43 RSEs, the lowest R^2 value is 0.9715 and the mean is 0.9961. As a result, these equations are sufficiently accurate and well-suited for use in conceptual design trades. Examples of such trades are provided, including demonstrations using the RSEs to (1) select a launch vehicle given an orbit inclination and altitude, (2) visualize orbit altitude and inclination constraints given a spacecraft mass, and (3) calculate the sensitivity of orbital parameters to mass growth. Suited for a variety of applications, the set of RSEs provides a tool to the aerospace engineer allowing efficient, informed launch option trades and decisions early during design.
GT-FAST: A Point Design Tool for Rapid Fractionated Spacecraft Sizing and Synthesis

(Georgia Institute of Technology, 2009-09) Lafleur, Jarret M. ; Saleh, Joseph H.

In July 2007, DARPA issued a Broad Agency Announcement for the development of System F6, a flight demonstration of an architecture in which the functionality of a traditional monolithic satellite is fulfilled with a fractionated cluster of free-flying, wirelessly interconnected modules. Given the large number of possible architectural options, two challenges facing systems analysis of F6 are (1) the ability to enumerate the many potential candidate fractionated architectures and (2) the ability to analyze and quantify the cost and benefits of each architecture. One element necessary in enabling a probabilistic, valuecentric analysis of such fractionated architectures is a systematic method for sizing and costing the many candidate architectures that arise. The Georgia Tech F6 Architecture Synthesis Tool (GT-FAST) is a point design tool designed to fulfill this need by allowing rapid, automated sizing and synthesis of candidate F6 architectures. This paper presents the internal mechanics and some illustrative applications of GT-FAST. Discussed are the manner in which GT-FAST fractionated designs are specified, including discrete and continuous-variable inputs, as well as the methods, models, and assumptions used in estimating elements of mass, power, and cost. Finally, the paper concludes with sample outputs from GT-FAST for a notional fractionated architecture, an example of GT-FAST's trade study capability, and a partial validation of GT-FAST against the Jason-2 and TIMED satellites. The ease with which GT-FAST can be adapted to new fractionated spacecraft applications is highlighted, and avenues for potential future expansion of GT-FAST are discussed.