Doctor of Philosophy with a Major in Aerospace Engineering

Series

Doctor of Philosophy with a Major in Aerospace Engineering

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

Series Type

Degree Series

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Organizational Unit

Daniel Guggenheim School of Aerospace Engineering

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Publication Search Results

Now showing 1 - 9 of 9

Methods of Analysis and Design of Dynamical Systems Using Homogeneous Polynomial Lyapunov Functions

(Georgia Institute of Technology, 2023-03-23) Immanuel, Gidado-Yisa

Lyapunov functions are the mainstay for systems analysis and control. The ubiquitous quadratic Lyapunov function (QLF) successfully solves a large class of problems because the QLF is amenable to energy-based problems represented by ellipsoids that efficiently capture energy-type bounds and constraints. In contrast, using QLFs in the analysis and design of nonlinear systems introduces conservatism due to the inherent limitations of the associated ellipsoid as a covering for the stability region of the system. For example, analysis of peak-input bounded types of problems generally lacks closed-form solutions. Instead, the analysis utilizes approximations and relaxations, which are computationally expensive due to the norm expressing the bounds. Also, for switched linear systems, there may not exist a common QLF for an asymptotically stable switched system; however, it has been shown that there exist homogeneous Lyapunov functions (HLFs) that establish the stability of the system. This research investigates HLFs as generalizations of QLFs to generate better approximations of reachable sets and domains of attraction (DoA) of dynamical systems. Central to HLF construction is lifting the state vector x via a recursive Kronecker product to a higher degree, homogeneous form resident in a higher-dimensional space. This research demonstrates a method of HLF construction that provides good estimates of system characteristics, such as the DoA and reachable sets. The main contribution of this research is applying this methodology to improve the upper bounds of the induced L1 norm of a linear time-invariant system. This method requires no more than linear matrix inequalities (LMIs), and the problems are tractable with standard semidefinite programming (SDP). This method is demonstrated for the analysis of the L1 problem, as well as the stability of switched linear systems and implicit switched linear systems. Contributions are developed and demonstrated for homogeneous controllers constructed in the lifted space and projected to the original space.
The design, education and evolution of a robotic baby

(Georgia Institute of Technology, 2022-12-13) Zhu, Hanqing

Inspired by Alan Turing’s idea of a child machine, I introduce the formal definition of a robotic baby, an integrated system with minimal world knowledge at birth, capable of learning incrementally and interactively, and adapting to the world. Within the definition, fundamental capabilities and system characteristics of the robotic baby are identified and presented as the system-level requirements. As a minimal viable prototype, the Baby architecture is proposed with a systems engineering design approach to satisfy the system-level requirements, which has been verified and validated with simulations and experiments on a robotic system. The capabilities of the robotic baby are demonstrated in natural language acquisition and semantic parsing in English and Chinese, as well as in natural language grounding, natural language reinforcement learning, natural language programming and system introspection for explainability. Furthermore, the education and evolution of the robotic baby are illustrated with real-world robotic demonstrations. Inspired by the genetic inheritance in human beings, knowledge inheritance in robotic babies and its benefits regarding evolution are discussed.
Rotor-Rotor Interactions in the Design of Unmanned Aerial Systems

(Georgia Institute of Technology, 2022-07-28) Epps, Jeremy T.

This dissertation investigates the impact of rotor-rotor interactions on small Unmanned Aerial System (UAS) design. This work explores the aerodynamic effects of two rotor configurations, the first being non-coplanar overlapping rotors, tandem-rotors, and the second being the semi-coaxial rotor configuration, which is an adaptation of the traditional coaxial rotor configuration. This work is motivated by three UAS, two of which, the Tetracopter and the Dodecacopter, are designed and developed as a part of the work presented in this dissertation. The Tetracopter and Dodecacopter are multi-agent vehicles that implement multiple layers of non-coplanar overlapping rotors. The goal of these two vehicles is to implement a design where a multi-agent UAS can have the structural rigidity to withstand carrying payloads, whether the payload is carried above or below the vehicle while being as efficient as a multi-agent aircraft with coplanar rotors. The goal of the Y6sC is to show that the semi-coaxial rotor configuration allows a vehicle to be more efficient in hover than a traditional coaxial rotor configuration and that the semi-coaxial rotor configuration grants the vehicle more maneuverability than a traditional coaxial rotor configuration. This dissertation can be separated into two halves; the first half begins with the presentation of a thrust stand fabricated to collect data on both rotor configurations. This half also discusses the methods used to conduct these thrust stand experiments, the methods used to analyze the data, and discussions about the results and their comparison to established theories that predict the performance of these rotor configurations. A rotor configuration performance estimation method that is based on the empirical data collected is also presented, and the accuracy of this estimation method is validated. This estimation method is then used to estimate the optimal design of the Tetracopter and Dodecacopter, which accounts for the vehicle's weight and the performance of the vehicle's rotors which may be impacted by rotor-rotor interactions. The latter half of this dissertation discusses the design of the Dodecacopter along with the methods used to flight test the vehicle. The data produced from the flight tests are discussed, and estimations of the degradation in the vehicle's performance due to the rotor-rotor interactions are presented and discussed. The dissertation concludes with a brief discussion on the design implications derived from the results of the work presented.
Versatile and structurally efficient aerial systems assembled from polyhedral rotorcraft modules

(Georgia Institute of Technology, 2022-05-03) Garanger, Kevin

Autonomous multirotor vehicles have become widespread tools for many industries. They are used to perform tasks for a fraction of the cost than the traditional methods they supplant and with greater safety. Most payloads carried by drones for current applications are sensors used to gather data in otherwise hard-to-reach places or over large distances or areas quickly. Cargo transportation via autonomous drones is also being explored by several companies, as a mean to provide fast last-mile delivery, for intra-logistics, or to serve remote locations. A few companies have already demonstrated the usefulness of drones to deliver emergency medical supplies to places isolated from transportation networks. The wide variety of drone payloads, from today's numerous sensors to tomorrow's airlifted supplies, and the tight performance envelope of electrically powered platforms result in a myriad of purpose-built vehicles. Modular, reconfigurable autonomous vehicles that can adapt to diverse payloads have been proposed as a replacement of conventional systems for greater flexibility of operations. Because of the necessity to limit interactions between rotors, prior art has been mostly defined by modules that assemble in a horizontal plane.This assembly rule inevitably leads to a decrease in stiffness of vehicles as they grow in size and to several related issues. Novel modular rotorcraft designs and assembly schemes based on polyhedral modules intended to remedy these limitations are explored in this thesis. Structural and dynamical properties of the introduced modular vehicles are studied. In particular, these properties are characterized in a way making the determination of optimal vehicle configurations possible with efficient algorithms. Multiple modular configurations with different capabilities are studied as examples in this thesis. Finally, several prototypes that were designed, fabricated, and flown are presented.
TOWARDS TRACTABLE METHODS FOR FORMAL VERIFICATION OF AUTONOMY IN AEROSPACE SYSTEMS

(Georgia Institute of Technology, 2022-01-12) Klett, Corbin

Formal verification techniques for control systems are developed and applied to realworld aerospace systems, including experimental platforms as well as mathematical models that contain features closely resembling those found in real systems. Though prolific in academia, these analysis techniques are not prevalent in industry, where system-level requirements are commonly validated by rudimentary measures of system robustness such as gain and phase margin as well as by extensive simulation and testing. Conventional methods have proven their efficacy for the certification of safety-critical systems but are also incapable of exhaustively testing a system’s behaviors. Integrating more advanced mathematical techniques into system design and analysis workflows could enable additional autonomy capabilities, improve safety, and decrease development, operating, and certification costs. The verification strategies developed and demonstrated in this work rely on key results from nonlinear systems theory, real algebraic geometry, and convex optimization. First, a method for constructing homogeneous polynomial Lyapunov functions is presented for the class of nonlinear systems that can be represented by a linear time-varying or a switchedlinear system. Procedures are developed that produce improved certificates of set invariance, bounds on peak norms, and system stability margin. Additionally, an algorithm that uses a Lyapunov function certificate to search for a worst-case trajectory is developed and applied to several aerospace examples, including an attitude-controlled spacecraft. Characterization of the safe operating envelope for this spacecraft is demonstrated using Lyapunov theory. This result is integrated into a run-time assurance algorithm, which is shown to significantly increase the vehicle’s operational capabilities as demonstrated on an experimental hardware platform. Finally, strategies are proposed for the formal analysis of gas turbine engine control systems that offer advantages over some conventional practices.
Optimization-based design of fault-tolerant avionics

(Georgia Institute of Technology, 2021-12-13) Khamvilai, Thanakorn

This dissertation considers the problem of improving the self-consciousness for avionic systems using numerical optimization techniques, emphasizing UAV applications. This self-consciousness implies a sense of awareness for oneself to make a reliable decision on some crucial aspects. In the context of the avionics or aerospace industry, those aspects are SWaP-C as well as safety and reliability. The decision-making processes to optimize these aspects, which are the main contributions of this work, are presented. In addition, implementation on various types of applications related to avionics and UAV are also provided. The first half of this thesis lays out the background of avionics development ranging from a mechanical gyroscope to a current state-of-the-art electronics system. The relevant mathematics regarding convex optimization and its algorithms, which will be used for formulating this self-consciousness problem, are also provided. The latter half presents two problem formulations for redundancy design automation and reconfigurable middleware. The first formulation focuses on the minimization of SWaP-C while satisfying safety and reliability requirements. The other one aims to maximize the system safety and reliability by introducing a fault-tolerant capability via the task scheduler of middleware or RTOS. The usage of these two formulations is shown by four aerospace applications---reconfigurable multicore avionics, a SITL simulation of a UAV GNC system, a modular drone, and a HITL simulation of a fault-tolerant distributed engine control architecture.
Optimization-based Approaches to Safety-Critical Control with Applications to Space Systems

(Georgia Institute of Technology, 2021-07-30) Mote, Mark Leo

This thesis investigates the problem of safety-critical control for complex cyber-physical systems, with an emphasis on numerical optimization and autonomy applications in the space domain. First, a set-based approach is introduced for specifying mission constraints, and safety is formalized in the context of a set invariance framework. Next, the research investigates the problem of run time assurance (RTA), which relates to a control system architecture where a performance-oriented controller is augmented with a safety-driven element that filters the control signal in such a way that guarantees safety. The latter part of the thesis consists of application-specific research on various space systems. Autonomous rendezvous proximity operations and docking (ARPOD) is considered under proximity, collision-avoidance, and speed constraints. Natural motion trajectories are used to identify a set of passively safe parking orbits under the Clohessy-Wiltshire-Hill dynamics, and a mixed integer programming approach is used to generate safety-constrained optimal transfer trajectories to this set. The formulation is encoded into an RTA framework. The safety problem is considered for a torque-controlled spacecraft in free rotational motion, subject to line-of-sight constraints. A nondeterministic dynamics model is considered, and an RTA filter is constructed that relies on online computation of forward reachable sets around a recovery maneuver. The approach utilizes recent results from reachability theory in addition to optimization-based computation of invariant sets. Safety guarantees exist when a disturbance torque is bounded. The practicality of the approach is demonstrated with an application on a hardware testbed. Finally, the research studies the topic of harnessing collisional behavior for free-flying spacecraft. A framework is proposed for collision-inclusive trajectory optimization. Experimental comparisons of trajectories with and without collision-avoidance requirements demonstrate the capability of the collision-inclusive strategy to achieve significant performance improvements in realistic scenarios. Additionally, a safety application is considered, and the planner is utilized for the purpose of optimally mitigating damage in the presence of an inevitable collision.
Risk analysis framework for unmanned systems

(Georgia Institute of Technology, 2020-05-17) Dunham, Joel

Airspace regulatory agencies are currently focusing on risk assessment frameworks for integrating the operation of Unmanned Aerial Systems (UAS) into National Air Space (NAS). Multiple frameworks, such as the Specific Operations Risk Assessment (SORA) framework for the European Union and similar frameworks for the US, provide defined pathways to evaluate the risk and seek approval for UAS operations. These frameworks are primarily qualitative and are sufficiently flexible to incorporate quantitative approaches, many of which have been proposed and tested in literature. Most proposed quantitative methods are still under development. Likewise, real-time analysis methods, designed to provide decision-making to unmanned systems during operations, have been proposed. Current real-time analysis methods still suffer from limitations, such as only applying to specific operations. This research applies Dempster-Shafer theory and valuation networks, a framework for reasoning with uncertainty used extensively for risk analysis, to UAS risk analysis by creating extensions which allow this framework to learn risk relationships in the UAS ecosystem based on operational results and enable this framework to be used in real-time analysis onboard small UAS. These extensions are applied to an autonomous car scenario for testing the capabilities against known baselines, then applied to the UAS scenario for testing in simulation against a previously implemented real-time health monitoring system. Finally, these extensions are demonstrated in flight on a small UAS. Application to the UAS ecosystem and conclusions are addressed based on the results of these tests.
Elicitation and formal specification of run time assurance requirements for aerospace collision avoidance systems

(Georgia Institute of Technology, 2020-03-25) Hobbs, Kerianne L.

Run Time Assurance (RTA) systems are proposed as a complementary verification approach to facilitate near-term certification of advanced aerospace decision and control systems. RTA systems monitor the state of a cyber-physical system (CPS) online for violations of predetermined boundaries that trigger a switch to a simple, safety remediation controller. For example, automatic collision avoidance systems are RTA systems that monitor the CPS state for violations of proximity constraints and switch to a backup controller that assures safe separation. Design of RTA systems is generally ad hoc and specific to application, although common design elements and requirements of RTA systems cross applications and domains. This research elicits, formally specifies, and analyzes RTA-based collision avoidance system requirements for a conceptual spacecraft conducting autonomous close-proximity operations. First, the Automatic Ground Collision Avoidance System developed for aircraft is studied to identify common design elements and requirements of RTA last-instant collision avoidance systems that cross the air and space domains. Second, formal requirements specification templates are developed for a generalized RTA architecture that extends the simplex architecture by accounting for human interaction, system faults, and safety interlocks. Third, formal requirements are elicited through the process of formal specification as well as from common design elements and requirements, spacecraft guidance constraints in the literature, and a structured hazard assessment. Finally, the requirements are analyzed using compositional reasoning and formal model checking verification techniques.