Aerospace Engineering Commons^™

Optimization Of Active Rendezvous Trajectories By Genetic Algorithms, Marie Emmanuelle Ricour

Master's Theses - Daytona Beach

Trajectory optimization is and will remain a hot topic in the engineering field. Because analytical or exact solutions are often difficult and sometimes impossible to compute, there is a need for alternative and efficient methods. UnderWater Vehicles (UWV) trajectories and rendezvous trajectories of continuous low-thrust spacecraft are examined. One of the methods to solve such problems is the Genetic Algorithm (GA) method. In this work, a GA has been developed using Matlab®. It treats possible solutions to the studied problems as individuals and eventually converges to an optimal or near optimal solution. Genetic Algorithms have been used previously to solve …

Spacecraft Trajectory Design For Short Duration Near Earth Asteroid Missions, Synthia Mirlin Findlay

Mechanical & Aerospace Engineering Theses & Dissertations

Design of orbital trajectories using patched conic approximation methodology for short duration missions to newly detected, incoming near Earth asteroids, which are on close approach trajectories with Earth, is the focus of this thesis. The primary purpose for such missions is two fold. First, near Earth asteroids provide unique mission opportunities for solar system science where the celestial body of interest transits to Earth proximity and is studied in situ by probes having short duration trajectories, rather than sending long distance probes to the celestial body. Second, improved characterization of asteroid properties, compositions, and orbital states for reduction of uncertainties …

Maneuver Estimation Model For Geostationary Orbit Determination, Brian J. Hirsch

Theses and Dissertations

As an increasing number of geostationary satellites fill a limited number of orbital slots, collocation of satellites leads to a risk of close approach or misidentification. The ability to detect maneuvers made by these satellites using optical observations can help to prevent these problems. Such a model has already been created and tested using data from the Air Force Maui Optical and Supercomputing site. The goal of this research was to create a more robust model which would reduce the amount of data needed to make accurate maneuver estimations. The Clohessy-Wiltshire equations were used to model the relative motion of …

Characterizing And Controlling The Effects Of Differential Drag On Satellite Formations, James T. Wedekind

Theses and Dissertations

The ability to fly satellites in close formations represents a capability that could revolutionize the way satellite missions are designed in the future. This study examines three of the primary formation flying designs and characterizes the effects that an anomalous satellite with a slightly different cross-sectional area would have on the stability of the formation. Following the characterization of these effects, a controller is implemented to mitigate the cross-sectional area differences between the satellites. The results show that, with the addition of a straightforward controller, small cross-sectional area differences can be mitigated and corrected such that the satellites will remain …

The Effects Of Using Solar Radiation Pressure To Alleviate Fuel Requirements For Orbit Changing And Maintenance Of The Dscs Ii F-13 Satellite, Jody A. Paris

Theses and Dissertations

Orbit disposal and maintenance of aging satellites has become a significant concern over the past few years, as the increasing number of orbiting objects threatens to limit the launching of future satellites. Many of the satellites currently in orbit, however, were not built with disposal considerations. The DSCS II series was launched into orbit beginning in the 1970s, and many satellites are now without the fuel required to conventionally transition to a sanctioned disposal orbit. In GEO orbit the largest non-gravitational perturbation is solar radiation pressure. By adjusting the attitude of a satellite with a controller to maximize the perturbing …

Covariance Estimation And Autocorrelation Of Norad Two-Line Element Sets, Victor P. Osweiler

Theses and Dissertations

This thesis investigates NORAD two-line element sets (TLE) containing satellite mean orbital elements for the purpose of estimating a covariance matrix and formulating an autocorrelation relationship. Orbit propagation is performed using Simplified General Perturbations Number 4 (SGP4) analytical model as implemented within Satellite Took Kit. For a given satellite, TLEs from a span of two weeks are used to calculate position and velocity differences of estimated state vectors in order to characterize their variance behavior and compute a covariance matrix for the most recent TLE. Six satellites and eight time spans are investigated, with all state vector differences evaluated in …

Optimal Coverage Of Theater Targets With Small Satellite Constellations, Axel Rendon

Theses and Dissertations

The daylight passes of a low-Earth orbit satellite over a targeted latitude and longitude are optimized by varying the inclination and eccentricity of an orbit at different altitudes. This investigation extends the work by Emery et al, in which the optimal Right Ascension of the Ascending Node was determined for a circular, matched inclination orbit. The optimal values were determined by a numerical research method based on Emery et al's Matlab program. Results indicate that small increases in inclination raise the number of daylight passes up to 33%. These optimal inclinations depend on the satellite semi-major axis. Eccentricity increases also …

Maneuver Estimation Model For Relative Orbit Determination, Tara R. Storch

Theses and Dissertations

While the use of relative orbit determination has reduced the difficulties inherent in tracking geosynchronous satellites that are in close proximity, the problem is often compounded by stationkeeping operations or unexpected maneuvers. If a maneuver occurs, observations will no longer fit predicted data, increasing the risk of misidentification and cross-tagging. The goal of this research was to develop a model that will estimate the magnitude, direction, and time of a suspected maneuver performed by a collocated satellite in geosynchronous orbit. Relative motion was modelled using Hill's equations, and least squares estimation was employed to create both a linear non-maneuver model …

Orbit Estimation Algorithms For A Microsatellite Rendezvous With A Non-Cooperative Target, John P. Heslin

Theses and Dissertations

This study investigated the minimum requirements to establish a satellite tracking system architecture for a microsatellite to rendezvous with a non-cooperative target satellite. A prototype optical tracking system was reviewed with emphasis on a proposed tactical employment that could be used by technologically unsophisticated state or non-state adversaries. With the tracking system architecture selected, simulated tracking data was processed with a Non-Linear Least Squares batch orbit estimation algorithm and a Bayes sequential orbit determination filter to update the target satellite's state vector.

Maneuver Design For Fast Satellite Circumnavigation, Stanley D. Straight

Theses and Dissertations

The feasibility of satellite operations in close proximity to a reference satellite is of interest for both civilian and military applications. One such operation is circular circumnavigation in a time period less than the orbital period of the reference satellite. This thesis investigates a guidance scheme for such maneuvers involving impulsive burns at specific points within a specified toroidal region centered on the circular-orbiting reference satellite. Two analytical methods for determining the magnitude and direction of the impulses are demonstrated. These methods are then used as initial estimates in an optimization scheme to produce the minimum total required impulse.

Optimal Constellation Design For Orbital Munitions Delivery System, Jason Anderson

Theses and Dissertations

Rather than delivering conventional munitions through the airspace of uncooperative nations, a constellation of space-stored weapons could potentially target any point on the Earth and arrive within the time it takes to de-orbit and re-enter through the atmosphere. The research involves applying the dynamics of atmospheric re-entry to a Common Aero Vehicle (CAV) and defining a footprint of attainable touchdown points. The footprint is moved forward to create a swath representing all the possible touchdown points in a 90 minute window. A nominal constellation of CAVs is established using a streets of coverage technique, and both analytic studies and numeric …

Hybrid Control Strategies For Rapid, Large Angle Satellite Slew Maneuvers, David B. French

Theses and Dissertations

This research investigated hybrid control strategies for rapid satellite pointing. First, a detailed computer simulation model of AFIT's SIMSAT satellite simulator was constructed. Control strategies were developed to enable the system to perform large-angle, 3-axis slewing maneuvers using a combination of both thrusters and reaction wheels. To handle the non-linear model, a State Dependent Riccati Equation controller was programmed and successfully controlled the computer-modeled satellite for any given slewing maneuver. A simpler PD controller was then programmed and demonstrated on the computer simulation of SIMSAT, using a combination of thruster and reaction wheel control inputs for large-angle single axis maneuvers …

Orbit Determination For A Microsatellite Rendezvous With A Non-Cooperative Target, Brian L. Foster

Theses and Dissertations

This study investigated the minimum requirements to establish a satellite tracking system architecture for a hostile "parasitic microsatellite" to rendezvous with a larger, non-cooperative target satellite. Four types of tracking systems and their capabilities were reviewed with emphasis on "low-technology" level and/or mobile systems which could be used by technologically unsophisticated state or non-state adversaries. With the tracking system architecture selected, simulated tracking data was processed with a non- linear least squares orbit determination filter to determine and/or update the target satellite's state vector.

Mean Performance Optimization Of An Orbiting Distributed Aperture By Warped Aperture Image Plane Comparisons, Timothy W. Parker

Theses and Dissertations

This work models the aggregate performance of satellite receiver formations functioning as orbiting interferometers as compared to filled apertures of similar geometries. These models facilitate selecting initial conditions for formations such that their control-free dynamics yield interferometry performance with minimal errors as compared to the filled apertures. The solution method draws on the dynamic models of an orbiting planar satellite formation to define the size and shape of a reference aperture and to define the degrees of freedom for the formation members. The paths of formation elements yield geometries for which the aggregate performance of the array of discrete receivers …

Estimation Of Relative Satellite Formation Elements In Near Circular Orbits, Ralph E. Bordner Iii

Theses and Dissertations

Precise relative position determination of satellite formation elements in near circular orbits is the focus of this thesis. A Bayes filter is used for the estimator with the dynamics solution obtained by solving the time periodic, linearized system via Floquet theory. This approach is similar to that of the traditional Clohessy-Wiltshire treatment, however much more of the system's behavior is retained by using a linear, time periodic system. The dynamics model includes all zonal harmonics of the Earth as well as sectoral, tesseral, and air drag perturbations. The filter algorithm was fed three types of simulated measurements: relative Carrier-Phases Differential …

Solar Radiation Pressure Modeling Issues For High Altitude Satellites, Dayne G. Cook

Theses and Dissertations

Current satellite orbit propagation techniques employ a solar radiation pressure model that makes simplifying assumptions concerning the satellite and its orbital geometry. Solar radiation pressure, a non-gravitational perturbation, significantly affects satellite motion at high altitudes. The model currently in use by the Air Force for orbit determination includes the following assumptions: a constant cross-sectional area projected to the Sun, cylindrical Earth shadow for eclipse, and specular reflection. In reality, the satellite's cross-sectional area with respect to the Sun constantly changes, the Earth's shadow is conical, and reflection is both specular and diffuse. Additionally, the solar flux received at the Earth …

Navigation Of Satellite Clusters, Jeffrey S. Davis

Theses and Dissertations

The relative position determination of a cluster of satellites in near circular orbit was investigated in previous thesis work. The purpose of this thesis is to extend the concept to cover absolute position determination. A Bayes filter is used for the estimator with dynamics based on the two-body problem extended to account for J2 perturbations. Measurements consist of combining Global Positioning System (GPS) data for each satellite and range data between the satellites. Simulations were conducted investigating the accuracy obtainable when combining the measurements for input into the filter. Performance results consist of comparing the magnitude of the time error …

Orbit Estimation Using Track Compression And Least Squares Differential Correction, Vincent J. Chioma

Theses and Dissertations

This thesis develops two methods of compressing a track of radar observations of a satellite into a single state vector and associated covariance matrix, and a method of estimating orbits using results from multiple tracks. The track compression uses least squares differential correction to determine a state vector at the central observation time. The resulting state vectors and covariance matrices are then used to estimate the satellite's orbit, also using least squares differential correction. Numerical integration using two-body, J₂ and an atmospheric drag model is used to represent the dynamics. This orbit estimation produces a state vector which includes …

Optimal Non-Coplanar Launch To Quick Rendezvous, Gregory B. Sears

Theses and Dissertations

The purpose of this study was to determine the feasibility of launching a Delta Clipper-like vehicle on an optimal, non-coplanar trajectory to rendezvous with an earth orbiting object in one orbit or less. The focus of the research was to determine what such a trajectory would look like, and to determine the cost, in payload mass, of flying such a trajectory. A model for the ascent trajectory was developed using the dynamics equations of motion, an atmosphere model, and an aerodynamic model for the DC-Y concept vehicle. A boundary value problem was posed and solved for a coplanar rendezvous. The …

Relative Equilibria Of A Rigid Satellite In A Central Gravitational Field, Jeffrey A. Beck

Theses and Dissertations

We apply noncanonical Hamiltonian methods to examine relative equilibria of a rigid body in a central gravitational field. These equilibria correspond to fixed points of a reduced set of equations expressed in a rotating frame and are representative of an orbiting satellite with fixed attitude relative to an observer rotating at the orbital rate. Our objective is to clarify the relationship between the classical approximation and a recent noncanonical Hamiltonian treatment. In contrast to the classical approximation, the orbital and attitude equations of motion for the noncanonical system remain coupled and the general solution is a circular orbit for which …

Investigation Of An Alternative Technique For Measuring Turbulence In The Upper Atmosphere, Charles Patrick Leonard

Mechanical & Aerospace Engineering Theses & Dissertations

The capability of the Global Positioning System (GPS) as a tool for measuring turbulence in the upper atmosphere is presented. By studying experimental ground and flight test data, a methodology for extracting macroscale turbulence data from in situ measurements was developed.

A description of the GPS using a single nonprecision receiver is followed by data from ground and flight testing. Ground testing focused on determining the smallest turbulent scales discernible by the GPS receiver. Testing was also undertaken to compare turbulence data from the GPS with that of a simultaneously operating constant-temperature hot-wire anemometer, the conventional tool for making turbulence …

Optimal Continuous-Thrust Orbit Transfers, James D. Thorne

Theses and Dissertations

The minimum time orbital transfer problem for spacecraft with steerable, continuous thrust of constant magnitude may be solved using Euler-Lagrange theory, which leads to the optimal control law in terms of Lagrange multipliers. However, the initial values of the Lagrange multipliers are not known from the orbital boundary conditions. Using analytical and empirical results, the optimal initial costates are modeled as functions of the problem parameters which are the initial thrust acceleration, A, and the final orbit radius, H, in canonical units. For circle to circle, coplanar orbit transfers, these approximate initial costate models lead to convergence in the shooting …

Analysis Of Gravity-Gradient Satellite Attitude Inversion, Jules-Francois D. Desamours

Theses and Dissertations

The purpose of this research is to understand and describe the process by which the 1986 Polar BEAR gravity- gradient research satellite of John Hopkins University/Applied Physics Laboratory achieved an orbital attitude correction (re-inversion) from an inverted orientation through the utilization of its momentum wheel. Understanding this process provides an analytical foundation from which a universal attitude inversion process for other gravity-gradient satellites with similar anomalous motions may be sought and developed. The equations of motion for a gravity-gradient satellite with a momentum wheel are derived and implemented in FORTRAN for simulation of the dynamics of the spacecraft. Several re-inversion …

Full Lyapunov Exponent Placement In Reentry Trajectories, Michael H. Platt

Theses and Dissertations

This study investigated the ability to control the chaotic reentry of a Delta-Clipper like vehicle by setting the values of initial arid final principal dynamical directions as well as the Lyapunov exponents. A model of the original controlled reentry vehicle was created through the use of the equations of motion in conjunction with an atmospheric model. A modified linear quadratic regulator allowed the set up of a boundary value problem which specified the Lyapunov exponents and determined the gain matrix as a function of time. The gain matrix can eventually be used in the control system of the vehicle.

Optimization Of A Nutation Damper Attached To A Spin-Stabilized Satellite, Brady P. Hauboldt

Theses and Dissertations

This study uses linearized equations of motion for a rigid body with an attached spring-mass-damper to maximize the decay rate of a satellite's coning motion. An analysis of the numerical eigenvalues is presented which leads to an optimal relationship between relevant parameters: damper placement, spring constant, damping coefficient, system moments of inertia, and damper mass fraction. The coupled system's eigenvalues do not provide truly critical damping, thus the real eigenvalue parts are minimized in order to achieve damping which requires the minimum amount of time. A comparison between this optimal design method and a classical method concludes a noticeable improvement …

Compression Of A Radar Track Of A Near Earth Satellite Into An Earth Centered Inertial State Vector Using Least Squares Differential Correction, Garry L. Hall

Theses and Dissertations

This study investigated the use of a least squares differential corrector to compress the information contained in a single radar track of a Near Earth satellite into a six element, Earth Centered Inertial state vector and associated covariance matrix. Observations were generated using a truth model program based on two body, J2 geopotential, and atmospheric drag dynamics and consisted of simulated range, azimuth and elevation. Random Gaussian noise was added to the data to simulate real world random errors. The orbital dynamics used in the estimator consisted of two body and J2 geopotential effects which were approximated using a Taylor …

The Modal Solution To The Moon's Orbit Using Canonical Floquet Perturbation Theory, Kurt A. Vogel

Theses and Dissertations

Using the restricted three body problem, the equations of motion EOM and Hamiltonian are computed for the moons orbit in physical variables. A periodic orbit is found in the vicinity of the moons orbit, and classical Floquet theory is applied to the periodic orbit to give stability information and the complete solution to the equations of variation. Floquet theory also supplies a transformation from physical variables to modal variables. This transformation to modal variables is made canonical by constraining the initial transformation matrix to be symplectic. Actual lunar data is used to calculate the modes for the real moons orbit. …

An Approximate Solution For The Spinup Dynamics Of Near Axisymmetric Axial Gyrostats Using The Method Of Multiple Scales, Stewart J. Kowall

Theses and Dissertations

Approximate solutions for the spinup of a near axisymmetric gyrostat are derived using the straightforward expansion method and the method of multiple scales. Two method of multiple scale solutions are presented. The first is derived using cartesian coordinates while the second is derived using cylindrical coordinates. The multiple scales solutions are compared to numerically integrated results for oblate and prolate configurations. A comparison for flat spin recovery is also accomplished. Excellent results are obtained for oblate configurations. Trajectory separatrix crossings hindered the results for prolate configurations and flat spin recoveries.

Data Reduction With Least Squares Differential Correction Using Equinoctial Elements, Michael S. Wasson

Theses and Dissertations

This study investigates earth satellite orbit estimation on a track of range, azimuth, and elevation data from a single tracking station. The estimation routine is a least squares batch filter based solely on two-body orbital motion. Using equinoctial elements for the reference orbit avoids the numerical difficulties of the classical elements at eccentricities near zero and inclinations near zero or 90 degrees. Orbits for Mir, DMSP, Explorer, Cosmos, and GPS are investigated. The goal of this study is to reduce orbit information from observations (range, azimuth, and elevation) to an element set and a covariance matrix without considering perturbation effects. …

Canonical Floquet Perturbation Theory, David J. Pohlen

Theses and Dissertations

Classical Floquet theory is examined in order to generate a canonical transformation to modal variables for periodic system This transformation is considered canonical if the periodic matrix of eigenvectors is symplectic at the initial time. Approaches for symplectic normalization of the eigenvectors had to be examined for each of the different Poincare eigenvalue cases. Particular attention was required in the degenerate case, which depended on the solution of a generalized eigenvector. Transformation techniques to ensure real modal variables and real periodic eigenvectors were also needed. Periodic trajectories in the restricted three-body case were then evaluated using the canonical Floquet solution. …