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Daniel Guggenheim School of Aerospace Engineering

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College of Engineering

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Aerospace Design Group

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Aerospace Systems Design Laboratory (ASDL)

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Air Transportation Laboratory

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Cognitive Engineering Center

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Space Systems Design Laboratory (SSDL)

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Publication Search Results

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An 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.
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.
Generalized Heuristic Search Algorithms with Applications to Motion Planning and Multi-Agent Path Finding Problems

(Georgia Institute of Technology, 2022-08-01) Lim, Jaein

This 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.
Planning For Satellite Actuator Failures: A Falsification Approach Towards Certification of Contingency Controllers

(Georgia Institute of Technology, 2022-03-14) Brewer, John

Today, 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.
Applied Stochastic Optimal Control for Spacecraft Guidance

(Georgia Institute of Technology, 2021-04-30) Ridderhof, Jack

Optimal 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.
Games of Pursuit-Evasion with Multiple Agents and Subject to Uncertainties

(Georgia Institute of Technology, 2021-04-30) Makkapati, Venkata Ramana

Over 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.
Optimal covariance steering: Theory and its application to autonomous driving

(Georgia Institute of Technology, 2019-11-08) Okamoto, Kazuhide

Optimal control under uncertainty has been one of the central research topics in the control community for decades. While a number of theories have been developed to control a single state from an initial state to a target state, in some situations, it is preferable to simultaneously compute control commands for multiple states that start from an initial distribution and converge to a target distribution. This dissertation aims to develop a stochastic optimal control theory that, in addition to the mean, explicitly steers the state covariance. Specifically, we focus on the control of linear time-varying (LTV) systems with additive Gaussian noise. The task is to steer a Gaussian-distributed initial system state distribution to a target Gaussian distribution, while minimizing a state and control expectation-dependent quadratic cost under probabilistic state constraints. Notice that, in such systems, the system state keeps being Gaussian distributed. Because Gaussian distributions can be fully described by the first two moments, the proposed optimal covariance steering (OCS) theory allows us to control the whole distribution of the state and quantify the effect of uncertainty without conducting Monte-Carlo simulations. We propose to use a control policy that is an affine function of filtered disturbances, which utilizes the results of convex optimization theory and efficiently finds the solution. After the OCS theory for LTV systems is introduced, we extend the theory to vehicle path planning problems. While several path planning algorithms have been proposed, many of them have dealt with deterministic dynamics or stochastic dynamics with open-loop un- certainty, i.e., the uncertainty of the system state is not controlled and, typically, increases with time due to exogenous disturbances, which may lead to the design of potentially conservative nominal paths. A typical approach to deal with disturbances is to use a lower-level local feedback controller after the nominal path is computed. This unidirectional dependence of the feedback controller on the path planner makes the nominal path unnecessarily conservative. The path-planning approach we develop based on the OCS theory computes the nominal path based on the closed-loop evolution of the system uncertainty by simultaneously optimizing the feedforward and feedback control commands. We validate the performance using numerical simulations with single and multiple vehicle path planning problems. Furthermore, we introduce an optimal covariance steering controller for linear systems with input hard constraints. As many real-world systems have input constraints (e.g., air- craft and spacecraft have minimum/maximum thrust), this problem formulation will allow us to deal with realistic scenarios. In order to incorporate input hard constraints in the OCS theory framework, we use element-wise saturation functions and limit the effect of disturbance to the control commands. We prove that this problem formulation leads to a convex programming problem and demonstrate the effectiveness using simple numerical examples. Finally, we develop the OCS-based stochastic model predictive control (CS-SMPC) theory for stochastic linear time-invariant (LTI) systems with additive Gaussian noise subject to state and control constraints. In addition to the conventional terminal cost and terminal mean constraints, we introduce terminal covariance constraints in the stochastic model predictive control theory. The OCS theory efficiently computes the control commands that satisfy the terminal covariance constraints. The key benefit of the CS-SMPC algorithm is its ability to ensure stability and recursive feasibility of the controlled system. In addition, thanks to the efficient OCS theory, the proposed CS-SMPC theory is computationally less demanding than previous SMPC approaches. In order to verify the effectiveness, the CS-SMPC approach is also applied to the problem of self-driving vehicle control under uncertainty.
Path-planning algorithms in high-dimensional spaces

(Georgia Institute of Technology, 2019-01-15) Hauer, Florian M.

In this thesis, we discuss the problem of path-planning in high-dimensional spaces. Large search spaces tend to lead to slow algorithms in order to find a path or to converge towards the optimal solution of a path-planning problem. This thesis investigates both discrete and continuous search spaces. For discrete search spaces, the use of multi-scale data structure allows a planning algorithm to consider a region of space at different resolutions through the execution of the algorithm and to accelerate the execution of the algorithm. The proposed algorithm is proven to be complete, it will find a solution if one exists, or report that no solution exists. Multiple applications are presented with direct construction of the multi-scale map via perception algorithms, as well as a sampling approach for problems where constructing the multi-scale map is too expensive. For continuous search spaces, the thesis explores the use of classical optimization methods within the family of sampling-based planning algorithms. An experiment is first presented to show the convergence limits of sampling-based algorithms. Then an optimization formulation shows how samples of the search space can be repositioned in order to enhance the estimate of the value function of the problem. Finally, this optimization is integrated in the framework of Rapidly-exploring Random Trees to introduce the Deformable Rapidly-exploring Random Trees algorithm. This algorithm rapidly finds a feasible solution, similarly to the other RRT algorithms, and it also significantly increases the convergence rate of the solution thanks to the added optimization step. Analysis of the parameters and applications of the algorithm show significant improvement compared to the state-of-the-art algorithms.
Multiple-hypothesis vision-based landing autonomy

(Georgia Institute of Technology, 2018-08-23) Nakamura, Takuma

Unmanned aerial vehicles (UAVs) need humans in the mission loop for many tasks, and landing is one of the tasks that typically involves a human pilot. This is because of the complexity of a maneuver itself and flight-critical factors such as recognition of a landing zone, collision avoidance, assessment of landing sites, and decision to abort the maneuver. Another critical aspect to be considered is the reliance of UAVs on GPS (global positioning system). A GPS system is not a reliable solution for landing in some scenarios (e.g. delivering a package in an urban city, and a surveillance UAV repatriating a home ship with the jammed signals), and a landing solely based on a GPS extremely decreases the UAV operation envelope. Vision is promising to achieve fully autonomous landing because it is a rich-sensing, light, affordable device that functions without any external resource. Although vision is a powerful tool for autonomous landing, the use of vision for state estimation requires extensive consideration. Firstly, vision-based landing faces a problem of occlusion. The target detected at a high altitude would be lost at certain altitudes while a vehicle descends; however, a small visual target can not be recognized at high altitude. Second, standard filtering methods such as extended Kalman filter (EKF) face difficulty due to the complex dynamics of the measurement error created due to the discrete pixel space, conversion from the pixel to physical units, the complex camera model, and complexity of detection algorithms. The vision sensor produces an unfixed number of measurements with each image, and the measurements may include false positives. Plus, the estimation system is excessively tasked in realistic conditions. The landing site would be moving, tilted, or close to an obstacle. The available landing location may not be limited to one. In addition to assessing these statuses, understanding the confidence of the estimations is also the tasks of the vision, and the decisions to initiate, continue, and abort the mission are made based on the estimated states and confidence. The system that handles those issues and consistently produces the navigation solution while a vehicle lands eliminates one of the limitations of the autonomous UAV operation. This thesis presents a novel state estimation system for UAV landing. In this system, vision data is used to both estimate the state of the vehicle and map the state of the landing target (position, velocity, and attitude) within the framework of simultaneous localization and mapping (SLAM). Using the SLAM framework, the system becomes resilient to a loss of GPS and other sensor failures. A novel vision algorithm that detects a portion of the marker is developed, and the stochastic properties of the algorithm are studied. This algorithm extends the detectable range of the vision system for any known marker. However, this vision algorithm produces highly nonlinear, non-Gaussian, and multi-modal error distribution, and a naive implementation of filters would not accurately estimate the states. A vision-aided navigation algorithm is derived within extended Kalman particle filter (PF-EKF) and Rao-Blackwellized particle filter (RBPF) frameworks in addition to a standard EKF framework. These multi-hypothesis approaches not only deal well with a highly nonlinear and non-Gaussian distribution of the measurement errors of vision but also result in numerically stable filters. The computational costs are reduced compared to a naive implementation of particle filter, and these algorithms run in real time. This system is validated through numerical simulation, image-in-the-loop simulation, and flight tests.
Dynamic modeling and control of spacecraft robotic systems using dual quaternions

(Georgia Institute of Technology, 2018-04-06) Valverde, Alfredo

As of 2014, the space servicing market has a potential revenue of $3-$5B per year due to the ever-present interest to upkeep existing orbiting infrastructure. In space servicing, there is a delicate balance between system complexity and servicer capability. Basic module-exchange servicers decrease the complexity of the servicing spacecraft, but is likely to require a more complex architecture of the serviced satellite (the host) in terms of electrical and mechanical connections. With increasing dexterity of the servicing satellite, host satellites can remain closer to flight-proven heritage architectures, which is a practice commonly adopted to increase reliability of space missions. This increased dexterity is provided through the on-orbit exchange of end-effector tools appended to a robotic arm. The dynamic coupling between such an arm and the satellite base has been the subject of intense academic scrutiny and its understanding is essential to the success of robotic servicing missions. In this work, we address different phases of a servicing mission using the dual quaternion formalism. First, we propose a dual quaternion pose-tracking controller that adaptively estimates the mass properties of a spacecraft using either a continuous-time implementation of the concurrent learning framework, or a discretized implementation. The advantage of incorporating concurrent learning lies in enhancing the parameter convergence characteristics of the adaptation scheme. Next, we provide the derivation of the dynamic equations of motion for a spacecraft with a serial robotic manipulator. This derivation uses a Newton-Euler approach formulated in dual quaternion algebra. This model is subsequently adapted to perform end-effector pose stabilization and end-effector pose tracking using the Differential Dynamic Programming control framework. A generalization of the dual quaternion-based framework for modeling of spacecraft with a rooted tree topology and five different types of joints is provided. The formulation is validated on a two-arm robotic spacecraft. This model is then used to implement a generalizable modification to the concurrent learning algorithm that allows “aggressively” estimating the 77 parameters that compose the mass properties of the rigid bodies in the two-arm multibody system.