Browsing by Subject "Trajectory"
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Item A critical evaluation of modern low-thrust, feedback-driven spacecraft control laws(2012-12) Hatten, Noble Ariel; Ocampo, Cesar; Akella, MaruthiLow-thrust spacecraft trajectory optimization is often a difficult and time-consuming process. One alternative is to instead use a closed-loop, feedback-driven control law, which calculates the control using knowledge of only the current state and target state, and does not require the solution of a nonlinear optimization problem or system of nonlinear equations. Though generally suboptimal, such control laws are attractive because of the ease and speed with which they may be implemented and used to calculate feasible low-thrust maneuvers. This thesis presents the theoretical foundations for seven modern low-thrust control laws based on control law "blending" and Lyapunov control theory for a particle spacecraft operating in an inverse-square gravitational field. The control laws are evaluated critically to determine those that present the best combinations of thoroughness of method and minimization of user input required. The three control laws judged to exhibit the most favorable characteristics are then compared quantitatively through three numerical simulations. The simulations demonstrate the effectiveness of feedback-driven control laws, but also reveal several situations in which the control laws may perform poorly or break down altogether due to either theoretical shortcomings or numerical difficulties. The causes and effects of these issues are explained, and methods of handling them are proposed, implemented, and evaluated. Various opportunities for further work in the area are also described.Item Designing a laboratory model test program for developing a new offshore anchor(2015-05) Huang, Yunhan; Gilbert, Robert B. (Robert Bruce), 1965-; Rathje, Ellen MThe Flying Wing Anchor (patent pending) is a new anchor concept that combines the features of dynamically penetrating anchors, drag embedment anchors, and plate anchors. To study and optimize the behavior of the new anchor, this study developed a simplified predictive model and a new data acquisition system for performing physical model tests. The simplified predictive model couples a limit-equilibrium-based model for the anchor line and a plasticity-based model for the anchor to predict the embedment trajectory and holding capacity of the new anchor. The new data acquisition system is used to record data from sensors and control the movement of an electric motor. The system was developed by LabVIEW and demonstrated with a model test. The following major conclusions are drawn from this work about the behavior of this anchor concept in clay: (1) The pitch angle at the initiation of dive can be optimized to achieve the maximum dive depth and ultimate holding capacity. (2) The maximum depth of the dive is not strongly dependent on the undrained shear strength of the soil, while the ultimate holding capacity is proportional to the undrained shear strength of the soil at the maximum dive depth. (3) A smaller diameter of the line makes the anchor dive deeper and increases the ultimate capacity. (4) A deeper initial embedment depth after free fall makes the anchor dive deeper and increases the ultimate capacity. (5) A series of model tests to calibrate the simplified predictive model for the performance of the anchor should consist of varying the thickness of the line, the depth of initial embedment, the pitch angle at the initiation of dive, and the profile of undrained shear strength versus depth. It is recommended that model tests be conducted using the guidance presented in this thesis.Item High Resolution Study of Micro-Meter Particle Detachment and Resuspension on Different Surfaces(2012-08-16) Kassab, Asmaa 1983-In an effort to understand the resuspension phenomena, interactions of spherical micro-meter particles (glass beads (GB) and Stainless steel (SS)) were investigated experimentally on different surfaces (glass, ceramic, hardwood, metal and chemical agent resistant coated metal (CARC)). Particles were deposited on the lower surface of a 10 cm square wind tunnel by gravitational settling. Air flows were imposed from an open entrance at average velocities up to 16 m/s. Individual particle trajectories obtained by high-speed imaging reveal three different types of motion: rolling/bouncing, immediate liftoff and complex motion. Surface roughness significantly affects the particle initial motion prior to liftoff. The majority of particle trajectories from the glass substrate were parallel to the surface with complex motion, covering 25% of the total distance traveled in rolling/bouncing motion before liftoff. Hardwood substrates took the longest time for initial particle movement (t >1 s) causing a more rapid liftoff. The ceramic substrate showed the most rolling/bouncing motion, for 80% of the particles. Additionally, single layer detachment showed that the detachment percentage initially follow an exponentially increasing trend for a period of ~ 1 s, followed by a plateau phase for a period of 5 s. Changing velocity, substrate and particle size significantly affects GB particle detachment. Furthermore, detachment from the metal substrate was consistently higher than the CARC substrates. However, particle density is not a significant difference in the bigger particle size studied. Initial 3-D particle tracking showed that particles seem to travel in a constant angle to the left rather than going straight in the flow direction. A detachment mode model showed that the detachment by direct liftoff required a much higher speed than rolling motion with a minimum of 14 m/s for both GB70 and SS70 on glass and metal surface, and the velocity increased to 21 m/s for the smaller particle. Incorporating the different types of particle motion prior to liftoff into resuspension models, and how their relative contributions change with different particle and substrate materials, can potentially yield improved predictive capabilities.Item Initial guess and optimization strategies for multi-body space trajectories with application to free return trajectories to near-Earth asteroids(2014-08) Bradley, Nicholas Ethan; Russell, Ryan Paul, 1976-; Ocampo, CesarThis concept of calculating, optimizing, and utilizing a trajectory known as a ``Free Return Trajectory" to facilitate spacecraft rendezvous with Near-Earth Asteroids is presented in this dissertation. A Free Return Trajectory may be defined as a trajectory that begins and ends near the same point, relative to some central body, without performing any deterministic velocity maneuvers (i.e., no maneuvers are planned in a theoretical sense for the nominal mission to proceed). Free Return Trajectories have been utilized previously for other purposes in astrodynamics, but they have not been previously applied to the problem of Near-Earth Asteroid rendezvous. Presented here is a series of descriptions, algorithms, and results related to trajectory initial guess calculation and optimal trajectory convergence. First, Earth-centered Free Return Trajectories are described in a general manner, and these trajectories are classified into several families based on common characteristics. Next, these trajectories are used to automatically generate initial conditions in the three-body problem for the purpose of Near-Earth Asteroid rendezvous. For several bodies of interest, example initial conditions are automatically generated, and are subsequently converged, resulting in feasible, locally-optimal, round-trip trajectories to Near-Earth Asteroids utilizing Free Return Trajectories. Subsequently, a study is performed on using an unpowered flyby of the Moon to lower the overall DV cost for a nominal round-trip voyage to a Near-Earth Asteroid. Using the Moon is shown to appreciably decrease the overall mission cost. In creating the formulation and algorithms for the Lunar flyby problem, an initial guess routine for generic planetary and lunar flyby tours was developed. This continuation algorithm is presented next, and details a novel process by which ballistic trajectories in a simplistic two-body force model may be iteratively converged in progressively more realistic dynamical models until a final converged ballistic trajectory is found in a full-ephemeris, full-dynamics model. This procedure is useful for constructing interplanetary transfers and moon tours in a realistic dynamical framework; an interplanetary and an inter-moon example are both shown. To summarize, the material in this dissertation consists of: novel algorithms to compute Free Return Trajectories, and application of the concept to Near-Earth Asteroid rendezvous; demonstration of cost-savings by using a Lunar flyby; and a novel routine to transfer trajectories from a simplistic model to a more realistic dynamical representation.Item Patched conic interplanetary trajectory design tool(2011-12) Brennan, Martin James; Fowler, Wallace T.; Ocampo, CesarOne of the most important aspects of preliminary interplanetary mission planning entails designing a trajectory that delivers a spacecraft to the required destinations and accomplishes all the objectives. The design tool described in this thesis allows an investigator to explore various interplanetary trajectories quickly and easily. The design tool employs the patched conic method to determine heliocentric and planetocentric trajectory information. An existing Lambert Targeting routine and other common algorithms are utilized in conjunction with the design tool’s specialized code to formulate an entire trajectory from Earth departure to arrival at the destination. The tool includes many options for the investigator to accurately configure the desired trajectory, including planetary gravity assists, deep space maneuvers, and various departure and arrival conditions. The trajectory design tool is coded in MATLAB, which provides access to three dimensional plotting options and user adaptability. The design tool also incorporates powerful MATLAB optimization functions that adjust trajectory characteristics to find a configuration that yields the minimum spacecraft propellant in the form of change in velocity.Item Preliminary design of spacecraft trajectories for missions to outer planets and small bodies(2015-08) Lantukh, Demyan Vasilyevich; Russell, Ryan Paul, 1976-; Fowler, Wallace; Bettadpur, Srinivas; Guo, Yanping; Broschart, StephenMultiple gravity assist (MGA) spacecraft trajectories can be difficult to find, an intractable problem to solve completely. However, these trajectories have enormous benefits for missions to challenging destinations such as outer planets and primitive bodies. Techniques are presented to aid in solving this problem with a global search tool and additional investigation into one particular proximity operations option is discussed. Explore is a global grid-search MGA trajectory pathsolving tool. An efficient sequential tree search eliminates v∞ discontinuities and prunes trajectories. Performance indices may be applied to further prune the search, with multiple objectives handled by allowing these indices to change between trajectory segments and by pruning with a Pareto-optimality ranking. The MGA search is extended to include deep space maneuvers (DSM), v∞ leveraging transfers (VILT) and low-thrust (LT) transfers. In addition, rendezvous or nπ sequences can patch the transfers together, enabling automatic augmentation of the MGA sequence. Details of VILT segments and nπ sequences are presented: A boundaryvalue problem (BVP) VILT formulation using a one-dimensional root-solve enables inclusion of an efficient class of maneuvers with runtime comparable to solving ballistic transfers. Importantly, the BVP VILT also allows the calculation of velocity-aligned apsidal maneuvers (VAM), including inter-body transfers and orbit insertion maneuvers. A method for automated inclusion of nπ transfers such as resonant returns and back-flip trajectories is introduced: a BVP is posed on the v∞ sphere and solved with one or more nπ transfers – which may additionally fulfill specified science objectives. The nπ sequence BVP is implemented within the broader search, combining nπ and other transfers in the same trajectory. To aid proximity operations around small bodies, analytical methods are used to investigate stability regions in the presence of significant solar radiation pressure (SRP) and body oblateness perturbations. The interactions of these perturbations allow for heliotropic orbits, a stable family of low-altitude orbits investigated in detail. A novel constrained double-averaging technique analytically determines inclined heliotropic orbits. This type of knowledge is uniquely valuable for small body missions where SRP and irregular body shape are very important and where target selection is often a part of the mission design.Item Preliminary interplanetary trajectory design tools using ballistic and powered gravity assists(2015-08) Brennan, Martin James; Fowler, Wallace T.; Russell, Ryan; Bettadpur, Srinivas; Lightsey, E G; Olsen, CarriePreliminary interplanetary trajectory designs frequently use simplified two-body orbital mechanics and linked conics methodology to model the complex trajectories in multi-body systems. Incorporating gravity assists provides highly efficient interplanetary trajectories, enabling otherwise infeasible spacecraft missions. Future missions may employ powered gravity assists, using a propulsive maneuver during the flyby, improving the overall trajectory performance. This dissertation provides a complete description and analysis of a new interplanetary trajectory design tool known as TRACT (TRAjectory Configuration Tool). TRACT is capable of modeling complex interplanetary trajectories, including multiple ballistic and/or powered gravity assists, deep space maneuvers, parking orbits, and other common maneuvers. TRACT utilizes an adaptable architecture of modular boundary value problem (BVP) algorithms for all trajectory segments. A bi-level optimization scheme is employed to reduce the number of optimization variables, simplifying the user provided trajectory information. The standardized optimization parameter set allows for easy use of TRACT with a variety of optimization algorithms and mission constraints. The dissertation also details new research in powered gravity assists. A review of literature on optimal powered gravity assists is presented, where many optimal solutions found are infeasible for realistic spacecraft missions. The need was identified for a mission feasible optimal powered gravity assist algorithm using only a single impulsive maneuver. The solution space was analyzed and a complete characterization was developed for solution types of the optimal single-impulse powered gravity assist. Using newfound solution space characteristics, an efficient and reliable optimal single-impulse powered gravity assist BVP algorithm was formulated. The mission constraints were strictly enforced, such as maintaining the closest approach above a minimum radius and below a maximum radius. An extension of the optimal powered gravity assist research is the development of a gravity assist BVP algorithm that utilizes an asymptote ΔV correction maneuver to produce ballistic gravity assist trajectory solutions. The efficient algorithm is tested with real interplanetary mission trajectory parameters and successfully converges upon ballistic gravity assists with improved performance compared to traditional methods. A hybrid approach is also presented, using the asymptote maneuver algorithm together with traditional gravity assist constraints to reach ballistic trajectory solutions more reliably, while improving computational performance.Item Simulation of windborne debris trajectories(2005-08) Lin, Ning; Letchford, Christopher W.; Chen, XinzhongWindborne debris is possibly the major cause of building damage and destruction in strong wind events such as hurricanes and tornadoes. It has been long recognized that fast-flying debris can penetrate building envelopes, inducing internal pressurization and doubling the net loading on roofs, side walls, and leeward walls. Consequently, failed roofing structures, damaged wall cladding panels, and broken glass become debris sources, threatening downwind areas. Knowledge of debris aerodynamics is necessary for proper estimation of debris trajectory and for establishment of rational debris impact criteria. This research aims to investigate the aerodynamics of flying debris through simulating debris trajectories. Extensive wind-tunnel tests on 3D (compact-like), 2D (plate-like), and 1D (rod-like) debris are carried out in the Texas Tech University wind tunnel. The simulation procedure is introduced. Full-scale simulation is explored, employing a C-130 Hercules aircraft to generate strong winds. Three categories of parameters affecting debris trajectories are investigated: wind field, debris properties, and debris initial support. It is determined that although many parameters influence debris trajectory in the vertical direction, the Tachikawa parameter (1983) governs the horizontal trajectory of debris. Aerodynamic functions for debris horizontal trajectory are established based on both experimental data and theoretical equations of debris motion. These functions can be used to predict debris horizontal speed (at a given flight distance) and flight distance (for a given flight time). The application of these functions in debris impact criteria is discussed. The incorporation of these functions into debris risk analysis is recommended for the further research.Item Simulation of windborne debris trajectories(Texas Tech University, 2005-08) Lin, Ning; Letchford, Christopher W.; Chen, XinzhongWindborne debris is possibly the major cause of building damage and destruction in strong wind events such as hurricanes and tornadoes. It has been long recognized that fast-flying debris can penetrate building envelopes, inducing internal pressurization and doubling the net loading on roofs, side walls, and leeward walls. Consequently, failed roofing structures, damaged wall cladding panels, and broken glass become debris sources, threatening downwind areas. Knowledge of debris aerodynamics is necessary for proper estimation of debris trajectory and for establishment of rational debris impact criteria. This research aims to investigate the aerodynamics of flying debris through simulating debris trajectories. Extensive wind-tunnel tests on 3D (compact-like), 2D (plate-like), and 1D (rod-like) debris are carried out in the Texas Tech University wind tunnel. The simulation procedure is introduced. Full-scale simulation is explored, employing a C-130 Hercules aircraft to generate strong winds. Three categories of parameters affecting debris trajectories are investigated: wind field, debris properties, and debris initial support. It is determined that although many parameters influence debris trajectory in the vertical direction, the Tachikawa parameter (1983) governs the horizontal trajectory of debris. Aerodynamic functions for debris horizontal trajectory are established based on both experimental data and theoretical equations of debris motion. These functions can be used to predict debris horizontal speed (at a given flight distance) and flight distance (for a given flight time). The application of these functions in debris impact criteria is discussed. The incorporation of these functions into debris risk analysis is recommended for the further research.Item Space object translational and rotational state prediction and sensitivity calculation(2016-12) Hatten, Noble Ariel; Russell, Ryan Paul, 1976-; Akella, Maruthi R; Bettadpur, Srinivas V; Jones, Brandon A; Weisman, Ryan MWhile computing power has grown monumentally during the space age, the demands of astrodynamics applications have more than kept pace. Resources are taxed by the ever-growing number of Earth-orbiting space objects (SOs) that must be tracked to maintain space situational awareness (SSA) and by increasingly popular but computationally expensive tools like Monte Carlo techniques and stochastic optimization algorithms. In this dissertation, methods are presented to improve the accuracy, efficiency, and utility of SO state prediction and sensitivity calculation algorithms. The dynamical model of the low Earth orbit regime is addressed through the introduction of an upgraded Harris-Priester atmospheric density model, which introduces a smooth polynomial dependency on solar flux. Additional modifications eliminate singularities and provide smooth partial derivatives of the density with respect to SO state, time, and solar conditions. The numerical solution of the equations of motion derived from dynamics models is also addressed, with particular emphasis placed on six-degree-of-freedom (6DOF) state prediction. Implicit Runge-Kutta (IRK) methods are applied to the 6DOF problem, and customizations, including variable-fidelity dynamics models and parallelization, are introduced to maximize efficiency and take advantage of modern computing architectures. Sensitivity calculation -- a necessity for SSA and other applications -- via RK methods is also examined. Linear algebraic systems for first- and second-order state transition matrix calculation are derived by directly differentiating either the first- or second-order form of the RK update equations. This approach significantly reduces the required number of Jacobian and Hessian evaluations compared to the ubiquitous augmented state vector approach for IRK methods, which can result in more efficient calculations. Parallelization is once again leveraged to reduce the runtime of IRK methods. Finally, a hybrid special perturbation/general perturbation (SP/GP) technique is introduced to address the notoriously slow speed of fully coupled 6DOF state prediction. The hybrid method uses a GP rotational state prediction to provide low-fidelity attitude information for a high-fidelity 3DOF SP routine. This strategy allows for the calculation of body forces using arbitrary shape models without adding attitude to the propagated state or taking the small step sizes often required by full 6DOF propagation. The attitude approximation is obtained from a Lie-Deprit perturbation result previously applied to SOs in circular orbits subject to gravity-gradient torque and extended here to SOs in elliptical orbits. The hybrid method is shown to produce a meaningful middle ground between 3DOF SP and 6DOF SP methods in the accuracy vs. efficiency space.Item Trajectory Simulations of H2O, O3, and CO in the Upper Troposphere and Lower Stratosphere (UTLS)(2014-05-05) Wang, TaoThe purpose of this work is to simulate water vapor (H2O), ozone (O3), and carbon monoxide (CO) in the upper troposphere and lower stratosphere (UTLS) using a domain-filling, forward trajectory model. The influx of H2O to the UTLS is largely determined by the large-scale troposphere-to-stratosphere transport in the tropics, during which air is dehydrated across the cold tropical tropopause. In the domain-filling, forward trajectory model, trajectories are initialized in the upper troposphere, and the circulation is based on reanalysis wind fields. Along the trajectories, winds determine the pathways of parcels and temperature determines the H2O content through an idealized saturation calculation. Compared with the Aura Microwave Limb Sounder (MLS) measurements, this simple advection-condensation strategy yields reasonable results for H2O in the stratosphere in terms of both seasonal variability and vertical structures. The detailed global dehydration patterns are also revealed from this model and it improves our understanding of the H2O and its transport within the UTLS. Besides H2O, ozone (O3) and carbon monoxide (CO) are also important trace gases in the UTLS linked to circulation, transport and climate forcing (for O3). Combined with simple parameterization of chemical production and loss rates from the Whole Atmosphere Community Climate Model (WACCM), we also managed to simulate O3 and CO transport in the UTLS via this trajectory model. The trajectory modeled O3 and CO show good overall agreement with satellite observations from the MLS and the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS) in terms of spatial structure and seasonal variability. The trajectory model results also agree well with the Eulerian WACCM simulations. Analysis of the simulated tracers shows that seasonal variations in tropical upwelling exerts strong influence on O3 and CO in the tropical lower stratosphere, and the coupled seasonal cycles provide a useful test of the transport simulations. Interannual variations in the tracers are also closely coupled to changes in upwelling, and the trajectory model can accurately capture and explain observed changes. This demonstrates the importance of variability in tropical upwelling in forcing chemical changes in the tropical UTLS. Trajectory modeling of O3 and CO can provide useful tests for simplified understanding of transport and chemical processes in the UTLS, and provide complementary information to the H2O simulations, which are primarily constrained by tropopause temperatures. This model is easy to use, easy to diagnose, and the Lagrangian perspective makes it exceptionally useful in studying transport processes within the UTLS.