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Articles 241 - 270 of 13098
Full-Text Articles in Entire DC Network
Investigating The Performance Of Processed Stockpile Fly Ash For Low Carbon Concrete, Michael Mccarthy, Arfas Habeeb, Laszlo Csetenyi, Roderick Jones
Investigating The Performance Of Processed Stockpile Fly Ash For Low Carbon Concrete, Michael Mccarthy, Arfas Habeeb, Laszlo Csetenyi, Roderick Jones
World of Coal Ash Proceedings
Reducing embodied carbon in concrete has increasingly focused on clinker substitution through the use of supplementary cementitious materials (SCMs). However, the local availability of fly ash, a widely used SCM in the UK, offering benefits in this role, has reduced over the past decade, as coal-fired electricity generating plants have gradually been taken out of service. Attention has, therefore, increasingly focused on fly ash from stockpile and landfill sites to maintain supply, i.e., material not used following production and put into storage. Most UK fly ash originated from the burning of bituminous coal, producing low-lime siliceous material, which although undergoing …
Solar Solution For Closed Ccr Units And Adjacent Land, Chris Fairey
Solar Solution For Closed Ccr Units And Adjacent Land, Chris Fairey
World of Coal Ash Proceedings
Solar Solution for Closed CCR Units and Adjacent Land Chris Fairey1, Kenny Hughes1 1Watershed Geo, 1125 Sanctuary Pkwy, Suite 180, Alpharetta, GA 30009 KEYWORDS: Solar, Racking, Brownfield, Greenfield, Slopes, PowerCap® ABSTRACT With the reduction in coal fired power generation, there is a consistent trend in the industry to supplement generation with solar power. The property located within and surrounding these decommissioned power plants offers a significant opportunity to create a renewable solar power asset. The PowerCap® Nail to Rail System, developed by Watershed Geo, is an advanced solar racking solution designed for sites that do not require environmental closure such …
Abundances Of Elements In Global Coals, Shifeng Dai
Abundances Of Elements In Global Coals, Shifeng Dai
World of Coal Ash Proceedings
The abundance of elements in coal is important not only because it provides a solid scientific and practical foundation for various geochemical comparisons, but also because it helps address broader questions in Earth Sciences. In this study, data on major and trace elements in global coals comprising hundreds of thousands of coal samples were compiled from peer-reviewed journal articles, books, various databases, dissertations, and technical reports. These data formed the basis for estimating element abundances in global coals presented in this study. All collected data were rigorously screened for reliability, and any records with questionable quality were excluded from the …
Consolidation Modeling To Support Closure Planning Of An Upstream Raise Ccr Surface Impoundment Containing Fgd Material, Tanya Walkenbach, Craig Schuettpelz, Todd Stong, Shane Stockdill
Consolidation Modeling To Support Closure Planning Of An Upstream Raise Ccr Surface Impoundment Containing Fgd Material, Tanya Walkenbach, Craig Schuettpelz, Todd Stong, Shane Stockdill
World of Coal Ash Proceedings
Rainbow Energy Center’s (REC’s) Coal Creek Station has managed calcium sulfite flue gas desulfurization (FGD) material in composite-lined upstream raise surface impoundments since 2001. The upstream raise surface impoundment utilizes bottom ash (drainage zone) and fly ash (structural zone) produced at Coal Creek Station to contain the FGD placement. FGD material was hydraulically sluiced to the center of the 110-acre Upstream Raise 92 (UR92) coal combustion residual (CCR) unit between 2001 and 2021. The FGD was deposited to a maximum thickness of approximately 100 feet in the center of the unit. Significant consolidation of FGD material occurred with subsequent FGD …
Investigation Of A Historical Coal Combustion Residuals Management Unit (Ccrmu), Todd Stong, Shane Stockdill, Erin Hunter
Investigation Of A Historical Coal Combustion Residuals Management Unit (Ccrmu), Todd Stong, Shane Stockdill, Erin Hunter
World of Coal Ash Proceedings
Rainbow Energy Center’s (REC’s) Coal Creek Station has managed coal combustion residuals (CCR) in various engineered impoundments and landfills since plant operation began in 1978. Since then, waste containment methods have evolved resulting in significant changes to their CCR management practice. In the late 1980s and early 1990s REC closed several existing CCR units with natural soil liners and constructed several new CCR units with composite liner systems. One of the closed units was an area now referred to as North Section 16, an impoundment that received CCR including bottom ash, fly ash, and flue gas desulfurization material. North Section …
Transportation Logistics Panel, John Ward, Andrew Vollmer, Tracy Zea, Marci Jenks
Transportation Logistics Panel, John Ward, Andrew Vollmer, Tracy Zea, Marci Jenks
World of Coal Ash Proceedings
As the industry shifts from freshly generated ash to harvested materials and advanced utilization, logistics is becoming one of the primary drivers of project success or failure. This moderated panel will explore how sourcing, transportation, and storage realities are changing — and what project teams most often underestimate when working with harvested coal ash. Panelists will discuss what breaks, what becomes more complex, and how logistics considerations are reshaping planning and development.
Optimization Of Remedial Strategies For Ccr Site Corrective Action Through Advanced Geochemical Modeling, Cole Mayer, Pj Nolan
Optimization Of Remedial Strategies For Ccr Site Corrective Action Through Advanced Geochemical Modeling, Cole Mayer, Pj Nolan
World of Coal Ash Proceedings
The power industry is actively designing and implementing corrective measures for Coal Combustion Residuals (CCR). In many cases, these measures include active remedies such as pump and treat, in-situ injection, or reactive barriers, all of which demand a thorough understanding of the underlying geochemical system. Depending on the geochemical characteristics of an aquifer, different chemical reagents can achieve varying degrees of success or even be detrimental to the remediation of the site. Advanced geochemical modeling is an invaluable tool for developing a remedy that is optimized to the site-specific geological, hydrological, and geochemical environment. In the case study presented here, …
Application Of Stable Isotopes In An Alternative Source Demonstration, Alison O'Connor
Application Of Stable Isotopes In An Alternative Source Demonstration, Alison O'Connor
World of Coal Ash Proceedings
Stable isotope analysis is commonly used in age dating, provenance studies and to differentiate between sources of groundwater. Multiple studies have shown that strontium and boron isotopic ratios can be successfully used in identifying CCR impacts to groundwater. This talk presents an applied case study using boron and strontium isotopes in conjunction with additional geochemical approaches in an alternative source demonstration. Boron and strontium isotopes were measured in both groundwater and CCR leachate over sampling events from 2019 to 2025. The data revealed that strontium and boron isotopic signatures in groundwater near the CCR unit differed significantly from both site-specific …
Distinguishing Ccp From Nuclear Impacts In Groundwater, Lea Millet
Distinguishing Ccp From Nuclear Impacts In Groundwater, Lea Millet
World of Coal Ash Proceedings
As the energy transition from fossil fuels to other generation technologies continues, many companies worldwide are evaluating the feasibility of constructing nuclear power plants at sites previously used for coal-powered generation. Thermal power plant sites offer advantages for siting nuclear generation such as proximity to cooling water and grid connections; however existing impacts to groundwater from coal combustion product (CCP) management units may confound monitoring programs designed to detect impacts from nuclear operations. For example, boron and lithium may be present in waters associated with CCP management and nuclear power plant operations, and potassium that often has concentrations above background …
Ccr Landfill Closure Challenges, Solutions And Innovation, Jay Mokotoff, Drew Browning, Steve Applegate
Ccr Landfill Closure Challenges, Solutions And Innovation, Jay Mokotoff, Drew Browning, Steve Applegate
World of Coal Ash Proceedings
CCR landfills can present unique design and construction challenges for the industry when closing these units at the end of their life. In comparison to CCR surface impoundments, CCR landfills typically have greater flexibility under the CCR Rule for operations and beneficial use purposes and may not have defined closure dates which results in some of these closures extending further into the future. However, as coal burning plants continue to shudder, the closure of these landfills is rapidly approaching. This presentation will focus on the challenging site conditions, site specific considerations and potential solutions when designing and constructing the landfill …
Engineering Granulometry To Optimize Performance Of Reclaimed Ash, Russell Hill
Engineering Granulometry To Optimize Performance Of Reclaimed Ash, Russell Hill
World of Coal Ash Proceedings
As utility production of fresh fly ash declines, the concrete industry is turning to reclaimed and beneficiated materials to maintain reliable SCM supply. This transition creates an opportunity not only to secure volumes but to engineer improved performance. The ReCinis™ beneficiation process enables this by providing controls that tune particle-size distribution (PSD), sphericity, packing behavior, surface area, and surface activation. Processing trials show that blends combining fine ground fractions with spherical, broad-graded hydrocyclone overflow (OF) materials can balance high reactivity with favorable rheology. Mechanochemical activation during grinding appears to increase reactivity beyond what surface-area metrics alone predict, likely through removal …
Alternative Cover Permitting And The Ccr Rule, Evan Andrews, Victor Damasceno
Alternative Cover Permitting And The Ccr Rule, Evan Andrews, Victor Damasceno
World of Coal Ash Proceedings
Federal rules (40 CFR Parts 9, 257 and 261) that regulate coal combustion residuals (CCR) created a significant demand associated with closure of coal ash management and storage facilities using liner systems. Timelines associated with these facility closures combined with substantial project scale and potential for future mining /reuse has driven the need for closure systems that perform beyond the prescriptive soil / geomembrane caps outlined in the federal regulations. As outlined in section 257.102 (d)(3)(i) of the CCR Rule, the standard cover system must include an infiltration layer of at least 18 inches of earthen material and an erosion …
Sustainability And Waste Diversion At Tva Shawnee "Project Phoenix", Bryan Jacob, Shane Harris
Sustainability And Waste Diversion At Tva Shawnee "Project Phoenix", Bryan Jacob, Shane Harris
World of Coal Ash Proceedings
An engineered turf closure system can serve as an ideal foundation for a solar energy system to be installed atop coal combustion residual (CCR) impoundments. This approach not only enables productive power generation during the post-closure period, it also preserves opportunities for recovery and beneficial use of CCR material in the future. “Project Phoenix” at TVA’s Shawnee Fossil Plant offers an illustrative example. This paper will cover the sustainability benefits of the companion ClosureTurf® and PowerCap® systems installed at that site as well as waste diversion activities undertaken during construction to recycle as much as practical and minimize waste destined …
Demystifying Large Language Models: How Ai Is Transforming Data, Compliance, And Decision-Making In Coal Ash And Environmental Management, Scott Pfeiffer
Demystifying Large Language Models: How Ai Is Transforming Data, Compliance, And Decision-Making In Coal Ash And Environmental Management, Scott Pfeiffer
World of Coal Ash Proceedings
The environmental and coal combustion residuals (CCR) industries generate vast amounts of information—from groundwater monitoring reports and RCRA documentation to closure plans and analytical data. Managing, interpreting, and communicating this information is a growing challenge for utilities, regulators, and consultants alike. Large Language Models (LLMs), such as OpenAI’s GPT architecture, represent a breakthrough in how organizations can interact with their technical data. These models use deep neural networks trained on billions of words to understand, summarize, and generate language with human-like accuracy. When securely adapted for enterprise use, LLMs can automate routine reporting, extract data from technical documents, generate regulatory …
Expert Perspectives On The U.S. Coal Combustion Products Market – Now, Then, And The Future, Mark Rokoff, David Cox, Walter Lemaire, John Ward
Expert Perspectives On The U.S. Coal Combustion Products Market – Now, Then, And The Future, Mark Rokoff, David Cox, Walter Lemaire, John Ward
World of Coal Ash Proceedings
This panel discussion will explore the continued evolution of the U.S. coal combustion products market, with a focus on the impacts of dynamic regulatory and market forces. Invited expert panelists will share perspectives on developments over the past several years (building on discussions from WOCA 2022 and WOCA 2024), current conditions, and expected future trends—particularly those likely to shape the market between 2026 and 2030. The discussion will address the interrelated markets for engineering, construction, and beneficiation of ash from both operating and inactive plants. Panelists will offer perspectives relevant to the full coal ash industry, from owner/operator organizations to …
Subsurface Delineation Of Coal Combustion Residuals Using Multiple Geophysical Methods, Eric Hageman, Adam Rak, Thomas Jordan, Kate Mckinley
Subsurface Delineation Of Coal Combustion Residuals Using Multiple Geophysical Methods, Eric Hageman, Adam Rak, Thomas Jordan, Kate Mckinley
World of Coal Ash Proceedings
Geophysical techniques provide alternative methods of Coal Combustion Residual (CCR) delineation and characterization to supplement more invasive boring programs used for beneficial reuse planning. A demonstration project was designed to characterize the electromagnetic and seismic stratigraphy of CCR material and test the effectiveness of three geophysical techniques: Electrical Resistivity Imaging (ERI), Transient Electromagnetic (TEM) induction, and Multi-channel Analysis of Surface Wave (MASW). The demonstration project was completed at a dry-stack CCR unit containing a variety of CCR ash, gypsum, and thin layers of drainage aggregate (limestone). During a single-day deployment, several geophysical survey tests were conducted in specific areas of …
Analysis Of Approximations In Flash Thermal Diffusivity Measurements Using High‑Fidelity Simulations, Tage T. Burnett, Jakob G. Bates, Matthew R. Jones, Christopher R. Dillon, John Tencer
Analysis Of Approximations In Flash Thermal Diffusivity Measurements Using High‑Fidelity Simulations, Tage T. Burnett, Jakob G. Bates, Matthew R. Jones, Christopher R. Dillon, John Tencer
Faculty Publications
Thermal diffusivity is an important material property for understanding and characterizing transient behavior in many heat transfer applications. This study investigates the accuracy and approximations of inverse mathematical models for measuring thermal diffusivity of materials via the widely used Flash Method. High-fidelity simulations of the Flash Method in copper, silicon carbide, silicon, and glass were performed as numerical experiments and included physics such as in-depth absorption, radial conduction, and surface convection. Data from those numerical experiments were used to estimate material thermal diffusivity using seven traditional and new inverse models. Parker’s original model had relative errors 𝜖< 5% when the approximations it makes were enforced in numerical experiments. Newer models performed well even when experimental restrictions were relaxed. Models that include radial heat conduction were capable of accurately measuring thermal diffusivity (𝜖< 1%) when a Gaussian energy source was used. Models with radial conduction and in-depth material absorption of the laser source could calculate thermal diffusivity for semi-transparent materials such as silicon (𝜖< 1%) and even transparent materials like glass (𝜖< 10%). Convective losses from the material’s front surface had a negligible impact on measurements except for very low thermal diffusivity materials. Using temperatures from many locations of the test material’s surface increased resilience to noise, reducing the distribution of thermal diffusivity measurements by more than an order of magnitude. The models developed in this study could enable a more relaxed Flash Method experimental setup that maintains thermal diffusivity accuracy and extend the utility of the Flash Method to semitransparent materials.
Aerodynamic Performance Of Grid Fins As High Lift Devices, Luke Jeffrey Krick
Aerodynamic Performance Of Grid Fins As High Lift Devices, Luke Jeffrey Krick
Senior Honors Theses
Flaps are used in almost all aircraft to increase the amount of lift the wings can produce at low speeds. However, the flaps also increase the amount of drag experienced by the aircraft. The drag induced by the flaps causes energy loss and is unfavorable for aircraft effectiveness. In recent years, grid fins have become a popular choice for aircraft and armaments to control their orientation. First developed for launch escape towers, grid fins are made up of lines that cut the fin into many quadrants, leaving the fin with multiple rectangular shaped open areas. The aim of this study …
Engineering Design And Analysis Using Creo® Cad, Cae, And Manufacturing Applications, Swapnil Moon
Engineering Design And Analysis Using Creo® Cad, Cae, And Manufacturing Applications, Swapnil Moon
Open and Affordable Textbooks
This textbook presents a structured approach to computer-aided design using Creo, integrating CAD, CAE, and CAM workflows within a unified engineering framework. The material emphasizes parametric modeling, design intent, and feature-based modeling as foundations for creating robust and adaptable engineering models. Through progressively structured tutorials, students develop skills in part modeling, assemblies, engineering drawings, mechanism design, simulation, and manufacturing. The text incorporates real-world engineering components and workflows, including structural and thermal analysis, motion simulation, and toolpath generation, reflecting modern engineering practice. Designed for upper-division undergraduate and graduate students, this open educational resource supports hands-on learning and prepares students for industry-relevant …
Aquaculture Ecosystem Modeling Aeration Efficiency Optimization Using Cfd, Gabriela Reyes Gomez
Aquaculture Ecosystem Modeling Aeration Efficiency Optimization Using Cfd, Gabriela Reyes Gomez
Electronic Theses and Dissertations 2020 - Present
The Harbor Branch Oceanographic Institute (HBOI) is developing the Intelligent and Resource Efficient Pond Aquaculture (IREPA) project, which aims to improve aquaculture management through the integration of predictive models and automated technologies. This approach seeks to transition traditional practices toward data-driven systems capable of supporting informed decision-making for aeration management.
This study investigates the effectiveness of different aerator configurations on hydrodynamic circulation and dissolved oxygen (DO) distribution in aquaculture ponds using computational fluid dynamics (CFD). A model was developed in ANSYS Fluent, where the aerator was represented using a power-based formulation and implemented as a moving wall boundary condition. Dissolved …
Portable Humidity Chamber, Calvin Wright, Ian Heilers, Sam Taylor
Portable Humidity Chamber, Calvin Wright, Ian Heilers, Sam Taylor
Honors Capstones
This engineering project, sponsored by Crandall Stats and Sensors, focuses on improving the ability to test product performance under controlled environmental conditions by designing a portable humidity chamber capable of maintaining a stable relative humidity between 20 and 80 percent with a tolerance of ±0.5 percent. Consistent humidity is crucial for evaluating how moisture influences material properties, product reliability, and long-term durability in real production environments. Because Crandall conducts testing across multiple facility locations, the chamber must also be lightweight, transportable, and easy for operators to use without specialized training. Developing such a system provides the company with a valuable …
Harness: Hybrid Architecture For Resilience In Networked Engineering System Simulations, Daniel Scott
Harness: Hybrid Architecture For Resilience In Networked Engineering System Simulations, Daniel Scott
Graduate Theses and Dissertations
This dissertation presents the development of HARNESS, a unified, domain-agnostic framework for the modeling, optimization, and evaluation of complex systems under conditions of degradation and uncertainty. The research addresses a persistent challenge in systems engineering: the lack of a generalizable, behaviorally grounded approach for quantifying resilience and robustness across diverse domains. HARNESS integrates graph-theoretic dependency modeling, GPU-accelerated evolutionary optimization, and agent-based simulation into a modular architecture that enables both system design and diagnostic analysis. The framework models system interdependencies through user-defined components, parameters, and constraints, allowing architectures to evolve dynamically while maintaining structural validity. A mutation-only genetic algorithm with a …
Development Of A Novel Method For Simultaneously Testing Multiple Specimens To Evaluate Tension-Tension Fatigue Life, Mehedi Hasan Mahfuz
Development Of A Novel Method For Simultaneously Testing Multiple Specimens To Evaluate Tension-Tension Fatigue Life, Mehedi Hasan Mahfuz
All Graduate Theses and Dissertations, Fall 2023 to Present
The aim of this study is to develop a novel method for rapidly evaluating the tension–tension fatigue life of metals. Fatigue failure, which occurs when materials gradually weaken and fracture under repeated loading, is a critical concern in designing safe and reliable structures such as airplanes, cars, and bridges. Traditional fatigue testing methods are slow, costly, and typically limited to one specimen at a time. To address this, a high-throughput testing method was developed that allows multiple small-scale specimens to be tested simultaneously while following international testing standards. Using stainless steel sub-sized specimens scaled at 1:5 relative to the ASTM …
Optimization Of Stamped Tool Geometry Using Regression-Based Cost Models And Structural Constraints, Matthew J. Teague
Optimization Of Stamped Tool Geometry Using Regression-Based Cost Models And Structural Constraints, Matthew J. Teague
Mechanical Engineering Undergraduate Honors Theses
Stamped steel paint can openers are simple tools but still require sufficient strength for the end user and low material consumption for the manufacturer. The goal of this project is to optimize the stamped design of a paint can opener by reducing material cost while maintaining structural rigidity and device performance. This was achieved in part by simplifying the tool’s geometry so that an equation for the mass could be developed analytically and checked against the simulation’s outputs. First, a 25-run design of experiments was created that varied the shaft length and the endloop diameter. Next, a CAD model for …
A Multi-Criteria Decision And Spatial Modeling Framework For Socially Informed Advanced Air Mobility Implementation Planning, Noah Wesley Bretz
A Multi-Criteria Decision And Spatial Modeling Framework For Socially Informed Advanced Air Mobility Implementation Planning, Noah Wesley Bretz
Graduate Theses and Dissertations
Advanced air mobility (AAM) is an emerging mode of transportation that integrates advanced aircraft technologies, such as manned air taxis or unmanned freight drones, to transport people and goods across urban and regional environments. While these technologies promise to transform mobility, successful implementation depends heavily on community acceptance, which is shaped by multiple social factors. This study presents a multi-criteria decision framework to evaluate and prioritize the key social factors influencing AAM adoption. A literature review identified six primary social factors: safety, noise, privacy and cybersecurity, automation, environmental impact, and price and economics. The Analytical Hierarchy Process (AHP) was used …
Deep Learning For Predicting Impact Energy And Compression After Impact Strength Of Composite Materials Using C-Scan Images, K. T. Tan, Jason P. Mack, Faizan Mirza, Zhong-Hui Duan
Deep Learning For Predicting Impact Energy And Compression After Impact Strength Of Composite Materials Using C-Scan Images, K. T. Tan, Jason P. Mack, Faizan Mirza, Zhong-Hui Duan
University Research
Traditional assessment of post-impact performance in carbon fiber reinforced polymer (CFRP) composites often relies on simplified scalar metrics that fail to capture the complex spatial interactions driving failure. This study addresses this limitation by developing an automated, end-to-end deep learning framework that shifts from manual feature extraction to the direct interpretation of raw damage morphology from ultrasonic C-scans. Using a ResNet18-based convolutional neural network (CNN) trained on 1,428 augmented images, the model achieved coefficients of determination (R2) of 0.7948 ± 0.0847 for compression after impact (CAI) strength and 0.9436 ± 0.0098 for impact energy. Beyond prediction, this dual-purpose methodology serves …
Tau Beta Pi Engineering Mentorship Program, Tyler Black
Tau Beta Pi Engineering Mentorship Program, Tyler Black
Undergraduate Honors Capstone Projects
The purpose of this project is to design and implement a student-led engineering mentorship program directed by the members of the Utah Gamma Chapter of Tau Beta Pi on the Utah State University (USU) Logan campus. Retention data show that many undergraduate students who start engineering programs change their degree before graduation due to academic and social challenges that may be mitigated by the support of a peer mentor. The Tau Beta Pi Engineering Mentorship Program selects and trains upperclassman mentors to effectively mentor underclassman engineering students.
The design of the mentorship program is an application of backward design, where …
Extremum Seeking Compensation And Quantification Of Position Sensor Offset Error In Speed-Controlled Permanent Magnet Synchronous Motors, Tessa Biondo
Masters Theses
Position sensor offset errors present a persistent challenge in speed-controlled permanent magnet synchronous motor drives operating under field-oriented control. Even small, constant offsets in the measured rotor position can reduce torque effectiveness, requiring increased current and voltage demand to maintain the commanded speed and resulting in degraded speed regulation performance across a range of operating conditions. These effects are particularly problematic in speed-controlled systems, where speed loop dynamics cause increased electrical effort and limit overall performance. Many existing detection and compensation approaches are either dependent on the system model, require offline calibration, or are primarily designed for torque-controlled operation. This …
An Experimental Study On Turbine-Based Energy Harvesters For Thermal Underwater Gliders, Stephen Edward Coster
An Experimental Study On Turbine-Based Energy Harvesters For Thermal Underwater Gliders, Stephen Edward Coster
Theses and Dissertations
Buoyancy-driven underwater gliders have been optimized for long-duration missions primarily for continual monitoring of the ocean’s water column. However, longer missions and higher-powered sensors have increased the energy requirements of gliders. While current solutions aim to increase battery capacity, the development of energy-harvesting systems (EHMs) could greatly improve mission capabilities in both ability and duration. This thesis discusses the experimental testing of an underwater glider with an EHM as detailed in the theoretical study, “Development of a Turbine-Based Ocean Thermal Energy Harvesting Mechanism Applied to the Underwater Glider” by Hongbo Hou, PhD. The rear-mounted turbine captures energy using the kinetic …
Safe Control Design For Quadruped Locomotion In Unstructured Environments Using Linear Transfer Operators, Sriram Sundar Krishnamoorthy Shankara Narayanan
Safe Control Design For Quadruped Locomotion In Unstructured Environments Using Linear Transfer Operators, Sriram Sundar Krishnamoorthy Shankara Narayanan
All Dissertations
Deploying quadruped robots in unstructured, obstacle-rich environments requires control and planning methods that remain safe and reliable despite complex terrain geometry, limited sensing, and inevitable modeling errors. This thesis develops operator-theoretic tools for safe control design of robotic systems using linear transfer operators, with a focus on quadruped locomotion in unstructured environments. The central goal is to develop a unified operator-theoretic framework for safe control design based on the Perron–Frobenius (P–F) and Koopman operators. In particular, the thesis leverages \emph{density functions} to develop safe navigation frameworks in the dual space of densities. In the operator-theoretic perspective, the P–F operator governs …