Flower Constellations Research Articles

Method for Generating Closely Packed Orbital Shells and Orbital Capacity Implications

Shell-wise orbital coordination in low Earth orbit can improve space safety, simplify space traffic coordination and management, and optimize orbital capacity. This work describes two methods to generate 2D lattice flower constellations (2D-LFCs) that are defined with respect to either an arbitrary zonal, or zonal, sectoral, and tesseral Earth geopotential. By generating orbital shells that are periodic with respect to the Earth geopotential, it is possible to safely stack shells with vertical separation distances smaller than the osculating variation in semimajor axis and radial distance of each shell, or a corresponding Keplerian 2D-LFC propagated under an aspherical geopotential. These methods exploit previous work on constellations based on time distributions and designs of closed 2D-LFCs under arbitrary Earth geopotentials using repeating ground track orbits. Factors that influence the widths and shapes of these shells are identified. Additionally, simplified formulas for estimating shell geometry and thickness are presented. Based on these results, it is shown that geopotential-aware periodic orbital shells significantly increase the number of admissible orbital shells while preserving shell separation. Finally, this work shows that sequencing shells to group similar or ascending inclinations can further improve capacity versus arbitrary inclination ordering, particularly for smaller shell separation distances.

Orbital Tolerance and Intrinsic Orbital Capacity for Electric Propulsion Constellations

Large constellations are typically designed using sets of periodic orbits and satellite control boxes sized to ensure compatible phasing between coorbital constellation planes to prevent conjunction events. This work investigates how the control action for orbit maintenance influences feasible intrashell and intershell distances in a satellite constellation. Two-dimensional lattice flower constellations are simulated in an environment inclusive of orbital perturbations, with onboard sensors and an electric propulsion system constituting the satellite guidance, navigation, and control system. An analysis to define estimates for minimum separation distances is performed as a function of control, propulsion, orbit, environmental, and spacecraft characteristics. An estimate of the intrinsic (geometric) orbital capacity is proposed, based on current and advanced technologies, in order to quantify the number of admissible spacecraft and orbital shells in a selected altitude range. Simulation results are used to improve the fidelity of intrinsic orbital capacity estimates and to understand factors that influence the number of admissible satellite locations in low Earth orbit.

Optimal design and reconfiguration of flower constellations: An application to global disaster management

Unpredictable natural disasters are inevitable, and creating a communication satellite constellation that can continuously cover the entire Earth during disasters seems practically impossible. On the other hand, building up dedicated constellations associated with disaster areas does not make sense, either technically or temporally. This paper presents an optimal approach to providing timely and continuous communication coverage by optimal design and reconfiguration of flower constellations (FCs). In particular, the proposed approach addresses the optimal design of an FC and its formation by optimal satellites’ transfer from the last constellation and the remaining satellites from the previous reconfigurations. The multi-objective evolutionary algorithm (NSGA-II) is used to find optimal FC designs that minimize the height of perigee while simultaneously minimizing the number of satellites. In addition, the optimum assignment for transferring satellites to the designed FC is to minimize the total Δv for the reconfiguration by the particle swarm optimization (PSO) algorithm. In the end, the feasibility of the proposed approach is demonstrated by comparison optimal results.

Uniform Satellite Constellation Reconfiguration

This work focuses on the study of the reconfiguration strategies available for uniformly distributed satellite constellations and slotting architectures. Particularly, this paper deals with the cases of reducing, maintaining, and also increasing the number of available positions for satellites in a space structure, and takes into account the potential minimum distances between spacecraft in the configuration to assure the safety of the system. To that end, several approaches to solve the reconfiguration problem are presented based on the properties of 2D Lattice Flower Constellations and, more particularly, on the properties of uniformity and symmetries present in these uniform distributions.

Design of Constellations for GNSS Reflectometry Mission Using the Multiobjective Evolutionary Algorithms

In this simulation study, the operational GNSS satellites of Global Positioning System (GPS), Galileo, GLONASS, and BDS, which are currently in service, are used to transmit signals for GNSS Reflectometry (GNSS-R) measurement. LEO constellations composed of 8, 16 and 24 satellites and with two different patterns, the 2D-lattice flower constellation (2D-LFC) and the 3D-lattice flower constellation (3D-LFC), are designed considering the trade-off among three objectives, namely the visited coverage (<i>V C</i>), the revisited coverage (<i>RC</i>) and the total cost of the constellation. Two multi-objective evolution-ary algorithms (MOEAs), the non-dominated sorting genetic algorithm II (NSGA-II) and the multi-objective evolutionary algorithm based on decomposition (MOEA/D), are applied to solve this multi-objective optimization problem (MOP). The optimal constellations meeting the best trade-off for the three objectives are picked out, and the distributions of the reflected points observed by them are presented and compared. It is found that NSGA-II generally performs better with respect to the convergence and the diversity of the Pareto solutions. The optimal trade-off constellations are generally with inclinations of around 67&#x00B0; to 77&#x00B0; and orbital altitudes of nearly 1000 km. For certain number of satellites, the latitudinal and longitudinal distributions of the number of the reflected points observed by the optimal 2D-LFC and 3D-LFC are highly similar to each other. Moreover, with the resolution of 0.25&#x00B0;&#x00D7;0.25&#x00B0;, the VCs of the optimal 8-satellite and 16-satellite 3D-LFCs reach 58.30% and 79.59%, respectively, and the optimal 24-satellite 2D-LFC and 3D-LFC can achieve an average revisit time of about 11.0 h and 10.2 h, respectively.

Cost-Efficient LEO Navigation Augmentation Constellation Design under a Constrained Deployment Approach

The advantages of the Low Earth Orbit (LEO) satellite include low-latency communications, shorter positioning time, higher positioning accuracy, and lower launching, building, and maintenance costs. Thus, the introduction of LEO satellite constellation as a regional navigation augmentation system for the current navigation constellations is studied in this paper. To achieve the navigation performance requirement with the least system cost, a synthetic approach is presented to design and deploy a cost-efficient LEO navigation augmentation constellation over 108 key cities. To achieve lower construction costs, the constellation is designed to be deployed by constrained piggyback launches, which brings additional complexity to the constellation design. Two optimization models with discrete and continuous performance indices are established. They are solved by the genetic algorithm and differential evolution algorithm, and both Walker and Flower constellations are adopted. Results for 77 and 70 satellites are obtained. During the construction phase, a synthesis procedure containing five impulses is proposed by utilizing natural drift under J 2 perturbation. This work presents a method for designing the optimal LEO navigation constellation under a constraint deployment approach with the lowest construction cost and a strategy to deploy the constellation economically.

Efficient search of optimal Flower Constellations

We derive an analytical closed expression to compute the minimum distance (quantified by the angle of separation measured from the center of the Earth) between any two satellites located at the same altitude and in circular orbits. We also exploit several properties of Flower Constellations (FCs) that, combined with our formula for the distance, give an efficient method to compute the minimum angular distance between satellites, for all possible FCs with up to a given number of satellites.

2D Necklace Flower Constellations applied to Earth observation missions

This work focuses on the nominal design and later maintenance of satellite constellations based on the 2D Necklace Flower Constellations for their application in Earth observation missions. To that end, we introduce a generalization of the 2D Necklace Flower Constellations formulation to adapt the methodology to constellations whose satellites have different mission requirements, while still allowing to reduce the searching space in satellite constellation design. Moreover, this design is combined with its dual distribution in the Earth Centered–Earth Fixed reference frame to obtain additional information about the dynamic of the system, including the sub-satellite point revisiting time, or the relative to Earth distribution. This is used to optimize the constellation in terms of maximum uniformity of the distribution with respect to the Earth. Finally, a detailed example of application of this design methodology is presented, where a constellation based on satellites with different mission requirements is considered.

N-Dimensional congruent lattices using necklaces

This work introduces the n-dimensional congruent lattices using necklaces, a general methodology to generate uniform distributions in multidimensional modular spaces. The formulation presented in this manuscript constitutes the mathematical foundation of the most used satellite constellation designs, including Walker Constellations, and Lattice and Necklace Flower Constellations. These constellation design models are based on Number Theory and allow to obtain distributions that have some interesting properties of uniformity and large number of symmetries. This work includes the complete formulation of the methodology, proofs for existence and uniqueness of the distribution definitions, and several theorems that focus on the counting possibilities of design for the most common cases of study.

4D Lattice Flower Constellations

4D Lattice Flower Constellations is a new constellation design framework, based on the previous 2D and 3D Lattice theories of Flower Constellations, that focus on the generation of constellations whose satellites can have different semi-major axis and still present a constellation structure that is maintained during the dynamic of the system. This situation can arise when dealing with satellites with very different instruments, or when it is of interest to coordinate two different constellations. In that sense, 4D Lattice Flower Constellations constitutes the most general representation of the Flower Constellation formulation. In addition, the effects of the J2 perturbation are taken into account in order to generate distributions that maintain their initial design configuration under this perturbation for longer periods of time with a low fuel budget. Finally, examples of application are presented, showing the possibilities in satellite constellation design of this new approach.

Definition of Low Earth Orbit slotting architectures using 2D lattice flower constellations

This work proposes the use of 2D Lattice Flower Constellations (2D-LFCs) to facilitate the design of a Low Earth Orbit (LEO) slotting system to avoid collisions between compliant satellites and to optimize the available orbital volume. Specifically, this manuscript proposes the use of concentric orbital shells of admissible “slots” with stacked intersecting orbits that preserve a minimum separation distance between satellites at all times. The problem is formulated in mathematical terms and three approaches are explored: random constellations, single 2D-LFCs, and unions of 2D-LFCs. Each approach is evaluated in terms of several metrics including capacity, Earth coverage, orbits per shell, and symmetries. Additionally, a rough estimate for the capacity of LEO is generated, subject to certain minimum separation and station-keeping assumptions, and several trade-offs are identified to guide policy-makers interested in the adoption of a LEO slotting scheme for space traffic management.

Nominal definition of satellite constellations under the Earth gravitational potential

This work focuses on the definition of satellite constellations whose secular relative distributions are invariant under the perturbation produced by the Earth gravitational potential. This is done by defining the satellite distribution directly in the Earth-Centered–Earth-Fixed frame of reference and using the along-track time distances between satellites to define the satellite constellation configuration. In addition, in order to expand the possibilities of application of this design methodology, a general transformation between the formulations of Flower Constellations, Walker Constellations, and a relative to Earth formulation based on along-track and cross-track distances between satellites is obtained. This allows not only for a relation between these formulations, but also for the obtainment of the relative to Earth distribution of such constellations. Finally, an example of application of these methodologies is presented for a low Earth orbit.

On the Constellation Design of Multi-GNSS Reflectometry Mission Using the Particle Swarm Optimization Algorithm

Due to the great success of the CYclone Global Navigation Satellite System (CYGNSS) mission, the follow-on GNSS Reflectometry (GNSS-R) missions are being planned. In the perceivable future, signal sources for GNSS-R missions can originate from multiple global navigation satellite systems (GNSSs) including Global Positioning System (GPS), Galileo, GLONASS, and BeiDou. On the other hand, to facilitate the operational capability for sensing ocean, land, and ice features globally, multi-satellite low Earth orbit (LEO) constellations with global coverage and high spatio-temporal resolutions should be considered in the design of the follow-on GNSS-R constellation. In the present study, the particle swarm optimization (PSO) algorithm was applied to seek the optimal configuration parameters of 2D-lattice flower constellations (2D-LFCs) composed of 8, 24, 60, and 120 satellites, respectively, for global GNSS-R observations, and the fitness function was defined as the length of the time for the percentage coverage of the reflection observations reaches 90% of the globe. The configuration parameters for the optimal constellations are presented, and the performances of the optimal constellations for GNSS-R observations including the visited and the revisited coverages, and the spatial and temporal distributions of the reflections were further compared. Although the results showed that all four optimized constellations could observe GNSS reflections with proper temporal and spatial distributions, we recommend the optimal 24- and 60-satellite 2D-LFCs for future GNSS-R missions, taking into account both the performance and efficiency for the deployment of the GNSS-R missions.

Seeking Optimal GNSS Radio Occultation Constellations Using Evolutionary Algorithms

Given the great achievements of the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) mission in providing huge amount of GPS radio occultation (RO) data for weather forecasting, climate research, and ionosphere monitoring, further Global Navigation Satellite System (GNSS) RO missions are being followingly planned. Higher spatial and also temporal sampling rates of RO observations, achievable with higher number of GNSS/receiver satellites or optimization of the Low Earth Orbit (LEO) constellation, are being studied by high number of researches. The objective of this study is to design GNSS RO missions which provide multi-GNSS RO events (ROEs) with the optimal performance over the globe. The navigation signals from GPS, GLONASS, BDS, Galileo, and QZSS are exploited and two constellation patterns, the 2D-lattice flower constellation (2D-LFC) and the 3D-lattice flower constellation (3D-LFC), are used to develop the LEO constellations. To be more specific, two evolutionary algorithms, including the genetic algorithm (GA) and the particle swarm optimization (PSO) algorithm, are used for searching the optimal constellation parameters. The fitness function of the evolutionary algorithms takes into account the spatio-temporal sampling rate. The optimal RO constellations are obtained for which consisting of 6–12 LEO satellites. The optimality of the LEO constellations is evaluated in terms of the number of global ROEs observed during 24 h and the coefficient value of variation (COV) representing the uniformity of the point-to-point distributions of ROEs. It is found that for a certain number of LEO satellites, the PSO algorithm generally performs better than the GA, and the optimal 2D-LFC generally outperforms the optimal 3D-LFC with respect to the uniformity of the spatial and temporal distributions of ROEs.

Space-Enhanced Terrestrial Solar Power for Equatorial Regions

This Paper investigates the concept of solar mirrors in an Earth orbit to provide large-scale terrestrial equatorial solar farms with additional solar power during the hours of darkness. A flower constellation of mirrors is considered in highly eccentric orbits (semimajor ) in order to increase the time of visibility over the solar farms, and through this architecture, only two mirrors are needed to provide complete night coverage over three equatorial locations. Selecting the proper value for the orbit eccentricity, solar radiation pressure and Earth’s oblateness perturbations act on the mirrors so that the apsidal motion of the orbit due to these perturbations is synchronized with the apparent motion of the sun. Therefore, it can be guaranteed that the perigee always points toward the sun and that the mirrors orbit mostly above the night side of the Earth. With respect to geostationary orbit, the family of orbits considered in this Paper allows a passive means to overcome issues related to orbital perturbations. Moreover, because of the large slant range from geostationary orbits, a larger mirror is required to deliver the same energy that could be delivered from a lower orbit with a smaller mirror. As a result, a single antiheliotropic flower constellation composed of two mirrors of would be able to deliver energy in the range of 4.60–5.20 GW·h per day to solar farms on the equator. Finally, it is estimated that, deploying 90 of these constellations, the price of electricity could be reduced from 9.1 cents to 6 cents per .

Optimization of satellite constellation deployment strategy considering uncertain areas of interest

This paper presents an integrated framework to design a flexible multi-stage telecommunication satellite configuration deployment strategy considering the uncertainties in the evolution of the areas of interest over time. The constructed stochastic demand model considers multiple possible scenarios for the evolution of the areas of interest with probabilities based on the market share growth in each area. The optimization aims to find each stage's design with minimum expected lifecycle cost considering all possible scenarios. Each stage of the constellation, assumed to be Flower constellation with circular orbits, provides a regional coverage of the current area of interest as well as additional coverage for the potential future areas of interest. The proposed multi-stage satellite constellation enables the constellation designer to react flexibly and efficiently to the uncertain future expansion of the areas of interest. A case study reveals a reduction in the expected lifecycle cost for an optimized system compared with the all-in-single-stage system and global coverage constellation.

2D Necklace Flower Constellations

The 2D Necklace Flower Constellation theory is a new design framework based on the 2D Lattice Flower Constellations that allows to expand the possibilities of design while maintaining the number of satellites in the configuration. The methodology presented is a generalization of the 2D Lattice design, where the concept of necklace is introduced in the formulation. This allows to assess the problem of building a constellation in orbit, or the study of the reconfiguration possibilities in a constellation. Moreover, this work includes three counting theorems that allow to know beforehand the number of possible configurations that the theory can provide. This new formulation is especially suited for design and optimization techniques.

3-Dimensional Necklace Flower Constellations

A new approach in satellite constellation design is presented in this paper, taking as a base the 3D Lattice Flower Constellation Theory and introducing the necklace problem in its formulation. This creates a further generalization of the Flower Constellation Theory, increasing the possibilities of constellation distribution while maintaining the characteristic symmetries of the original theory in the design.

Establishing a Formation of Small Satellites in a Lunar Flower Constellation

The success of previous lunar science missions can be expanded upon by using a constellation of satellites to increase the lunar surface coverage. A constellation could also serve as a communications or GPS network for a lunar human base. Small-sats, deployed from a single mothercraft, are proposed to achieve a lunar constellation. The establishment of a single- and multi-petal constellation is investigated where the mothercraft does the primary deployment maneuvers. The constellation lifetime and closed-loop maintenance are addressed once higher order lunar gravity fields and Earth/solar perturbations are included.

Satellite constellation design for telecommunication in Antarctica

Summary This paper addresses the problem of designing a small satellite constellation suitable for communications in Antarctica. This study has been motivated by the increasing international interests in having permanent bases in Antarctica to perform experiments in physics, atmospheric sciences, geology, and biology to name a few key areas. The existing and planned scientific expeditions in Antarctica require continuous and reliable communication services, especially during emergencies. Geostationary Earth orbit satellites do not cover this high latitude adequately, and constellations using circular orbits would require too many satellites to provide continuous regional coverage, thus increasing cost prohibitively. A three-satellite constellation using elliptical orbits is proposed to address this issue. The critical inclination has been selected to predominantly keep the satellites over Antarctica, where the satellites will dwell most of the time. This configuration has been obtained by using the two-dimensional lattice flower constellation design theory: a minimum parameter design methodology that enforces all three satellites in the same trajectory as seen from the Earth rotating frame. This aspect provides the continuous coverage necessary for reliable communications using only a small number of satellites. Copyright © 2015 John Wiley & Sons, Ltd.