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Satellites’ full ground track (a) and close-up (b) for a solution in Case 12 (best 74% area coverage and 9 hours of ART). Red line: ground track of sat #1, pink line: ground track of sat #2, and blue line: ground track of sat #3. Pink triangle: area covered by sat #1 and red star: area covered by sat #2.
Source publication
This paper focuses on maximizing the percent coverage and minimizing the revisit time for a small satellite constellation with limited coverage. A target area represented by a polygon defined by grid points is chosen instead of using a target point only. The constellation consists of nonsymmetric and circular Low Earth Orbit (LEO) satellites. A glo...
Citations
... Ortore et al. [11] used the ground subsatellite trajectory analysis method to determine the satellites distribution on elliptic orbit plane and achieved a fixed revisit frequency for a specific region. Savitri et al. [12] used multiobjective genetic algorithm to optimize the orbit of asymmetric and circular low-orbit constellation, taking maximizing coverage and minimizing revisit time as the objectives. Xiangyue and others [13] designed a reconfigurable constellation for disaster monitoring; in the constellation, satellites could leap over disaster region by orbit maneuver. ...
The configuration optimization design of Low Earth Orbit observation mega constellation in complex space environment is a nonlinear problem that is difficult to solve analytically. In this paper, a constellation design method is proposed, considering satellite imaging width, formation flying of subgroup satellites, and global uniform coverage by payloads. Firstly, a configuration of satellites with the same subsatellite trajectory is proposed, and its orbital analytical expression under J2 perturbation is provided. Then, the relative motion feature points are extracted near the orbit of each satellite, and a group of uniform natural accompanying satellites are set to corresponding points. Afterwards, the orbit parameters of satellite and its companions are set as initial values, and the precise orbits under the High Precision Orbit Propagator model are solved in the neighborhood by using the Nondominated Sort Particle Swarm Optimization algorithm. Finally, the correctness of the configuration design method is verified by numerical simulation.
... In addressing the optimization problem, a genetic algorithm was utilized to minimize the objective function due to the high modality of the problem (i.e., many local minima with a large design space). The genetic algorithm has been widely used for various applications in orbital mechanics (e.g., [25][26][27][28][29][30][31][32]. Furthermore, a non-gradient based optimization (i.e., a golden section search) was used in a similar space-based solar power study [16], which investigated a comparable objective function for geometric efficiency optimization to the one used in this paper, but with a smaller design space (i.e., restricted to equatorial orbits and equatorial ground locations) [16]. ...
... Once a specific definition is determined, the problem becomes a multi-objective optimization problem over a space with both discrete and continuous variables. Multi-objective heuristic optimization algorithms have been applied to this constellation optimization problem including the following classes: evolutionary algorithms [5,[20][21][22][23][24][25][26] and ant colony optimization [27]. Evolutionary algorithms have several well studied algorithms with simple implementations for multi-objective optimizaton [28]. ...
... Evolutionary algorithms have several well studied algorithms with simple implementations for multi-objective optimizaton [28]. The evolutionary algorithm class can further be broken down into generic evolutionary algorithms [5,20,25] and genetic algorithms [20,[22][23][24]26]. Genetic algorithms provide the benefit of directly handling mixed variable types [20], yet they do not necessarily handle constraints well. ...
... For the purposes of this paper a square area of operation with legs of 100 km has been selected. This area was discretized into sets of latitude and longitude pairs for the calculation of specific metrics [5,22,24,37]. In stage two, there are multiple bases across the surface with each base having a 100 km square area of operation. ...
Cislunar operations are expected to rise dramatically within the next decade, requiring a comparable increase in PNT and communications services. However, current PNT systems are at capacity and need to be augmented to serve a cislunar space domain, specifically in the form of novel cislunar PNT architectures. This paper studies the problem of the deployment of PNT and communications satellites, specifically, the problem of deployment strategies spanning multiple stages over extended periods of time. A set of stage definitions will be determined along with areas of potential user activity. A novel application of the hidden gene genetic algorithm to the constellation optimization problem is presented. A design space exploration is presented with comparisons of circular and elliptical constellations. Optimization results from the first stage are also provided. It is shown that acceptable performance can be achieved with a low number of deployed satellites and that strong trade-offs exist between performance and stability.
... When compared to a single satellite, a constellation provides several better points Savitri et al. (2017), although, to describe the path of the constellation are necessary six additional parameters per satellite, eccentricity (e), semi-major axis (a), inclination (i), Longitude of the ascending node (Ω), argument of periapsis (ω) and the true anomaly (θ) Curtis (2015). There are different types of constellations, such as Delta patterns Walker (1970), Rosette constellations Ballard (1980) and Streets of Coverage Lueders and Ginsberg (1974) and It is possible to compare the efficiency between each one of the constellation types considering the need for site-specific orbits of interest, the choice of a launch vehicle, the robustness of the satellites, the need for communication between satellites, and the need to mitigate collisions with space debris. ...
... This inability to make maneuvers indicates the importance of choosing the best orbit. Based on the literature review, diverse authors conducted studies on the design and optimization of nanosatellites constellation systems (Abdelkhalik and Gad, 2011;Lewis, 2021;Marsili-Libelli and Alba, 2000;Melaku and Kim, 2023;Meziane-Tani et al., 2016;Savitri et al., 2017). For the problem of optimization, the best approach is using the evolutionary algorithm, which is highly inspired by the work of Charles Darwin, the Darwinian natural selection theory for evolution Darwin (2004). ...
... The optimization problems are defined as presented in Tab. 1, where t com is the communication time t f light is the satellite flight time, i is the orbit inclination, SM A is the semi-major axis and Raan is the right ascension of the ascending node. In order to solve the optimization problem, it was chosen the genetic algorithm as solver (Confessore et al., 2001;Goldberg and Goldberg, 1989;Marsili-Libelli and Alba, 2000;Melaku and Kim, 2023;Meziane-Tani et al., 2016;Petrovski et al., 1998;Savitri et al., 2017;Thengade and Dondal, 2012). This algorithm is stochastic, uses the natural phenomena of genetic inheritance and Darwinism for survival, and borrows the vocabulary from genetics. ...
The Brazilian Data Collection System (SBCD) comprises geostationary satellites and a series of devices and ground stations available to operate with such space systems in order to acquire data, mostly environmental, and feed climate and defense analysis in the Brazilian territory. However, the high cost of large satellite projects prevents the large-scale production of these systems, which, together with the restrictions on the availability of mostly national communication protocols, shows the tendency of the SBCD to become obsolete in the coming decades. Under this scenario, the Cata-rina Constellation project was created, to develop a constellation of nanosatellites that could be added to the SBCD, to lower the cost of replacing space systems, foster the Santa Catarina space industry and strengthen the relationship of the so-called triple helix, formed by industry, government and universities. However, for such a constellation to efficiently replace possible geostationary satellites, mission requirements must be fulfilled considering crucial design and operation variables for the constellation's operation, such as the number of satellites, chosen orbit parameters and launch time windows. In order to optimize communication between the satellites of Catarina Constellation's Fleet A and its designated earth stations, initially the ground station of Natal/RN and the Data Collection Platform based on Florianópolis/SC, a genetic algorithm orbit optimization was conducted for a CubeSat. The inclinations of 30, 50 and 98 degrees were considered as cases of study and the optimization was performed using inclination and Satellite altitude as design variables. The genetic algorithm uses the roulette selection algorithm with single-point crossover and mutation to define the offspring and elitism to ensure that the best solution was kept during the generations, in order to decrease the computational cost, the evolutionary differentiation strategy was used. The first results show that when compared the communication time for inclinations between 30 • and 130 • the fraction of communication, the time of communication time over the total flight time, is about 1%.
... In the field of satellite constellations, Savitri et al. employed GA in [1] to optimize trajectories, maximizing coverage while minimizing revisit time. Rughani et al. in [2] utilized GA to optimize orbital trajectories for spacecraft swarms, facilitating collaborative tasks in space and collision avoidance. ...
This paper introduces an innovative approach to explore the capabilities of Quantum Annealing (QA) for trajectory optimization in dynamic systems. The proposed method involves transforming trajectory optimization problems into equivalent binary optimization problems using Quadratic Unconstrained Binary Optimization (QUBO) representation. The procedure is general and adaptable, making it applicable to a wide range of optimal control problems that entail the satisfaction of dynamic, boundary, and path constraints. Specifically, the trajectory is discretized and approximated using polynomials. In contrast to the conventional approach of determining the polynomial degree (n) solely based on the number of boundary conditions, a specific factor is introduced in our method to augment the polynomial degree. As a result, the ultimate polynomial degree is calculated as a composite of two components: n = l + (m−1), where m denotes the count of boundary conditions and l signifies the number of independent variables. By leveraging inverse dynamics, the control required to follow the approximated trajectory can be determined as a linear function of independent variables l. As a result, the optimization function, which is represented by the integral of the square of the control, can be formulated as a QUBO problem and the QA is employed to find the optimal binary solutions.
... Genetic algorithms have been used in many other investigations of satellite constellation design [29] for similar reasons. Analytic solutions to coverage calculations are limited [30], though they can be used to reduce the search space for heuristic approaches [31]. ...
... Therefore, a lot of studies can be sorted including such an optimization algorithm. Savitri et al. used a combined genetic algorithm to design multiobjective optimization to maximize the percent coverage and minimize the revisit time for a small satellite constellation in circular low Earth orbit (LEO) [Savitri et al., 2017]. They used six orbital elements as optimization design variables. ...
In this study, performance of a low earth orbit Walker satellite constellation (LWSC) is analyzed as a Regional Navigation Satellite System (RNSS) for Türkiye. A reference LWSC is designed with respect to the Walker method. Geometric dilution of precision (GDOP) is used as a figure of merit. A software is developed to design and analyze the Walker satellite constellation. Results are compared with the current Global Positioning System (GPS) constellation. Both LWSC and reference GPS constellations are visualized in Systems Tool Kit (STK). The software is also corrected with STK.
... 26] and Genetic Algorithm [e.g. 27] have also been proven useful to solve astrodynamics problems [28,29]. The success of the optimization process depends on the choice of the optimization algorithm, the analytical model, and the quality of the input data, among others factors. ...
The growing population of man-made objects with the build up of mega-constellations not only increases the potential danger to all space vehicles and in-space infrastructures (including space observatories), but above all poses a serious threat to astronomy and dark skies. Monitoring of this population requires precise satellite characterization, which is is a challenging task that involves analyzing observational data such as position, velocity, and light curves using optimization methods. In this study, we propose and analyze the application of two optimization procedures to determine the parameters associated with the dynamics of a satellite: one based on the Theory of Functional Connections (TFC) and another one based on the Nelder-Mead heuristic optimization algorithm. The TFC performs linear functional interpolation to embed the constraints of the problem into a functional. In this paper, we propose to use this functional to analytically embed the observational data of a satellite into its equations of dynamics. After that, any solution will always satisfy the observational data. The second procedure proposed in this research takes advantage of the Nealder-Mead algorithm, that does not require the gradient of the objective function, as alternative solution. The accuracy, efficiency, and dependency on the initial guess of each method is investigated, analyzed, and compared for several dynamical models. These methods can be used to obtain the physical parameters of a satellite from available observational data and for space debris characterization contributing to follow-up monitoring activities in space and astronomical observatories.
... In their work, they assumed that no more than eight of each type of launcher to be available to deploy the constellation within the given deployment schedule. Savitri et al. [15] proposed an approach based on the objective of designing a small satellite constellation with limited coverage. A Genetic Algorithm (GA) was used to optimize five out of six orbital elements. ...
The surge in small satellite constellations is spurred by the recent cost reductions in launching capabilities. This has facilitated the development of affordable constellations in Low Earth Orbit (LEO). Commercial space components are revolutionizing LEO systems, with a particular focus on electric propulsion. Deployment strategies and space mobility are also gaining significant attention. To ensure a successful constellation deployment, careful consideration should be given to factors such as launcher selection. A proposed concurrent engineering methodology utilizes optimization techniques to identify optimal combinations of launchers, propulsion systems, and deployment strategies. The methodology is demonstrated through a constellation deployment scenario, showcasing its effectiveness.
... Evolutionary algorithms are frequently used to solve these problems as they can keep a diverse solution set. The genetic algorithm (GA) is a widely used global optimization method, among evolutionary algorithms, due to its ability to locate a global optimum solution for a set of nonlinear multi-objective problems [10,22,23]. ...
... NSGA-II calculates the nondominated solution set at each generation until the maximum generation or a given convergence criterion is achieved. Several studies have used NSGA-II for constellation design optimization problems, resulting in a good performance [12,[22][23][24]. ...
The increasing demand for low-cost space-borne Earth observation missions has led to small satellite constellation systems development. CubeSat platforms can provide a cost-effective multiple-mission space system using state-of-the-art technology. This paper presents a new approach to CubeSat constellation design for multiple missions using a multi-objective genetic algorithm (MOGA). The CubeSat constellation system is proposed to perform multi-missions that should satisfy global Earth observation and regional disaster monitoring missions. A computational approach using a class of MOGA named non-dominated sorting genetic algorithm II is implemented to optimize the proposed system. Pareto optimal solutions are found that can minimize the number of satellites and the average revisit time (ART) for both regional and global coverage while maximizing the percentage coverage. As a result, the study validates the feasibility of implementing the CubeSat constellation design with an acceptable level of performance in terms of ART and percentage coverage. Moreover, the study demonstrates CubeSat’s ability to perform a multi-missions.
