Challenging science requirements and complex space missions are driving the need for fast and robust space trajectory design and simulation tools. The main aim of this thesis is to develop new and improved high performance algorithms and solution techniques for commonly encountered problems in astrodynamics. Five major problems are considered and their state-of-the art algorithms are systematically improved. Theoretical and methodological improvements are combined with modern computational techniques, resulting in increased algorithm robustness and faster runtime performance. The five selected problems are 1) Multiple revolution Lambert problem, 2) High-fidelity geopotential (gravity field) computation, 3) Ephemeris computation, 4) Fast and accurate sensitivity computation, and 5) High-fidelity multiple spacecraft simulation. The work being presented enjoys applications in a variety of fields like preliminary mission design, high-fidelity trajectory simulation, orbit estimation and numerical optimization. Other fields like space and environmental science to chemical and electrical engineering also stand to benefit.

Baigiamajame magistro darbe nagrinėjamas šešiakojo roboto judėjimas. Pateikiami vienos kojos atvirkštinės kinematikos uždavinio sprendimai Denavito ir Hartenbergo bei geometriniu metodais. Analizuojamas vienos kojos trajektorijos sudarymo metodas ir pateikiams jos aprašymo būdas. Pateikiami galimi trajektorijų pavyzdžiai. Sudaroma trikojės roboto eisenos seka bei diagrama. Darbe pateikiamas roboto valdymo algoritmas ir valdymo programa, atsižvelgiant į apibrėžtus variklių valdymo kriterijus. Eksperimentiškai tiriamas roboto judėjimas lygiu paviršiumi taikant trikoję eiseną. Pagal rezultatus koreguojama eisena. Atliekami trajektorijos pakartojimo tikslumo bandymai. Įvertinus rezultatus pateikiamos baigiamojo darbo išvados ir pasiūlymai. / Hexapod robot locomotion is analyzed in this paper. Inverse kinematics solutions are proposed for one leg using Denavit-Hartenberg and geometric methods. Trajectory forming for one leg is analyzed and solution for delineating trajectory is introduced. Possible leg trajectory examples are presented. Tripod gait sequence and diagram is designed for robot. Work presents robot control algorithm and program according to motor control parameters. Robot locomotion over regular terrain using tripod gait is tested. Gait then is corrected according to test results. Tests are made for trajectory repeating accuracy. Conclusions and solutions are made according to results.

<p>This dissertation presents a novel distributed optimal control (DOC) problem formulation that is applicable to multiscale dynamical systems comprised of numerous interacting systems, or agents, that together give rise to coherent macroscopic behaviors, or coarse dynamics, that can be modeled by partial differential equations (PDEs) on larger spatial and time scales. The DOC methodology seeks to obtain optimal agent state and control trajectories by representing the system's performance as an integral cost function of the macroscopic state, which is optimized subject to the agents' dynamics. The macroscopic state is identified as a time-varying probability density function to which the states of the individual agents can be mapped via a restriction operator. Optimality conditions for the DOC problem are derived analytically, and the optimal trajectories of the macroscopic state and control are computed using direct and indirect optimization algorithms. Feedback microscopic control laws are then derived from the optimal macroscopic description using a potential function approach.</p><p>The DOC approach is demonstrated numerically through benchmark multi-agent trajectory optimization problems, where large systems of agents were given the objectives of traveling to goal state distributions, avoiding obstacles, maintaining formations, and minimizing energy consumption through control. Comparisons are provided between the direct and indirect optimization techniques, as well as existing methods from the literature, and a computational complexity analysis is presented. The methodology is also applied to a track coverage optimization problem for the control of distributed networks of mobile omnidirectional sensors, where the sensors move to maximize the probability of track detection of a known distribution of mobile targets traversing a region of interest (ROI). Through extensive simulations, DOC is shown to outperform several existing sensor deployment and control strategies. Furthermore, the computation required by the DOC algorithm is proven to be far reduced compared to that of classical, direct optimal control algorithms.</p> / Dissertation

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<p>The missed-thrust problem is a modern challenge in the field of mission design. While some methods exist to quantify its effects, there still exists room for improvement for algorithms which can fully anticipate and plan for a realistic set of missed-thrust events. The present work investigates the use of machine learning techniques to provide a robust controller for a low-thrust spacecraft. The spacecraft’s thrust vector is provided by a neural network controller which guides the spacecraft to the target along a trajectory that is robust to missed thrust, and the controller does not need to re-optimize any trajectories if it veers off its nominal course. The algorithms used to train the controller to account for missed thrust are supervised learning and neuroevolution. Supervised learning entails showing a neural network many examples of what inputs and outputs should look like, with the network learning over time to duplicate the patterns it has seen. Neuroevolution involves testing many neural networks on a problem, and using the principles of biological evolution and survival of the fittest to produce increasingly competitive networks. Preliminary results show that a controller designed with these methods provides mixed results, but performance can be greatly boosted if the controller’s output is used as an initial guess for an optimizer. With an optimizer, the success rate ranges from around 60% to 96% depending on the problem.</p> <p><br></p> <p>Additionally, this work conducts an analysis of a novel hyperbolic rendezvous strategy which was originally conceived by Dr. Buzz Aldrin. Instead of rendezvousing on the outbound leg of a hyperbolic orbit (traveling away from Earth), the spacecraft performs a rendezvous while on the inbound leg (traveling towards Earth). This allows for a relatively low Delta-v abort option for the spacecraft to return to Earth if a problem arose during rendezvous. Previous work that studied hyperbolic rendezvous has always assumed rendezvous on the outbound leg because the total Delta-v required (total propellant required) for the insertion alone is minimal with this strategy. However, I show that when an abort maneuver is taken into consideration, inserting on the inbound leg is both lower Delta-v overall, and also provides an abort window which is up to a full day longer.</p>

This paper will investigate the development of a landing footprint for a re-entry vehicle. Vehicles can re-enter the atmosphere with a range of orientations, velocities and flight path angles. The central question is whether a vehicle with any combination of these states can be brought to an acceptable landing condition at a particular landing site and with a particular landing speed. To aide in this investigation several models must be implemented, including that of the atmosphere, the vehicles, the Earth, and the aerodynamics. A detailed analysis of the aerodynamic model will be treated, and the equations of motion subject to these aerodynamic laws will then be compared to results from existing atmospheric reentry software. The principles of optimization will then be employed to generate the footprint of landable states, based on maximum and minimum possible downrange distances, for two vehicle concepts.

Applying reinforcement learning to control systems enables the use of machine learning to develop elegant and efficient control laws. Coupled with the representational power of neural networks, reinforcement learning algorithms can learn complex policies that can be difficult to emulate using traditional control system design approaches. In this thesis, three different model-free reinforcement learning algorithms, including Monte Carlo Control, REINFORCE with baseline, and Guided Policy Search are compared in simulated, continuous action-space environments. The results show that the Guided Policy Search algorithm is able to learn a desired control policy much faster than the other algorithms. In the inverted pendulum system, it learns an effective policy up to three times faster than the other algorithms. In the cartpole system, it learns an effective policy up to nearly fifteen times faster than the other algorithms.

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There is a need for a fuel-optimal required time of arrival (RTA) mode for aircraft flight management systems capable of enabling controlled time of arrival functionality in the presence of wind speed forecast uncertainty. A computationally tractable two-stage stochastic algorithm utilizing a data-driven, location-specific forecast uncertainty model to generate forecast uncertainty scenarios is proposed as a solution. Three years of Aircraft Communications Addressing and Reporting Systems (ACARS) wind speed reports are used in conjunction with corresponding wind speed forecasts from the Rapid Update Cycle (RUC) forecast product to construct an inhomogeneous Markov model quantifying forecast uncertainty characteristics along specific route through the national airspace system. The forecast uncertainty modeling methodology addresses previously unanswered questions regarding the regional uncertainty characteristics of the RUC model, and realizations of the model demonstrate a clear tendency of the RUC product to be positively biased along routes following the normal contours of the jet stream. A two-stage stochastic algorithm is then developed to calculate the fuel optimal stage one cruise speed given a required time of arrival at a destination waypoint and wind forecast uncertainty scenarios generated using the inhomogeneous Markov model. The algorithm utilizes a quadratic approximation of aircraft fuel flow rate as a function of cruising Mach number to quickly search for the fuel-minimum stage one cruise speed while keeping computational footprint small and ensuring RTA adherence. Compared to standard approaches to the problem utilizing large scale linear programming approximations, the algorithm performs significantly better from a computational complexity standpoint, providing solutions in fractional power time while maintaining computational tractability in on-board systems.

This dissertation progressively addresses research problems related to the trajectory optimization for fuel cell powered UAVs, from propulsion system model development, to optimal trajectory analyses and optimal trajectory applications. A dynamic model of a fuel cell powered UAV propulsion system is derived by combining a fuel cell system dynamic model, an electric motor dynamic model, and a propeller performance model. The influence of the fuel cell system dynamics on the optimal trajectories of a fuel cell powered UAV is investigated in two phases. In the first phase, the optimal trajectories of a fuel cell powered configuration and that of a conventional gas powered configuration are compared for point-to-point trajectory optimization problems with different performance index functions. In the second phase, the influence of the fuel cell system parameters on the optimal fuel consumption cost of the minimum fuel point-to-point optimal trajectories is investigated. This dissertation also presents two applications for the minimum fuel point-to-point optimal trajectories of a fuel cell powered UAV: three-dimensional minimum fuel route planning and path generation, and fuel cell system size optimization with respect to a UAV mission.