Lee, Sang Hyun (2015-05). Coverage Optimization Using Lattice Flower Constellations. Doctoral Dissertation. Thesis uri icon

abstract

  • Recently developed satellite systems require a group of satellites acting in concert with one another to meet mission objectives. Specifying a constellation by defining all the orbit elements for each satellite is complex, inconvenient, and computationally impossible for constellations with many satellites. There are many degrees of freedom in the parameters for constellations such as number of orbital planes, number of satellites in the orbital plane, orbital inclination and altitude. Therefore, an efficient way to design to a constellation is to adopt some orbital elements with common value and some other derived by algorithms and various algorithms have been proposed. Among them, the Lattice Flower Constellations theory is more suitable to optimization of constellation design because it is a minimum parameterization theory and because this design methodology contains most of the existing methodologies as subsets. The main contributions of this dissertation are 1) the development of an algorithm which provides uniform points on a sphere for fast evaluation of coverage fitness functions, 2) the presentation of a set of three non-classical constellation missions using Lattice Flower Constellations, and 3) the investigation of a new class of orbits, called "J2-propelled," and associated constellations which are particularly suitable in the three-dimensional lattice theory of flower constellations. For global coverage missions, fitness functions for constellation design are computed using globally distributed points. Most of the grid data sets are provided with a fixed step in latitude and longitude. Therefore, conventionally computed points are distributed with a fixed step in latitude and longitude. Since these are certainly not uniform distributions of points on the Earth, mainly due to the increase of point density at high latitude regions, converting these data into an "equivalent" distribution of points (with different weights) is needed. This will allow the data sets to be dramatically decreased to small amount data sets with appropriate values and, consequently, computational burden is then reduced using \equivalent" uniformly distributed points. For elliptical constellations, the Lattice Flower Constellations require nine design parameters of which six are integers. For circular constellations, there are five required design parameters of which three are integers. A general optimization technique implies finding the optimal values of these parameters. This dissertation introduces a general process to perform constellation optimization for any specific optimality definition, that is, for any specific space mission. To demonstrate the feasibility and the effectiveness of the proposed approach this optimization tool is applied to three distinct types of space missions: a) global radio occultation, b) interferometric imaging, and c) constrained communication missions. The results obtained validate the proposed methodology. A linear theory to design orbits and constellations where the Earth oblateness perturbation, the J2 perturbation, generates dynamics that are periodic in an inertial or in a rotating frame is presented. In J2-propelled orbits, the linear (secular) J2 effect is used instead of being fought to allow the satellites accessing specific 3-dimensional volumes around the Earth. The main motivation is to design space missions (satellites and constellations) able to measure physical quantities (e.g., magnetic or electric fields) in large space volumes by limiting the control costs to compensate the other gravitational and non-gravitational orbital perturbations only.
  • Recently developed satellite systems require a group of satellites acting in concert with one another to meet mission objectives. Specifying a constellation by defining all the orbit elements for each satellite is complex, inconvenient, and computationally impossible for constellations with many satellites. There are many degrees of freedom in the parameters for constellations such as number of orbital planes, number of satellites in the orbital plane, orbital inclination and altitude. Therefore, an efficient way to design to a constellation is to adopt some orbital elements with common value and some other derived by algorithms and various algorithms have been proposed. Among them, the Lattice Flower Constellations theory is more suitable to optimization of constellation design because it is a minimum parameterization theory and because this design methodology contains most of the existing methodologies as subsets.

    The main contributions of this dissertation are 1) the development of an algorithm which provides uniform points on a sphere for fast evaluation of coverage fitness functions, 2) the presentation of a set of three non-classical constellation missions using Lattice Flower Constellations, and 3) the investigation of a new class of orbits, called "J2-propelled," and associated constellations which are particularly suitable in the three-dimensional lattice theory of flower constellations.

    For global coverage missions, fitness functions for constellation design are computed using globally distributed points. Most of the grid data sets are provided with a fixed step in latitude and longitude. Therefore, conventionally computed points are distributed with a fixed step in latitude and longitude. Since these are certainly not uniform distributions of points on the Earth, mainly due to the increase of point density at high latitude regions, converting these data into an "equivalent" distribution of points (with different weights) is needed. This will allow the data sets to be dramatically decreased to small amount data sets with appropriate values and, consequently, computational burden is then reduced using equivalent" uniformly distributed points.

    For elliptical constellations, the Lattice Flower Constellations require nine design parameters of which six are integers. For circular constellations, there are five required design parameters of which three are integers. A general optimization technique implies finding the optimal values of these parameters. This dissertation introduces a general process to perform constellation optimization for any specific optimality definition, that is, for any specific space mission. To demonstrate the feasibility and the effectiveness of the proposed approach this optimization tool is applied to three distinct types of space missions: a) global radio occultation, b) interferometric imaging, and c) constrained communication missions. The results obtained validate the proposed methodology.

    A linear theory to design orbits and constellations where the Earth oblateness perturbation, the J2 perturbation, generates dynamics that are periodic in an inertial or in a rotating frame is presented. In J2-propelled orbits, the linear (secular) J2 effect is used instead of being fought to allow the satellites accessing specific 3-dimensional volumes around the Earth. The main motivation is to design space missions (satellites and constellations) able to measure physical quantities (e.g., magnetic or electric fields) in large space volumes by limiting the control costs to compensate the other gravitational and non-gravitational orbital perturbations only.

publication date

  • May 2015