Spacecraft Formation Research Articles

Reconfigurable Guidance Strategy for Compensating Actuator Faults in Spacecraft Formation Flying

The capacity to keep a desired topology with a requested accuracy plays a significant role in every spacecraft formation-flying operation. These missions can be terminated in case of an unexpected spacecraft fault, preventing the system from returning to its nominal configuration. This paper presents and tests a new recovery solution, called Reconfigurable Guidance Strategy (RGS), for the spacecraft formation-flying control problem subject to a look-in-place permanent thruster fault. The proposed method relies on autonomously and in real-time reconfiguring the guidance function to compensate for the loss of the spacecraft actuation system. The performance and cost of the RGS have been tested in a high-fidelity simulation scenario, the 42 spacecraft simulator developed by NASA Goddard Space Flight Center, taking into account orbital and rotational nonlinear coupled dynamics, high-order perturbation models, and actuator and sensor models. The numerical simulation results have demonstrated the proposed recovery strategy’s effectiveness, feasibility, and robustness.

Spacecraft formation flying orbital control for earth observation mission

Synthetic Aperture Radar (SAR) sensors have gained much attention for multiple civil use cases, where NewSpace startups have launched and planning to launch sensors to orbit to harvest the unique capabilities of SAR for the Earth Observation (EO) market. Unlike optical, SAR can capture images in all lighting conditions and penetrate cloud cover, generating exceptional use cases, which makes SAR the most reliable sensor. For example, monitoring soil deformation with millimeter accuracy, oil spills, crop lodging, and typical EO use cases of optical sensors that are unable to penetrate the clouds or see at night. However, SAR is still limited in civil use cases because it is tough to interpret. In addition, unlike government users who can consume the SAR data directly, most civil end-users need analytics on top of the data. To unlock the potential civil use cases, many experts believe that optical EO data should be fused with SAR at the EO upstream, thus suggesting optical and SAR sensors fly in formation. Spacecraft Formation Flying (SFF) is one of the key technology enablers for space exploration and EO space missions. This paper presents an SFF EO mission (SAR and Optical) design considering orbit requirements to maximize user objectives inspired by OptiSAR™ Constellation.

Consensus SE(3)-Constrained Extended Kalman Filter for Close Proximity Orbital Relative Pose Estimation

In this paper, a recently proposed SE(3)-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(3)-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(3)-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.

Distributed control of spacecraft formation under [formula omitted] perturbation in the port-Hamiltonian framework

To control the relative position and relative velocity of spacecraft formation, a time-varying nonlinear relative motion model under J2 perturbation in an elliptical orbit is established in the port-Hamiltonian (PH) framework, and a distributed control law for spacecraft formation is developed using the consensus algorithm for parameter estimation and the passivity-based control (PBC) method based on the state-error interconnection and damping assignment (IDA) technique. First, the influence of J2 perturbation on the potential energy and orbit parameters in the model is considered when the relative motion model is built in the PH frame, and the expression of the relative motion acceleration under J2 perturbation is given. Second, to solve the problem that the state of the chief spacecraft cannot be directly obtained from the deputy spacecraft under distributed communication, a consensus-based parameter estimation method is introduced, the estimated parameter of the chief spacecraft is applied to the relative motion model in the PH frame, and a state error model with the estimated parameters derived from the consistency algorithm is established. Then, after the stability analysis is conducted on the desired PH system containing the estimated parameter values, the desired Hamiltonian energy function with the estimated parameters is designed according to the time-varying errors of the relative equilibrium states of the deputy spacecraft and the errors between deputy spacecraft, and the distributed control law of spacecraft formation is derived based on the state-error IDA-PBC method. Finally, the expected relative motion trajectory designed based on the TH equation is used to simulate a spacecraft formation under J2 perturbation, and the results indicate that the spacecraft can quickly converge to the expected formation under the influence of the control law.

Self-learning for translational control of elliptical orbit spacecraft formations

PurposeThis paper aims to investigate the relative translational control for multiple spacecraft formation flying. This paper proposes an engineering-friendly, structurally simple, fast and model-free control algorithm.Design/methodology/approachThis paper proposes a tanh-type self-learning control (SLC) approach with variable learning intensity (VLI) to guarantee global convergence of the tracking error. This control algorithm utilizes the controller's previous control information in addition to the current system state information and avoids complicating the control structure.FindingsThe proposed approach is model-free and can obtain the control law without accurate modeling of the spacecraft formation dynamics. The tanh function can tune the magnitude of the learning intensity to reduce the control saturation behavior when the tracking error is large.Practical implicationsThis algorithm is model-free, robust to perturbations such as disturbances and system uncertainties, and has a simple structure that is very conducive to engineering applications.Originality/valueThis paper verified the control performance of the proposed algorithm for spacecraft formation in the presence of disturbances by simulation and achieved high steady-state accuracy and response speed over comparisons.

Trajectory tracking PID passivity-based control of spacecraft formation flying around Sun-Earth L2 point in the port-Hamiltonian framework

Spacecraft formation flying for interferometric observations around the 2nd Lagrange point in the Sun-Earth system (SEL2) is currently focal point in deep space exploration research, which demands high precision in relative position control of spacecraft. This paper proposes the relative motion dynamics of satellite formations around the L2 point in the port-Hamiltonian framework, and establishes a high-precision nonlinear dynamics model. PID passivity-based control (PID-PBC) is widely used in engineering. However, existing methods of PID-PBC cannot address the trajectory tracking issues in port-Hamiltonian systems. Utilizing the contraction properties of the port-Hamiltonian system, this paper proposes the trajectory tracking PID-PBC (tPID-PBC) approach, effectively resolving trajectory tracking issues for formation dynamics around L2 point in port-Hamiltonian framework. The paper details explicit solutions of the Partial Differential Equations (PDE) for the tPID-PBC method and its controller structure, and references the trajectories of interferometric observation formations, to verify the method’s effectiveness through numerical simulation. The presented control approach is applicable across generic port-Hamiltonian systems, offering substantial theoretical value.

Distributed finite‐time attitude coordination control of spacecraft formations with multiple constraints

SummaryThis paper addresses the issue of distributed finite‐time attitude coordination control of spacecraft formations with multiple constraints on angular velocities and control torques. First, the multiple constrained problem is transformed into a bounded issue by virtue of the nonlinear transformation technique and an input saturation model. Next, the nearest neighbor rule is applied to deal with the problem of the unavailability of the leader's information to all followers. Then, a distributed attitude coordination control algorithm is derived to enforce that all attitude tracking errors can converge to a neighborhood around the origin in finite time even when there exist multiple constraints and external disturbances imposed on spacecraft systems. Finally, several numerical simulation examples are presented to illustrate the efficiency of the derived method.

Distributed prescribed-time coordinated control of spacecraft formation flying under input saturation

This paper studies the prescribed-time relative motion control problem of spacecraft formation flying under input saturation. Using prescribed-time theory, a prescribed-time sliding mode is designed such that the states on the sliding mode converge to the equilibrium in the prescribed time. Based on the prescribed-time sliding mode, a prescribed-time relative motion tracking controller is developed, which guarantees fast formation maneuvers with feasible fuel consumption and strong robustness under input saturation. Furthermore, a simulation example is carried out to verify the effectiveness of the proposed controller.

Fixed-time coordination control for 6-DOF attitude-orbit coupled spacecraft formation flying

This paper presents a distributed fixed-time control protocol for 6-DOF(degree-of-freedom) attitude-orbit coupled spacecraft formation flying with external disturbances. Firstly, the 6-DOF attitude-orbit coupled dynamics is established. The communication topology between the spacecraft in the formation is described by a directed graph. Secondly, a fixed-time disturbance observer (FxTDO) is designed to ensure that the estimation errors of the unknown external disturbances can converge to zero in fixed time. Thirdly, based on non-singular fixed-time terminal sliding mode (NFFTSM) surface, the fixed-time coordination control protocol is proposed combined with the fixed-time disturbance observer, which can guarantee that each spacecraft can track their desirable positions and attitudes in fixed time. The stability of the closed-loop system is proved through Lyapunuov method. Finally, simulation results for a formation with one virtual leader and five followers demonstrate the effectiveness of the proposed control scheme.

Robust attitude coordinated control for gravitational-wave detection spacecraft formation with large-scale communication delays

This paper concentrates on robust attitude control issues for spacecraft formation in gravitational-wave detection missions. Notably, with the large-scale communication delays brought by the million kilometers-scale inter-satellite distance, the exponential convergence of the closed-loop delayed system is firstly achieved via a new delay-dependent nominal attitude coordinated control scheme. Then, a finite-time disturbance observer is deployed to reconstruct the unknown lumped disturbance from internal uncertainties and the external environment. Meanwhile, an integral sliding manifold is embedded in the delay-dependent attitude controller for superior systems’ robustness. Finally, two simulation examples illustrate the feasibility and effectiveness of the proposed attitude control strategy for in-orbit gravitational-wave detection spacecraft systems.

Cooperative control method of multiple spacecraft formation based on graphtheory

Spacecraft cluster is a new way of multi-vehicle cooperation and a major problem in the current space distribution system. A large number of core technologies of spacecraft cluster technology need to be simulated, analyzed and verified on the ground. On this basis, this article proposes the construction of a spacecraft system model and a dynamic model, and designs a path planning method that combines the spacecraft system model with the a* algorithm. And use the Morphin search tree algorithm to improve the A-star algorithm, and then simulate and analyze the spacecraft formation control scheme. The simulation results of trajectory planning show that after running the model for 21 ms, the improved A* algorithm achieved the expected error. Its MAE value is 10 - 4, achieving good path planning effect. The research plan can effectively achieve control of spacecraft formation and meet the needs of collaborative tasks and navigation route planning.

Attitude consensus coordination algorithm for spacecraft formation under compound disturbance

To address the attitude coordination and consensus tracking problem in the multi-spacecraft system, a distributed attitude-coordinated strategy based on the Fixed-time theory is proposed. An observer based on second-order integral sliding mode is designed to accurately estimate the compound disturbance, which consists of external disturbance and inertia uncertainties. On the basis of the observed information, a distributed Fixed-time attitude coordination controller is proposed, which can guarantee the attitude tracking errors converge to zero in a fixed time. System stability is analyzed by using the Lyapunov function. Finally, simulations and comparison analysis demonstrate the effectiveness and superiority of the proposed control scheme.

Searching for new physics in the Solar System with tetrahedral spacecraft formations

Searching for new physics in the Solar System with tetrahedral spacecraft formations

Spacecraft Formation Keeping and Reconfiguration Using Optimal Visual Servoing

This paper proposes a direct visual servoing system for spacecraft guidance in formation flying scenarios. The proposed image-based visual servoing system uses image information for planning and executing formation acquisition, reconfiguration, and maintenance maneuvers. The system assumes that LEDs are located at specific points on the satellites, enabling the visual servoing controller to rely on continuous tracking of these features in the camera’s image plane. Analytical developments demonstrate that the proposed optimal visual control system is stable and optimal, and it acts on both the orbital and attitude dynamics of the spacecraft, considering circular and elliptical reference orbits. The distributed image-based controller defines a cost function that minimizes control efforts, and the paper proses an optimal framework for developing controllers that address the issue. A ROS-based simulation tool was used to test the proposed visual servoing controller in a realistic small-sat formation flying scenario. Results indicate that the proposed distributed control strategy is viable and robust against environmental perturbations and disturbances in sensing and actuation.

Fixed-Time Coordinated Attitude Control for spacecraft formation flying via event-triggered and delayed communication

This article tackles the challenge of achieving fixed-time coordinated attitude control for spacecraft formation flying when dealing with event-triggered and delayed communication. First and foremost, we introduce a fixed-time observer that leverages event-triggered, time-delayed information to enable follower spacecraft to access the leader’s commands within a directed, switching topology. In particular, the observer possesses the ability to effectively mitigate the impact of communication delays on information propagation. Following this, a fixed-time controller that empowers each follower to precisely follow the leader’s trajectory while maintaining the formation configuration is devised. Ultimately, we validate the feasibility and superiority of the proposed algorithm through numerical simulations and practical spacecraft ground experiments conducted with planar air-floating robots.

Dynamic event‐triggered orbit coordination for spacecraft formation via a self‐learning sliding mode control approach

SummaryThis article investigates the issue of orbit coordination control for a class of multi‐spacecraft formation systems in presence of limited communication and external disturbance. To solve the limitation of communication sources, a dynamic event trigger (DET) mechanism is developed to reduce the communication frequency between the follower spacecrafts. Subsequently, we explore a robust DET mechanism‐based distributed self‐learning sliding mode control design, in which a variable learning intensity‐based iterative learning algorithm is designed to approximate and compensate space perturbation. This approach can guarantee an event triggering sequence without Zeno phenomenon and accurate coordination control for formation configuration simultaneously. Compared with the traditional event‐triggered control and other state‐of‐the‐art approaches, the distributed DET control scheme achieves higher control accuracy of formation configuration meanwhile requires less communication resource. Finally, a series of numerical simulations demonstrate the feasibility and superiority of the event triggered control method.

Formation-flying interferometry in geocentric orbits

Context. Spacecraft formation flying serves as a method of astronomical instrumentation that enables the construction of large virtual structures in space. The formation-flying interferometry generally requires very high control accuracy, and extraterrestrial orbits are typically selected. To pave the way for comprehensive missions, proposals have been made for preliminary space missions, involving nano- or small satellites, to demonstrate formation-flying interferometry technologies, especially in low Earth orbits. From a theoretical perspective, however, it is unknown where and to what extent feasible regions for formation-flying interferometry should exist in geocentric orbits. Aims. This study aims to demonstrate the feasibility of formation-flying interferometry in geocentric orbits in which various perturbation sources exist. Geocentric orbits offer the advantage of economic accessibility and the availability of proven formation-flying technologies tailored for Earth orbits. Its feasibility depends on the existence of specific orbits that satisfy a small-disturbance environment with good observation conditions. Methods. Spacecraft motions in Earth orbits subjected to perturbations are analytically modeled based on celestial mechanics. The magnitudes of the accelerations required to counteract these perturbations are characterized by parameters such as the semimajor axis and the size of the formation. Results. Small-perturbation regions tend to appear in higher-altitude and shorter-separation regions in geocentric orbits. Candidate orbits are identified in high Earth orbits for the triangular laser-interferometric gravitational-wave telescope, which is 100 km in size, and in medium Earth orbits for the linear astronomical interferometer, which is 0.5 km in size. A low Earth orbit with a separation of approximately 0.1 km may be suitable for experimental purposes. Conclusions. Geocentric orbits are potentially applicable for various types of formation-flying interferometry.

Trajectory Planning for Spacecraft Formation Reconfiguration Using Saturation Function and Difference-of-Convex Decomposition

Trajectory Planning for Spacecraft Formation Reconfiguration Using Saturation Function and Difference-of-Convex Decomposition

Noncooperative Target Finite-Time Surrounding Control of Spacecraft Formation

This paper proposes a novel distributed control method for surrounding a noncooperative target that has maneuverability by spacecraft formation. A relative orbit error dynamic model between the target and the formation is established dependent on a reference spacecraft under the 2-body assumption. To estimate and compensate for the target’s control input rapidly, a novel finite-time extended state observer is developed. It is stable in the sense of fast finite-time uniformly ultimately bounded stability. A fast terminal sliding mode controller is proposed for finite-time convergence of the system. Simulation examples are implemented to show the effectiveness of proposed algorithm.

Learning-Based Reconfiguration of Charged Spacecraft Formation in Geomagnetic Field.

This article introduces a novel approach for spacecraft formation flying utilizing Lorentz-augmented techniques. It demonstrates that the relative motion among spacecraft, driven by the Lorentz force, possesses equilibrium states beneficial for formation maintenance. However, for effective formation reconfiguration, reliance solely on the Lorentz force is insufficient; low thrust is also necessary. To address this, this article proposes an optimal control framework based on reinforcement learning (RL). It derives the nonlinear dynamics of relative motion within the geomagnetic field, considering intersatellite Lorentz force, atmospheric drag, and Earth's gravitational harmonics. The study employs Lagrangian coherent structure analysis to identify relative equilibrium configurations and develops an RL-based optimal control strategy for real-time formation reconfiguration. By leveraging optimal demonstrations, the framework guides the agent's actions to match these demonstrations over time, especially when encountering out-of-distribution states. Numerical simulations confirm the method's optimality, robustness, and real-time performance, highlighting its potential in achieving optimal control and adapting to varying environment in future space missions.