Doctor of Philosophy with a Major in Aerospace Engineering

Series

Doctor of Philosophy with a Major in Aerospace Engineering

Permanent Link

https://hdl.handle.net/1853/72952

Series Type

Degree Series

Associated Organization(s)

Organizational Unit

Daniel Guggenheim School of Aerospace Engineering

The Daniel Guggenheim School of Aeronautics was established in 1931, with a name change in 1962 to the School of Aerospace Engineering

Full item page

Publication Search Results

Now showing 1 - 10 of 1197

Feedback Interconnection of Dissipative Systems and Accelerated Learning for Adaptive Control

(Georgia Institute of Technology, 2024-12-08) Somers, Luke

In this research, we develop partial stability theorems for nonlinear continuous-time and discrete-time dissipative feedback systems. Specifically, by invoking additional structural constraints on the forward and feedback loop system storage functions, we develop feedback interconnection partial stability results for dissipative nonlinear dynamical systems. Our results provide extensions of the positivity and small gain theorems for guaranteeing partial stability of feedback interconnected systems. Moreover, we introduce the notion of strongly dissipative dynamical systems. In particular, we construct a stronger version of the dissipation inequality that implies system dissipativity and generalizes the notion of strict dissipativity but unlike strict dissipativity, which for a closed dynamical system implies asymptotic stability, the closed dynamical system possesses the property that system trajectories converge to a Lyapunov stable equilibrium state in finite time. Next, we develop new continuous-time, momentum-based adaptive laws for identification and control by augmenting higher-order tuners into the integral gradient and recursive least squares algorithms. In addition, we develop an online learning algorithm for solving the Bellman equation for affine in the control discrete-time nonlinear uncertain dynamical systems. To ensure accelerated learning of our algorithm in generating optimal control policies, we use an actor-critic structure predicated on higher-order tuner laws. Finally, we merge our strong dissipativity framework with our momentum-based adaptive control architecture to develop adaptive controllers with finite time guarantees.
Absolute and Autonomous Spacecraft Navigation Using Line-of-Sight Measurements

(Georgia Institute of Technology, 2024-12-08) Henry, Sebastien Daniel Jacques

Increasing activities in the space domain drive the need for better navigation solutions. Optical navigation (OPNAV) is particularly attractive because it allows one to navigate autonomously using different beacons like stars, planets, moons, asteroids, and other spacecraft. However, there are still technical hurdles to overcome about autonomous OPNAV. The evermore stringent mission requirements call for efficient OPNAV solutions that provide the best state estimation possible. Moreover, the need for efficient algorithms is further motivated by the fact that cameras increase in resolution while new image processing pipelines often allow for the extraction of more measurements. Finally, autonomous navigation pipelines need recovery procedures in case of filter failure or simply as a redundancy check. This work specifically treats the case of line-of-sight (LOS) measurements and focuses on four contributions. One of the most fundamental algorithms used in computer vision is triangulation. Triangulation serves a dual purpose: reconstructing shapes from multiple pictures and estimating the position of a camera when observing known features. The first contribution reviews the state-of-the-art in triangulation and develops a complete non-iterative framework for an uncertainty-aware statistically optimal solution: linear optimal sine triangulation (LOST). LOST gives similar results as iterative schemes but at a fraction of the computational cost. LOST is applied to space exploration in a second contribution. More specifically, effects like relativity, planetary uncertainty, and light time-of-flight are important in celestial navigation. LOST is used to analyze the impact of those effects and seamlessly integrates them into the navigation solution. LOST for planet identification in the image in the case of a full lost-in-space problem. Finally, LOST is adapted to the pushbroom camera model. The third contribution considers a problem adjacent to triangulation, the perspective-n-point (PnP). At the difference with triangulation, the PnP further needs to estimate the camera rotation on top of the position. The PnP is very relevant for robot navigation. The linear optimal sine framework is extended to solve this harder problem and demonstrates faster performance compared to other optimal methods. Finally, the fourth contribution tackles the use of LOS in the case of a formation flying initial orbit determination (IOD). For this, the LOS measurements are augmented with knowledge of the range by the inter-satellite communication. The developed solution allows the recovery of the inertial orbits of multiple spacecraft that can then initialize navigation filters.
Investigation of Ammonia Kinetics Using Shock Tube and Laser Absorption Spectroscopy

(Georgia Institute of Technology, 2024-12-08) Peng, Yuzhe

The implementation of ammonia (NH3) as a carbon-free energy vector and practical fuel is considered a key component in a sustainable energy system. The synthesis of green NH3 provides a viable storage and transport solution for renewable electricity, while the substitution of fossil-based fuel sources with NH3 in power generation gas turbines and transportation engines could deliver immediate decarbonization results in sectors that are hard to electrify. As challenges surrounding the low reactivity and high nitrogen oxide (NOx) emissions remain major obstacles, an improved understanding of the chemical kinetics of NH3 is critical to the development of practical combustion systems. This dissertation is concerned with the investigation of NH3 chemical kinetics at high temperatures and pressures relevant to combustion in gas turbines, leveraging the capability of shock tube and laser absorption spectroscopy (LAS). The ignition delay time (IDT) measurements of NH3/(H2)/O2/Ar mixtures are conducted behind reflected shock waves at a range of temperatures between 941 and 1941 K and pressures between 11 and 30 atm. As one of the focuses of this work, the effect of fuel concentration is systematically studied for the first time over a wide range of NH3 mole fractions in mixture from 1.14% to 21.88% and compared with a number of current kinetic models. Experimental observations and kinetic analyses reveal fuel-concentration-dependent model deficiencies, and the oxidation paths of H2NO/HNOH forming HNO are found to possibly have a major impact on the autoignition of NH3 through the HO2/H2O2 chemistry. The effects of equivalence ratio and H2 blending are also investigated for their relevance to both NH3 combustion in practical devices and addressing the observed fuel-concentration-dependent model deficiencies. Findings from experiments and kinetic analyses are used to inform the optimization of two selected models, each showing good performance at one end of the fuel concentration range. The updated rate parameters of selected reactions lead to significantly improved model predictions of experimental data from this work at both low and high fuel concentrations, whereas moderate improvements are seen at certain conditions and mixed results at others in the validation against data from literature. Since the updates are mostly informed by experiments and kinetic analyses limited to the autoignition of NH3 mixtures, more work is needed in the future to improve the existing kinetic models. A diode-laser-based absorption sensor for NH3 detection is also developed to aid the investigation of NH3 chemical kinetics in this work. The sensor takes advantage of the affordability and robustness of near-infrared (NIR) diode lasers and three NH3 absorption transitions near 2.2 μm. Built upon a previous study in literature with a similar setup, this work provides the first detailed lineshape characterization of the absorption feature to determine the collisional broadening coefficients in a static absorption cell and their temperature dependences for O2, N2, Ar, and air behind shock waves at temperatures up to 1480 K and pressures up to 6.5 atm, allowing for accurate NH3 detection at a wider range of conditions. The sensor is used for NH3 time history measurements to help ascertain IDT in autoignition experiments and to monitor fuel decay in NH3 pyrolysis experiments. The experimental and analytical work presented in this dissertation contributes to the knowledge of NH3 combustion in two major aspects: providing new observations focusing on high-fuel-concentration IDTs and reliable datasets for model validation and development. The kinetic analysis based on experimental data obtained in this work reveals the importance of H2NO/HNOH oxidation pathways that warrants future investigation.
Reduced-Order Modeling Techniques for Aircraft Design in High-Dimensional Spaces

(Georgia Institute of Technology, 2024-12-06) Mufti, Bilal

Future aircraft designs are expected to meet rigorous performance demands, including enhanced fuel efficiency and high-speed capabilities, all while adhering to stringent environmental regulations that call for reduced noise levels and lower emissions. The design of these aircraft necessitates the early use of high-fidelity simulation tools during the conceptual design phase, where these simulations are applied in various areas, including multidisciplinary analysis, design optimization, uncertainty quantification, and design space exploration. However, the high computational cost associated with these tools renders them impractical for such applications. Surrogate models offer a computationally economical alternative, replacing these intensive simulations with efficient mathematical models. While data-fit surrogate models predict scalar outputs, Reduced-Order Models (ROMs) extend this capability to predict field solutions, capturing the underlying physics crucial for early-stage aircraft design. To enable the exploration of revolutionary aircraft designs and capture subtle design nuances, it is crucial to develop these ROMs over high-dimensional design spaces. However, constructing such ROMs presents challenges due to (1) large input dimensionality, leading to the curse of dimensionality, (2) the high computational cost of training, and (3) the prediction of nonlinearities, such as shock waves within flow fields. This dissertation's primary objective is to develop or enhance methods to address these three challenges, structured into three research areas. For the first research area, we address the challenge of high input dimensionality by introducing a model-based active subspace method for supervised input dimensionality reduction. This method leverages direct function evaluations to identify the active subspace, enhancing computational efficiency. Notably, it circumvents the need for gradient information and the complex formulations often associated with active subspace methods, making it well-suited for the construction of ROMs over high-dimensional design spaces. To address the second research challenge concerning the high computational cost, we develop a multi-fidelity reduced-order modeling approach that combines Procrustes manifold alignment with dimensionality reduction techniques. This method applies dimensionality reduction to both input and output spaces within a multi-fidelity framework, facilitating a cost-effective construction of ROMs in high-dimensional design spaces. Procrustes alignment ensures consistent integration of various field data types, enhancing model flexibility and efficiency, while the dimensionality reduction techniques mitigate potential issues related to high dimensionality. In the third research area, we tackle the challenge of predicting nonlinearities by proposing a nonlinear ROMs framework based on deep learning and manifold learning, specifically designed to handle flow fields with complex variations, such as shock waves in transonic and supersonic regimes. This framework combines convolutional neural networks (CNNs) for extracting nonlinear shape modes and manifold learning for field prediction, accurately capturing and reconstructing shock-related features. The resulting method enhances predictive accuracy for applications where nonlinear behavior is critical, allowing for precise characterization of these phenomena. This dissertation provides methods that span different points on the cost-versus-accuracy spectrum, enabling aircraft designers to make informed choices based on their requirements for prediction accuracy and computational budgets. While these methods are developed for aircraft design applications, they can also be considered machine learning and deep learning techniques applicable to a wide range of engineering design problems. In summary, this thesis introduces three methods: (1) a computationally efficient model-based active subspace approach for supervised input dimension reduction, (2) a multi-fidelity framework for high-dimensional ROMs construction, and (3) a nonlinear ROM framework utilizing deep learning and manifold learning to predict complex field solutions.
Adapting the Past for Future Flight: Preliminary Design Framework for Long Duration O&S Aerospace Programs

(Georgia Institute of Technology, 2024-12-05) Roush, Karl

Aerospace programs face significant challenges due to their immense scale, extended timelines, and substantial budgets. While the reuse of heritage technologies helps reduce costs and mitigate risks, it introduces complications as these elements often struggle to meet modern requirements. This incompatibility, coupled with increasingly lengthy post-design phases, leads to substantial operations and support (O&S) challenges. While certainly a known issue, these constraints have been documented as worsening in GAO reports, OIG investigations, RAND studies, Congressional Reports, and more. These challenges have taken a priority role in programs’ considerations as evidenced by the command media updates across NASA, the DOD, and commercial entities. Past efforts to tackle this issue exist, but they often lack applicability to the unique aerospace context, particularly regarding long-term O&S considerations. Attempts at modeling the supply base are confined to broad characterizations and lack the means to communicate disruptive rare events- which are more likely to occur as O&S duration increases. This research addresses three key gaps in the field: O&S best practices are ill-suited for heritage technology reuse, the shallow and dynamic aerospace supply base in modeling approaches is not captured, and communication of rare events over an extended O&S phase is lacking. Correspondingly, the research delivers three main contributions. First, it identifies shortfalls in existing producibility best practices and revises them for heritage technology reuse through a comprehensive case study of the Space Shuttle Program. Second, it enhances supply base modeling by implementing a distributional approach to learning rates and associated cost projections, validated using NASA's standard PCEC tool and a novel retrospective LCC estimate for the Space Shuttle. Third, it integrates concepts from portfolio management and extreme value theory to create a toolkit for evaluating rare events in the context of cost estimates and O&S considerations. The legacy of the Space Shuttle continues today with the Space Launch System (SLS) containing many heritage elements and an expectedly long O&S duration, in line with the major themes of this work. Applying the contributions of this work to the SLS program revealed improved adherence to the modified best practices, potential substantial underestimation in NASA's public cost projections, and reduced likelihood of extreme cost outliers for SLS relative to the Shuttle program. In today's fiscally cautious space environment, the challenge lies in strategically leveraging prior resources while considering financial realities over long O&S horizons. The efforts of this research work aim not only to ensure the long-term viability of projects like SLS under this dual mandate, but also to contribute to broader efforts in planning the next generation of space exploration programs. It provides actionable guidance and valuable tools for immediate use by designers, planners, cost estimators, and engineers, paving the way for the next era of human spaceflight.
Thermoelectromagnetic Fluid Management in Microgravity

(Georgia Institute of Technology, 2024-12-04) Hart, Samuel T.

Modern microgravity fluid management is dominated by capillary systems, mechanical pumps, and positive expulsion devices such as bladders. These technologies, either singularly or in combination, are able to achieve the fluid management needs of most space missions. However, in the age of small spacecraft, increasing human spaceflight, and long-term space habitation, there is a desire for smaller, more reliable, and higher-performing fluid management systems. This research proposes and demonstrates the use of thermal phase change and electromagnetic devices to create improved fluid management technologies. The applications of these technologies range from propellant management and life support to heat transfer. This work first proposes several methods of phase separation for saturated or cryogenic fluids in conformal tanks using thermal, capillary, and electromagnetic means. The viability of a thermal phase change fluid management device is then demonstrated in laboratory tests, and the primary factors contributing to its performance are analyzed. Finally, electromagnetic forces are applied to dynamic fluid management in a small-scale cooling loop for spacecraft. An electromagnetic pump is developed and demonstrated in a benchtop prototype loop.
VIDEC-CFD: A Methodology for Variational Integration of a Discrete Exterior Calculus-Based Computational Fluid Dynamics Formulation

(Georgia Institute of Technology, 2024-12-02) Leibenguth, Chase

Computational Fluid Dynamics has revolutionized the design process of aerospace systems in the decades since its introduction. The improvements provided by CFD in conjunction with physical experiments have enabled database creation for aerospace design, design cycle cost and time reductions, and experimental extrapolation corrections for full-scale flight vehicles at in-flight Reynolds Numbers. Despite such valuable applications, there are critical shortcomings in current CFD methodologies. Turbulent vortex formation, shedding, and interactions with the surrounding flow field are difficult to resolve without significant financial and computational cost and complexity. Furthermore, fundamental invariants, such as circulation and angular momentum, are not conserved in discretized space-time. These quantities may be conserved at the limit of a steady-state solution or an infinitely refined mesh, however, not all problems have such properties. Failing to preserve these invariants will affect the final obtained solution. An area of research that shows promise involves Consistent Spatial Discretization and Discrete Exterior Calculus-based CFD solvers. The governing equations of fluid mechanics are re-derived using operators from Discrete Differential Geometry and Topology. These operators enable the inherent, exact conservation of theorems, such as Stokes' or Noether's, in the flow domain. Discrete analogs have been constructed that take these operators from a continuous domain to a discretized space. So far, DEC-based solvers have been derived and applied to viscous and inviscid incompressible flows using only the continuity and momentum equations. No turbulence models were required to resolve turbulent phenomena that arose as flows moved from inviscid to highly viscous. The inherent preservation of underlying geometric quantities related to the governing equations and fundamental physical invariants on a discretized domain mitigated the need for additional models. Application of variational integrators enabled discrete time integration that preserves fundamental invariants during numerical integration in time. However, all of these methodologies relied specifically on the divergence-free velocity field present in an incompressible flow. The goal of the following research is to extend the cited methodologies to include the energy and entropy equations for modeling viscous, compressible, subsonic flows. The energy equation is essential to this extension to account for viscous dissipation effects on a compressible fluid. The entropy equation is included alongside specific variable definitions to ensure the combined set of continuous and discrete governing equations are Thermodynamically Consistent. That requirement ensures the governing equations inherently satisfy the 1st and 2nd Laws of Thermodynamics topologically. The first major research contribution is the derivation of the full set of governing equations of fluid mechanics from a Least Action Principle obtained from a symmetric Lie-Bracket and anti-symmetric Poisson Bracket. The second contribution is the derivation of a coordinate free representation of the viscous dissipation function in terms of DEC operators for a viscous, compressible, homogenous, single-phase Newtonian fluid.
Topology optimization with natural frequency and structural stability criteria using eigenvector aggregates

(Georgia Institute of Technology, 2024-11-25) Li, Bao

Topology optimization is a powerful tool for designing lightweight, high-performance structures by optimizing material distribution to meet specific performance objectives. One of the most challenging applications of topology optimization involves ensuring structural stability and achieving the desired natural frequencies of the design by formulating problems as generalized eigenvalue problems. Eigenvectors provide essential information on the mode shapes for a structure, offering insights into tailoring its behavior to specific requirements. However, imposing eigenvector constraints in topology optimization is challenging due to the non-differentiability of repeated eigenvalues, the complexity of balancing competing objectives, and the high computational cost of calculating eigenvector derivatives. This thesis addresses these challenges by introducing an innovative eigenvector aggregation approach to handle eigenvector constraints in topology optimization. It presents a comprehensive study of the eigenvector aggregate, including its applications in natural frequency and buckling optimization, as well as the ability to hand the repeated eigenvalues. Additionally, this work presents efficient methods for computing eigenvector-based derivatives and validates these methods in the thermal, natural frequency, and buckling optimization problems. Furthermore, this thesis investigates nonlinear initial post-buckling problems and introduces efficient optimization criteria based on Koiter asymptotic theory for post-buckling performance optimization. It presents a novel two-layer adjoint-based sensitivity analysis for Koiter-based optimization, significantly reducing the computational cost.
From Strategic Planning to Tactical Adjustments: An eVTOL Trajectory Management Framework for Urban Air Mobility

(Georgia Institute of Technology, 2024-09-05) Kim, Seulki

Urban Air Mobility (UAM) is emerging as a revolutionary transportation concept aimed at alleviating ground traffic congestion in densely populated urban areas. By utilizing electric Vertical Takeoff and Landing (eVTOL) aircraft, UAM promises to provide rapid, efficient, and environmentally friendly air transportation for short to medium distances within and between cities. The increasing urbanization of the global population, coupled with advancements in electric propulsion, battery technology, and automation, has motivated significant interest in UAM as a potential solution to ground transportation challenges. However, the realization of UAM operations faces several critical barriers. These include the need for comprehensive airspace management, the development of reliable aircraft, and integration with existing urban infrastructure and communities. Particularly, the motivation for this research stems from the unique operational complexities associated with managing multiple eVTOL flights in complex urban environments. These aircraft are anticipated to operate at low heights in obstacle-rich settings, relying on limited battery energy storage and subject to specific electrical and thermal powertrain constraints. The vertical takeoff and landing capabilities, while advantageous for urban operations, also impose significant power demands and rapidly deplete energy reserves. Additionally, the current technological limitations in battery energy density and their non-linear discharge behavior present challenges in energy management and flight planning. Currently, trajectory management for conventional aircraft is primarily handled through a combination of pre-flight planning by airline dispatchers and real-time adjustments by pilots and air traffic controllers. Given the novel operational characteristics of UAM, however, traditional human-driven trajectory management systems may not suffice for the anticipated high traffic densities, rapid-paced operations envisioned for UAM, where a numerous number of aircraft will need to navigate through constrained urban airspace while adhering to strict energy and safety constraints. Moreover, the need for rapid decision-making in dynamic urban environments, especially during contingencies such as en-route diversions, necessitates more agile and automated management approaches. Consequently, these challenges underscore the necessity for an advanced automated system capable of ensuring safe, energy-efficient, and scalable management of eVTOL trajectories. In response, this dissertation addresses these challenges through the development of an automated trajectory management framework for eVTOL UAM aircraft. The framework is designed to enable safe, energy-efficient trajectory generation and dynamic adjustments in response to evolving flight circumstances. Specifically, it consists of two primary components: a strategic planner and a tactical planner. The strategic planner, developed using mixed-integer linear programming (MILP), generates pre-departure trajectories that optimize battery energy efficiency and collision avoidance, taking into account intricate powertrain constraints. This component successfully integrates operational constraints specific to manned eVTOL fights into the MILP formulation, allowing for the generation of trajectories that adhere to aviation regulations and standard flight procedures. Additionally, the development of a battery discharge model and thermal prediction capability enables to generate battery energy-efficient trajectories for multiple aircraft with the prediction capability of electrical and thermal profiles of powertrain along trajectories. Notably, this prediction of electrical and thermal behaviors along the trajectory help enable accurate pre-departure safety assessments to prevent potential energy deficits and powertrain issues during flights. The tactical planner, built upon a Receding Horizon MILP (RH-MILP) approach, provides real-time trajectory adjustments and manages in-flight contingencies. This component demonstrates rapid computational efficiency, with trajectory recalculations completed in less than a second, allowing for dynamic adaptation to changing flight conditions. Furthermore, the creation of a diversion decision-making and planning tool aids pilots in selecting optimal alternate landing sites during contingencies, considering real-time aircraft and powertrain states. Complementing the strategic planner, the tactical planner facilitates real-time adjustments to planned trajectories in response to evolving flight conditions and unforeseen contingencies. It employs a Receding Horizon MILP (RH-MILP), which allows for dynamic trajectory modifications while maintaining computational efficiency. Experiments demonstrate that the RH-MILP can generate real-time, energy-efficient trajectories for multiple eVTOL aircraft within a fraction of a second, significantly outperforming standalone MILP in terms of computational time. In addition, the tactical planner incorporates a diversion decision-making and planning tool that helps pilots manage in-flight contingencies by automatically selecting the best alternate landing sites and continuously adjusting the trajectory until safe diversion is completed. Several case studies demonstrate the tool's effectiveness in managing contingency scenarios, such as unexpected vertiport closures and partial battery pack disconnections. The integration of these components forms a trajectory management framework capable of effectively managing UAM trajectories under both regular and irregular operational scenarios. To validate the proposed framework, several real-world use cases were simulated in the Southern California region, chosen for its unique geographical and urban characteristics. These use cases demonstrated the framework's capability in generating conflict-free trajectories through complex terrains and urban environments. One case study showcased the optimization of trajectories for a flight, navigating mountainous terrain while adhering to airspace regulations and powertrain constraints. Another case study simulated high-density UAM operations in Los Angeles city, optimizing trajectories for 50 aircraft departing or arriving at 10 vertiports within a 30-minute period. These simulations validated the framework's scalability and its ability to handle diverse operational scenarios, including multi-hop missions and in-flight contingencies such as unexpected vertiport closures and partial battery pack disconnections. Ultimately, this automated trajectory management framework is expected to offer considerable benefits to UAM stakeholders, including pilots, operators, and air traffic controllers. UAM operators could leverage this framework to optimize flight planning and improve operational efficiency, pilots is able to receive enhanced decision support, particularly during off-nominal situations, and finally air traffic controllers could more effectively manage high-density urban air traffic. In conclusion, this research contributes to the advancement of UAM by addressing critical challenges in trajectory management. The developed framework demonstrates the potential for safe, efficient, and scalable eVTOL operations in complex urban environments, potentially accelerating the integration of this innovative transportation mode into urban airspace.
Hazard Detection and Avoidance for Autonomous Spacecraft Landing

(Georgia Institute of Technology, 2024-08-26) Tomita, Kento

As the feasibility of autonomous spacecraft landing is increasingly demonstrated by space agencies and private space companies, the demand for even more advanced capabilities grows, with the aim of achieving anytime and anywhere global and safe landing capabilities across the solar system—a milestone articulated by NASA’s Precision Landing and Hazard Avoidance (PL&HA) program. A notable challenge in this endeavor is the need for real-time terrain mapping and processing, along with the appropriate guidance, navigation, and control (GNC) technologies to perform autonomous hazard detection and avoidance (AHDA). This dissertation presents novel mathematical formulations and methods for the design and development of next-generation AHDA technology. Specifically, this study focuses on terrain mapping and processing algorithms for onboard hazard detection (HD) and the guidance problem under safe landing site uncertainty. We begin by improving the state-of-the-art (SOTA) model-based HD algorithm by applying deep learning techniques. Given the safety-critical application of planetary landings, an uncertainty-aware learning-based HD algorithm is developed for improved reliability. Next, in Chapters 3 and 4, we address the landing safety evaluation under topographic uncertainty. Topographic uncertainty is often inevitable due to the hardware limitations of sensing instruments and challenging operational conditions, but in-depth studies and effective algorithmic solutions remain limited. Chapter 3 investigates the uncertainty quantification of landing safety under topographic uncertainty and proposes a semi-analytical evaluation method. In Chapter 4, novel real-time stochastic terrain mapping and processing algorithms are developed. We develop a real-time Gaussian digital elevation map (DEM) construction algorithm and a real-time stochastic HD algorithm compatible with the Gaussian DEM input. The novel stochastic terrain mapping and processing algorithm is shown to outperform the SOTA algorithm in terms of both prediction reliability and computational cost. Finally, Chapter 5 formulates the hazard detection and avoidance (HDA) guidance problem and presents novel solution approaches. The HDA guidance problem is unique, where the objective is to maximize the probability of a safe landing, with the major uncertainty being the landing safety over the terrain. This dissertation presents several illustrative examples as proof-of-concept to demonstrate the value of the proposed work.