Orbital Maneuvering Research Articles

Earth shadow time/accelerometer/GNSS-based geosynchronous transfer orbit determination method for electric propulsion satellite

Autonomous orbital maneuvering of an electric propulsion satellite in geosynchronous transfer orbit (GTO) requires more accurate autonomous orbit determination (OD). Implementing the traditional autonomous OD method for the electric propulsion satellites may result in the accumulation of measurement errors and dynamic errors from orbit extrapolation, which significantly restrict the OD accuracy. Fortunately, an electric propulsion satellite in GTO can sense the transit time in or out of the Earth shadow according to the output power change of the solar array. Therefore, an Earth shadow time/accelerometer/GNSS-based geosynchronous transfer OD method for electric propulsion satellites is proposed in this paper. First, a system state model with dynamics is established for the entire orbit transfer process. Second, measurement models that use the measurement information from the accelerometer, GNSS, and the transit time into or out of the Earth shadow are established. Third, a sequential filtering estimation approach is designed to solve the problem of asynchronous data fusion for autonomous OD. Comparison simulations demonstrate the effectiveness and superiority of the proposed method.

Fuel-Efficient and Fault-Tolerant CubeSat Orbit Correction via Machine Learning-Based Adaptive Control

The increasing deployment of CubeSats in space missions necessitates the development of efficient and reliable orbital maneuvering techniques, particularly given the constraints on fuel capacity and computational resources. This paper presents a novel two-level control architecture designed to enhance the accuracy and robustness of CubeSat orbital maneuvers. The proposed method integrates a J2-optimized sequence at the high level to leverage natural perturbative effects for fuel-efficient orbit corrections, with a gated recurrent unit (GRU)-based low-level controller that dynamically adjusts the maneuver sequence in real-time to account for unmodeled dynamics and external disturbances. A Kalman filter is employed to estimate the pointing accuracy, which represents the uncertainties in the thrust direction, enabling the GRU to compensate for these uncertainties and ensure precise maneuver execution. This integrated approach significantly enhances both the positional accuracy and fuel efficiency of CubeSat maneuvers. Unlike traditional methods, which either rely on extensive pre-mission planning or computationally expensive control algorithms, our architecture efficiently balances fuel consumption with real-time adaptability, making it well-suited for the resource constraints of CubeSat platforms. The effectiveness of the proposed approach is evaluated through a series of simulations, including an orbit correction scenario and a Monte Carlo analysis. The results demonstrate that the integrated J2-GRU system significantly improves positional accuracy and reduces fuel consumption compared to traditional methods. Even under conditions of high uncertainty, the GRU-based control layer effectively compensates for errors in thrust direction, maintaining a low miss distance throughout the maneuvering period. Additionally, the GRU’s simpler architecture provides computational advantages over more complex models such as long short-term memory (LSTM) networks, making it more suitable for onboard CubeSat implementations.

Discrete search-based determination of a local orbital frame in unknown environments

A local orbital frame is an important and often applied coordinate frame in attitude and orbit control. Usually, a navigation filter estimates the position and velocity vector, which are used to build up this reference frame. It is beneficial for many space applications, such as communication or Earth observation missions, or for conducting orbit control maneuvers to change the orbit plane. Furthermore, satellite formation flying can require an orbital frame to describe relative motion. This work investigates the feasibility of determining the local-vertical local horizontal (LVLH) frame without full knowledge of the orbit. This scenario often applies to non-characterized small bodies like asteroids or comets. A discrete search method is used to determine the complete LVLH frame in real-time, assuming that one axis, a line-of-sight vector to the body’s center of mass, is known. By minimizing an objective function, the remaining axes can be determined. The estimated parameters are the inclination and the right ascension of the ascending node of the osculating orbit plane. This study investigates the feasibility of this concept and then applies it to perturbed orbits and sensor noise. The proposed method demonstrates that a discrete search can determine the LVLH frame. The approach can be seen as a step toward increasing the autonomy of a spacecraft near small bodies with unknown environments.

Orbit determination for spacecraft with continuous low-thrust using nonsingular Thrust-Fourier-Coefficients and filtering-through approach

Orbit determination using optical survey measurements for cataloging spacecraft encounters new obstacles from mega-constellations. These challenges arise from the sparse observations, and the frequent occurrences of unknown maneuvers which are difficult to model using traditional methods. By utilizing 14 Fourier coefficients, the Thrust-Fourier-Coefficients (TFC) model can effectively represent the averaged variations of orbital elements caused by arbitrary maneuvers. However, this model contains systematic offsets that will reduce the accuracy of orbit determination, and is unsuitable for spacecraft in nearly circular orbits. This paper first replaces the classical Keplerian elements of the previous TFC model with the nonsingular elements. Then detailed analytical expressions for model offsets have been derived based on Kozai’s orbit-averaging method. A process noise covariance matrix related to the model offsets has been added to the iterated extended Kalman filter to compensate for the unmodeled dynamics and enhance the accuracy. Simulations based on this modified method demonstrate that the accuracy of orbit determination for maneuvering satellites can meet the requirements of catalog maintenance even with sparse observations.

Swarm-to-swarm orbital pursuit method under delta-v maneuver for space pursuit-evasion

This paper investigates the orbital pursuit strategy for spacecraft swarms, where both pursuers and evaders possess limited delta-v maneuvering capabilities. Given that swarms can consist of numerous members, ranging from dozens to thousands, the swarm-to-swarm problem has significant coupling effects that cannot be solved by merely superimposing one-to-one or few-to-few problems. Otherwise, one would cause a dimension explosion in decision-making space. To avoid this issue, the swarm orbital pursuit problem is divided into two coupled problems: swarm target allocation and orbital maneuver. First, considering the relative orbit state between pursuers and evaders and estimated orbital maneuver costs of pursuit, the swarm target allocation problem is formulated into three coupled sub-problems, i.e., target allocation order, target allocation for sub-swarms, and target allocation for individuals. These sub-problems are solved by the presented double-layer contract net protocol algorithm to maximize task completion efficiency. Then, the orbital maneuver problem is decomposed into two coupled problems to maximize pursuit benefits, i.e., long-range rendezvous, and close-distance game maneuvers. For the long-range rendezvous, the optimal Lambert algorithm is developed to efficiently obtain the discrete optimal pursuit time and corresponding orbital transfer maneuver. To address close-distance games more proficiently, a hybrid orbital maneuver algorithm, combining the proximal policy optimization and the Lambert algorithm is proposed. Finally, comparison simulations verified the effectiveness and superiority of the proposed method.

Observability-Aware Differential Dynamic Programming with Impulsive Maneuvers

In autonomous space systems, the reliability of navigation systems is essential. Observability in autonomous orbit determination techniques depends on the spacecraft’s orbital motion, making the design of autonomous navigation systems and orbital maneuvers a coupled process. This study develops a stable and efficient algorithm based on differential dynamic programming to design maneuver sequences that improve navigation performance. Our approach incorporates the Fisher information matrix into a cost function to quantify state observability and facilitates its convergence using a semi-analytic gradient and Hessian derived under impulsive maneuvers. Two numerical examples show the validity and effectiveness of our algorithm. The results indicate the stability and efficiency in determining maneuver sequences and the improvement of state estimation accuracy along an optimized trajectory. It is also applicable to other observability-aware optimal control problems because the algorithm is independent of specific systems.

The Trajectory Prediction of Spacecraft under the Influence of Gyroscopic Effect Generated during Non-Keplerian Motion

Due to perturbation forces and control forces, trajectories of spacecraft around the Earth are usually non-Keplerian orbits, which may result in a gyroscopic effect. To meet the complex demands of space operations in the future, the trajectory prediction of spacecraft under the influence of the gyroscopic effect generated during non-Keplerian motion needs to be studied in depth. The paper investigated the trajectory of spacecraft under the gyroscopic effect generated during non-Keplerian motion. Firstly, according to the similarity between the spacecraft precession motion and the gyroscopic precession, as well as the definition of the “gyroscopic effect” of high-speed rotating bodies, the “gyroscopic effect” generated during the non-Keplerian motion of spacecraft around the earth was defined. Then, taking a continuous radial thrust orbit as an example, the dynamics equations of spacecraft under the influence of gyroscopic effect were deduced. Through theoretical analysis and numerical simulation, the trajectory of spacecraft under the influence of the gyroscopic effect generated during non-Keplerian motion was investigated. Finally, the paper simulated the examples and tested the performance of the proposed method. Simulation results show that a large gyroscopic moment may be generated in some non-Keplerian motion of the spacecraft. The greater the rotational angular velocity of the orbital plane, the greater the gyroscopic moment. Due to the gyroscopic effect, there is a significant deviation in the orbit and the orbital elements compared to those without considering the gyroscopic effect, which indicates that the influence of the gyroscopic effect generated during non-Keplerian motion on the orbit of the spacecraft cannot be ignored. It can be seen from the simulation results that the gyroscopic effect has a significant influence on the trajectory of spacecraft. In some special cases, the gyroscopic effect can be utilized reasonably to save fuel and realize low-energy orbit maneuver control technology in actual space missions; but the control should be considered for the spacecraft to bring it back to the desired orbit in most cases. It is necessary to study the trajectory of spacecraft under the influence of gyroscopic effect. The method and conclusions proposed can provide a theoretical reference for spacecraft trajectory prediction and future large-scale fast orbital maneuvers to meet the needs of complex space operations.

Space-Based Passive Orbital Maneuver Detection Algorithm for High-Altitude Situational Awareness

Orbital maneuver detection for non-cooperative targets in space is a key task in space situational awareness. This study develops a passive maneuver detection algorithm using line-of-sight angles measured by a space-based optical sensor, especially for targets in high-altitude orbit. Emphasis is placed on constructing a new characterization for maneuvers as well as the corresponding detection method. First, the concept of relative angular momentum is introduced to characterize the orbital maneuver of the target quantitatively, and the sensitivity of the proposed characterization is analyzed mathematically. Second, a maneuver detection algorithm based on the new characterization is designed in which sliding windows and correlations are utilized to determine the mutation of the maneuver characterization. Subsequently, a numerical simulation system composed of error models, reference missions and trajectories, and computation models for estimating errors is established. Then, the proposed algorithm is verified through numerical simulations for both long-range and close-range targets. The results indicate that the proposed algorithm is effective. Additionally, the sensitivity of the proposed algorithm to the width of the sliding window, accuracy of the optical sensor, magnitude and number of maneuvers, and different relative orbit types is analyzed, and the sensitivity of the new characterization is verified using simulations.

Navigation performance analysis of Earth–Moon spacecraft using GNSS, INS, and star tracker

Global Navigation Satellite System (GNSS) can provide an approach for spacecraft autonomous navigation in earth–moon space to make up for the insufficiency of earth-based tracking, telemetry, and control systems. However, its weak power and poor observation geometry near the moon causes new problems. After the GNSS signal characteristics and satellite visibility were evaluated in Phasing Orbit and Lunar Transfer Orbit, we proposed an adaptive Kalman filter based on the Carrier-to-Noise ratio (C/N0) and innovation vector to weaken the influence of GNSS accuracy attenuation as much as possible. The experimental results show that the spacecraft position and velocity accuracy are better than 10 m and 0.1 m/s near the Earth, and better than 50 m and approximately 0.2 m/s near the moon use GNSS with the proposed adaptive algorithms. Additionally, because of the deterioration of navigation performance based on the orbit filter during orbital maneuvering, we used accelerometer data to compensate for the dynamic model to maintain navigation performance. The results of the experiment provide a reference for subsequent studies.

Precise Orbit Determination for Maneuvering HY2D Using Onboard GNSS Data

The Haiyang-2D (HY2D) satellite is the fourth ocean dynamics environment monitoring satellite launched by China. The satellite operates on a re-entry frozen orbit, which necessitates orbital maneuvers to maintain its designated path once the satellite’s sub-satellite point deviates beyond a certain threshold. However, the execution of orbit maneuvers presents a significant challenge to the field of Precise Orbit Determination (POD). The thesis selects the on-board GPS data of HY2D satellite in December 2023 and five maneuvering days of that year. Employing a multifaceted approach that includes the assessment of observational data quality, orbit overlap, external orbit validation, and SLR (Satellite Laser Ranging) verification, the research delves into precise orbit determination during both maneuver and non-maneuver periods. The results indicate that: (1) The average number of satellites tracked by the receiver is 6.4; (2) During the non-maneuver periods, the average RMS (Root Mean Square) value of the radial difference in the 6-h overlapping arc segment is 0.66 cm, and the three-dimensional position difference is about 1.16 cm; (3) When compared with the precision science orbits (PSO) provided by CNES (Centre National d’Études Spatiales), the average values of the RMS values of the differences in the radial (R), transverse (T), and normal (N) directions during the non-maneuver and maneuver periods are respectively 1.32 cm, 2.31 cm, 1.92 cm and 3.04 cm, 8.78 cm, 2.72 cm. (4) The SLR verification of the orbit revealed a residual RMS of 2.24 cm. This suggests that by incorporating the modeling of maneuver forces during the maneuver periods, the impact of orbital maneuvers on orbit determination can be mitigated.

Maneuver strategies of Starlink satellite based on SpaceX-released ephemeris

In the face of huge collision risks posed by the Starlink mega-constellation, the detection of unpredictable orbital maneuvers of Starlink satellites emerges as an important topic of Space Situational Awareness (SSA). The ephemerides released by the SpaceX company on the Space-track website provide a timely and valuable opportunity for addressing this problem. Based on the mean orbital elements extracted from Starlink ephemerides released at the end of 2023, the maneuver strategies, including maneuver frequency and characteristics of Starlink satellites in different orbital phases, are discussed, and the start time and end time with error ranges of confirmed maneuvers are acquired. It is found that operational satellites in Shell 1 perform an orbit maintenance maneuver approximately every 2 days, while those in Shells 2–5 execute a maneuver roughly once a day. Moreover, the parking satellites maneuver approximately every 0.25 days on average. As for satellites in the climbing orbit and the deorbiting orbit, they maneuver around every 0.1 days. The maneuver strategies of Starlink summarized in this paper can contribute to optimizing the observation plan of the Starlink constellation.

Control strategy for trading off solar power and control input while rendezvous and docking

This paper presents a novel strategy for decoupling the attitude and orbit equations of a CubeSat for rendezvous and docking with an uncontrollable cooperative target. For computing a safe trajectory, the proposed control algorithm takes into account the solar energy received by the CubeSat. The CubeSat is equipped with a thruster for orbit maneuvers, magnetic coils for attitude control, and four fixed single-sided rectangular solar panels. The coupled dynamics arising from the dynamical model of the spacecraft is solved using a novel weighted vector-based approach. This paper presents a linearized nonlinear optimal control problem arising in small spacecrafts while trying to maximize solar energy input in the rendezvous and docking process. An intermediate orbit is defined and used to divide the problem into two different optimal control problems: rendezvous optimization and docking optimization problems. A geometrical approach based on the shape of the chaser and the target is contemplated for collision avoidance while docking. The proposed controller design is modified whenever the sunlight is obstructed by the Earth, and the maneuvering controls are redesigned accordingly for optimal rendezvous and docking. Numerical simulations have been carried out to show the efficacy of the proposed concept for steering the trade-off between solar energy and control input during the rendezvous and docking of CubeSat with a tumbling target.

A simplified GNSS/LEO joint orbit determination method

Joint orbit determination (JOD) of Global Navigation Satellite Systems (GNSS) satellites and low Earth orbit (LEO) satellites has been substantiated as an efficacious approach to compensate for the ground station geometry. In the traditional JOD, the precise orbit determination (POD) of LEO satellite is mainly processed by the reduced-dynamic approach, however, this approach involves complex calculations and the credibility of the determined positions diminishes when LEO satellites undergo orbital maneuvers. Therefore, a simplified JOD method is designed that employs kinematic approach to determine the LEO satellites orbit. To verify the effectiveness of the proposed method, the orbit of GPS satellites and LEO satellites are jointly estimated utilizing the regional and global networks. 8 LEO satellites, including GRACE-C/D, SWARM-A/B/C, SENTINEL-3A/B, and JASON-3, are chosen for JOD. The comparative analysis between the proposed method and traditional method are achieved in terms of GPS orbit accuracy, LEO orbit accuracy, computation time and the JOD performance during LEO maneuvers. Under regional station scenario, the GPS orbit accuracy determined using the proposed method and the traditional method is 3.64 cm and 2.52 cm, respectively. In the case of global station scenario, the accuracies are 1.71 cm and 1.64 cm. Additionally, the traditional method yields superior enhancement and higher accuracy of the LEO orbits. However, it exhibits a noticeable increase in computation time compared to the proposed method and the performance of JOD declines significantly when LEO satellites undergo orbital maneuvers. Alternatively, although the accuracy of the LEO orbits using the proposed method is comparatively lower, it offers a substantial reduction in the overall network computation time compared to traditional method. Moreover, the proposed method based on LEO kinematic precise orbit determination (KPOD) is nearly unaffected by orbital maneuvers of LEO satellites, presenting unique advantages in practical data processing.

Enhancing the trustworthiness of chaos and synchronization of chaotic satellite model: a practice of discrete fractional-order approaches

Accurate development of satellite maneuvers necessitates a broad orbital dynamical system and efficient nonlinear control techniques. For achieving the intended formation, a framework of a discrete fractional difference satellite model is constructed by the use of commensurate and non-commensurate orders for the control and synchronization of fractional-order chaotic satellite system. The efficacy of the suggested framework is evaluated employing a numerical simulation of the concerning dynamic systems of motion while taking into account multiple considerations such as Lyapunov exponent research, phase images and bifurcation schematics. With the aid of discrete nabla operators, we monitor the qualitative behavioural patterns of satellite systems in order to provide justification for the structure’s chaos. We acquire the fixed points of the proposed trajectory. At each fixed point, we calculate the eigenvalue of the satellite system’s Jacobian matrix and check for zones of instability. The outcomes exhibit a wide range of multifaceted behaviours resulting from the interaction with various fractional-orders in the offered system. Additionally, the sample entropy evaluation is employed in the research to determine complexities and endorse the existence of chaos. To maintain stability and synchronize the system, nonlinear controllers are additionally provided. The study highlights the technique’s vulnerability to fractional-order factors, resulting in exclusive, changing trends and equilibrium frameworks. Because of its diverse and convoluted behaviour, the satellite chaotic model is an intriguing and crucial subject for research.

A multi-point decentralized control for mitigating vibration of flexible space structures using reaction wheel actuators

The vibration with large amplitude and low frequency of the flexible space structures is prone to affect the attitude stability and pointing precision of the spacecraft. To mitigate the vibration of the flexible space structures, a multi-point decentralized control strategy using reaction wheel (RW) actuators is proposed and investigated in this paper. The motion equations of the solar array with multiple RW actuators are derived in modal coordinate representation. To suppress the overall response of the structure, the decentralized control strategy using RW actuators is designed based on the natural frequencies and mode shapes. The stability and the effect of closed-loop dynamic system is theoretically proved. The comparative studies under sun-pointing of the solar array and the rest-to-rest orbital maneuver conditions are presented to show the control performance of the RW actuators. The results indicate that, with 2% increase in total mass from the addition of the actuators, the vibration attenuation time can be decreased by 85.25% and 94.16% for the vibration excited by the sun-pointing and the rest-to-rest orbital maneuver, respectively. The experimental results demonstrate the effectiveness of the proposed decentralized control method. Theoretical analysis, numerical simulation and experimental study are conducted to demonstrate the validity of the proposed vibration mitigation approach and its potential application in the spacecraft design.

Autonomous Mission Planning for Spacecraft On-orbit Service Based on Hybrid Variant Particle Swarm Optimization

For the complex on-orbit service (OOS) mission planning problem, an improved hybrid variant particle swarm optimization (PSO) method was proposed to improve the fuel utilization efficiency of spacecraft. Firstly, considering the time and fuel constraints, a model for OOS mission planning under the scenario of multiple target spacecrafts is established. The Lambert orbit maneuver method is used and the problem is transformed into a large-scale hybrid nonlinear integer programming problem. Next, an improved hybrid variant PSO algorithm is designed to optimize the fuel performance cost, and its simple structure and lightweight operation facilitate autonomous planning, considering the limited computing power of the onboard computer. The hybrid algorithm is composed of discrete particle swarm optimization (DPSO) and PSO, so it has a strong ability to search for the optimal service sequence and orbit maneuver time simultaneously. Moreover, the adaptive and variant operators are used to improve the searching ability and avoid falling into local optimal solutions. Finally, simulation experiments show that the proposed method can quickly give optimal results, reducing fuel consumption effectively in the OOS mission and improving the OOS capability of the spacecraft.

Simultaneously Adjusting Deployment Strategies for Mega-Constellations Using Low-Thrust Maneuvers

Deploying a constellation can be costly and inefficient. The ultimate goal is to position multiple satellites into designated orbital slots with the fewest launches and lowest energy consumption. This paper presents a method for simultaneous right ascension of the ascending node (RAAN) and argument of latitude (AOL) adjustments using continuous low thrust. Firstly, how changes in the semimajor axis and inclination affect the RAAN and the AOL is analyzed. A control method is proposed, and all satellites are sequentially placed from the injection orbit to the working orbit at specific time intervals. Because the RAAN and AOL are coupled with each other, a priority control strategy is introduced. This strategy ensures that the AOL is accurately satisfied within the time between each maneuver. Next, equations that correlate the RAAN and the AOL with the orbit inclination deviation and maneuver interval time are established. By studying the maneuver time intervals and inclination compensations, a highly accurate synchronized deployment scheme can be obtained. A simulation experiment based on the OneWeb constellation is carried out. In the simulation, 80 satellites are launched by just one rocket. By employing the proposed method, the constellation is successfully deployed. Results from the simulation verified the effectiveness of the proposed algorithm, which may be employed for rapid deployment of a mega-constellation in the future.

An approximate optimal control method for 6-DOF spacecraft

In this paper, an approximate optimal control method based on adaptive dynamic programming (ADP) is proposed for the proximity operations with six degrees of freedom (6-DOF) relative motion control of spacecraft. Firstly, the dynamic model is normalized and dimension-reduced to avoid the excessive gradient change of the neural network. Then, a nonlinear disturbance observer is designed to deal with the disturbance. Finally, using ADP ‘s reinforcement learning idea, a single-critic neural network is constructed to solve the approximate optimal control strategy and minimize the cost function. The simulation results show that the designed controller can achieve the attitude and orbit maneuvering targets, and the overall energy consumption is approximately optimal.

Tangential velocity constraint for orbital maneuvers with Theory of Functional Connections

Maneuvering a spacecraft in the cislunar space is a complex problem, since it is highly perturbed by the gravitational influence of both the Earth and the Moon, and possibly also the Sun. Trajectories minimizing the needed fuel are generally preferred in order to decrease the mass of the payload. A classical method to constrain maneuvers is mathematically modeling them using the Two Point Boundary Value Problem (TPBVP), defining spacecraft positions at the start and end of the trajectory. Solutions to this problem can then be obtained with optimization techniques like the nonlinear least squares conjugated with the Theory of Functional Connections (TFC) to embed the constraints, which recently became an effective method for deducing orbit transfers. In this paper, we propose a tangential velocity (TV) type of constraints to design orbital maneuvers. We show that the technique presented in this paper can be used to transfer a spacecraft (e.g. from the Earth to the Moon) and perform gravity assist maneuvers (e.g. a swing-by with the Moon). In comparison with the TPBVP, solving the TV constraints via TFC offers several advantages, leading to a significant reduction in computational time. Hence, it proves to be an efficient technique to design these maneuvers.

Basic Orbit Design and Maneuvers for Satellite Constellations Deployed Using Momentum Exchange Tethers

This article describes a new alternative approach to satellite constellation deployment by incorporating momentum exchange tethers (METs). Traditional methods of deploying satellite constellations have limitations, typically involving costly propulsion systems and extended dispersion times. METs offer a novel solution by efficiently transferring momentum between tethered objects, reducing the need for onboard propellants and streamlining the deployment process. This article discusses orbit design and maneuvers for different mission architectures using asymmetrical and symmetrical tether release techniques to deploy satellites into designated orbits. In addition, a short walkthrough of designing one possible constellation is given, showing how quickly a MET-deployed constellation can be established in low Earth orbit (LEO). This work contributes to ongoing research investigating the applicability of METs in satellite constellation deployments, which could potentially be a new opportunity for MET technology to start seeing routine usage in the space environment, and also enable new constellation architectures that have not yet been realized.