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Daniel Guggenheim School of Aerospace Engineering
Daniel Guggenheim School of Aerospace Engineering
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ItemAn Information-Theoretic Framework for Resource-Aware Abstraction and Planning for Autonomous Agents(Georgia Institute of Technology, 2023-07-26) Larsson, Daniel T.In the modern era of autonomy, autonomous systems have seen deployment in a number of both terrestrial and extraterrestrial applications including drone delivery systems, warehouse robotics, aerial surveillance, self-driving cars, and mars exploration. However, the systems deployed in the aforementioned applications differ in their size, sensing ability, on-board information-processing resources, as well as their communication capabilities. Consequently, to develop the next-generation of independent and self-sufficient intelligent systems, frameworks that endow autonomous systems the ability to tailor their information processing for decision-making, planning, and perception, in accordance with their on-board resources in a task-specific manner is of paramount importance. For this reason, we consider in this dissertation, the development of approaches for resource-aware, task-driven abstraction in autonomous systems. The process of abstraction, or equivalently, the identification of relevant and irrelevant information, is a task humans perform subconsciously everyday. The ability to focus on details that are task-relevant, and abstract away those that are not, is considered cornerstone to human intelligence and information processing. Inspired by their ability to simplify problems by removing irrelevant details, researchers within the intelligent systems community have leveraged the power of abstractions to reduce the complexity of solving real-world problems in autonomous decision-making and control. However, despite their role in enabling autonomous agents to solve complex problems, the design of abstractions has been traditionally handled by system engineers, who provide heuristic, domain-specific knowledge that guides the construction of the reduced-order representations. For this reason, a growing interest in the development of frameworks that design task-relevant abstractions for autonomous agents has emerged, motivated largely by the central role of abstraction in intelligent systems. To design task-relevant abstractions requires the preservation of relevant information through the process of compression. A formal treatment of these notions has been considered by information-theorists, who have developed a number of powerful frameworks for signal compression that rigorously capture the trade-off between relevant information retention and compression when encoding signals for transmission across capacity-limited communication channels. Of particular interest is the information-bottleneck (IB) framework, which formulates an optimization problem to design encoders that maximize compression while remaining maximally retentive regarding task-relevant information. In recent years, frameworks that employ IB-like approaches in order to design latent representations for autonomous systems have been developed, but with varying degrees of success, reproducibility, and theoretical guarantees. Motivated by these observations we, in this dissertation, develop frameworks that leverage ideas from information-theoretic signal compression to generate and design abstractions for autonomous systems. The frameworks allow for task-specific, multi-resolution, hierarchical tree abstractions to be obtained that are not provided to the system a priori, and instead emerge as a function of the agent's resource constraints. In more detail, this dissertation contributes by drawing on the connection between hierarchical data structures and signal encoders to introduce an information-theoretic hierarchical tree-search problem which leverages the IB-principle to design multi-scale abstractions for autonomous systems that can be tailored to system resource-constraints. To solve our problem, we develop an algorithm, called Q-tree search, which employs a dynamic-programming-like pruning rule which we formally establish results in the optimal tree solution to our information-theoretic problem. Moreover, we show how the hard-constrained version of our problem may be realized as an integer linear program, thereby allowing multi-scale abstractions to be designed subject to hard system resource constraints, such as limited on-board memory. We discuss the connection between the two formulations, and establish a formal bridge between them by leveraging ideas from duality and relaxation theory. An algorithm for choosing the trade-off parameter in the soft-constrained, Q-tree search, problem as a function of the setting of the hard-constraint is proposed which leverages the structure of the problem and so-called tree phase-transitions to select the trade-off parameter by maximizing the dual function of the hard-constrained formulation. We then develop a framework that employs hierarchical abstraction, specifically those generated by Q-tree search, to reduce the computational complexity of planning in a principled manner that endows agents the ability to trade path-cost (quality) and environment information (resolution) in a rigorous fashion. A generalized formulation of the information-theoretic abstraction problem is then presented which considers the design of multi-scale hierarchical representations in the presence of multiple information sources. The generalized approach allows for both task-relevant and task-irrelevant information sources to be specified, and has connections with concepts from information-theoretic privacy. Importantly, the generalized method enables the creation of multi-resolution hierarchical abstractions of environments containing probabilistic semantic information, thereby allowing semantic-information driven abstractions to be generated that can be tailored to retain (and/or discard) desirable (undesirable) semantic classes (e.g., grass, asphalt, etc.). To solve the generalized problem, we develop the G-tree search algorithm and formally show that the proposed algorithm returns the optimal solution (i.e., multi-resolution tree). Finally, this dissertation contributes by developing a joint map-building and compression algorithm that simultaneously builds and compresses three-dimensional (3D) octree data structures containing (probabilistic) semantic information. The map-building and compression algorithm builds a Bayesian multi-class semantic octree from semantically-labeled point-cloud data which is subsequently compressed by a modified version of the G-tree search algorithm. We demonstrate the ability of our approach to compress large, semantically rich, outdoor environments built from real-world data, and show how the semantically-driven abstractions may be employed to create informed colored-graphs for semantic-planning.
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ItemMethods of Analysis and Design of Dynamical Systems Using Homogeneous Polynomial Lyapunov Functions(Georgia Institute of Technology, 2023-03-23) Immanuel, Gidado-YisaLyapunov 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.
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ItemGeneralized Heuristic Search Algorithms with Applications to Motion Planning and Multi-Agent Path Finding Problems(Georgia Institute of Technology, 2022-08-01) Lim, JaeinThis thesis investigates novel ways of leveraging generalized interpretations of heuristics to solve complex motion planning problems with completeness and bounded suboptimality guarantees. A set of heuristic search algorithms is developed to utilize relaxed notions of relevancy to more efficiently solve path planning, motion planning and multi-agent path finding problems. The main focus of this thesis is to demonstrate how using generalized heuristics based on the relaxed notions of relevancy helps the hereto developed search algorithms focus their computational efforts to make better progress towards finding a solution. The theoretical properties of the developed algorithms are extensively studied, and their numerical performances are benchmarked against state-of-the-art algorithms across various robotic platforms. This thesis proceeds with a brief introduction and background on existing heuristic search algorithms and their limitations in solving real world planning problems, delineating our contributions in Chapter 1. The main contributions of this thesis follow in the consequent four chapters, where four distinct planning frameworks are presented: hierarchically abstracted path planning, lazy replanning, colored planning, and multi-agent path finding. Each framework is dealt in greater detail in each of the four consequent chapters. Chapter 2 considers planning on hierarchically abstracted graphs by utilizing distributed abstract information as heuristics to find a globally refined solution. Chapter 3 considers lazy replanning which utilizes previous search results as heuristics to facilitate a new plan, while delaying expensive edge evaluations. Chapter 4 considers using semantic information as heuristics to guide search in a principled way. Finally, the multi-agent path finding problem is considered in Chapter 5, namely, the problem of finding a set of collision-free paths for a team of agents while minimizing some global cost, focusing on how the ideas presented in the preceding chapters help produce an efficient algorithm. The thesis is concluded in Chapter 6 with a discussion on potential future research directions.
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ItemPlanning For Satellite Actuator Failures: A Falsification Approach Towards Certification of Contingency Controllers(Georgia Institute of Technology, 2022-03-14) Brewer, JohnToday, more satellites are being launched at a rate never experienced before. This is due, in part, to the miniaturization of the technology and the increasing reliance on smaller satellites which are cheaper to build, launch, and replace compared to the large monolithic satellites of the past. However, these small satellites still possess strikingly high failure rates that are often the result of design issues, the lack of testing, and uncertainties in hardware components. As satellites grow in complexity, incorporate more features, and are built at a faster rate, the ability to design and test successful systems becomes urgent and difficult. This thesis aims to present a falsification approach to the automated verification and validation approach to satellite systems. Specifically, we seek to address how falsification techniques can be used to test and validate contingency plan controllers designed to rescue a satellite in the event an actuator failure occurs. These contingency control schemes are complicated implementations which, not only require unique controllers capable of stabilizing a satellite that has lost controllability, but they must also perform identification of the failure that has occurred and invoke the switching needed from the primary controller to a backup controller most suitable to handle the failure experienced by the satellite. Verifying these types of complex control structures by hand is difficult, so the development and demonstration of an automated framework capable of performing this challenging task would not only be a valuable contribution to the current state of spacecraft technology, but would also lead to a significant reduction in the failure rate of satellites seen in the space community over the past 20 years.
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ItemApplied Stochastic Optimal Control for Spacecraft Guidance(Georgia Institute of Technology, 2021-04-30) Ridderhof, JackOptimal control theory has been successfully applied to a wide range of a problems in spacecraft trajectory optimization. Historically, the identification and management of uncertainty in spaceflight applications has been a separate endeavor from optimal trajectory design, with the exception of heuristic margins applied on the deterministic optimal trajectory. Following a stochastic optimal control approach, on the other hand, leads to the direct consideration of uncertainty for the design of closed-loop trajectories with probabilistic constraints. Resulting control laws are designed with respect to all possible trajectory and control input realizations, and the performance is evaluated over measures of the aggregate, or expected, state and control trajectories. This dissertation focuses on specific applications of stochastic optimal control for spacecraft guidance, namely: powered descent guidance (PDG), atmospheric entry guidance, and aerocapture guidance. In addition, extensions are developed, which have further applications for spacecraft guidance, to the general theory of applying convex optimization to jointly steer the mean and covariance of stochastic systems, subject to probabilistic constraints. For minimum-fuel PDG, the problem of setting non-conservative thrust margins is addressed by application of minimum-variance, covariance-constrained stochastic optimal control. The resulting closed-loop PDG process does not, with high probability, either saturate thrust commands or deviate too far from the desired landing site. Next, entry guidance in an atmosphere with spatially-dependent random variations in the atmospheric density is posed as a chance-constrained stochastic optimal control problem; the resulting targeting accuracy is shown to be better than the current state-of-the-art Apollo-derived entry guidance. Finally, in order to address the problem of aerocapture guidance around a planet with an unknown atmosphere, a successive convex programming-based method is developed to solve chance-constrained stochastic optimal control problems for systems acting in the presence of a Gaussian random field. In a numerical example of an aerocapture mission with bank angle control, the developed method is used to solve for a control law that explicitly minimizes the 99th percentile of the required Delta-V, subject to constraints on the probability distribution of the closed-loop bank angle during atmospheric flight.
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ItemGames of Pursuit-Evasion with Multiple Agents and Subject to Uncertainties(Georgia Institute of Technology, 2021-04-30) Makkapati, Venkata RamanaOver the past decade, there have been constant efforts to induct unmanned aerial vehicles (UAVs) into military engagements, disaster management, weather monitoring, and package delivery, among various other applications. With UAVs starting to come out of controlled environments into real-world scenarios, uncertainties that can be either exogenous or endogenous play an important role in the planning and decision-making aspects of deploying UAVs. At the same time, while the demand for UAVs is steadily increasing, major governments are working on their regulations. There is an urgency to design surveillance and security systems that can efficiently regulate the traffic and usage of these UAVs, especially in secured airspaces. With this motivation, the thesis primarily focuses on airspace security, providing solutions for safe planning under uncertainties while addressing aspects concerning target acquisition and collision avoidance. In this thesis, we first present our work on solutions developed for airspace security that employ multiple agents to capture multiple targets in an efficient manner. Since multi-pursuer multi-evader problems are known to be intractable, heuristics based on the geometry of the game are employed to obtain task-allocation algorithms that are computationally efficient. This is achieved by first analyzing pursuit-evasion problems involving two pursuers and one evader. Using the insights obtained from this analysis, a dynamic allocation algorithm for the pursuers, which is independent of the evader's strategy, is proposed. The algorithm is further extended to solve multi-pursuer multi-evader problems for any number of pursuers and evaders, assuming both sets of agents to be heterogeneous in terms of speed capabilities. Next, we consider stochastic disturbances, analyzing pursuit-evasion problems under stochastic flow fields using forward reachability analysis, and covariance steering. The problem of steering a Gaussian in adversarial scenarios is first analyzed under the framework of general constrained games. The resulting covariance steering problem is solved numerically using iterative techniques. The proposed approach is applied to the missile endgame guidance problem. Subsequently, using the theory of covariance steering, an approach to solve pursuit-evasion problems under external stochastic flow fields is discussed. Assuming a linear feedback control strategy, a chance-constrained covariance game is constructed around the nominal solution of the players. The proposed approach is tested on realistic linear and nonlinear flow fields. Numerical simulations suggest that the pursuer can effectively steer the game towards capture. Finally, the uncertainties are assumed to be parametric in nature. To this end, we first formalize optimal control under parametric uncertainties while introducing sensitivity functions and costates based techniques to address robustness under parametric variations. Utilizing the sensitivity functions, we address the problem of safe path planning in environments containing dynamic obstacles with an uncertain motion model. The sensitivity function based-approach is then extended to address game-theoretic formulations that resemble a "fog of war" situation.