Control and Optimization for Aerospace Systems with Stochastic Disturbances, Uncertainties, and Constraints

The topic of this dissertation is the control and optimization of aerospace systems under the influence of stochastic disturbances, uncertainties, and subject to chance constraints. This problem is motivated by the uncertain operating environments of many aerospace systems, and the ever-present push to extract greater performance from these systems while maintaining safety. Explicitly accounting for the stochastic disturbances and uncertainties in the constrained control design confers the ability to assign the probability of constraint satisfaction depending on the level of risk that is deemed acceptable and allows for the possibility of theoretical constraint satisfaction guarantees. Along these lines, this dissertation presents novel contributions addressing four different problems: 1) chance-constrained path planning for small unmanned aerial vehicles in urban environments, 2) chance-constrained spacecraft relative motion planning in low-Earth orbit, 3) stochastic optimization of suborbital launch operations, and 4) nonlinear model predictive control for tracking near rectilinear halo orbits and a proposed stochastic extension. For the first problem, existing dynamic and informed rapidly-expanding random trees algorithms are combined with a novel quadratic programming-based collision detection algorithm to enable computationally efficient, chance-constrained path planning. For the second problem, a previously proposed constrained relative motion approach based on chained positively invariant sets is extended in this dissertation to the case where the spacecraft dynamics are controlled using output feedback on noisy measurements and are subject to stochastic disturbances. Connectivity between nodes is determined through the use of chance-constrained admissible sets, guaranteeing that constraints are met with a specified probability. For the third problem, a novel approach to suborbital launch operations is presented. It utilizes linear covariance propagation and stochastic clustering optimization to create an effective software-only method for decreasing the probability of a dangerous landing with no physical changes to the vehicle and only minimal changes to its flight controls software. For the fourth problem, the use of suboptimal nonlinear model predictive control (NMPC) coupled with low-thrust actuators is considered for station-keeping on near rectilinear halo orbits. The nonlinear optimization problems in NMPC are solved with time-distributed sequential quadratic programming techniques utilizing the FBstab algorithm. A stochastic extension for this problem is also proposed. The results are illustrated using detailed numerical simulations.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/162992/1/awbe_1.pd

A Framework for Offline Risk-aware Planning of Low-altitude Aerial Flights during Urban Disaster Response

Disaster response missions are dynamic and dangerous events for first responders. Active situational awareness is critical for effective decision-making, and unmanned aerial assets have successfully extended the range and output of sensors. Aerial assets have demonstrated their capability in disaster response missions via decentralized operations. However, literature and industry lack a systematic investigation of the algorithms, datasets, and tools for aerial system trajectory planning in urban disasters that optimizes mission performance and guarantee mission success. This work seeks to develop a framework and software environment to investigate the requirements for offline planning algorithms and flight risk models when applied to aerial assets exploring urban disaster zones. This is addressed through the creation of rapid urban maps, efficient flight planning algorithms, and formal risk metrics that are demonstrated in scenario-driven experiments using Monte Carlo simulation. First, rapid urban mapping strategies are independently compared for efficient processing and storage through obstacle and terrain layers. Open-source data is used when available and is supplemented with an urban feature prediction model trained on satellite imagery using deep learning. Second, sampling-based planners are evaluated for efficient and effective trajectory planning of nonlinear aerial dynamic systems. The algorithm can find collision-free, kinodynamic feasible trajectories using random open-loop control targets. Alternative open-loop control commands are formed to improve the planning algorithm’s speed and convergence. Third, a risk-aware implementation of the planning algorithm is developed that considers the uncertainty of energy, collisions, and onboard viewpoint data and maps them to a single measure of the likelihood of mission failure. The three modules are combined in a framework where the rapid urban maps and risk-aware planner are evaluated against benchmarks for mission success, performance, and speed while creating a unique set of benchmarks from open-source data and software. One, the rapid urban map module generates a 3D structure and terrain map within 20 meters of data and in less than 5 minutes. The Gaussian Process terrain model performs better than B-spline and NURBS models in small-scale, mountainous environments at 10-meter squared resolution. Supplementary data for structures and other urban landcover features is predicted using the Pix2Pix Generative Adversarial Network with a 3-channel encoding for nine labels. Structures, greenspaces, water, and roads are predicted with high accuracy according to the F1, OIU, and pixel accuracy metrics. Two, the sampling-based planning algorithm is selected for forming collision-free, 3D offline flight paths with a black-box dynamics model of a quadcopter. Sampling-based planners prove successful for efficient and optimal flight paths through randomly generated and rapid urban maps, even under wind and noise uncertainty. The Stable-Sparse-RRT, SST, algorithm is shown to improve trajectories for minimum Euclidean distance more consistently and efficiently than the RRT algorithm, with a 50% improvement in finite-time path convergence for large-scale urban maps. The forward propagation dynamics of the black-box model are replaced with 5-15 times more computationally efficient motion primitives that are generated using an inverse lower-order dynamics model and the Differential Dynamic Programming, DDP, algorithm. Third, the risk-aware planning algorithm is developed that generates optimal paths based on three risk metrics of energy, collision, and viewpoint risk and quantifies the likelihood of worst-case events using the Conditional-Value-at-Risk, CVaR, metric. The sampling-based planning algorithm is improved with informative paths, and three versions of the algorithm are compared for the best performance in different scenarios. Energy risk in the planning algorithm results in 5-35% energy reduction and 20-30% more consistency in finite-time convergence for flight paths in large-scale urban maps. All three risk metrics in the planning algorithm generally result in more energy use than the planner with only energy risk, but reduce the mean flight path risk by 10-50% depending on the environment, energy available, and viewpoint landmarks. A final experiment in an Atlanta flooding scenario demonstrates the framework’s full capability with the rapid urban map displaying essential features and the trajectory planner reporting flight time, energy consumption, and total risk. Furthermore, the simulation environment provides insight into offline planning limitations through Monte Carlo simulations with environment wind and system dynamics noise. The framework and software environment are made available to use as benchmarks in the field to serve as a foundation for increasing the effectiveness of first responders’ safety in the challenging task of urban disaster response.Ph.D

Path Planning for Aircraft Under Threat of Detection from Ground-Based Radar with Uncertainty in Aircraft and Radar States

Mission planners for manned and unmanned aircraft operating within the detection range of ground-based radar systems are often concerned with the probability of detection. Several factors influence the probability of detection, including aircraft position and orientation, radar position, and radar performance parameters. Current path planning algorithms assume that these factors are known with certainty, but in practice, these factors are estimated and have some uncertainty. This dissertation explores methods to consider the uncertainty in the detection factors for an aircraft path planner. First, the detection model is extended to include uncertainty in the aircraft position and orientation, radar position, and radar parameters. Second, an efficient method to estimate the aircraft position and orientation uncertainty is presented that enables rapid path evaluation. Third, the extended radar model and efficient aircraft uncertainty calculation are incorporated into a path planner that evaluates the sources of uncertainty and provides actionable information to the mission planner

A methodology for the validated design space exploration of fuel cell powered unmanned aerial vehicles

Unmanned Aerial Vehicles (UAVs) are the most dynamic growth sector of the aerospace industry today. The need to provide persistent intelligence, surveillance, and reconnaissance for military operations is driving the planned acquisition of over 5,000 UAVs over the next five years. The most pressing need is for quiet, small UAVs with endurance beyond what is capable with advanced batteries or small internal combustion propulsion systems. Fuel cell systems demonstrate high efficiency, high specific energy, low noise, low temperature operation, modularity, and rapid refuelability making them a promising enabler of the small, quiet, and persistent UAVs that military planners are seeking. Despite the perceived benefits, the actual near-term performance of fuel cell powered UAVs is unknown. Until the auto industry began spending billions of dollars in research, fuel cell systems were too heavy for useful flight applications. However, the last decade has seen rapid development with fuel cell gravimetric and volumetric power density nearly doubling every 2-3 years. As a result, a few design studies and demonstrator aircraft have appeared, but overall the design methodology and vehicles are still in their infancy. The design of fuel cell aircraft poses many challenges. Fuel cells differ fundamentally from combustion based propulsion in how they generate power and interact with other aircraft subsystems. As a result, traditional multidisciplinary analysis (MDA) codes are inappropriate. Building new MDAs is difficult since fuel cells are rapidly changing in design, and various competitive architectures exist for balance of plant, hydrogen storage, and all electric aircraft subsystems. In addition, fuel cell design and performance data is closely protected which makes validation difficult and uncertainty significant. Finally, low specific power and high volumes compared to traditional combustion based propulsion result in more highly constrained design spaces that are problematic for design space exploration. To begin addressing the current gaps in fuel cell aircraft development, a methodology has been developed to explore and characterize the near-term performance of fuel cell powered UAVs. The first step of the methodology is the development of a valid MDA. This is accomplished by using propagated uncertainty estimates to guide the decomposition of a MDA into key contributing analyses (CAs) that can be individually refined and validated to increase the overall accuracy of the MDA. To assist in MDA development, a flexible framework for simultaneously solving the CAs is specified. This enables the MDA to be easily adapted to changes in technology and the changes in data that occur throughout a design process. Various CAs that model a polymer electrolyte membrane fuel cell (PEMFC) UAV are developed, validated, and shown to be in agreement with hardware-in-the-loop simulations of a fully developed fuel cell propulsion system. After creating a valid MDA, the final step of the methodology is the synthesis of the MDA with an uncertainty propagation analysis, an optimization routine, and a chance constrained problem formulation. This synthesis allows an efficient calculation of the probabilistic constraint boundaries and Pareto frontiers that will govern the design space and influence design decisions relating to optimization and uncertainty mitigation. A key element of the methodology is uncertainty propagation. The methodology uses Systems Sensitivity Analysis (SSA) to estimate the uncertainty of key performance metrics due to uncertainties in design variables and uncertainties in the accuracy of the CAs. A summary of SSA is provided and key rules for properly decomposing a MDA for use with SSA are provided. Verification of SSA uncertainty estimates via Monte Carlo simulations is provided for both an example problem as well as a detailed MDA of a fuel cell UAV. Implementation of the methodology was performed on a small fuel cell UAV designed to carry a 2.2 kg payload with 24 hours of endurance. Uncertainty distributions for both design variables and the CAs were estimated based on experimental results and were found to dominate the design space. To reduce uncertainty and test the flexibility of the MDA framework, CAs were replaced with either empirical, or semi-empirical relationships during the optimization process. The final design was validated via a hardware-in-the loop simulation. Finally, the fuel cell UAV probabilistic design space was studied. A graphical representation of the design space was generated and the optima due to deterministic and probabilistic constraints were identified. The methodology was used to identify Pareto frontiers of the design space which were shown on contour plots of the design space. Unanticipated discontinuities of the Pareto fronts were observed as different constraints became active providing useful information on which to base design and development decisions.Ph.D.Committee Chair: Mavris, Dimitri; Committee Member: Nam, Taewoo; Committee Member: Parekh, David; Committee Member: Soban, Danielle; Committee Member: Volovoi, Vital

Air Force Institute of Technology Research Report 2020

This Research Report presents the FY20 research statistics and contributions of the Graduate School of Engineering and Management (EN) at AFIT. AFIT research interests and faculty expertise cover a broad spectrum of technical areas related to USAF needs, as reflected by the range of topics addressed in the faculty and student publications listed in this report. In most cases, the research work reported herein is directly sponsored by one or more USAF or DOD agencies. AFIT welcomes the opportunity to conduct research on additional topics of interest to the USAF, DOD, and other federal organizations when adequate manpower and financial resources are available and/or provided by a sponsor. In addition, AFIT provides research collaboration and technology transfer benefits to the public through Cooperative Research and Development Agreements (CRADAs). Interested individuals may discuss ideas for new research collaborations, potential CRADAs, or research proposals with individual faculty using the contact information in this document

UAS Path Planning for Dynamical Wildfire Monitoring with Uneven Importance

Unmanned Aircraft Systems (UASs) offer many benefits in wildfire monitoring when compared to traditional wildfire monitoring technologies. When planning the path of an UAS for wildfire monitoring, it is important to consider the uneven propagation nature of the wildfire because different parts of the fire boundary demand different levels of monitoring attention (importance) based on the propagation speed. In addition, many of the existing works adopt a centralized approach for the path planning of the UASs. However, the use of centralized approaches is often limited in terms of applicability and adaptability. This work focuses on developing decentralized UAS path planning algorithms to autonomously monitor a spreading wildfire considering uneven importance. The algorithms allow the UASs to focus on the most active regions of a wildfire while still covering the entire fire perimeter. When monitoring a relatively smaller and spatially static fire, a single UAS might be adequate for the task. However, when monitoring a larger wildfire that is evolving dynamically in space and time, efficient and optimized use of multiple UASs is required. Based on this need, we also focus on decentralized and importance-based multi-UAS path planning for wildfire monitoring. The design, implementation, analysis, and simulation results have been discussed in details for both single-UAS and multi-UAS path planning algorithms. Experiment results show the effectiveness and robustness of the proposed algorithms for dynamic wildfire monitoring