Proper engine selection for Reusable Launch Vehicles (RLVs) is a key factor in the design of low cost reusable launch systems for routine access to space. RLVs typically use combinations of different types of engines used in sequence over the duration of the flight. Also, in order to properly choose which engines are best for an RLV design concept and mission, the optimal trajectory that maximizes or minimizes the mission objective must be found for that engine configuration. Typically this is done by the designer iteratively choosing engine combinations based on his/her judgment and running each individual combination through a full trajectory optimization to find out how well the engine configuration performed on board the desired RLV design. This thesis presents a new method to reliably predict the optimal engine configuration and optimal trajectory for a fixed design of a conceptual RLV in an automated manner. This method is accomplished using the original code Steele-Flight. This code uses a combination of a Genetic Algorithm (GA) and a Non-Linear Programming (NLP) based trajectory optimizer known as GPOPS II to simultaneously find the optimal engine configuration from a user provided selection pool of engine models and the matching optimal trajectory. This method allows the user to explore a broad range of possible engine configurations that they wouldn't have time to consider and do so in less time than if they attempted to manually select and analyze each possible engine combination. This method was validated in two separate ways. The codes ability to optimize trajectories was compared to the German trajectory optimizer suite known as ASTOS where only minimal differences in the output trajectory were noticed. Afterwards another test was performed to verify the method used by Steele-Flight for engine selection. In this test, Steele-Flight was provided a vehicle model based on the German Saenger TSTO RLV concept and models of turbofans, turbojets, ramjets, scramjets and rockets. Steele-Flight explored the design space through the use of a Genetic Algorithm to find the optimal engine combination to maximize payload. The results output by Steele-Flight were verified by a study in which the designer manually chose the engine combinations one at a time, running each through the trajectory optimization routine to determine the best engine combination. For the most part, these methods yielded the same optimal engine configurations with only minor variation. The code itself provides RLV researchers with a new tool to perform conceptual level engine selection from a gathering of user provided conceptual engine data models and RLV structural designs and trajectory optimization for fixed RLV designs and fixed mission requirement. / Master of Science

<p dir="ltr">The electrification of pneumatic or hydraulic system on aircraft has been shown effective in reducing the fuel burn. Recently, electrifying propulsive loads has attracted a lot of atten- tion to further improve fuel economy. This work focuses on tools to facilitate more electric aircraft at conceptual design stage, particularly assuming a turbo-generator architecture. Specifically, we develop a simulation tool, mimicking SUAVE [1], which allows mission and fuel burn analysis. Major differences from SUAVE include more detailed models of compo- nents in the electric propulsive branch and degrees of freedom to adjust the velocity profile along the entire mission. Based on the simulator, this work further proposes to leverage a gradient-free optimization technique, which optimizes the optimal velocity profile along the entire mission to minimize fuel burn. Simulation results on two aircraft designs, a con- ventional Boeing 737-800 and NASA-STARC-ABL, verify the effectiveness of the proposed tools.</p>

Trajectory modeling is one of the most important aspects of any mission design. The trajectory should be able to propagate the S/C to the final destination while optimizing the flight duration, the total change in velocity and also the total launch mass. The Spacecraft Trajectory Optimizer (STO) tool described in this report first solves the Gauss Lambert problem and generates initial departure and arrival conditions which can also be expressed as porkchop plots. These initial conditions are then used as input to optimize the flight steps which are based on a patched conic approximation with the elliptical transfer with respect to the Sun and the hyperbolic transfers at the departure and arrival planet's sphere of influence. The tool is completely based on MATLAB 2007 or later and uses ODE45 for trajectory propagation and FMINCON with Active-set algorithm for optimization. The results obtained in house were compared with four Mars Sample return orbits calculated at ESOC and there is a very good correlation between the required change in velocities and transfer duration for e.g. Orbit case: O22S, ESOC values: total Delta V = 3.946 - 4.119 [km/s], TOF = 329 - 342 [days] &amp; STO values: Delta V = 3:986 [km/s] &amp; TOF = 335 [days]. The in house data was also used as an input in the System Tool Kit (a professional trajectory calculation software) for modeling an interplanetary trajectory to Mars and the S/C arrived at Mars without any optimization. Therefore, even though the STO does not have all the capabilities of a professional software it can be used for preliminary mission analysis as it offers quite accurate results for interplanetary transfers. / <p>Validerat; 20131127 (global_studentproject_submitter)</p>

A real-time computer algorithm to control and optimize aircraft flight profiles is described and applied to a three-dimensional minimum-time intercept mission. The proposed scheme has roots in two well-known techniques: singular perturbations and neighboring-optimal guidance. Use of singular-perturbation ideas is made in terms of the assumed trajectory-family structure. A heading/energy family of prestored point-mass-model state-Euler solutions is used as the baseline in this scheme. The next step is to generate a near-optimal guidance law that will transfer the aircraft to the vicinity of this reference family. The control commands fed to the autopilot consist of the reference controls plus correction terms which are linear combinations of the altitude and path-angle deviations from reference values, weighted by a set of precalculated gains. In this respect the proposed scheme resembles neighboring-optimal guidance. However, in contrast to the neighboring-optimal guidance scheme, the reference control and state variables as well as the feedback gains are stored as functions of energy and heading in the present approach. A detailed description of the feedback laws and of some of the mathematical tools used to construct the controller is presented. The construction of the feedback laws requires a substantial preflight computational effort, but the computation times for on-board execution of the feedback laws are very modest. Other issues relating to practical implementation are addressed as well. Numerical examples, comparing open-loop optimal and approximate feedback solutions for a sample high-performance fighter, illustrate the attractiveness of the guidance scheme. Optimal three-dimensional flight in the presence of a terrain limit is studied in some detail. / Ph. D. / incomplete_metadata

A satellite launch vehicle not subjected to any perturbations, external or internal, could be guided along a trajectory by following a stored, pre-computed steering program. In practice, perturbations do occur, and in order to take account of them and to achieve an accurate injection, a closed loop guidance system is required. Guidance algorithm is developed by solving the optimal control problem. Closed form solution is difficult because the necessary conditions are in the form of Two Point Boundary Value Problems (TBVP) or Multi Point Boundary Value Problems (MPBVP). Development of non-iterative guidance algorithm is taken as a prime objective of this thesis to ensure reliable on-board implementation. If non-iterative algorithms are required, the usual practice is to approximate the system equations to derive closed form solutions. In the present work, approximations cannot be used because the algorithm has to cater to a wide variety of vehicles and missions. Present development adopts an alternate approach by splitting the reconfigurable algorithm development in to smaller sub-problems such that each sub-problem has closed form solution. The splitting is done in such a way that the solution of the sub-problems can be used as building blocks to construct the final solution. By adding or removing the building blocks, the algorithm can be configured to suit specific requirements. Chapter 1 discusses the motivation and objectives of the thesis and gives a literature survey. In chapter 2, Classical Flat Earth (CFE) guidance algorithm is discussed. The assumptions and the nature of solution are closely analyzed because CFE guidance is used as the baseline for further developments. New contribution in chapter 2 is the extension of CFE guidance for a generalized propulsion system in which liquid and solid engines are present. In chapter 3, CFE guidance is applied for a mission with large pitch steering angles. The result shows loss of optimality and performance. An algorithm based on regular perturbation is developed to compensate for the small angle approximation. The new contribution in chapter 3 is the development of Regular Perturbation based FE (RPFE) guidance as an extension of CFE guidance. RPFE guidance can be configured as CFE guidance and FEGP. Algorithms presented up to chapter 3 are developed to inject a satellite in to orbits with unspecified inertial orientation. Communication satellite missions demand injection in to an orbit with a specific inertial orientation defined by argument of perigee. This problem is formulated using Calculus of Variations in chapter 4. A non-iterative closed form solution (Predicted target Flat Earth or PFE guidance) is derived for this problem. In chapter 5, PFE guidance is extended to a multi-stage vehicle with a constraint on the impact point of spent lower stage. Since the problem is not analytically solvable, the original problem is split in to three sub-problems and solved. Chapter 6 has two parts. First part gives theoretical analysis of the sub-optimal strategies with special emphasis to guidance. Behavior of predicted terminal error and control commands in presence of plant approximations are theoretically analyzed for a class of optimal control problems and the results are presented as six theorems. Chapter 7 presents the conclusions and future works.

A study has been performed to determine the advantages and disadvantages of variable thrust and variable specific impulse (Isp) trajectories for solar system exploration. There have been several numerical research efforts for variable thrust, variable Isp, power-limited trajectory optimization problems. All of these results conclude that variable thrust, variable Isp (variable specific impulse, or VSI) engines are superior to constant thrust, constant Isp (constant specific impulse, or CSI) engines. However, most of these research efforts assume a mission from Earth to Mars, and some of them further assume that these planets are circular and coplanar. Hence they still lack the generality. This research has been conducted to answer the following questions: - Is a VSI engine always better than a CSI engine or a high thrust engine for any mission to any planet with any time of flight considering lower propellant mass as the sole criterion? - If a planetary swing-by is used for a VSI trajectory, is the fuel savings of a VSI swing-by trajectory better than that of a CSI swing-by or high thrust swing-by trajectory? To support this research, an unique, new computer-based interplanetary trajectory calculation program has been created. This program utilizes a calculus of variations algorithm to perform overall optimization of thrust, Isp, and thrust vector direction along a trajectory that minimizes fuel consumption for interplanetary travel. It is assumed that the propulsion system is power-limited, and thus the compromise between thrust and Isp is a variable to be optimized along the flight path. This program is capable of optimizing not only variable thrust trajectories but also constant thrust trajectories in 3-D space using a planetary ephemeris database. It is also capable of conducting planetary swing-bys. Using this program, various Earth-originating trajectories have been investigated and the optimized results have been compared to traditional CSI and high thrust trajectory solutions. Results show that VSI rocket engines reduce fuel requirements for any mission compared to CSI rocket engines. Fuel can be saved by applying swing-by maneuvers for VSI engines, but the effects of swing-bys due to VSI engines are smaller than that of CSI or high thrust engines.

Recently there has been a tremendous growth of research emphasizing control of unmanned aerial vehicles (UAVs) either in isolation or in teams. As a matter of fact, UAVs increasingly find their way to applications, especially in military and law enforcement (e.g., reconnaissance, remote delivery of urgent equipment/material, resource assessment, environmental monitoring, battlefield monitoring, ordnance delivery, etc.). This trend will continue in the future, as UAVs are poised to replace the human-in-the-loop during dangerous missions. Civilian applications of UAVs are also envisioned such as crop dusting, geological surveying, search and rescue operations, etc. In this thesis we propose a new online multiresolution path planning algorithm for a small UAV with limited on-board computational resources. The proposed approach assumes that the UAV has detailed information of the environment and the obstacles only in its vicinity. Information about far-away obstacles is also available, albeit less accurately. The proposed algorithm uses the fast lifting wavelet transform (FLWT) to get a multiresolution cell decomposition of the environment, whose dimension is commensurate to the on-board computational resources. A topological graph representation of the multiresolution cell decomposition is constructed efficiently, directly from the approximation and detail wavelet coefficients. Dynamic path planning is sequentially executed for an optimal path using the A* algorithm over the resulting graph. The proposed path planning algorithm is implemented on-line on a small autopilot. Comparisons with the standard D*-lite algorithm are also presented. We also investigate the problem of generating a smooth, planar reference path from a discrete optimal path. Upon the optimal path being represented as a sequence of cells in square geometry, we derive a smooth B-spline path that is constrained inside a channel that is induced by the geometry of the cells. To this end, a constrained optimization problem is formulated by setting up geometric linear constraints as well as boundary conditions. Subsequently, we construct B-spline path templates by solving a set of distinct optimization problems. For an application to the UAV motion planning, the path templates are incorporated to replace parts of the entire path by the smooth B-spline paths. Each path segment is stitched together while preserving continuity to obtain a final smooth reference path to be used for path following control. The path following control for a small fixed-wing UAV to track the prescribed smooth reference path is also addressed. Assuming the UAV is equipped with an autopilot for low level control, we adopt a kinematic error model with respect to the moving Serret-Frenet frame attached to a path for tracking controller design. A kinematic path following control law that commands heading rate is presented. Backstepping is applied to derive the roll angle command by taking into account the approximate closed-loop roll dynamics. A parameter adaptation technique is employed to account for the inaccurate time constant of the closed-loop roll dynamics during actual implementation. Finally, we implement the proposed hierarchical path control of a small UAV on the actual hardware platform, which is based on an 1/5 scale R/C model airframe (Decathlon) and the autopilot hardware and software. Based on the hardware-in-the-loop (HIL) simulation environment, the proposed hierarchical path control algorithm has been validated through the on-line, real-time implementation on a small micro-controller. By a seamless integration of the control algorithms for path planning, path smoothing, and path following, it has been demonstrated that the UAV equipped with a small autopilot having limited computational resources manages to accomplish the path control objective to reach the goal while avoiding obstacles with minimal human intervention.

In the event of an onboard emergency, air transport pilots are remarkably adept at safely landing their aircraft. However, the tasks of selecting an alternate landing site and developing a safe path to land are very difficult in the high workload, high stress environment of a cockpit during an emergency. The purpose of this research was to develop an automated path planning aid which would assist the pilot in the completion of these tasks. A prototype was developed to test this concept experimentally. The experiment was also intended to gather further information about how pilots think about and accomplish this task as well as the best ways to assist them. In order to better understand the priorities and processes pilots use when dealing with emergency planning, a survey of airline pilots was conducted. The results of this survey highlighted the fact that each emergency is unique and has its own set of factors which are critically important. One factor which is important in many emergencies is the need to land quickly. The survey responses indicated that one of the most important characteristics of a useful tool is that it should provide pertinent information in an easy to use manner, and should not divert too much attention from their other tasks. A number of design goals drove the development of the prototype aid. First, the aid was to work within current aircraft, without requiring substantial redesign on the cockpit. Second, the aid was to help improve pilots' performance without increasing their workload. Finally, the aid was designed to assist pilots in obtaining and processing critical information which influences the site selection and path development tasks. One variation of the aid included a filter dial which allowed pilots to quickly reduce the number of options considered, another variation of the aid did not include such a dial. These two variations of the aid were tested in order to assess the impact of the addition of the filter dial to the system. Though many of the results did not prove to be statistically significant, they suggest that the addition of a filter dial improved the quality of the selected landing site; however, it also increased the time required for the selection. The results were obtained in both familiar and unfamiliar emergencies. The dial was shown to improve the time to complete the task in the case of unfamiliar emergencies. The experiment also compared an optimal ranking system to a non-optimal system, for which results showed no significant difference between the two. This may imply that while pilots did not tend to over rely on the ranking system, under-reliance may need to be addressed by training and a better understanding of the factors which impact the rankings. The participants found that the aid facilitates quick and easy access to critical information. The aid was also useful for processing this information by filtering out options which were inappropriate for a given scenario through the use of the filter dial. The participants also made recommendations about possible improvements which could be made to the system such as better filter settings which are more similar to the way that pilots think about their options.

Future ambitious solar system exploration missions are likely to require ever larger propulsion capabilities and involve innovative interplanetary trajectories in order to accommodate the increasingly complex mission scenarios. Two recent advances in trajectory design can be exploited to meet those new requirements: the use of low-thrust propulsion which enables larger cumulative momentum exchange relative to chemical propulsion; and the consideration of low-energy transfers relying on full multi-body dynamics. Yet the resulting optimal control problems are hypersensitive, time-consuming and extremely difficult to tackle with current optimization tools. Therefore, the goal of the thesis is to develop a methodology that facilitates and simplifies the solution finding process of low-thrust optimization problems in multi-body environments. Emphasis is placed on robust techniques to produce good solutions for a wide range of cases despite the strong nonlinearities of the problems. The complete trajectory is broken down into different component phases, which facilitates the modeling of the effects of multiple bodies and makes the process less sensitive to the initial guess. A unified optimization framework is created to solve the resulting multi-phase optimal control problems. Interfaces to state-of-the-art solvers SNOPT and IPOPT are included. In addition, a new, robust Hybrid Differential Dynamic Programming (HDDP) algorithm is developed. HDDP is based on differential dynamic programming, a proven robust second-order technique that relies on Bellman's Principle of Optimality and successive minimization of quadratic approximations. HDDP also incorporates nonlinear mathematical programming techniques to increase efficiency, and decouples the optimization from the dynamics using first- and second-order state transition matrices. Crucial to this optimization procedure is the generation of the sensitivities with respect to the variables of the system. In the context of trajectory optimization, these derivatives are often tedious and cumbersome to estimate analytically, especially when complex multi-body dynamics are considered. To produce a solution with minimal effort, an new approach is derived that computes automatically first- and high-order derivatives via multicomplex numbers. Another important aspect of the methodology is the representation of low-thrust trajectories by different dynamical models with varying degrees of fidelity. Emphasis is given on analytical expressions to speed up the optimization process. In particular, one novelty of the framework is the derivation and implementation of analytic expressions for motion subjected to Newtonian gravitation plus an additional constant inertial force. Example applications include low-thrust asteroid tour design, multiple flyby trajectories, and planetary inter-moon transfers. In the latter case, we generate good initial guesses using dynamical systems theory to exploit the chaotic nature of these multi-body systems. The developed optimization framework is then used to generate low-energy, inter-moon trajectories with multiple resonant gravity assists.

This thesis presents an integrated framework for online obstacle avoidance of rotary-wing unmanned aerial vehicles (UAVs), which can provide UAVs an obstacle field navigation capability in a partially or completely unknown obstacle-rich environment. The framework is composed of a LIDAR interface, a local obstacle grid generation, a receding horizon (RH) trajectory optimizer, a global shortest path search algorithm, and a climb rate limit detection logic. The key feature of the framework is the use of an optimization-based trajectory generation in which the obstacle avoidance problem is formulated as a nonlinear trajectory optimization problem with state and input constraints over the finite range of the sensor. This local trajectory optimization is combined with a global path search algorithm which provides a useful initial guess to the nonlinear optimization solver. Optimization is the natural process of finding the best trajectory that is dynamically feasible, safe within the vehicle's flight envelope, and collision-free at the same time. The optimal trajectory is continuously updated in real time by the numerical optimization solver, Nonlinear Trajectory Generation (NTG), which is a direct solver based on the spline approximation of trajectory for dynamically flat systems. In fact, the overall approach of this thesis to finding the optimal trajectory is similar to the model predictive control (MPC) or the receding horizon control (RHC), except that this thesis followed a two-layer design; thus, the optimal solution works as a guidance command to be followed by the controller of the vehicle. The framework is implemented in a real-time simulation environment, the Georgia Tech UAV Simulation Tool (GUST), and integrated in the onboard software of the rotary-wing UAV test-bed at Georgia Tech. Initially, the 2D vertical avoidance capability of real obstacles was tested in flight. Then the flight test evaluations were extended to the benchmark tests for 3D avoidance capability over the virtual obstacles, and finally it was demonstrated on real obstacles located at the McKenna MOUT site in Fort Benning, Georgia. Simulations and flight test evaluations demonstrate the feasibility of the developed framework for UAV applications involving low-altitude flight in an urban area.