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Daniel Guggenheim School of Aerospace Engineering

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End date: 2017 × Start date: 2017 × Item Type: Publication × search.filters.applied.f.isOrgUnitOfPublicationTitle: Daniel Guggenheim School of Aerospace Engineering × search.filters.applied.f.resourcesubtype: Dissertation ×

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Now showing 1 - 10 of 43
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Learning control via probabilistic trajectory optimization

2017-11-29 , Pan, Yunpeng

A central problem in the field of robotics is to develop real-time planning and control algorithms for autonomous systems to behave intelligently under uncertainty. While classical optimal control provides a general theoretical framework, it relies on strong assumption of full knowledge of the system dynamics and environments. Alternatively, modern reinforcement learning (RL) offers a computational framework for controlling autonomous systems with minimal prior knowledge and user intervention. However, typical RL approaches require many interactions with the physical systems, and suffer from slow convergence. Furthermore, both optimal control and RL have the difficulty of scaling to high-dimensional state and action spaces. In order to address these challenges, we present probabilistic trajectory optimization methods for solving optimal control problems for systems with unknown or partially known dynamics. Our methods share two key characteristics: (1) we incorporate explicit uncertainty into modeling, prediction and decision making using Gaussian processes; (2) our algorithms bypass the \textit{curse of dimensionality} via local approximation of the value function or linearization of the Hamilton-Jacobi-Bellman (HJB) equation. Compared to related approaches, our methods offer superior combination of data efficiency and scalability. We present experimental results and comparative analyses to demonstrate the strengths of the proposed methods. In addition, we develop fast Bayesian approximate inference methods which enable probabilistic trajectory optimizer to perform real-time receding horizon control. It can be used to train deep neural network controllers that map raw observations to actions directly. We show that our approach can be used to perform high-speed off-road autonomous driving with low-cost sensors, and without on-the-fly planning and optimization.

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Stochastic optimal control - a forward and backward sampling approach

2017-11-15 , Exarchos, Ioannis

Stochastic optimal control has seen significant recent development, motivated by its success in a plethora of engineering applications, such as autonomous systems, robotics, neuroscience, and financial engineering. Despite the many theoretical and algorithmic advancements that made such a success possible, several obstacles remain; most notable are (i) the mitigation of the curse of dimensionality inherent in optimal control problems, (ii) the design of efficient algorithms that allow for fast, online computation, and (iii) the expansion of the class of optimal control problems that can be addressed by algorithms in engineering practice. The aim of this dissertation is the development of a learning stochastic control framework which capitalizes on the innate relationship between certain nonlinear partial differential equations (PDEs) and forward and backward stochastic differential equations (FBSDEs), demonstrated by a nonlinear version of the Feynman-Kac lemma. By means of this lemma, we are able to obtain a probabilistic representation of the solution to the nonlinear Hamilton-Jacobi-Bellman PDE, expressed in form of a system of decoupled FBSDEs. This system of FBSDEs can then be simulated by employing linear regression techniques. We present a novel discretization scheme for FBSDEs, and enhance the resulting algorithm with importance sampling, thereby constructing an iterative scheme that is capable of learning the optimal control without an initial guess, even in systems with highly nonlinear, underactuated dynamics. The framework we develop within this dissertation addresses several classes of stochastic optimal control, such as L2, L1, risk sensitive control, as well as some classes of differential games, in both fixed-final-time as well as first-exit settings.

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Integrated architecture analysis and technology evaluation for systems of systems modeled at the subsystem level

2017-11-13 , Trent, Douglas James

A lack of knowledge during conceptual design results in two primary challenges: overruns in cost and schedule due to frequent design changes and combinatorial explosion of alternatives due to large, discrete categorical design spaces. Due to the significant impact subsystem-level technologies have on the cost and schedule of a design, they should be considered during the conceptual design of systems of systems in an effort to reduce this lack of knowledge. To integrate architecture analysis and technology evaluation at the subsystem level, several questions and hypotheses are posed during a discussion of a general concept exploration process to guide the development of a new framework. The Dynamic Rocket Equation Tool (DYREQT) and a collection of subsystem-level in-space transportation models were developed to provide a modeling and simulation environment capable of producing the necessary data for experimentation. DYREQT provides the capability to integrate user-developed subsystem models for space transportation architecture analysis and design. Results from the experiments led to conclusions which guided the definition of the Integrated Architecture and Technology Exploration (IntegrATE) framework. This new framework enables integrated architecture analysis and technology evaluation at the subsystem level in an effort to increase design knowledge during the conceptual design process. IntegrATE provides flexibility such that it can be tailored to a wide range of problems. It also provides a high degree of transparency throughout to help reduce the likelihood of bias towards individual architectures or technologies. Finally, the IntegrATE framework and DYREQT were demonstrated on a notional manned Mars 2033 design study to highlight the utility of these new developments.

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Simulation of full-scale combustion instabilities in small-scale rigs using actively controlled boundary conditions

2017-11-09 , Kim, Yong Jea

The onset of combustion instabilities (CIs) has hindered the development and performance of combustion systems employed in industrial, power generation and propulsion systems for many decades. Investigating CIs in actual “full-scale” engine tests are not practical because of the exorbitant cost of such tests, the large space required to house the full-sized engine, and the inability to equip full-scale engines with diagnostic systems. Because of these difficulties, most studies of CIs to date were performed in “small-scale” setups that were geometrically similar to but smaller than the full-scale engines combustors. While testing with these small-scale setups reduced the cost of testing and produced important results, the acoustic modes excited in the small-scale setups had considerably higher frequencies that did not simulate the lower frequency oscillations that are excited in the unstable full-scale engines. The above discussion indicates that in order to study the driving of CIs in full-scale engines in small-scale rigs, the latter must simulate the acoustic environments, the combustion processes, and the interactions between these processes in the unstable full-scale engine. This study developed a real time active acoustic boundary control approach to simulate the acoustic environment of the full-scale engine in the small-scale rig. For the study of the driving mechanism of longitudinal CIs, the small-scale rig consists of a shorter section of the full-scale engine and the “missing part” of the full-scale engine (consists of what has been “left over” after the small-scale rig has been removed from the full-scale combustor); see the first figure in Summary in this thesis. The goal of the actively controlled small-scale rig is to experimentally study the processes taking place in the corresponding region of small-scale rig section in an unstable full-scale engine. To attain this goal, the active control system (ACS) needs to generate an acoustic impedance at the actively controlled boundary of the small-scale rig that equals to the acoustic impedance at the corresponding location in the full-scale unstable engine. If this is accomplished, the acoustic oscillations in the small-scale rig and the corresponding region of small-scale rig section in full-scale engine would be identical. This study has developed a real time ACS, which enables the small-scale tube rig to simulate the longitudinal acoustic oscillations in the full-scale tubes (or engine), with the one-dimensional cold flow setup. In this setup, the speaker at the left end of the small-scale tube rig generated acoustic oscillations that simulate the driving by the combustion process, and the speaker at the right end was actively controlled to simulate the acoustic field of the full-scale system. It was demonstrated that the developed, actively controlled, small-scale, rig can simulate travelling and standing waves oscillations that are encountered in longer full-scale tubes. Additionally, this rig was used to demonstrate that standing acoustic waves CI in full-scale tubes having different lengths could be simulated in the developed, actively controlled, small-scale rig. This study also developed a theoretical model that determines in real time the acoustic boundary condition (BC) that must be generated by the ACS at the boundaries of a small-scale rig that simulates transverse (tangential) CI in an annular combustor similar to those used in gas turbines and jet engines. In this case, the small-scale rig consists of a small section of the annular combustor and the “missing part” of the full-scale engine (consists of what has been “left over” after the small-scale sector-rig has been removed from the annular combustor); see the second figure in Summary in this thesis. To determine the BCs that needed to be established at the boundaries of the actively controlled, small-scale rig, the developed model accounts for the effects of the combustion processes and flows through the reactants supply injectors and exhaust nozzles in the “missing part” of the engine, and for the presence of a tangential mean flow in the annular combustor. The developed model was numerically validated and used to investigate the effects of the exhaust nozzle, combustion process, and tangential mean flow component upon the characteristics of tangential CIs in an annular combustor. For example, its numerical solutions demonstrated that the presence and direction of the mean tangential flow component critically affect the characteristics of tangential (spinning) instabilities and an initially standing wave disturbance gradually transforms itself into a spinning wave that rotates around the annular combustor in the direction of the tangential mean flow; this finding is in agreement with previous experimental observations that have not been explained to date.

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Ambush games in discrete and continuous environments

2017-11-22 , Boidot, Emmanuel

We consider an autonomous navigation problem, whereby a traveler aims at traversing an environment in which an adversary sets an ambush. A two players zero- sum game is introduced, describing the initial strategy of the traveler and the ambusher based on a description of the environment and the traveler initial location and desired goal. The process is single-step in the sense that agents do not reevaluate their strategy after the traveler has started moving. Players’ strategies are computed as probabilistic path distributions, a realization of which is the path chosen by the traveler and the ambush location chosen by the ambusher. A parallel is drawn between the discrete problem, where the traveler moves on a network, and the continuous problem, where the traveler moves in a compact subset of R2. Analytical optimal policies are derived. Assumptions from the Minimal Cut - Maximal Flow literature for continuous domains are used. The optimal value of the game is shown to be related to the maximum flow on the environment for sub-classes of games where the reward function for the ambusher is uniform. This proof is detailed in the discrete and continuous setups. In order to relax the assumptions for the computation of the players’ optimal strategies, a sampling-based approach is proposed, inspired by re- cent sampling-based motion planning techniques. Given a uniform reward function for the ambusher, optimal strategies of the sampled ambush game are proven to converge to the optimal strategy of the continuous ambush game under some sampling and connectivity constraints. A linear program is introduced that allows for the computation of optimal policies. The sampling-based approach is more general in the sense that it is compatible with constrained motion primitives for the traveler and non-uniform reward functions for the ambusher. The sampling-based game is used to create example applications for situ- ations where no analytic solution of the Continuous Ambush Game have been identified.This leads to more interesting games, applicable to real-world robots using modern motion planning algorithms. Examples of such games are setups where the traveler’s motion satis- fies Dubins’ kinematic constraints and setups where the reach of the ambusher is dependent on the speed of the traveler.

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A methodology for risk-informed launch vehicle architecture selection

2017-11-13 , Edwards, Stephen James

Modern society in the 21st century has become inseparably dependent on human mastery of the near-Earth regions of space. Billions of dollars in on-orbit assets provide a set of fundamental, requisite services to such diverse domains as telecom, military, banking, and transportation. While orbiting satellites provide these services, launch vehicles (LVs) are unquestionably the most critical piece of infrastructure in the space economy value chain. The past decade has seen a significant level of activity in LV development, including some fundamental changes to the industry landscape. Every space-faring nation is engaged in new program developments; most notable, however, is the surge in commercial investments and development efforts, which has been spurred by a combination of private investments by wealthy individuals, new government policies and acquisition strategies, and the increased competition that has resulted from both. In all the LV programs of today, affordability is acknowledged as the single biggest objective. Governments seek assured access to space that can be realized within constrained budgets, and commercial entities vie for survival, profitability, and market-share. From literature, it is clear that the biggest opportunity for affecting affordability resides in improving decision-making early on in the design process. However, a review of historical LV architecture studies shows that very little has changed over the past 50 years in how early architecting decisions are analyzed. In particular, architecture analyses of alternatives are still conducted deterministically, despite uncertainty being at its highest in the very early stages of design. This thesis argues that the ``design freedom'' that exists early on manifests itself as volitional uncertainty during the LV architect's deliberation, motivating the objective statement ``to develop a methodology for enabling risk-informed decision making during the architecture selection phase of LV programs.'' NASA's Risk-Informed Decision Making process is analyzed with respect to the particulars of the LV architecture selection problem. The most significant challenge is found to be LV performance modeling via trajectory optimization, which is not well suited to probabilistic analysis. To overcome this challenge, an empirical modeling approach is proposed. However, this in turn introduces the challenge of generalizing the empirical model, as creating distinct performance models for every architecture concept under consideration is considered infeasible. A review of the main drivers in LV trajectory performance observes T/W not only to be one of the parameters with most sensitivity, but also reveals it to be a functional in its true form. Based on the performance-driving nature of the T/W profile, and the fact that in its infinite-dimensional form it offers a common basis for representing diverse architectures, functional regression techniques are proposed as a potential means of constructing an architecture-spanning empirical performance model. A number of techniques are formulated and tested, and prove capable of supporting the LV performance modeling in support of risk-informed architecture selection.

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Experimental investigation of transverse acoustic instabilities

2017-11-09 , Smith, Travis Edward

This work presents 5 kHz stereo PIV and OH PLIF measurements as well as OH* and CH* chemiluminescence measurements of transversely forced swirl flames. The presence of transverse forcing on this naturally unstable flow both influences the natural instabilities, as well as amplifies disturbances that may not necessarily manifest themselves during natural oscillations. By manipulating the structure of the acoustic forcing field, both axisymmetric and helical modes are preferentially excited away from the frequency of natural instability. Additionally, forced and self-excited transverse acoustic instability studies to date have strong coupling between the transverse and axial acoustic fields near the flame. This is significant, as studies suggest that it is not the transverse disturbances themselves, but rather the induced axial acoustic disturbances, that control the bulk of the heat release response. The work first presents a method for spatially interpolating the phase locked r-z and r-θ planar velocity and flame position data, extracting the full three-dimensional structure of the helical disturbances. These helical disturbances are also decomposed into symmetric and antisymmetric disturbances about the jet core, showing the subsequent axial evolution (in magnitude and phase) of each of these underlying disturbances. Then experiments performed with essentially the same transverse acoustic wave field, but with and without axial acoustics, show that significant heat release oscillations are only excited in the former case. The results show that the axial disturbances at the nozzle exit are the dominant cause of the heat release oscillations. These observations support the theory that the key role of the transverse motions is to act as the “clock” for the instability, setting the frequency of the oscillations while having a negligible direct effect on the actual heat release fluctuations. They also show that transverse instabilities can be damped by either actively canceling the induced axial acoustics in the nozzle (rather than the much larger energy transverse combustor disturbances), or by passively tuning the nozzle impedance to drive an axial acoustic velocity node at the nozzle outlet.

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A time accurate fluid-structure interaction framework using a Cartesian grid CFD solver

2017-11-15 , Bopp, Matthew Scott

The landing of the Mars Science Laboratory (MSL) in 2012 demonstrated the limits of supersonic planetary entry technology through the use of a disk-gap-band parachute deployed from behind the aeroshell capsule. With the eventual goal of sending humans to Mars, the payload requirements are estimated to increase by a factor of 40, far outside the current technological envelope. With a density of less than 1% of Earth's, the Martian atmosphere makes the task of generating aerodynamic drag very challenging. Larger aeroshells produce more drag, but the vehicle is then too large to fit as payload inside a rocket. By utilizing inflatable aerodynamic decelerators, the drag area can be significantly increased, while the pre-deployed configuration has high packing efficiency. New technologies bring with them the requirement to study their behavior, and characterize their flight limits. Wind tunnel tests are difficult due scaling concerns, and flight tests are costly and time consuming. Thus, accurate computational modeling of the fluid-structure interactions (FSI) is critical in the development of aerodynamic decelerators. Much of the current research in FSI focuses on high fidelity analysis, which is often very computationally expensive, and requires significant user intervention. The current work fills a niche where the analysis time and human interaction is reduced, by utilizing an adaptive, Cartesian grid framework for solving the computational fluid dynamics (CFD). A time accurate, partitioned coupling strategy is employed to study FSI applied to flexible materials under high dynamic pressure loads. The structural dynamics is solved using LS-DYNA, and care must be taken at the interface boundary conditions to reduce numerical errors. The development of this tool has relied on a complete re-write of the in-house CFD code, NASCART-GT, where significant improvements have been made in computational efficiency and scalability. CFD simulations with prescribed motions are studied in order to validate the fluid dynamics of high speed flows with non-stationary boundary conditions, and to study the effects of solution-based grid adaption for these simulations. The interaction with rigid body dynamics is presented in simulations of the free flight dynamics of the MSL capsule. FSI simulations are then presented for a series of test cases, where the physics is validated for the unsteady, time accurate coupling of 1-D piston motion and 2-D beam deformation. Finally, steady state and time accurate simulations of an inflatable aerodynamic decelerator demonstrate the effectiveness of the current methodology in furthering the development of decelerator technologies.

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Geometric nonlinearity effects on the behavior of sandwich structures

2017-11-13 , Yuan, Zhangxian

The Extended High-order Sandwich Panel Theory (EHSAPT) accounts for the axial rigidity, the transverse compressibility, and the shear effect of the core. Thus, it is suitable for sandwich composites made of a wide range of core materials, including soft cores and stiff cores. However, its analytical solution is only available to particular cases, i.e., sandwich panels with simply supported edges and subjected to sinusoidally distributed transverse loads. To obtain its solutions under general boundary conditions and loadings, a special finite element is first proposed to implement the EHSAPT with the finite element method. The proposed method extends the application of the EHSAPT and can easily handle arbitrary combinations of boundary conditions and loadings. Small deformation and infinitesimal strain were considered in the EHSAPT. In this dissertation, the EHSAPT is further developed to include geometric nonlinearities. Both faces and core are considered undergoing large deformation and moderate rotation. The weak form nonlinear governing equations of static behavior are derived from the principle of minimum total potential energy, and the equations of motion for dynamic response are derived from Hamilton's principle. The geometric nonlinearity effects on both static behavior and dynamic response of sandwich structures are investigated. In the literature, there are various simplifying assumptions adopted in the kinematic relations of the faces and the core when considering the geometric nonlinearities in sandwich structures. It is common that only one nonlinear term that appears in faces is included, and the core nonlinearities are neglected. A critical assessment of these assumptions, as well as the effects of including the other nonlinear terms in the faces and the core is made. It shows that the geometric nonlinearities of the core have significant effects on the behavior of sandwich structures. The stability behavior is very important to sandwich structures. The compressive strength of the thin faces and the overall behavior of sandwich structure can be realized only if it is stabilized against buckling. As a compound structure, a sandwich structure has more complicated stability behavior than an ordinary beam. The compressibility of the core significantly affects the stability response and contributes to the local instability phenomenon. Therefore, despite the global buckling (Euler buckling), very common in ordinary beams and plates, wrinkling, characterized as short-wave buckling, may also occur in sandwich structures. The stability investigation of sandwich structures is carried out based on the derived weak form nonlinear governing equations. The buckling analysis, which determines the buckling mode shape and critical buckling load at a convenient manner, and the nonlinear post-buckling analysis, which evaluates the post-buckling response of sandwich structures, are both presented. Both wrinkling and global buckling are observed. It is shown that although the axial rigidity of the core usually is hundreds times smaller than that of the faces, which is often negligible in the static analysis, it has significant influence on the stability response.

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The effects of ozone addition on flame propagation and stabilization

2017-11-09 , Gao, Xiang

Combustion plays a vital role in transportation and power generation. However, concerns of efficiency, emission, and operations at extreme conditions highlight the needs to enhance combustion process. If the rate-limiting chemical pathways can be modified, the ignition and combustion process could be dramatically accelerated. Following this idea, addition of ozone (O3) is proposed as a potential solution. O3 is one of the strongest oxidizers. It can be efficiently and economically produced in situ at high pressures, and transported to the desired region from an injection location to modify fuel oxidization and control the combustion process. To serve as a basis for future application on practical combustion systems, this dissertation investigates the effects of O3 addition on two fundamental combustion processes: the propagation of laminar premixed flames and the stabilization of non- premixed jet flames in autoignitive environment. Previous studies have shown that O3 addition can enhance flame propagation, stability and ignition, but the dependence on pressure and temperature were not clear. Furthermore, few studies have been conducted on the effects of ozonolysis reactions, which are rapid even at room temperature for unsaturated hydrocarbons. The results presented in this dissertation are an attempt to address these questions. The effects of O3 addition on the propagation of laminar premixed flames are investigated with respect to pressure, initial temperature, O3 concentration and fuel kinetics. For alkane/air premixed laminar flames, high-pressure Bunsen flame experiments in the present work show that the enhancement in laminar flame speed (SL) increases with pressures. This is due to the fact that O3 decomposition, which releases reactive oxygen atoms, becomes a more dominant O3 consumption pathway at higher pressure. Simulations show that adding O3 at higher initial temperature is not as effective as lower initial temperatures. A nearly linear relation between the enhancement and O3 concentration is observed at room temperature and atmospheric pressure. If the fuel is changed from alkanes to C2H4, an unsaturated hydrocarbon species, ozonolysis reactions take place in the premixing process. When the heat released from ozonolysis reactions is lost, decrease in SL is observed. In contrast, if ozonolysis reaction are frozen, either by cooling the reactants or decreasing the pressure, enhancement of SL by O3 addition is observed. The study on flame stabilization with O3 addition is conducted with a non-premixed jet burner in a quartz tube using C2H4 as the fuel. At low-dilution conditions, autoignition events are initiated by ozonolysis reactions. The autoignition timescale is further investigated quantitatively. Overall, this timescale decreases as the inlet velocity increases. At such autoignitive conditions created by ozonolysis reactions, the stabilization of a lifted non-premixed flame is fundamentally different from non-autoignitive conditions. Propagation is enhanced due to the “preprocessing” of fuel by ozonolysis reactions, after which the mass burning velocity of the reactants is increased as shown by simulation. This can increase the propagation speed by several times. In summary, for the premixed laminar flame propagation, the present results explain the pressure, initial temperature, and fuel dependence of enhancement of flame propagation by O3 addition. A more comprehensive understanding is thus contributed. Furthermore, this dissertation explores ozonolysis reactions as an alternative to create a platform to conduct fundamental research on flame in autoignitive environment.

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