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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. • Satellite swarm pursuit problem is transformed to the coupled problem with swarm target allocation and orbital maneuvers. • Swarm target allocation is formulated as a coupled problem with target order, allocations for subgroups and individuals. • An improved DLCNP algorithm is proposed to pursue a reasonable target allocation solution for higher task efficiency. • Optimal Lambert algorithm is developed to obtain the optimal maneuver strategyfor long-range rendezvous. • A hybrid algorithm combining PPO and the Lambert algorithm is presented to get closed-loop control for close-distance games. [ABSTRACT FROM AUTHOR]

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Parasitic SAR formation can be flown at low altitude using smaller satellites and adding potential to conventional SAR mission From the orbital point of view, the main issue is related to the differential aerodynamic drag, which rapidly disrupts the formation. In this ambit, this paper proposes a case study of an along-track distributed parasitic receiver flying in formation with PLATiNO-1. Formation maintenance is the core contribution, highlighting how the active control of both altitude and in-plane anomalies leads to an unfeasible ΔV. Then, the active control of the altitude around the nominal value, which naturally controls anomaly shift, is proposed, modeled, and applied to the presented case study. It is shown that the annual ΔV can be reduced to the m/s range. [ABSTRACT FROM AUTHOR]

The space constellation of the BeiDou navigation satellite system (BDS) is a hybrid constellation containing medium earth orbit (MEO) satellites, geostationary earth orbit (GEO) satellites, and inclined geosynchronous orbit (IGSO) satellites. Due to the geosynchronous characteristics of GEO and IGSO, GEO satellites and IGSO satellites often need to perform orbital maneuvers, which can affect the signal-in-space (SIS) availability performance of BeiDou satellites. A two-step detection method for BeiDou satellite orbital maneuvers has been proposed in this paper. The first step is to identify orbital maneuvers based on time series analysis of broadcast ephemeris, and the second step is to verify orbital maneuvers based on bidirectional orbit prediction. The two-step detection method was used to detect the orbital maneuvers of BeiDou satellites in 2019. Through the double guarantees of identification and verification, the detection accuracy of BeiDou satellite orbital maneuvers has been effectively improved. And the orbital maneuver detection results are continued to be used to assess the SIS availability of BeiDou satellites. The results show that the availability loss of GEO satellite orbital maneuvers is about 0.45%–1.07%, and the availability loss of IGSO satellite orbital maneuvers is about 0.12%–0.19%.

Copyright of Transactions of Nanjing University of Aeronautics & Astronautics is the property of Editorial Department of Journal of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

By developing an analytical model considering the J 2 perturbation and small eccentricity, the effects of an in-track maneuver on the umbra and penumbra arcs of near-circular orbits are analyzed. The effectiveness of the analytical model is validated by comparing it with the numerical difference and a published model for the cylindrical eclipse. Three major conclusions are draw. First, the proposed analytical model agrees well with the numerical difference method in common situations, and the effect of an in-track maneuver on the eclipse arc center is much smaller than that on the eclipse arc length. Second, although the precision of the proposed analytical model decreases as the eccentricity increases, the effects of a small in-track maneuver on the orbital eclipse could be considered as small values in common situations. Those effects could be notable as the maneuver magnitude increases. Third, when the orbital sun angle approaches the critical angle defined by the ratio of the Earth radius to the satellite's semimajor axis, the effects of an in-track maneuver on the penumbra arc length could not be a small value any more, the precision of the analytical model would be considerably degraded. In the neighborhood of the critical angle, the differences between the effects of an in-track maneuver on the umbra, penumbra and cylindrical eclipse reach the maximum. Moreover, the reasons for the properties presented above are successfully explained by the analytical partial derivatives in the developed model. [ABSTRACT FROM AUTHOR]

The BeiDou navigation satellite system (BDS) comprises geostationary earth orbit (GEO) satellites as well as inclined geosynchronous orbit (IGSO) and medium earth orbit (MEO) satellites. Owing to their special orbital characteristics, GEO satellites require frequent orbital maneuvers to ensure that they operate in a specific orbital window. The availability of the entire system is affected during the maneuver period because service cannot be provided before the ephemeris is restored. In this study, based on the conventional dynamic orbit determination method for navigation satellites, multiple sets of instantaneous velocity pulses parameters which belong to one of pseudo-stochastic parameters were used to simulate the orbital maneuver process in the orbital maneuver arc and establish the observed and predicted orbits of the maneuvered and non-maneuvered satellites of BeiDou regional navigation satellite system (BDS-2) and BeiDou global navigation satellite system (BDS-3). Finally, the single point positioning (SPP) technology was used to verify the accuracy of the observed and predicted orbits. The orbit determination accuracy of maneuvered satellites can be greatly improved by using the orbit determination method proposed in this paper. The overlapping orbit determination accuracy of maneuvered GEO satellites of BDS-2 and BDS-3 can improve 2–3 orders of magnitude. Among them, the radial orbit determination accuracy of each maneuvered satellite is basically better than 1 m. simultaneously, the combined orbit determination of the maneuvered and non-maneuvered satellites does not have a great impact on the orbit determination accuracy of the non-maneuvered satellites. Compared with the multi GNSS products (indicated by GBM) from the German Research Centre for Geosciences (GFZ), the impact of adding the maneuvered satellites on the orbit determination accuracy of BDS-2 satellites is less than 9 %. Furthermore, the orbital recovery time and the service availability period are significantly improved. When the node of the predicted orbit is traversed approximately 3 h after the maneuver, the accuracy of the predicted orbit of the maneuvered satellite can reach that of the observed orbit. The SPP results for the BDS reached a normal level when the node of the predicted orbit was 2 h after the maneuver. [ABSTRACT FROM AUTHOR]

An analytical nonlinear model for elastic planar motion of a tethered spacecraft (TS) is presented and used to investigate the mode characteristics and analyze the nonlinear vibrations induced by the orbital maneuver. Dynamic characteristics such as frequency densification caused by variation of solar panel length, mode localization, and mode interchanging phenomenon caused by acceleration variation are investigated. Two prerequisites and the mechanisms for the occurrence of the complete mode interchanging phenomenon are discussed in detail. Nonlinear phenomena were observed such as hardening, jumping, and third-order superharmonic resonance. Dynamic responses of TS with and without considering the geometrical nonlinearity of the tether were obtained and used to show the influence of the tether's nonlinearity on the whole system. The influence of the tether's nonlinearity was strengthened with the increase of the excitation amplitude. Numerical results showed that the geometrical nonlinearity of tether has a significant influence on the dynamical responses and residual vibrations of the whole tethered spacecraft. [ABSTRACT FROM AUTHOR]

With the continuous development of space rendezvous technology, more and more attention has been paid to the study of spacecraft orbital pursuit-evasion differential game. Therefore, we propose a pursuit-evasion game algorithm based on branching improved Deep Q Networks to obtain a space rendezvous strategy with non-cooperative target. Firstly, we transform the optimal control of space rendezvous between spacecraft and non-cooperative target into a survivable differential game problem. Next, in order to solve this game problem, we construct Nash equilibrium strategy and test its existence and uniqueness. Then, in order to avoid the dimensional disaster of Deep Q Networks in the continuous behavior space, we construct a TSK fuzzy inference model to represent the continuous space. Finally, in order to solve the complex and timeconsuming self-learning problem of discrete action sets, we improve Deep Q Networks algorithm, and propose a branching architecture with multiple groups of parallel neural Networks and shared decision modules. The simulation results show that the algorithm achieves the combination of optimal control and game theory, and further improves the learning ability of discrete behaviors. The algorithm has the comparative advantage of continuous space behavior decision, can effectively deal with the continuous space chase game problem, and provides a new idea for the solution of spacecraft orbit pursuit-evasion strategy. [ABSTRACT FROM AUTHOR]

Aiming at the singularity of real-time model transition probability correction using model likelihood function comparison with traditional interacting multiple model (IMM) algorithm, an improved adaptive IMM algorithm is proposed based on the proposed correction function. Firstly, combining the white noise model with the extended Kalman filter (EKF) algorithm, the non maneuvering model EKFI and maneuvering model EKF2 are designed as the model set of IMM algorithm. Secondly, the prediction model adopts the nonlinear relative orbit dynamic equation suitable for the elliptical reference orbit to improve the prediction accuracy of the model. Finally, the effect of rate measurement information on reducing the peak error of maneuvering target tracking is analyzed. The simulation results show that the tracking accuracy of the improved model transition probability adaptive imm-ekf algorithm is significantly improved and better than the existing methods. After introducing the rate measurement information, the maximum peak error and estimation accuracy are improved. [ABSTRACT FROM AUTHOR]

Sloshing phenomenon in spacecraft fuel tank during orbital maneuver, causes adverse effects on spacecraft attitude. Therefore, before orbital maneuvers, modeling fuel sloshing and determining appropriate method for controlling it has to be carried out. The aim of this paper is to model slosh dynamics by using double pendulum model in two-dimensional space. Spacecraft maneuver and pendulums motion are considered in 2D-coordinate, so coupled spacecraft and pendulums dynamic system are 5 degrees of freedom systems. Here, linear control methods (PD and LQR), and also nonlinear control methods (Lyapunov and fuzzy) are determined to stabilize dynamic parameters of the introduced system. Simulation results show that designed controllers have good performance to achieve stabilization of the parameters.

A new strategy is presented for the optimal transfer of non-coplanar elliptical orbits based on sequential multi-Lambert trajectories. The proposed method tries to minimize the control effort during the orbit transfer. The main advantages of the proposed method include transfer between arbitrary initial and final orbits, utilizing desired number of impulses, and covering all possible transfer trajectories to achieve the target. The position and time instant of impulses are considered as the design variables which determine utilizing the well-known optimization method of pseudo-Newton. Performance of the proposed method is investigated and verified through some numerical simulations. It is also shown that the proposed method converges to the celebrated Hahmann’s maneuver in transfer between two coplanar orbital orbits.

This paper proposes a solution for multiple-impulse orbital maneuvers near circular orbits for special cases where orbital observations are not globally available and the spacecraft is being observed through a limited window from a ground or a space-based station. The current study is particularly useful for small private launching companies with limited access to global observations around the Earth and for orbital maneuvers around other planets for which the orbital observations are limited to the in situ equipment. An appropriate cost function is introduced for the sake of minimizing the total control/impulse effort as well as the orbital uncertainty. It is subsequently proved that for a circle-to-circle maneuver, the optimization problem is quasi-convex with respect to the design variables. For near circular trajectories the same cost function is minimized via a gradient based optimization algorithm in order to provide a sub-optimal solution that is efficient both with respect to energy effort and orbital uncertainty. As a relevant case study, a four-impulse orbital maneuver between circular orbits under Mars gravitation is simulated and analyzed to demonstrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The present paper aims to study the cumulative collision probability of a target that crosses a cloud of particles that has the orbital parameters of each individual element modified by a close approach with the Earth. Clouds of this type are formed when natural or man-made bodies explode for some reason. After an explosion like that, the individual particles have different trajectories. The clouds are specified by a non-uniform distribution of semi-major axis and eccentricity of their particles which are assumed to pass close to the Earth, making a close approach that modifies the trajectory of every single particle that belongs to the cloud. This study makes simulations considering separately two different clouds based on the patched conics model to obtain the new trajectories of each particle and to analyze the density of the whole cloud. Then it is possible to map the new distribution of the orbital elements of the fragments that constituted the cloud, using the distribution as initial conditions. After calculating the spatial density for the whole cloud, it is possible to obtain the cumulative collision probability for one space vehicle that crosses the cloud. These pieces of information are important when planning satellite missions where a spacecraft passes close to a cloud of this type, because we can determine values to study the risks of collision and the possible maneuvers that need to be made to avoid them. [ABSTRACT FROM AUTHOR]

A new shape-based geometric method (SBGM) is proposed for generation of multi-impulse transfer trajectories between arbitrary coplanar oblique orbits via a heuristic algorithm. The key advantage of the proposed SBGM includes a significant reduction in the number of design variables for an N-impulse orbital maneuver leading to a lower computational effort and energy requirement. The SBGM generates a smooth transfer trajectory by joining a number of confocal elliptic arcs such that the intersections share common tangent directions. It is proven that the well-known classic Hohmann transfer and its bi-elliptic counterpart between circular orbits are special cases of the proposed SBGM. The performance and efficiency of the proposed approach is evaluated via computer simulations whose results are compared with those of optimal Lambert maneuver and traditional methods. The results demonstrate a good compatibility and superiority of the proposed SBGM in terms of required energy effort and computational efficiency. • A shape-based geometric method (SBGM) is proposed for impulsive orbital transfer. • The SBGM is used for maneuvers between coplanar oblique elliptic orbits. • The relationships between SBGM, Hohmann and bi-elliptic maneuvers are investigated. • It is shown that how the proposed SBGM is computationally efficient. • It is shown that how the optimal SBGM has considerable low costs. [ABSTRACT FROM AUTHOR]

• Spin-stabilized method is applied to eliminate velocity pointing error. • Analytical solutions with nonzero initial conditions are derived. • Mechanism research on spinning thrusting Cubesat is carried out. • The mechanism analysis can be used on Cubesat parameters design. To solve the problem of thrust vector misalignment from the Cubesat center of mass during orbital maneuver, spin-stabilized method is applied to eliminate velocity pointing error. Spinning thrusting Cubesat model involves the effects of mass variation and jet damping is established. Analytical solutions for the angular velocity, nutation angle, Euler angle, and inertial velocity with nonzero initial conditions are derived. Simulations show that the analytical solutions closely match numerical simulations. Based on the analytical solutions, the velocity pointing error influencing factors is analyzed. The results show that the velocity pointing error caused by initial transverse velocity, nutation angle and transverse disturbance torque can be reduced by raising the spin rate, but the initial Euler angle need to be limited. Also, the spinning thrusting maneuver can allow for a lower spin rate by increasing the axial moment of inertia. [ABSTRACT FROM AUTHOR]

The orbital dynamics basis for orbital plane change maneuver using chemical propulsion is the impulsive orbital change theory in practical engineering. The orbital plane change theory using continuous thrust suitable for electric propulsion is studied in this paper. A set of nonsingular orbital variational equations using quaternion is used to investigate the orbital motion of spacecraft under constant normal acceleration departing from a Keplerian circular orbit firstly. Results show that the orbit of spacecraft under continuous constant normal acceleration is a circular orbit over the gravitational center on the same spherical surface as the initial orbit, and it is tangent to the initial circular orbit at the initial position. Continuous and discontinuous maneuver strategies are then designed using the previous theory, and they are validated by numerical simulations. Results indicate that the strategy can work effectively. [ABSTRACT FROM AUTHOR]

The present paper has the goal of studying the changes of the orbital parameters of each individual element of a cloud of particles that makes a close approach with the Earth. Clouds of particles are formed when natural or man-made bodies explode for some reason. After an explosion like that, the center of mass of the cloud follows the same orbit of the body that generated the explosion, but the individual particles have different trajectories. The cloud is specified by a distribution of semi-major axis and eccentricity of their particles. This cloud is assumed to pass close to the Earth, making a close approach that modifies the trajectory of every particle that belongs to the cloud. The present paper makes simulations based in the "Patched-Conics" model to obtain the new trajectories of each particle. Then, it is possible to map the new distribution of the Keplerian elements of the particles that constituted the cloud, using the previous distribution as initial conditions. These information are important when planning satellite missions having a spacecraft passing close to a cloud of this type, because it is possible to obtain values for the density and amplitude of the cloud, so finding the risks of collision and the possible maneuvers that need to be made in the spacecraft to avoid the collisions. [ABSTRACT FROM AUTHOR]

Many responsive civilian or military space missions require that a certain ground site of interest be visited in a fairly short period (e.g., 12 h or less). To this end, a constellation must be utilized, since a single satellite is usually unable to fulfill such a task if the ground site is selected on the whole terrestrial surface responding to random user requirements. In this paper, the design approaches of such a constellation for responsive visiting based on ground track adjustment are investigated. By using the difference in orbit period between the maneuvered satellite and the reference satellite to make the ground track shift, reachable domain belts are generated. In terms of orbit maneuvering, two- and one-impulse maneuvers are analyzed and compared. Based on the reachable domain belts of a single satellite, two constellation design methods are proposed. The first one is an analytical method which is presented to achieve global reach and implemented by uniformly splicing together the widest belts of all satellites within the range of [0°, 180°]. The second one is an optimized method proposed to further reduce the number of satellites, by splicing together all the reachable domain belts rather than only the widest belts in the equator. A hybrid algorithm that consists of the genetic algorithm and the pattern search algorithm is proposed to minimize the number of satellites. Numerical examples are provided to illustrate the two proposed constellation design methods and validate the global reach performance. [ABSTRACT FROM AUTHOR]

In orbital maneuvering, the mass variation due to fuel consumption has an obvious impact on the dynamics of tethered system, which cannot be neglected. The contributions of the work are mainly shown in two aspects: 1) the improvement of the model; 2) the analysis of dynamics characteristics. As the mass is variable, and the derivative of the mass is directly considered in the traditional Lagrange equation, the expression of generalized force is complicated. To solve this problem, the coagulated derivative is adopted in the paper; besides, the attitude dynamics equations derived in this paper take into account the effect of mass variation and the drift of orbital trajectory at the same time. The bifurcation phenomenon, the pendular motion angular frequency, and amplitudes of tether vibration revealed in this paper can provide a reference for the parameters and controller design in practical engineering. In the article, a dumbbell model is adopted to analyze the dynamics of tethered system, in which the mass variation of base satellite is fully considered. Considering the practical application, the case of orbital transfer under a transversal thrust is mainly studied. Besides, compared with the analytical solutions of librational angles, the effects of mass variation on stability and librational characteristic are studied. Finally, in order to make an analysis of the effect on vibrational characteristic, a lumped model is introduced, which reveals a strong coupling of librational and vibrational characteristics. [ABSTRACT FROM AUTHOR]

The thrust vector control (TVC) scheme is a powerful method in spacecraft attitude control. Since the control of a small spacecraft is being studied here, a solid rocket motor (SRM) should be used instead of a liquid propellant motor. Among the TVC methods, gimbaled-TVC as an efficient method is employed in this paper. The spacecraft structure is composed of a body and a gimbaled-SRM where common attitude control systems such as reaction control system (RCS) and spin-stabilization are not presented. A nonlinear two-body model is considered for the characterization of the gimbaled-thruster spacecraft where, the only control input is provided by a gimbal actuator. The attitude of the spacecraft is affected by a large exogenous disturbance torque which is generated by a thrust vector misalignment from the center of mass (C.M). A linear control law is designed to stabilize the spacecraft attitude while rejecting the mentioned disturbance torque. A semi-analytical formulation of the region of attraction (RoA) is developed to ensure the local stability and fast convergence of the nonlinear closed-loop system. Simulation results of the 3D maneuvers are included to show the applicability of this method for use in a small spacecraft. [ABSTRACT FROM AUTHOR]

The orbital maneuvers of Global Navigation Satellite System (GNSS) Constellations will decrease the performance and accuracy of positioning, navigation, and timing (PNT). Because satellites in the Chinese BeiDou Navigation Satellite System (BDS) are in Geostationary Orbit (GEO) and Inclined Geosynchronous Orbit (IGSO), maneuvers occur more frequently. Also, the precise start moment of the BDS satellites' orbit maneuvering cannot be obtained by common users. This paper presented an improved real-time detecting method for BDS satellites' orbit maneuvering and anomalies with higher timeliness and higher accuracy. The main contributions to this improvement are as follows: (1) instead of the previous two-steps method, a new one-step method with higher accuracy is proposed to determine the start moment and the pseudo random noise code (PRN) of the satellite orbit maneuvering in that time; (2) BDS Medium Earth Orbit (MEO) orbital maneuvers are firstly detected according to the proposed selection strategy for the stations; and (3) the classified non-maneuvering anomalies are detected by a new median robust method using the weak anomaly detection factor and the strong anomaly detection factor. The data from the Multi-GNSS Experiment (MGEX) in 2017 was used for experimental analysis. The experimental results and analysis showed that the start moment of orbital maneuvers and the period of non-maneuver anomalies can be determined more accurately in real-time. When orbital maneuvers and anomalies occur, the proposed method improved the data utilization for 91 and 95 min in 2017. [ABSTRACT FROM AUTHOR]

The frequent maneuvering of BeiDou Geostationary Orbit (GEO) and Inclined Geosynchronous Orbit (IGSO) satellites affects the availability of real-time orbit, and decreases the accuracy and performance of positioning, navigation and time (PNT) services. BeiDou satellite maneuver information cannot be obtained by common users. BeiDou broadcast ephemeris is the only indicator of the health status of satellites, which are broadcast on an hourly basis, easily leading to ineffective observations. Sometimes, identification errors of satellite abnormity also appear in the broadcast ephemeris. This study presents a real-time robust detection method for a satellite orbital maneuver with high frequency and high reliability. By using the broadcast ephemeris and pseudo-range observations, the time discrimination factor and the satellite identification factor were defined and used for the real-time detection of start time and the pseudo-random noise code (PRN) of satellites was used for orbital maneuvers. Data from a Multi-GNSS Experiment (MGEX) was collected and analyzed. The results show that the start time and the PRN of the satellite orbital maneuver could be detected accurately in real time. In addition, abnormal start times and satellite abnormities caused by non-maneuver factors also could be detected using the proposed method. The new method not only improves the utilization of observations for users with the data effective for about 92 min, but also promotes the reliability of real-time PNT services. [ABSTRACT FROM AUTHOR]

Because there are different types of BeiDou constellations with participating geostationary orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites, the maneuvering frequency of BeiDou satellites is higher than that of other navigation systems. The satellite orbital maneuvers lead to orbital parameter failure for several hours from broadcast ephemeris. Due to the missing initial orbit, the maneuvering thrust, and the period of orbital maneuvering, the orbit products of maneuvering satellites cannot be provided by the International Global Navigation Satellite System (GNSS) Service (IGS) and International GNSS Monitoring and Assessment System (iGMAS). In addition, the period of unhealthy status and the orbital parameters of maneuvering satellites in broadcast ephemeris are unreliable, making the detection of orbital maneuver periods more difficult. Here, we develop a method to detect orbital maneuver periods involving two key steps. The first step is orbit prediction of maneuvering satellites based on precise orbit products. The second step is time period detection of orbit maneuvering. The start time detection factor is calculated by backward prediction orbit and pseudo-range observations, and the end time detection factor is calculated by forward prediction orbit and pseudo-range observations. Data of stations from the Multi-GNSS Experiment (MGEX) and iGMAS were analyzed. The results show that the period of orbit maneuvering could be detected accurately for BeiDou GEO and IGSO satellites. In addition, the orbital maneuver period of other GNSS medium Earth orbit (MEO) satellites could also be determined by this method. The results of period detection for orbit maneuvering provide important reference information for precision orbit and clock offset determination during satellite maneuvers.