The next generation of reusable launch vehicles (RLVs) require significant improvements in guidance methods in order to reduce cost, increase safety and flexibility, whilst allowing for possible autonomous operation. Research has focused on the ascent and hypersonic re-entry flight phases. This thesis presents a new method for trajectory design, optimisation and guidance of RLVs during the terminal area flight phases. The terminal area flight phase is the transitional phase from hypersonic re-entry to the approach and landing phase. The trajectory design, optimisation and guidance methods within this thesis are an evolution of previous work conducted on the ascent and re-entry flight phases of RLVs. The methods are modified to incorporate the terminal area flight phase through the adaption of the problem definition and the inclusion of the speed brake setting as a steering parameter. The methods discussed and developed in this thesis are different to previous methods for the terminal area flight phase as they encompass optimisation, trajectory design and guidance based on the definition of the steering parameters. The NLPQL nonlinear optimiser contained within the International Mathematics Standards Library (IMSL) is utilised for trajectory design and optimisation. Real-time vehicle guidance is achieved using the restoration steps of an accelerated Gradient Projection Algorithm (GPA). The methods used are evaluated in a three degrees of freedom (3DOF) simulation environment. To properly evaluate the programs and gain a better understanding of the terminal area flight phase, two different vehicles are utilised within this study. These vehicles are the German sub-orbital Hopper concept vehicle, a previously proposed replacement for the Ariane series of launch vehicles and the recently cancelled joint National Aeronautics and Space Administration (NASA) and Lockheed Martin sub-orbital test bed vehicle, X-33. The two vehicles each have a terminal area flight phase, but their mission profiles and vehicle characteristics are significantly different. The Hopper vehicle is a winged re-entry vehicle, whereas the X-33 vehicle is a lifting body. The trajectory design method takes into account the initial and final conditions, in-flight restrictions such as dynamic pressure and vehicle loads as well as safety margins. The designed trajectories are evaluated to analyse the terminal area flight phase and to assist in the development of the guidance program. The guidance method is evaluated utilising an program consisting of two parts, a real world simulator with high order models and a representation of the on-board guidance computer, the predictor, which uses low order models for computational efficiency. The guidance method is evaluated against a variety of off-nominal conditions to account for dispersions within the high order real world models and common errors experienced by re-entry vehicles. These off-nominal conditions include atmospheric disturbances, winds, aerodynamic, mass, navigation, steering and initial condition errors. The results of this study include a detailed analysis of the terminal area flight phase highlighting the major influences for vehicle and trajectory design. The study also confirms the applicability of the non-linear programming method utilising the vehicle steering parameters as a viable option for trajectory design and guidance. A comparison to other available results highlights the strengths and weaknesses of the proposed method. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1282342 / Thesis (Ph.D.)--School of Mechanical Engineering, 2007.

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

The increasing market of small and affordable space systems requires fast and reliablelaunch capabilities to cover the current and future demand. This project aims to studyand implement guidance and control schemes for vertical ascent and descent phases ofa reusable launcher. Specifically, the thesis focuses on developing and applying ModelPredictive Control (MPC) and optimisation techniques to several kino-dynamic modelsof rockets. Moreover, the classical MPC method has been modified to include a decreasingfactor for the horizon used, enhancing the performance of the guidance and control.Multiple scenarios of vertical launch, landing and full fligth guidance on Earth and Mars,along with Monte Carlo analysis, were carried out to demonstrate the robustness of thealgorithm against different initial conditions. The results were promising and invite tofurther research.

Solutions to trajectory optimization problems are carried out by the direct and indirect methods. Under broad heading of these methods, numerous algorithms such as collocation, direct, indirect and multiple shooting methods have been developed and reported in the literature. Each of these algorithms has certain advantages and limitations. For example, direct shooting technique is not suitable when the number of nonlinear programming variables is large. Indirect shooting method requires analytical derivatives of the control and co-states function and a poorly guessed initial condition can result in numerical unstable values of the adjoint variable. Multiple shooting techniques can alleviate some of these difficulties by breaking down the trajectory into several segments that help in reducing the non-linearity effects of early control on later parts of the trajectory. However, multiple shooting methods then have to handle more number of variables and constraints to satisfy the defects at the segment joints. The sie of the nonlinear programming problem in the collocation method is also large and proper locations of grid points are necessary to satisfy all the path constraints. Stochastic methods such as Genetic algorithms, on the other hand, also require large number of function evaluations before convergence. To overcome some of the limitations of the conventional methods, improved solution techniques are developed. Three improved methods are proposed for the solution of trajectory optimization problems. They are • a genetic algorithm employing dominance and diploidy concept. • a collocation method using chebyshev polynomials , and • a hybrid method that combines collocation and direct shooting technique A conventional binary-coded genetic algorithm uses a haploid chromosome, where a single string contains all the variable information in the coded from. A diploid, as the name suggests, uses pair of chromosomes to store the same characteristic feature. The diploid genetic algorithm uses a dominant map for decoding genotype into a stable, consistent phenotype. In dominance, one allele takes precedence over another. Diploidy and dominance helps in retaining the previous best solution discovered and shields them from harmful selection in a changing environment. Hence, diploid and dominance affect a king of long-term memory in the genetic algorithm. They allow alternate solutions to co-exist. One solution is expressed and the other is held in abeyance. In the improved diploid genetic algorithm, dominant and recessive genes are defined based on the fitness evaluation of each string. The genotype of fittest string is declared as the dominant map. The dominant map is dynamic in nature as it is replaced with a better individual in future generations. The concept of diploidy and dominance in the improved method mimics closer to the principles used in human genetics as compared to any such algorithms reported in the literature. It is observed that the improved diploid genetic algorithm is able to locate the optima for a given trajectory optimization problem with 10% lower computational time as compared to the haploid genetic algorithm. A parameter optimization problem arising from an optimal control problem where states and control are approximated by piecewise Chebyshev polynomials is well known. These polynomials are more accurate than the interpolating segments involving equal spaced data. In the collocation method involving Chebyshev polynomials, derivatives of two neighboring polynomials are matched with the dynamics at the nodal points. This leads to a large number of equality constraints in the optimization problem. In the improved method, derivative of the polynomial is also matched with the dynamics at the center of segments. Though is appears the problem size is merely increased, the additional computations improve the accuracy of the polynomial for a larger segment. The implicit integration step size is enhanced and overall size of the problem is brought down to one-fourth of the problem size defined with a conventional collocation method using Chebyshev polynomials. Hybrid method uses both collocation and direct shooting techniques. Advantages of both the methods are combined to give more synergy. Collocation method is used in the starting phase of the hybrid method. The disadvantage of standalone collocation method is that tuning of grid points is required to satisfy the path constraints. Nevertheless, collocation method does give a good guess required for the terminal phase of the hybrid method, which uses a direct shooting approach. Results show nearly 30% reduction in computation time for the hybrid approach as compared to a method in which direct shooting alone is used, for the same initial guess of control. The solutions obtained from the three improved methods are compared with an indirect method. The indirect method requires derivations of the control and adjoint equations, which are difficult and problem specific. Due to sensitivity of the costate variables, it is often difficult to find a solution through the indirect method. Nevertheless, these methods do provide an accurate result, which defines a benchmark for comparing the solutions obtained through the improved methods. Trajectory design and optimization of a RLV(Reusable Launch Vehicle) Demonstrator mission is considered as a test problem for evaluating the performance of the improved methods. The optimization problem is difficult than a conventional launch vehicle trajectory optimization problem because of the following two reasons. • aerodynamic lift forces in the RLV add one more dimension to the already complex launch vehicle optimization problem. • as RLV performs a sub orbital flight, the ascent phase trajectory influences the re-entry trajectory. Both the ascent and re-entry optimization problem of the RLV mission is addressed. It is observed that the hybrid method gives accurate results with least computational effort, as compared with other improved techniques for the trajectory optimization problem of RLV during its ascent flight. Hybrid method is then successfully used during the re-entry phase and in designing the feasible optimal trajectories under the dispersion conditions. Analytical solutions obtained from literature are used to compare the optimized trajectory during the re-entry phase. Trajectory optimization studies are also carried out for the off-nominal performances. Being a thrusting phase, the ascent trajectory is subjected to significant deviations, mainly arising out of solid booster performance dispersions. The performance index during rhe ascent phase is modified in a novel way for handling dispersions. It minimizes the state errors in a least square sense, defined at the burnout conditions ensure possibilities of safe re-entry trajectories. The optimal trajectories under dispersion conditions serve as a benchmark for validating the closed-loop guidance algorithm that is developed for the ascent phase flight. Finally, an on-line trajectory command-reshaping algorithm is developed which meets the flight objectives under the dispersion conditions. The guidance algorithm uses a pre-computed trajectory database along with some real-time measured parameters in generating the optimal steering profiles. The flight objectives are met under the dispersion conditions and the guidance generated steering profiles matches closely with the optimal trajectories.