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Reconfiguration and Recovery of Formation Flying Spacecraft in Eccentric OrbitsRoscoe, Christopher William Thomas 22 September 2009 (has links)
The problem of reference trajectory reconfiguration and long-term uncontrolled recovery of a formation of spacecraft is considered in an eccentric orbit under the influence of the J2 perturbation. Reference trajectories considered are the Projected Circular Orbit, Along-Track Orbit, and their eccentric modifications. Reconfiguration is accomplished using two, finite-pulse thrusts, modeled as impulses. The state transition matrix (STM) is calculated by four methods: (i) analytically from the Hill-Clohessy-Wiltshire equations, (ii) numerical integration using a fourth-order Runge-Kutta method, (iii) from the fundamental matrix of the linearized equations of motion, and (iv) computing the STM for the relative mean orbital elements, the geometric method. Only the geometric method takes into account J2, and it is shown to perform the transfers most accurately of all the methods. The methods are also applied to the reconfiguration maneuvers of the University of Toronto's CanX 4/5 formation flying mission.
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Reconfiguration and Recovery of Formation Flying Spacecraft in Eccentric OrbitsRoscoe, Christopher William Thomas 22 September 2009 (has links)
The problem of reference trajectory reconfiguration and long-term uncontrolled recovery of a formation of spacecraft is considered in an eccentric orbit under the influence of the J2 perturbation. Reference trajectories considered are the Projected Circular Orbit, Along-Track Orbit, and their eccentric modifications. Reconfiguration is accomplished using two, finite-pulse thrusts, modeled as impulses. The state transition matrix (STM) is calculated by four methods: (i) analytically from the Hill-Clohessy-Wiltshire equations, (ii) numerical integration using a fourth-order Runge-Kutta method, (iii) from the fundamental matrix of the linearized equations of motion, and (iv) computing the STM for the relative mean orbital elements, the geometric method. Only the geometric method takes into account J2, and it is shown to perform the transfers most accurately of all the methods. The methods are also applied to the reconfiguration maneuvers of the University of Toronto's CanX 4/5 formation flying mission.
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Automatic algorithm for accurate numerical gradient calculation in general and complex spacecraft trajectoriesRestrepo, Ricardo Leon 21 February 2012 (has links)
An automatic algorithm for accurate numerical gradient calculations has been developed. The algorithm is based on both finite differences and Chebyshev interpolation approximations. The novelty of the method is an automated tuning of the step size perturbation required for both methods. This automation guaranties the best possible solution using these approaches without the requirement of user inputs. The algorithm treats the functions as a black box, which makes it extremely useful when general and complex problems are considered. This is the case of spacecraft trajectory design problems and complex optimization systems. An efficient procedure for the automatic implementation is presented. Several examples based on an Earth-Moon free return trajectory are presented to validate and demonstrate the accuracy of the method. A state transition matrix (STM) procedure is developed as a reference for the validation of the method. / text
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A Comparative Study of Estimation Models for Satellite Relative MotionDesai, Uri 02 October 2013 (has links)
The problem of relative spacecraft motion estimation is considered with application to various reference and relative orbits. Mean circular and elliptic orbits are analyzed, with relative orbits ranging in size from 1 km to 10 km. Estimators are built for three propagation models: (i) Gim-Alfriend State Transition Matrix, (ii) the J2-Linearized Equations of Motion for Circular Orbits, and (iii) the Clohessy-Wiltshire Equations of Motion. Two alternative models were developed in an attempt to ac- count for unmodeled nonlinearities: (i) Biased Clohessy-Whiltshire Equations, and (ii) J2 -Linearized State Transition Matrix. Two estimation techniques are presented in an attempt to explore and determine which propagation model minimizes the error residual: the linear Kalman filter is presented under the assumption of vector based, GPS-type measurements; the extended Kalman filter is analyzed assuming angle-range, optical-type measurements. Sampling time is varied to look at the effect of measurement frequency. It is assumed that the orbit of one of the satellites, the chief, is known reasonably well.
This work showed that the error residuals from the state estimates were minimized when the propagation technique utilized was the Gim-Alfriend State Transition Matrix. This supports conclusions that are obtained outside of the estimation problem. Additionally, the error residuals obtained when the propagation technique was the Clohessy-Wiltshire Equations is comparable to the more complicated models. Unmodeled nonlinearities affect the magnitude of the error residuals. As expected, the Gim-Alfriend STM comes closest to the truth; for smaller eccentricities (0.005), the Clohessy-Wiltshire EOM show minor deviations from the truth. As the eccentricity increases, the linear models begin to diverge greatly from the true response. The additional two models (the biased CW equations, and the linear STM) show decent performance under specific conditions. The former accounts for some of the unaccounted for nonlinearities. The latter exhibits comparable performance to the Gim-Alfrien STM for circular reference orbits. However, in each case, as the nonlinearity of the problem increases, the accuracy of the model decreases.
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New methods for estimation, modeling and validation of dynamical systems using automatic differentiationGriffith, Daniel Todd 17 February 2005 (has links)
The main objective of this work is to demonstrate some new computational methods
for estimation, optimization and modeling of dynamical systems that use automatic
differentiation. Particular focus will be upon dynamical systems arising in Aerospace
Engineering. Automatic differentiation is a recursive computational algorithm, which
enables computation of analytically rigorous partial derivatives of any user-specified
function. All associated computations occur, in the background without user
intervention, as the name implies. The computational methods of this dissertation are
enabled by a new automatic differentiation tool, OCEA (Object oriented Coordinate
Embedding Method). OCEA has been recently developed and makes possible efficient
computation and evaluation of partial derivatives with minimal user coding. The key
results in this dissertation details the use of OCEA through a number of computational
studies in estimation and dynamical modeling.
Several prototype problems are studied in order to evaluate judicious ways to use
OCEA. Additionally, new solution methods are introduced in order to ascertain the
extended capability of this new computational tool. Computational tradeoffs are studied
in detail by looking at a number of different applications in the areas of estimation,
dynamical system modeling, and validation of solution accuracy for complex dynamical
systems. The results of these computational studies provide new insights and indicate
the future potential of OCEA in its further development.
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