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Trajectory Planning for Mission Survivability of Autonomous Vehicles in Moderately to Extremely Uncertain Environments
Trajectory planning is a particularly challenging task for autonomous vehicles when there are moderate to extreme uncertainties in their operating environment, i.e., where the trajectories of hazards are partially known to completely unknown. In this paper, we propose a receding horizon control strategy with novel trajectory planning policies that enable dynamic updating of the planned trajectories of autonomous vehicles. The proposed policies utilize two metrics: (1) the number of feasible trajectories; and (2) the robustness of the feasible trajectories. We measure the effectiveness of the suggested policies in terms of mission survivability, which is defined as the probability that the primary mission is accomplished or, if that is not possible, the vehicle lands safely at an alternative site. We show that a linear combination of both metrics is an effective objective function when there is a mix of partially known and unknown uncertainties. When the operating environment is dominated by unknown disturbances, maximizing the number of feasible trajectories results in the highest mission survivability. These findings have significant implications for achieving safe aviation autonomy.
Safe Landing on Uncertain Terrain - The Pillars of Europa Lander DDL
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Multihierarchy Gaussian Process Models for Probabilistic Aerodynamic Databases using Uncertain Nominal and Off-Nominal Configuration Data
Probabilistic aerodynamic databases are a crucial component of the development lifecycle for aerospace vehicles. A key challenge when building aerodynamic databases is that most data used to construct them represent various simplifications of the real flight vehicle. For example, wind tunnel models often simplify the vehicle geometry and surface roughness characteristics, while CFD computations often make simplifications to the physics being modeled, such as fully laminar or turbulent calculations. Multifidelity data fusion models rely on a user being able to define a hierarchy of fidelity levels anchored to some "truth" data. This approach is unsatisfactory when no data can be considered to accurately reflect real flight conditions. In this work, we provide an alternative approach by presenting a consistent mathematical framework for building probabilistic aerodynamic databases in the form of a conditional probability distribution described by an ensemble of multifidelity Gaussian Processes. Instead of relying on a single hierarchy of data fidelity levels, the presented framework identifies a "nominal" configuration and potential corrections to the nominal which represent specific physical phenomena not represented in the nominal data. The nominal and correction functions themselves are constructed as multifidelity Gaussian Processes and linearly combined to form an ensemble model which fuses the uncertainties associated nominal and correction models. Results obtained using the proposed framework on a simplified Orion Crew Module wind tunnel dataset demonstrate the predictive capability of the multihierarchy framework. We further demonstrate the benefits of such a probabilistic aerodynamic database approach through function sampling and computing the conditional distributions of derived quantities, such as the trim angle of attack and aerodynamic coefficients at trim.
Multihierarchy Gaussian Process Models for Probabilistic Aerodynamic Databases using Uncertain Nominal and Off-Nominal Configuration Data
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Small-Sample Estimator Decisions – Certainly Uncertain in Human Spaceflight at NASA
Within statistics when estimating means, we rely heavily on the Central Limit Theorem (CLT) to aid in our inference, however in cases where the CLT does not apply we begin to be strongly limited in our choices. If a violation to the CLT comes in the form of small samples and unknown population variance, yet we maintain the assumption of normality, the use of t-distributions is perfectly valid. We explore cases where population normality is not assumed, where sample sizes are small, and where some actionable estimate of the central tendency of a distribution is needed such as for spaceflight operational decisions. Here we identify different scenarios based on measures taken from spaceflight, characterizing performance of estimators of central tendency within our set of simulations. We examine bias and variability of standard estimators of central tendency as they apply to varying small sample sizes and varying population distributions. Further work in this area is needed to develop a framework or set of guidelines for individuals set in these situations. Even with limited information, decisions need to be made.
Statistically Consistent Dispersions of Line Loads to Uncertain Integrated Forces and Moments
This work presents a method to generate line loads that are consistent with integrated force and moment constraints, while also following the statistical distribution underlying known line load data. The motivation for this method is to address a particular problem that can arise during the pre-flight analysis of an ascent vehicle. That problem is constructing separate databases, for line loads and integrated aerodynamic coefficients, that contain different data and thus different amounts of quantified uncertainty. A dispersed line load method is described and applied to a data set generated by 29 computational fluid dynamics simulations at various angles of attack and sideslip. The statistical similarity of the generated line loads to the known data is confirmed by using the Maximum Mean Discrepancy 2-sample test. The promising results from this novel method are compared against results from applying an existing line load adjustment procedure to the same data set. Finally, potential future avenues of research are briefly discussed.
The uncertain future of mountaintop-removal-mined landscapes 2: Modeling the influence of topography and vegetation
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Accounting for uncertain 3-D elastic structure in fault slip estimates
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Calibration of a radiation quality model for sparse and uncertain data
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Uncertain and negative evidence in continuous time Bayesian networks
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Determination of robust stability margin for second-order systems
Robust stabilization of uncertain systems has been extensively investigated and the stability test for the whole set of uncertain parameters has been reduced to a finite number of test points, four points for the characteristic polynomial with independent coefficients. As a result the robust stability margin can be determined using a reasonable amount of computation. It is impossible to apply the results of the test to a practical system as the coefficients of the characteristic polynomial for a physical system are usually functions of uncertain parameters. However, many physical systems may be represented by a second-order mass-spring-damper system with a special multilinear form in its characteristic polynomial. This paper investigates second-order mass-spring-damper systems and the reduction of the number of test points. It is shown that such a system with arbritrary compensators always has a multilinear characteristic polynomial. It is also shown that a line in the two-dimensional parameter space forms the boundary after the mapping of a multilinear characteristic polynomial and this interior extreme line forms a conic curve in the complex plane. The boundary of uncertain domain for a multilinear polynomial with two uncertainty parameters can be determined analytically using this curve, and the four sides image of a square of the uncertain parameter. Therefore, the stability margin may be determined by checking the intersections of the boundary with the zero point. A similar procedure can be used for second-order systems with more than two uncertainty parameters when parameter optimization is used in determining the boundary.
Parametric uncertainty modeling for application to robust control
Viewgraphs and a paper on parametric uncertainty modeling for application to robust control are included. Advanced robust control system analysis and design is based on the availability of an uncertainty description which separates the uncertain system elements from the nominal system. Although this modeling structure is relatively straightforward to obtain for multiple unstructured uncertainties modeled throughout the system, it is difficult to formulate for many problems involving real parameter variations. Furthermore, it is difficult to ensure that the uncertainty model is formulated such that the dimension of the resulting model is minimal. A procedure for obtaining an uncertainty model for real uncertain parameter problems in which the uncertain parameters can be represented in a multilinear form is presented. Furthermore, the procedure is formulated such that the resulting uncertainty model is minimal (or near minimal) relative to a given state space realization of the system. The approach is demonstrated for a multivariable third-order example problem having four uncertain parameters.
A Modeling Approach to Support Changeability Analysis and Management of Earth Observation Portfolios
Earth observing (EO) mission portfolios provide data on many geophysical parameters that collectively inform our understanding of the Earth system. To observe large-scale climate trends, it is important to collect data on many parameters over time. However, gaps may occur between missions due to formulation complexity, development delays, and uncertain events in operations. These gaps may impact the ability to provide sustained measurements. Developing a balanced EO mission portfolio is key to supporting study of the Earth system. Yet, decision-making at the portfolio level is a complex task because missions often address multiple parameters. Currently, the likelihood of data gaps is often assessed for an individual parameter, but decisions and events can impact data collection for many parameters. This poster introduces a modeling approach that supports management of the many parameter impacts of decisions and uncertain events. The approach provides a foundation for analyzing changeability in EO mission portfolios. Changeability analysis provides insight into a portfolio’s sensitivity to changes caused by decisions or uncertain events. The model is developed to analyze two aspects of changeability, robustness and flexibility, in EO mission portfolios. In context of these portfolios, the authors define robustness as a portfolio’s ability to provide sustained measurements despite future uncertainties, and they define flexibility as the availability of decision alternatives that contribute to parameter coverage at little detriment to the rest of the portfolio. The proposed model characterizes a portfolio’s sensitivity to change by capturing mission-parameter interconnectivity and redundancy in parameter coverage. The model can be analyzed to identify events that can create substantial gaps, thereby revealing focus areas for mitigation efforts. The model can also be analyzed to identify gap mitigation decisions that may improve parameter coverage with little detriment to the rest of the portfolio, thereby revealing favorable pathways for portfolio improvement. Developing a process for identifying these threats and opportunities will be the focus of future work. A parallel poster proposes a standard for visualizing and communicating portfolio-level impacts of decisions and uncertain events.
Gaussian membership functions are most adequate in representing uncertainty in measurements
In rare situations, like fundamental physics, we perform experiments without knowing what their results will be. In the majority of real-life measurement situations, we more or less know beforehand what kind of results we will get. Of course, this is not the precise knowledge of the type 'the result will be between alpha - beta and alpha + beta,' because in this case, we would not need any measurements at all. This is usually a knowledge that is best represented in uncertain terms, like 'perhaps (or 'most likely', etc.) the measured value x is between alpha - beta and alpha + beta.' Traditional statistical methods neglect this additional knowledge and process only the measurement results. So it is desirable to be able to process this uncertain knowledge as well. A natural way to process it is by using fuzzy logic. But, there is a problem; we can use different membership functions to represent the same uncertain statements, and different functions lead to different results. What membership function do we choose? In the present paper, we show that under some reasonable assumptions, Gaussian functions mu(x) = exp(-beta(x(exp 2))) are the most adequate choice of the membership functions for representing uncertainty in measurements. This representation was efficiently used in testing jet engines to airplanes and spaceships.
Robust linear quadratic designs with respect to parameter uncertainty
The authors derive a linear quadratic regulator (LQR) which is robust to parametric uncertainty by using the overbounding method of I. R. Petersen and C. V. Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. It is shown that, when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. A worst-case disturbance in the direction of the uncertainty is also considered. It is proved that performance robustness has been increased with the robust LQR when compared to a mismatched LQR design where the controller is designed on the nominal system, but applied to the actual uncertain system.
Robust stabilization of the Space Station in the presence of inertia matrix uncertainty
This paper presents a robust H-infinity full-state feedback control synthesis method for uncertain systems with D11 not equal to 0. The method is applied to the robust stabilization problem of the Space Station in the face of inertia matrix uncertainty. The control design objective is to find a robust controller that yields the largest stable hypercube in uncertain parameter space, while satisfying the nominal performance requirements. The significance of employing an uncertain plant model with D11 not equal 0 is demonstrated.
Reliability, Risk and Cost Trade-Offs for Composite Designs
Risk and cost trade-offs have been simulated using a probabilistic method. The probabilistic method accounts for all naturally-occurring uncertainties including those in constituent material properties, fabrication variables, structure geometry and loading conditions. The probability density function of first buckling load for a set of uncertain variables is computed. The probabilistic sensitivity factors of uncertain variables to the first buckling load is calculated. The reliability-based cost for a composite fuselage panel is defined and minimized with respect to requisite design parameters. The optimization is achieved by solving a system of nonlinear algebraic equations whose coefficients are functions of probabilistic sensitivity factors. With optimum design parameters such as the mean and coefficient of variation (representing range of scatter) of uncertain variables, the most efficient and economical manufacturing procedure can be selected. In this paper, optimum values of the requisite design parameters for a predetermined cost due to failure occurrence are computationally determined. The results for the fuselage panel analysis show that the higher the cost due to failure occurrence, the smaller the optimum coefficient of variation of fiber modulus (design parameter) in longitudinal direction.