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- Message from the Guest Editors of the Special Issue on Precise Orbit
Determination-
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PubDate: 2024-09-01
- Perturbed initial orbit determination
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Abstract: Abstract An algorithm for robust initial orbit determination (IOD) under perturbed orbital dynamics is presented. By leveraging map inversion techniques defined in the algebra of Taylor polynomials, this tool returns a highly accurate solution to the IOD problem and estimates a range centered on the aforementioned solution in which the true orbit should lie. To meet the specified accuracy requirements, automatic domain splitting is used to wrap the IOD routines and ensure that the local truncation error, introduced by a polynomial representation of the state estimate, remains below a predefined threshold. The algorithm is presented for three types of ground-based sensors, namely range radars, Doppler-only radars, and optical telescopes, by considering their different constraints in terms of available measurements and sensor noise. Finally, the improvement in performance with respect to a Keplerian-based IOD solution is demonstrated using large-scale numerical simulations over a subset of tracked objects in low Earth orbit. 
PubDate: 2024-09-01
- Autonomous navigation of an asteroid orbiter enhanced by a beacon
satellite in a high-altitude orbit-
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Abstract: Abstract This study aims to assess the autonomous navigation performance of an asteroid orbiter enhanced using an inter-satellite link to a beacon satellite. Autonomous navigation includes the orbit determination of the orbiter and beacon, and asteroid gravity estimation without any ground station support. Navigation measurements were acquired using satellite-to-satellite tracking (SST) and optical observation of asteroid surface landmarks. This study presents a new orbiter–beacon SST scheme, in which the orbiter circumnavigates the asteroid in a low-altitude strongly-perturbed orbit, and the beacon remains in a high-altitude weakly-perturbed orbit. We used Asteroid 433 Eros as an example, and analyzed and designed low- and high-altitude orbits for the orbiter and beacon. The navigation measurements were precisely modeled, extended Kalman filters were devised, and observation configuration was analyzed using the Cramer–Rao lower bound (CRLB). Monte Carlo simulations were carried out to assess the effects of the orbital inclination and altitudes of the orbiter and beacon as key influencing factors. The simulation results showed that the proposed SST scheme was an effective solution for enhancing the autonomous navigation performance of the orbiter, particularly for improving the accuracy of gravity estimation. 
PubDate: 2024-09-01
- Designing a concurrent detumbling and redirection mission for asteroid
mining purposes via optimization-
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Abstract: Abstract Asteroids may contain valuable minerals. A method to exploit asteroid mines is to transfer them closer to the Earth for further mining processes. In this work, we optimally mount a set of fixed-angle spacecraft thrusters on the surface of an asteroid to conduct concurrent detumbling and redirecting to the desired orbit. The optimization objective reconciles the minimum duration of the mission with the minimum required fuel as well as the maximum uniformity of the fuel distribution required for all thrusters. Each thruster can respond to redirection and detumbling commands simultaneously. Redirection and detumbling are performed via the directional adaptive guidance method and PID controllers, respectively, and the weight factors for each orbital element and the gains of the rotational control channels are also optimized in the process. We use the particle swarm optimization algorithm to evaluate the objective function by simulating the entire mission to find the optimal design. The rotational control damps the tumbling of the asteroid without interfering with the simultaneous redirection process and eventually fixes the asteroid in the optimally selected orientation in the inertial reference frame. The rotational velocity and attitude of the asteroid are controlled via separate PID controllers, which are set robustly. We can effectively optimize the mission by collectively tuning both the system’s rotational and redirection behaviors as well as the thrusters’ configuration and optimally selecting the final attitude of the asteroid. 
PubDate: 2024-08-20
- Luring cooperative capture guidance strategy for the pursuit—evasion
game under incomplete target information-
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Abstract: Abstract In this work, we attempt to investigate a luring cooperative guidance strategy for three-player inducer–defender–attacker engagement with field-of-view (FOV) and overload constraints against an attacker with speed advantages under incomplete information. We formulate the three-player inducer–defender–attacker engagement problem as the pursuit–evasion (defender–attacker) game problem. On this basis, an analytical luring cooperative guidance strategy based on backstepping control is proposed to facilitate the defender with zero overloads intercepting the attacker. Additionally, under incomplete information, we offer a parameter delay design approach to delay the unknown parameters and state design. Afterward, an improved adaptive update law is devised to address the incomplete information. The proposed luring cooperative guidance, which incorporates backstepping control and an improved adaptive update law, can guarantee that the defender captures the attacker with zero overloads under luring by the inducer. Additionally, the proposed design adopts the directed communication topology network structure. Finally, we also execute simulations that demonstrate the effectiveness of the designed luring cooperative guidance strategy and reveal that it can be extended to double-hierarchical interception and four-on-two engagement interception. 
PubDate: 2024-08-14
- Low-energy Earth–Moon transfer autonomous guidance considering
high-fidelity orbital dynamics-
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Abstract: Abstract This technical note presents a practical approach to low-energy Earth–Moon transfer autonomous guidance considering high-fidelity orbital dynamics. Initially, autonomous guidance, delineated as a trajectory-tracking problem, is addressed within the framework of a predesigned reference trajectory solution, accompanied by empirical trajectory correction maneuver allocation. A series of two-point boundary value problems is subsequently formulated to incorporate guidance velocity increments. An algorithm employing quasilinearization, discretization, and recursion is proposed to address these boundary value problems, which results in enhanced convergence performance compared with traditional differential-correction-based guidance methods. Finally, a Monte Carlo analysis demonstrates the efficacy of the proposed autonomous guidance approach, indicating its potential for onboard applications. 
PubDate: 2024-08-09
- Near-optimal maneuver design for high-accuracy trans-lunar injection with
highly elliptical phasing loops-
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Abstract: Abstract To match the trans-lunar injection with high accuracy, a near-optimal orbit control method for phasing loops is proposed. Sensitivity analysis was performed based on Gauss’s variational equations, and a near-optimal orbit control strategy was developed. A sequential shooting method was proposed to reduce the dimensions of each shooting problem and improve convergence. To satisfy the accessibility requirements of ground facilities, a maneuvering location adjustment strategy is proposed. The advantage of the delta-V saving of the near-optimal method was verified by comparing with the differential correction method. The robustness of the practical method was verified using Monte Carlo simulations with high-fidelity dynamics. The results of this study can be applied to midcourse correction of phasing loops before the trans-lunar injection of a lunar probe. 
PubDate: 2024-08-09
- Precise orbit determination for Tianwen-1 during mapping phase
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Abstract: Abstract The mapping phase is a key stage of the Tianwen-1 orbiter. It has the longest exploration time and gathers abundant radio tracking data via the Chinese deep space network. Thus, it also provides opportunities for radio science research topics such as the Mars gravity field model, ephemeris, and radio occultation experiments. At this stage, the need for imaging takes the highest priority, leading to frequent attitude adjustments for the spacecraft, which presents challenges for Precise Orbit Determination (POD). To improve the accuracy of the spacecraft’s orbit, this study analyzes the effects of arc length, the empirical acceleration, and the solar radiation pressure parameters on POD, considering the limited number of radio tracking observations. For one-day arcs, the POD is not able to adequately account for wheel off-loading and a few unknown forces with limited observations, but reasonable fitting is performed for the wheel off-loading occurring during tracking periods or the gap between two tracking periods. When extending the POD arc to three days, the estimated empirical acceleration can be well-fitted and reflects the aggregation feature, but the solar radiation pressure parameter has little impact on POD results. The root mean square of two-way range-rate residuals after POD is about 0.18–0.35 mm/s; the orbital position accuracy of 60% of the arcs is better than 100 m. 
PubDate: 2024-07-04
- Initial orbit determination of some cislunar orbits based on short-arc
optical observations-
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Abstract: Abstract Ground- and space-based optical observation is an efficient way to catalog objects in the cislunar space. Initial orbit determination based on optical data is still an open problem for cislunar objects. The motion of these objects usually follows the law of three bodies instead of the two-body one, so current algorithms based on the two-body relation should be revised. Moreover, due to the long duration of most cislunar objects, optical observations of even hours can cover only a small fraction of one orbit, making the initial orbit determination of these objects a typical too-short-arc problem, which is difficult. A way to address this problem is to use the admissible region. In this study, an efficient algorithm constrained by the admissible region is proposed. It is easy to implement because it uses only simple iterations. Its efficiency is proven by comparing it with that of one traditional initial orbit determination algorithm. 
PubDate: 2024-06-15
DOI: 10.1007/s42064-024-0210-z
- Controlled deployment of a long tether to operate as a partial space
elevator-
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Abstract: Abstract The deployment of a long tether to operate as a partial space elevator, starting from a nucleus in geostationary orbit, is studied. Uncontrolled deployment is an inherently unstable process because the center of orbit gradually decreases from the geostationary altitude when deployment progresses. It is also observed that the elasticity of the tether has an important effect on deployment stability. It is shown that the application of a transverse force on the main spacecraft, determined by using linear state feedback and appropriate gains, can stabilize the deployment. An LQR controller is developed. Simulations of the dynamics of the system are carried out using this controller for various parametric values of tether elasticity, deployment rates, etc., to evaluate the efficacy of the controller. 
PubDate: 2024-06-10
DOI: 10.1007/s42064-024-0225-5
- Real-time hybrid method for maneuver detection and estimation of
non-cooperative space targets-
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Abstract: Abstract A novel hybrid scheme for the maneuver detection and estimation of a noncooperative space target was proposed in this study. The optical measurements, together with the range and range rate measurements from the ground-based radars, were used in the tracking scenarios. In many tracking scenarios, radar resources for non-cooperative targets are constrained, particularly for near-earth targets, where multiple objects can only be tracked by a single radar at a time. This limitation hinders the accurate estimation of noncooperative target maneuvers, and can at times result in target loss. Existing literature has addressed this issue to some extent through various maneuvering target-tracking methods. To address this problem, a hybrid maneuver detection and estimation method that combines the input detection and estimation extended kalman filter and the weighted nonlinear least squares method is presented. Simulation results demonstrate that the proposed method outperforms the previous method, offering more accurate and efficient estimations. 
PubDate: 2024-06-06
DOI: 10.1007/s42064-024-0203-y
- Message from the Guest Editors of the Special Issue on Tethered Satellite
System-
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PubDate: 2024-06-01
DOI: 10.1007/s42064-024-0231-7
- Analytical libration control law for electrodynamic tether system with
current constraint-
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Abstract: Abstract This study focuses on stabilizing the libration dynamics of an electrodynamic tether system (EDTS) using generalized torques induced by the Lorentz force. In contrast to existing numerical optimization methods, a novel analytical feedback control law is developed to stabilize the in-plane and out-of-plane motions of a tether by modulating the electric current only. The saturation constraint on the current is accounted for by adding an auxiliary dynamic system to the EDTS. To enhance the robustness of the proposed controller, multiple perturbations of the orbital dynamics, modeling uncertainties, and external disturbances are approximated using a neural network in which the weighting matrix and approximation error are estimated simultaneously, such that these perturbations are well compensated for during the control design of the EDTS. Furthermore, a dynamically scaled generalized inverse is utilized to address the singular matrix in the control law. The closed-loop system is proven to be ultimately bounded based on Lyapunov stability theory. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed analytical control law. 
PubDate: 2024-06-01
DOI: 10.1007/s42064-023-0174-4
- Collision-avoidance strategy for a spinning electrodynamic tether system
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Abstract: Abstract Spinning electrodynamic tether systems (SEDTs) have promising potential for the active removal of space debris, the construction of observation platforms, and the formation of artificial gravity. However, owing to the survivability problem of long tethers, designing collision-avoidance strategies for SEDTs with space debris is an urgent issue. This study focuses on the design of collision-avoidance strategies for SEDTs with an electrodynamic force (Ampere force). The relative distance between the debris and the SEDT is first derived, and then two collision-avoidance strategies are proposed according to the two different cases. When debris collides closer to a lighter subsatellite, a stationary avoidance strategy is proposed to change the spatial position of the subsatellite by adjusting only the angular motion of the tether, which maintains the original orbit of the SEDT. When debris collides closer to a heavier main spacecraft, a comprehensive avoidance strategy is proposed to change the spatial position of the SEDT by slightly modifying the orbital height and changing the tether angular motion simultaneously. The numerical results illustrate that the proposed strategies promptly avoid potential collisions of an SEDT with space debris without significant changes in the orbital parameters of the SEDT. 
PubDate: 2024-06-01
DOI: 10.1007/s42064-023-0175-3
- Optimal orbit transfer of single-tether E-sail with inertially fixed spin
axis-
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Abstract: Abstract This study analyzes the optimal transfer trajectory of a spacecraft propelled by a spin-stabilized electric solar wind sail (E-sail) with a single conducting tether and a spin axis with a fixed direction in an inertial (heliocentric) reference frame. The approach proposed in this study is useful for rapidly analyzing the optimal transfer trajectories of the current generation of small spacecraft designed to obtain in-situ evidence of the E-sail propulsion concept. In this context, starting with the recently proposed thrust model for a single-tether E-sail, this study discusses the optimal control law and performance in a typical two-dimensional interplanetary transfer by considering the (binary) state of the onboard electron emitter as the single control parameter. The resulting spacecraft heliocentric trajectory is a succession of Keplerian arcs alternated with propelled arcs, that is, the phases in which the electron emitter is switched on. In particular, numerical simulations demonstrated that a single-tether E-sail with an inertially fixed spin axis can perform a classical mission scenario as a circle-to-circle two-dimensional transfer by suitably varying a single control parameter. 
PubDate: 2024-05-13
DOI: 10.1007/s42064-023-0194-0
- Dynamic analysis of tethered defunct satellites with solar panels
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Abstract: Abstract A precise dynamic model for towing and removing a defunct satellite with solar panels in orbit using a tethered net often has low computational efficiency owing to the complex contact and collision between the net and panels, which is not conducive to research. To solve this problem, a “single main tether–multiple subtether” bifurcation structure with beads was employed as the tethered net model. This study investigated the dynamics of tethered defunct satellites with solar panels, particularly the behavior of the attitude of the tethered satellite, oscillation of the main tether, and vibration of solar panels under different conditions. The results showed that different attachment configurations of the subtethers and the flexibility of the main tether have an evident impact on the dynamic characteristics of the system. 
PubDate: 2024-05-13
DOI: 10.1007/s42064-024-0206-8
- Precise orbit determination for low Earth orbit satellites using GNSS:
Observations, models, and methods-
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Abstract: Abstract Spaceborne global navigation satellite system (GNSS) has significantly revolutionized the development of autonomous orbit determination techniques for low Earth orbit satellites for decades. Using a state-of-the-art combination of GNSS observations and satellite dynamics, the absolute orbit determination for a single satellite reached a precision of 1 cm. Relative orbit determination (i.e., precise baseline determination) for the dual satellites reached a precision of 1 mm. This paper reviews the recent advancements in GNSS products, observation processing, satellite gravitational and non-gravitational force modeling, and precise orbit determination methods. These key aspects have increased the precision of the orbit determination to fulfill the requirements of various scientific objectives. Finally, recommendations are made to further investigate multi-GNSS combinations, satellite high-fidelity geometric models, geometric offset calibration, and comprehensive orbit determination strategies for satellite constellations. 
PubDate: 2024-04-11
DOI: 10.1007/s42064-023-0195-z
- Spaceborne and ground-based sensor collaboration: Advancing resident space
objects’ orbit determination for space sustainability-
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Abstract: Abstract The limited space around the Earth is getting cluttered with leftover fragments from old missions, creating a real challenge. As more satellites are launched, even debris pieces as small as 5 mm must be tracked to avoid collisions. However, it is an arduous and challenging task in space. This paper presents a technical exploration of ground-based and in-orbit space debris tracking and orbit determination methods. It highlights the challenges faced during on-ground and in-orbit demonstrations, identifies current gaps, and proposes solutions following technological advancements, such as low-power pose estimation methods. Owing to the numerous atmospheric barriers to ground-based sensors, this study emphasizes the significance of spaceborne sensors for precise orbit determination, complemented by advanced data processing algorithms and collaborative efforts. The ultimate goal is to create a comprehensive catalog of resident space objects (RSO) around the Earth and promote space environment sustainability. By exploring different methods and finding innovative solutions, this study contributes to the protection of space for future exploration and the creation of a more transparent and precise map of orbital objects. 
PubDate: 2024-03-14
DOI: 10.1007/s42064-023-0193-1
- Evaluation of E-sail parameters on central spacecraft attitude stability
using a high-fidelity rigid–flexible coupling model-
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Abstract: Abstract This study examines the impact of electric solar wind sail (E-sail) parameters on the attitude stability of E-sail’s central spacecraft by using a comprehensive rigid–flexible coupling dynamic model. In this model, the nodal position finite element method is used to model the elastic deformation of the tethers through interconnected two-node tensile elements. The attitude dynamics of the central spacecraft is described using a natural coordinate formulation. The rigid–flexible coupling between the central spacecraft and its flexible tethers is established using Lagrange multipliers. Our research reveals the significant influences of parameters such as tether numbers, tether’s electric potential, and solar wind velocity on attitude stability. Specifically, solar wind fluctuations and the distribution of electric potential on the main tethers considerably affect the attitude stability of the spacecraft. For consistent management, the angular velocities of the spacecraft must remain at target values. Moreover, the attitude stability of a spacecraft has a pronounced dependence on the geometrical configuration of the E-sail, with axisymmetric E-sails proving to be more stable. 
PubDate: 2024-03-13
DOI: 10.1007/s42064-023-0190-4
- A comparative assessment of gravitational field modeling methods for
binary asteroid landing-
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Abstract: Abstract The tradeoff between accuracy and efficiency in gravitational field modeling for binary asteroid landing is one of the challenges in dynamical analyses. Four representative gravitational modeling methods are employed and compared in this study. These are the sphere–sphere model, ellipsoid–sphere model, inertia integral-polyhedron method, and finite element method. This study considers the differences between these four models, particularly their effects on the landing dynamics of a lander. A framework to simulate the coupled orbit–attitude motion of a lander in a binary system is first established. Numerical simulations are then performed on the natural landings on the second primary of the (66391) Moshup–Squannit system. The results show significant differences in the final landing dispersions, settling time, and sliding distance when applying the simplified models. On the basis of the modeling accuracy and computational efficiency, the finite element method should be chosen for future missions. 
PubDate: 2024-03-13
DOI: 10.1007/s42064-024-0202-z
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