Search Results (46)

Satellite formation flying faces significant challenges in maintaining its desired configurations due to various orbital perturbations, particularly in low-Earth-orbit environments. This paper presents a novel approach to generating fuel-optimal reference trajectories for in-track satellite formations by incorporating both the Earth’s oblateness ($J_2$ perturbation) and the inherent nonlinearity of the two-body problem. The resulting indirect optimal control problem is solved using Pontryagin Neural Networks (PoNNs). The proposed method transforms the conventional two-point boundary value problem into a mathematical programming problem, enabling the efficient computation of optimal trajectories. The effectiveness of our approach is validated through extensive numerical simulations at different inclinations of the chief satellite (0–90°) and cross-track separation distances (1–400 km), demonstrating significant reductions in annual fuel consumption compared to conventional approaches. The feasibility of these optimal trajectories is verified through closed-loop simulations using a PD controller, confirming their practical applicability in realistic mission scenarios. This research contributes to enhancing the long-term sustainability of satellite formation flying missions by optimizing fuel efficiency while maintaining precise formations. Full article

The high-repetition-rate dual-microcomb interferometry, characterized by its high precision, rapid measurement speed, and ease of integration, shows significant promise in applications such as precision spectroscopy and high-speed precision ranging. As dual-microcomb interferometry usually requires a specific difference in repetition rates, tuning the repetition rate of the microcomb is crucial for integrating dual-microcomb sources and enhancing the measurement performance, including the precision and the update rate. This work demonstrates a coherent dual-microcomb system driven by a single continuous-wave fiber laser at 1560.49 nm. The system employs a hybrid tuning method combing single-sideband (SSB) modulation for precision pump frequency control (enabling continuous repetition rate tuning across a 4.34 MHz range) with thermal control for coarse tuning. The linear dependence between the repetition rate and pump modulation frequency shows a measured coefficient of 143.58 kHz/GHz. This method enables dual microcombs with MHz-level repetition rate tuning, significantly relaxing the fabrication and pairing requirements for microresonators. The advancement is particularly valuable for dual-comb spectroscopy and ranging applications, including gas detection and satellite formation flying. Full article

In satellite formation flying, maintaining a predefined safety distance between the reference satellite and its accompanying satellites is critical to prevent collisions—a requirement that traditional control methods fail to satisfy. This paper proposes a novel safety control algorithm that enforces the relative position constraint as a formal safety condition. Specifically, we construct a high-order control barrier function (HOCBF) tailored to the dynamics of satellite formations, which defines a safety set that guarantees collision avoidance. By formulating and solving a quadratic programming problem embedded with the HOCBF, we obtain a safe controller that ensures the forward invariance of the safety set. Simulation results demonstrate that our controller effectively maintains the required safety distance and prevents collisions under various disturbance scenarios, outperforming conventional methods in terms of response speed and robustness. These findings confirm the practical advantages of the proposed approach for safe satellite formation flying. Full article

In this paper, a recently proposed $SE\left(3\right)$-constrained extended Kalman filter (EKF) is extended to formulate a strategy for relative orbit estimation in a space-based sensor network. The resulting consensus $SE\left(3\right)$-constrained EKF utilizes space-based sensor fusion and is applied to the problem of spacecraft proximity operations and formation flying. The proposed filter allows for the state (i.e., pose and velocities) estimation of the deputy satellite while accounting for measurement error statistics using the rotation matrix to represent attitude. Via a comparison with a conventional filter in the literature, it is shown that the use of the proposed consensus $SE\left(3\right)$-constrained EKF can improve the convergence performance of the existing filter for satellite formation flying. Moreover, the benefits of faster convergence and consensus speed by using communication networks with more connections are illustrated to show the significance of the proposed sensor fusion strategy in spacecraft proximity operations. Full article

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. Full article

The PIESAT-01 constellation is the world’s first multi-baseline distributed synthetic aperture radar (SAR) constellation with a “Cartwheel” formation. The “Cartwheel” formation is a unique formation in which four satellites fly in companion orbits, ensuring that at any given moment, the main satellite remains at the center, with three auxiliary satellites orbiting around it. Due to this unique configuration of the PIESAT-01 constellation, four images of the same region and six pairs of baselines can be obtained with each shot. So far, there has been no imaging and interference research based on four-satellite constellation measured data, and there is an urgent need to explore algorithms for the “Cartwheel” configuration imaging and digital surface model (DSM) production. This paper introduces an improved bistatic SAR imaging algorithm under the four-satellites interferometric mode, which solves the problem of multi-orbit nonparallelism in imaging while ensuring imaging coherence and focusing ability. Subsequently, it presents an interferometric processing method for the six pairs of baselines, weighted fusion based on elevation ambiguity from different baselines, to obtain a high-precision DSM. Finally, this paper selects the Dingxi region of China and other regions with diverse terrains for imaging and DSM production and compares the DSM results with ICESat-2 global geolocated photon data and TanDEM DSM data. The results indicate that the accuracy of PIESAT-01 DSM meets the standards of China’s 1:50,000 scale and HRTI-3, demonstrating a high level of precision. Moreover, PIESAT-01 data alleviate the reliance on simulated data for research on multi-baseline imaging and multi-baseline phase unwrapping algorithms and can provide more effective and realistic measured data. Full article

Satellite formation flying technology currently represents a focal point in space mission research. Traditional spacecraft payload performance and lifespan are often constrained by propellant limitations. Electromagnetic Formation Flying (EMFF), a propellant-free formation flying technique, has garnered widespread attention. Its inherent strong nonlinearity and coupling present challenges for high-precision control within EMFF. This paper presents the relative motion dynamics of a two-satellite EMFF in the port-Hamiltonian framework and constructs an accurate nonlinear model of the dynamics. Utilizing the concept of Interconnection and Damping Assignment and nonlinear disturbance observer, a composite disturbance-rejection passivity-based controller is designed, offering a method for controlling the magnetic dipole strength of formation satellites. Finally, numerical simulations are conducted to demonstrate the viability of the proposed dynamics model and control strategy. Full article

This paper created a flight trajectory model of five uncrewed aerial vehicles (UAVs) in the geocentric coordinate system, provided the UAVs fly in the specified formation. Based on this model, equations for determining the position of a selected member of a group of UAVs were created, provided that the group communicates with each other in its telecommunications network. The simulation confirmed that if we know the exact coordinates of the four member UAVs of the group and their distances from the leader of the group, then the mean value of the error in determining its position in flight is equal to 0.044 m, and the variance is equal to 2.9 m². We consider these errors to be methodological errors of the proposed method. Next, we checked how the error of determining the position of the group leader depends on the distance measurement errors between the individual UAVs and the group leader. The simulation confirmed that if errors in measuring the distance between individual UAVs and the group leader are from 0.01 m to 12.0 m, the mean values of group commander position determination errors range from 0.11 m to 34.6 m. The simulation result showed that to accurately determine the group commander’s position, the distance measurement errors between individual UAVs and the group commander must be less than 1.9 m. The research results showed that the telemetry method can be used to determine the position of individual members of the UAV group. The advantage of this method is that it does not require the reception of signals from satellite navigation systems, which can be interfered with under certain conditions. The disadvantage of the method is the need to synchronize the time bases of individual UAVs that communicate in the telecommunications network. Full article

In recent years, the number of expected missions to the Moon has increased significantly. With limited terrestrial-based infrastructure to support this number of missions, as well as restricted visibility over intended mission areas, there is a need for space navigation system autonomy. Autonomous on-board navigation systems in the lunar environment have been the subject of study by a number of authors. Suggested systems include optical navigation, high-sensitivity Global Navigation Satellite System (GNSS) receivers, and navigation-linked formation flying. This paper studies the interoperable nature and fusion of proposed autonomous navigation systems that are independent of Earth infrastructure, given challenges in distance and visibility. This capability is critically important for safe and resilient mission architectures. The proposed elliptical frozen orbits of lunar navigation satellite systems will be of special interest, investigating the derivation of orbit determination by non-terrestrial sources utilizing celestial observations and inter-satellite links. Potential orbit determination performances around 100 m are demonstrated, highlighting the potential of the approach for future lunar navigation infrastructure. Full article

This paper investigates the performance of the forthcoming lunar navigation satellite systems for estimating not only the position of an onboard receiver in a lunar inertial reference frame but also, and with a consistent accuracy, the relative position between two or more spacecraft in proximity. This could be the case of two spacecraft performing a rendezvous, of a lander released by an orbiter, or the case of the permanent relative navigation service for a formation of satellites around the Moon. The considered observables are the pseudorange and pseudorange-rate measurements provided by the upcoming lunar communication and navigation system (LCNS), expected to support lunar missions. A single-stage Kalman filter is implemented, and its performance is demonstrated through error statistics, which are then compared to what can be achieved with sequential filtering. Full article

In this paper, the problem of autonomous optimal absolute orbit keeping for a satellite mission in Low Earth Orbit using electric propulsion is considered. The main peculiarity of the approach is to support small satellite missions in which the platform is equipped with a single thruster nozzle that provides acceleration on a single direction at a time. This constraint implies that an attitude maneuver is necessary before or during each thrusting arc to direct the nozzle into the desired direction. In this context, an attitude guidance algorithm specific for the orbit maneuver has been developed. A Model Predictive Control scheme is proposed, where the attitude kinematics are coupled with the orbital dynamics in order to obtain the optimal guidance profiles in terms of satellite state, reference attitude, and thrust magnitude. The proposed control scheme is developed exploiting formation flying techniques where the reference orbit is that of a virtual spacecraft that the main satellite is required to rendezvous with. In addition to the controller design, the closed-loop configuration is presented supported by numerical simulations. The efficacy of the proposed autonomous orbit-keeping approach is shown in several application scenarios. Full article

The paper presents a study of decentralized control for a satellite formation flying mission that uses differential lift and drag to enforce the relative positioning requirements. All spacecraft are equipped with large sunlight reflectors so that, given the appropriate lighting conditions, the formation as a whole can be made visible from the Earth as a configurable pixel image in the sky. The paper analyzes the possibility of achieving a pre-defined lineup of the formation by implementing decentralized aerodynamic-based control through the orientation of sunlight reflectors relative to the incoming airflow. The required relative trajectories are so-called projected circular orbits which ensure the rotation of the image with the orbital period. The choice of the reference trajectory for each satellite is obtained by minimizing the total sum of relative trajectory residuals. The control law is based on the linear-quadratic regulator with the decentralized objective function of reducing the mean deviation of each satellite’s trajectory relative to the other satellites. The accuracy of the required image construction and convergence time depending on the initial conditions and orbit altitude are studied in the paper. Full article

A satellite formation operating in low-altitude orbits is subject to perturbations associated to the higher-order harmonics of the gravitational field, which cause a degradation of the formation configurations designed based on the unperturbed model of the Hill–Clohessy–Wiltshire equations. To compensate for these effects, periodic reconfiguration maneuvers are necessary, requiring the prior allocation of a propellant mass budget and, eventually, the use of resources from the ground segment, having a non-negligible impact on the complexity and cost of the mission. Using the Hamiltonian formalism and canonical transformations, a model is developed that allows designing configurations for formation flying invariant with respect to the zonal harmonic perturbation. $J_n$ invariant configurations can be characterized, selecting the drift rate (or boundedness condition) and the amplitude of the oscillations, based on four parameters which can be easily converted in position and velocity components for the satellites of the formation. From this model, a guidance strategy is developed to inject a satellite approaching another spacecraft into a bounded relative trajectory about it and the optimal time for the maneuver, minimizing the total $\mathrm{\Delta }V$, is identified. The effectiveness of the model and of the guidance strategy is verified on some scenarios of interest for formations operating in a sun-synchronous and a medium-inclination low Earth orbit and a medium-inclination lunar orbit. Full article

Space-based Earth Observation (EO) systems have undergone a continuous evolution in the twenty-first century. With the help of space-based Maritime Domain Awareness (MDA), specially Automatic Identification Systems (AIS), their applicability across the world’s waterways, among others, has grown substantially. This research work explores the potential applicability of Synthetic Aperture Radar (SAR) and Distributed Satellite Systems (DSS) for the MDA operation. A robust multi-baseline Along-Track Interferometric Synthetic Aperture Radar (AT-InSAR) Formation Flying concept is proposed to combine several along-track baseline observations effectively for single-pass interferometry. Simulation results are presented to support the feasibility of implementing this acquisition mode with autonomous orbit control, using low-thrust actuation suitable for electric propulsion. To improve repeatability, a constellation of this formation concept is also proposed to combine the benefits of the DSS. An MDA application is considered as a hypothetical mission to be solved by this combined approach. Full article

Beamwidth-reconfigurable antennas are useful for the intersatellite link of low earth orbit formation flying and constellation, as they prevent unauthorized satellites from eavesdropping. In this article, a circularly polarized slot array antenna based on a half-mode substrate-integrated waveguide (HMSIW) for the K-band beamwidth reconfiguration is proposed using a new radio frequency (RF) switch structure and a pair of modified −45° and +45° linearly polarized HMSIW slot arrays for the dual operation of a single-pole double-throw (SPDT)/a power divider (PD) and easy integration with other components, respectively. The RF switch structure consists of a T-junction PD, λ/4 lines, and beam lead PIN diodes with current control resistors and without a DC block circuit for low DC power consumption and size reduction. The −45°/+45° linearly polarized HMSIW slot arrays providing linear and circular polarizations (LP and CP, respectively) are operated for CP. The use of a short-circuited termination instead of dissipative termination results in easier integration with other components because the 16 radiating slots consume most of the input power. The dimension of the beamwidth-reconfigurable antenna including the bottom metal layer is 157.2 × 23.3 × 0.254 mm³ (12.5λ₀ × 1.86λ₀ × 0.0202λ₀). The RF switch for the SPDT shows the insertion losses of 1.8–2.3 and 16.7–24.2 dB and an isolation of 20.9–33.4 dB for both outputs within the 10-dB bandwidth. The RF switch for the PD has an insertion loss of 3.9–4.8 dB. The one- and two-antenna operation modes of the CP antenna provide the gains of 9.44 and 6.99 dBic, the axial ratios of 2.24 and 3.47 dB, and the horizontal beamwidths of 35.8° and 78.2°, respectively. Full article