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Accurate sensing and control are important for high-performance formation control of spacecraft systems. This paper presents a strategy of disturbance estimation and distributed predefined-time control for the formation of multi-spacecraft systems with uncertainties based on a disturbance observer. The process begins by formulating a kinematics model for the relative motion of spacecraft, with the formation's communication topology represented by a directed graph for the formation system of the spacecraft. A disturbance observer is then developed to estimate the disturbances, and the estimation errors can be convergent in fixed time. Following this, a disturbance-estimation-based sliding mode control is proposed to guarantee the predefined-time convergence of the multi-spacecraft formation system, regardless of initial conditions. It allows each spacecraft to reach its desired position within a set time frame. The results of the analysis of the multi-spacecraft formation system are also provided. Finally, an example simulation of a five-spacecraft formation flying system is provided to demonstrate the presented formation control method. [ABSTRACT FROM AUTHOR]

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. • Spacecraft formation attitude control in gravitational-wave detection is studied. • Large-scale communication delays (LCD) among formation members are firstly modeled. • An attitude coordinated controller is put forward to handle the LCD. • An integral sliding manifold with disturbance observer is embedded for superior robustness. [ABSTRACT FROM AUTHOR]

• A preassigned finite-time attitude synchronization controller is proposed for multiple rigid spacecraft systems by using two designed barrier Lyapunov functions. • The convergence time of the designed controller can be preassigned according to different space task requirements and it is independent of the initial condition of the system states and control parameters. • The steady-state error of the closed-loop system can be limited to a certain range by the appropriate choice of the controller parameters. This paper investigates the preassigned finite-time attitude synchronization control for the spacecraft formation with a dynamic virtual leader under an undirected connected graph. Each follower is described by a rigid spacecraft model subjects to parameter uncertainty, actuator saturation, and the disturbance. First, two fixed-time sliding mode estimators are introduced to estimate the reference attitude variable and the reference angular velocity, respectively. Then, by selecting the attitude errors as the system states, an attitude tracking error system for the spacecraft formation is established. An extended state observer is applied for computing the total disturbance in the attitude tracking error system. Based on the estimations of the extended state observer and two sliding mode estimators, a novel distributed controller is proposed to force the states of the established attitude tracking error system converge to a small region in preassigned finite time by using two modified time-varying barrier Lyapunov functions. The practical preassigned finite-time stability of the resulting closed-loop system is proven by Lyapunov stability theory. Finally, some simulations are provided to illustrate the effectiveness and advantages of the developed preassigned finite-time attitude synchronization control scheme. [ABSTRACT FROM AUTHOR]

Summary: This 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. [ABSTRACT FROM AUTHOR]

Accurate sensing and control are important for high-performance formation control of spacecraft systems. This paper presents a strategy of disturbance estimation and distributed predefined-time control for the formation of multi-spacecraft systems with uncertainties based on a disturbance observer. The process begins by formulating a kinematics model for the relative motion of spacecraft, with the formation’s communication topology represented by a directed graph for the formation system of the spacecraft. A disturbance observer is then developed to estimate the disturbances, and the estimation errors can be convergent in fixed time. Following this, a disturbance-estimation-based sliding mode control is proposed to guarantee the predefined-time convergence of the multi-spacecraft formation system, regardless of initial conditions. It allows each spacecraft to reach its desired position within a set time frame. The results of the analysis of the multi-spacecraft formation system are also provided. Finally, an example simulation of a five-spacecraft formation flying system is provided to demonstrate the presented formation control method.

This paper addresses the trajectory planning and control problem of multi-spacecraft formation reconstruction in the presence of obstacles. By expressing spacecraft dynamics relative to a leader spacecraft in the formation, an integrated planning and control approach named predictive null-space-based behavior control (PNSBC) is proposed. First, a planner using null-space-based behavior control (NSBC) is designed at an upper layer to resolve multi-task conflicts. Here, both global tasks, e.g. formation keeping, and local tasks, e.g. obstacle avoidance, are considered. Second, a tracking controller is designed at the bottom layer using decentralized model predictive control. Unlike traditional two-layer approaches that treat planning and control separately, the proposed PNSBC integrates the planning and control in two ways: 1) the planner provides reference trajectories for the controller to track; 2) the model predictive control (MPC) controller provides predicted trajectories that can be employed by the planner for future task priority predictions, which extends the capability of NSBC from one-step planning to multi-step predicting. In addition, the computational burden of the MPC controller is greatly reduced by putting the nonlinear obstacle avoidance constraints into the planner as a local task. Simulation results show that such integrated approach has better performance in terms of safety constraint guarantee, fuel consumption and travel distance when compared against traditional non-integrated approaches, or all-in-one MPC methods, while constraints and task objectives are fully satisfied. [ABSTRACT FROM AUTHOR]

As the number of satellites in orbit increases, the issue of flight safety in spacecraft formation orbit control has become increasingly prominent. With this in mind, this paper designs a second-order terminal sliding mode controller for spacecraft formation obstacle avoidance based on an artificial potential function (APF). To demonstrate the effectiveness of the controller, this paper first constructs a Lyapunov function to prove its stability and then verifies its theoretical validity through numerical simulation. Finally, a satellite simulator is used for semi-physical simulation to verify the practical effectiveness of the controller proposed in this paper. [ABSTRACT FROM AUTHOR]

In order to meet the position and attitude requirements of spacecrafts and test masses for gravitational-wave detection missions, the attitude-orbit coordination control of multiple spacecrafts and test masses is studied. A distributed coordination control law for spacecraft formation based on dual quaternion is proposed. By describing the relationship between spacecrafts and test masses in the desired states, the coordination control problem is converted into a consistent-tracking control problem in which each spacecraft or test mass tracks its desired states. An accurate attitude-orbit relative dynamics model of the spacecraft and the test masses is proposed based on dual quaternions. A cooperative feedback control law based on a consistency algorithm is designed to achieve the consistent attitude tracking of multiple rigid bodies (spacecraft and test mass) and maintain the specific formation configuration. Moreover, the communication delays of the system are taken into account. The distributed coordination control law ensures almost global asymptotic convergence of the relative position and attitude error in the presence of communication delays. The simulation results demonstrate the effectiveness of the proposed control method, which meets the formation-configuration requirements for gravitational-wave detection missions. [ABSTRACT FROM AUTHOR]

The article discusses the collaborative relative navigation problem for near-circular orbiting small satellites in close-range under GNSS denied environment. Topics include the orbital propagation model for the relative motion of multi-spacecraft is established based on Hill-Clohessy-Wiltshire dynamics; consensus constraint model for the relative orbit state is constructed by introducing the geometry constraint between the spacecraft, and digital simulations conducted to verify the algorithm.

This paper investigates the finite-time relative position coordinated control problem of distributed spacecraft formation without velocity information over limited communication bandwidth. In this design, a dynamic event triggered transmission scheme among spacecraft is designed to reduce communication burden, and a finite-time extended state observer is proposed to estimate the velocity information and the effects of non-linearity and disturbance of each spacecraft. A fast terminal sliding mode control law is developed to achieve finite-time coordination of the overall spacecraft formation. Finally, a numerical simulation is presented to demonstrate the effectiveness of the proposed control strategy.

In the presence of compound disturbances, a multi-spacecraft cooperative collision avoidance capture control method based on disturbance observer was proposed, which can solve the problem of low speed rolling non-cooperative target close-range capture in space. Firstly, a relative motion model of attitude and orbit coupling is established. Secondly, the disturbance observer is used to estimate and cancel the compound disturbance in the capture process. At the same time, the hyperquadric surfaces are used to describe the shape of space non-cooperative targets and capture spacecraft to establish a composite artificial potential field, and a robust control law with collision avoidance function is also designed. Finally, the stability of the controlled system is proved by using Lyapunov function, and the collision avoidance performance of the system is analyzed. Numerical simulations are carried out to evaluate the effectiveness of the proposed control scheme.

In this paper, the attitude-orbit coupled control problem for multi-spacecraft formation with limited communication capability and actuator failure is investigated. For the purpose of solving this problem, an event-triggered attitude-orbit coupled fault-tolerant control strategy is proposed. First, an integrated nonlinear dynamic model including the coupling characteristics of the attitude and orbit is established based on the Kane equation. Second, the nonlinear dynamic model is linearized at the reference state to facilitate the controller design. Third, a dynamic event-triggered mechanism is designed and an event-triggered fault-tolerant control law is developed. The stability of closed-loop control systems can be ensured under the designed control law and a sufficient condition that Zeno's behavior can be avoided is presented. Finally, simulation results are given to show the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

A switching neural network control scheme, consisting of the adaptive neural network controller and sliding mode controller, is proposed for underactuated formation reconfiguration in elliptic orbits with the loss of either the radial or in-track thrust. By using the inherent coupling of system states, the switching neural network technique is then adopted to estimate the unmatched disturbances and design the underactuated controller to achieve underactuated formation reconfiguration with high precision. The adaptive neural network controller works in the active region, and the disturbances composed of linearization errors and external perturbations are approximated by radial basis function neural networks. The adaptive sliding mode controller works outside the active region, and the upper bound of the approximation errors is estimated by the adaptation law. The stability of the closed-loop control system is proved via the Lyapunov-based approach. The numerical simulation results have demonstrated the rapid, high-precision and robust performance of the proposed controller compared with the linear sliding mode controller. [ABSTRACT FROM AUTHOR]

• An attitude observer is designed for each element of the three-vehicle heterogeneous formation. • The attitude observers converge to zero error for almost all initial conditions. • In simulations with sensor noise, the observer reduces the errors of the reconstructed attitudes. Constrained formations of vehicles are interesting in a variety of space mission scenarios for their potential ability to solve complex problems with relatively simple and specialized individual systems. However, the analysis of such formations can present some challenges. In this paper, an attitude observer is designed with the intent of applying it to three-vehicle heterogeneous formations with no line of sight between two of the vehicles. Each vehicle measures directions to other vehicles and independent inertial reference vectors. The relative direction between the two vehicles with no line of sight cannot be measured. Under some assumptions, these relative measurements yield a reconstructed attitude, which, together with the angular velocities measured by rate gyros, drive the observers. The attitude observers are identical and independently applied to each vehicle. Their design is based on the Lagrange-d'Alembert principle of variational mechanics, considering only kinematic models. The attitude observers are locally exponentially stable and each estimation error is shown to converge to zero error for almost all initial conditions. Finally, a series of numerical Monte Carlo simulations of the discrete-time form of the observers validate the stability and convergence characteristics of the observers under the appropriate assumptions on the availability of a reconstructed attitude. [ABSTRACT FROM AUTHOR]

In order to meet the position and attitude requirements of spacecrafts and test masses for gravitational-wave detection missions, the attitude-orbit coordination control of multiple spacecrafts and test masses is studied. A distributed coordination control law for spacecraft formation based on dual quaternion is proposed. By describing the relationship between spacecrafts and test masses in the desired states, the coordination control problem is converted into a consistent-tracking control problem in which each spacecraft or test mass tracks its desired states. An accurate attitude-orbit relative dynamics model of the spacecraft and the test masses is proposed based on dual quaternions. A cooperative feedback control law based on a consistency algorithm is designed to achieve the consistent attitude tracking of multiple rigid bodies (spacecraft and test mass) and maintain the specific formation configuration. Moreover, the communication delays of the system are taken into account. The distributed coordination control law ensures almost global asymptotic convergence of the relative position and attitude error in the presence of communication delays. The simulation results demonstrate the effectiveness of the proposed control method, which meets the formation-configuration requirements for gravitational-wave detection missions.

This paper investigates the issues of iterative learning algorithm-based robust thruster fault reconstruction and reconfigurable fault-tolerant control for spacecraft formation flying systems subject to space perturbations. Motivated by sliding mode methodology, a novel iterative learning observer (ILO) was developed to robustly reconstruct the thruster faults. Based on the fault signals obtained from the ILO, a learning output–feedback fault-tolerant control (LOF2TC) approach was explored such that the closed-loop spacecraft formation configuration was accurately maintained in the presence of space perturbations and thruster faults. Numerical simulations were employed to demonstrate the effectiveness and superiority of the proposed ILO-based fault-reconstructing approach and LOF2TC-based configuration maintenance approach for spacecraft formation flying systems. [ABSTRACT FROM AUTHOR]

Spacecraft formation maneuvering will inevitably induce flexible vibration from flexible appendages of spacecraft such as solar array appendages or antennae, which leads to complex disturbances with unknown fundamental frequencies. To achieve high performance of spacecraft formation flying, a novel adaptive iterative learning disturbance observer based on adaptive notch filter is designed to estimate and compensate unknown multi-frequency disturbances. Different from existing results on iterative learning disturbance observer, the newly proposed observer can estimate effectively both low-frequency disturbances and high-frequency periodic disturbances. Based on the proposed observer, an output feedback pose tracking law is derived by combining the proposed velocity observer and a feedback controller in dual quaternions description. The stability of the closed-loop system is approved based on the Lyapunov framework. Finally, the effectiveness and accuracy of the proposed observer and controller are demonstrated successfully by numerical simulations. • Developed a novel adaptive iterative learning control for flexible spacecraft formation. • Developed adaptive iterative learning observer to estimate multi-frequency disturbances. • Formulated 6DOF spacecraft formation maneuvering by dual quaternions. [ABSTRACT FROM AUTHOR]

This paper investigates distributed adaptive fault-tolerant control schemes for spacecraft formation subject to external disturbances, model uncertainties and communication delays. Two novel adaptive fault-tolerant control approaches are presented based on directed communication interaction. The developed adaptive laws are used to estimate the actuator effectiveness, the spacecraft masses and the upper bound on external disturbances. Then, an adaptive fault-tolerant control algorithm with time-varying communication delays is proposed. In particular, the conditions on the controller parameters and the communication delays necessary to assure the asymptotic stability of the closed-loop system are given. Finally, numerical simulations are presented to validate the effectiveness of the two proposed fault-tolerant control schemes for the spacecraft formation system.

This article examines the problem of finite‐time fault‐tolerant output feedback attitude control for spacecraft formation system with guaranteed performance, in the presence of uncertainties, external disturbances, actuator faults, and input saturation. First, a neural network (NN) based finite‐time observer is established for follower spacecraft to observe its angular velocity, where the NN is utilized to approximate the unknown uncertainties. Furthermore, based on the information from the angular velocity observer, backstepping procedure, and barrier Lyapunov function technique, a distributed finite‐time controller with only attitude measurement is proposed. Unlike the existing finite‐time control scheme, the tracking errors keep inside their predefined feasible regions with guaranteed transient and steady‐state performance. A theoretical proof shows that the finite‐time stability of the closed‐loop system can be achieved. Finally, numerical simulation results are presented to illustrate the effectiveness and fine performance of the proposed finite‐time observer and controller for the attitude control system. [ABSTRACT FROM AUTHOR]

In this paper, the attitude-orbit coupled control problem for multi-spacecraft formation with limited communication capability and actuator failure is investigated. For the purpose of solving this problem, an event-triggered attitude-orbit coupled fault-tolerant control strategy is proposed. First, an integrated nonlinear dynamic model including the coupling characteristics of the attitude and orbit is established based on the Kane equation. Second, the nonlinear dynamic model is linearized at the reference state to facilitate the controller design. Third, a dynamic event-triggered mechanism is designed and an event-triggered fault-tolerant control law is developed. The stability of closed-loop control systems can be ensured under the designed control law and a sufficient condition that Zeno’s behavior can be avoided is presented. Finally, simulation results are given to show the effectiveness of the proposed control method.

A switching neural network control scheme, consisting of the adaptive neural network controller and sliding mode controller, is proposed for underactuated formation reconfiguration in elliptic orbits with the loss of either the radial or in-track thrust. By using the inherent coupling of system states, the switching neural network technique is then adopted to estimate the unmatched disturbances and design the underactuated controller to achieve underactuated formation reconfiguration with high precision. The adaptive neural network controller works in the active region, and the disturbances composed of linearization errors and external perturbations are approximated by radial basis function neural networks. The adaptive sliding mode controller works outside the active region, and the upper bound of the approximation errors is estimated by the adaptation law. The stability of the closed-loop control system is proved via the Lyapunov-based approach. The numerical simulation results have demonstrated the rapid, high-precision and robust performance of the proposed controller compared with the linear sliding mode controller.

The cooperative attitude control is addressed for spacecraft formation with unreliable communication and signal quantization among spacecrafts.First,to save the data rate and bandwidth among the spacecrafts,a signal quantization communication strategy is proposed among each two spacecrafts in the formation,and a terminal sliding mode attitude control law is developed to ensure the asymptotic stability of the spacecraft formation attitude synchronization systems.Second,to compensate the effects of communication delay and signal quantization,an exponent-logarithmic sliding mode surface design is presented, based on which a cooperative attitude control strategy is developed for spacecraft formation to achieve desirable attitude in finite-time.Finally,a simulation example with four spacecrafts in a formation system is provided to verify the effectiveness of the proposed cooperative control method. [ABSTRACT FROM AUTHOR]

This paper investigates the issues of iterative learning algorithm-based robust thruster fault reconstruction and reconfigurable fault-tolerant control for spacecraft formation flying systems subject to space perturbations. Motivated by sliding mode methodology, a novel iterative learning observer (ILO) was developed to robustly reconstruct the thruster faults. Based on the fault signals obtained from the ILO, a learning output–feedback fault-tolerant control (LOF2TC) approach was explored such that the closed-loop spacecraft formation configuration was accurately maintained in the presence of space perturbations and thruster faults. Numerical simulations were employed to demonstrate the effectiveness and superiority of the proposed ILO-based fault-reconstructing approach and LOF2TC-based configuration maintenance approach for spacecraft formation flying systems.

This paper proposes an adaptive tracking control scheme for multi-spacecraft formation with inter-collision avoidance, obstacle dodging, and connectivity preservation. The proposed scheme is distributed, i.e., each spacecraft only needs to communicate with its neighbours. Both connectivity preservation and distributed networking are critical features for small spacecraft formation with limited computation and communication capacities. New artificial potential functions are defined to preserve the connectivity of neighbour spacecraft while avoiding their inter-collision as well as collision with obstacles. An adaptive sliding-mode controller is designed for reaching and maintaining the predetermined formation configuration while satisfying the safety assurance requirements, including inter-collision avoidance, obstacle dodging, and connectivity preservation. The stability of the controller is proven through the Lyapunov analysis, in the presence of gravitational, solar radiation pressure, and atmosphere drag perturbations and dynamic uncertainties. The performance of the control scheme is demonstrated through several comparative simulation studies. [ABSTRACT FROM AUTHOR]

This article studies the reliable and coordinated control problem of formation flying spacecraft without velocity measurement. External disturbances and directed communication topology, which explicitly has bounded communication delays, are considered. A novel observer is preliminarily designed to ensure a precise and fast estimation of immeasurable velocity. A virtual velocity input is then synthesized for the kinematics. In accordance, a finite-time and velocity-free controller is finally developed for the dynamics with the virtual velocity precisely followed after a finite time. The velocity-free control strategy can ensure the formation spacecraft to follow their desired relative trajectories in a coordinated manner. Numerical simulation is also conducted to validate the performance of the designed scheme. [ABSTRACT FROM AUTHOR]

This paper investigates a novel leader-following attitude control approach for spacecraft formation under the preassigned two-layer performance with consideration of unknown inertial parameters, external disturbance torque, and unmodeled uncertainty. First, two-layer prescribed performance is preselected for both the attitude angular and angular velocity tracking errors. Subsequently, a distributed two-layer performance controller is devised, which can guarantee that all the involved closed-loop signals are uniformly ultimately bounded. In order to tackle the defect of statically two-layer performance controller, learning-based control strategy is introduced to serve as an adaptive supplementary controller based on adaptive dynamic programming technique. This enhances the adaptiveness of the statically two-layer performance controller with respect to unexpected uncertainty dramatically, without any prior knowledge of the inertial information. Furthermore, by employing the robustly positively invariant theory, the input-to-state stability is rigorously proven under the designed learning-based distributed controller. Finally, two groups of simulation examples are organized to validate the feasibility and effectiveness of the proposed distributed control approach. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the distributed coordinated attitude tracking control problem for spacecraft formation with time-varying communication delays under the condition that the dynamic leader spacecraft is a neighbor of only a subset of follower spacecrafts. We consider two cases for the leader spacecraft: i) the attitude derivative is constant, and ii) the attitude derivative is time-varying. In the first case, a distributed estimator is proposed for each follower spacecraft by using its neighbors' information with communication delays. In the second case, to express the dynamic leader's attitude, an improved distributed observer is developed to estimate the leader's information. Based on the estimated values, adaptive coordinated attitude tracking control laws are designed to compensate for parametric uncertainties and unknown disturbances. By employing the Lyapunov–Krasovskii functional approach, the attitude tracking errors and estimation errors are proven to converge to zero asymptotically. Numerical simulations are presented to illustrate the effectiveness of theoretical results. Highlights • The distributed attitude tracking control is investigated for spacecraft formation. • Parametric uncertainties and disturbances are coped with via the adaptive technique. • The time-varying communication delay cases are investigated. • The Lyapunov–Krasovskii functional approach and LMI approach are employed. [ABSTRACT FROM AUTHOR]

This paper investigates robust adaptive coordinated attitude tracking issue for spacecraft formation flying system with nonrigid and rigid spacecraft under directed communication topology, where the inertia and external disturbances are totally unknown time-varying. A novel robust adaptive attitude tracking coordination control algorithm is proposed to regulate the attitude of the spacecraft to a common time-varying reference state. The control law is robust adaptive against external disturbances and time-varying inertia under the directed topology. In addition, a dynamic adjustment function is designed to limit the amplitude of control torque. Simulation results validate the effectiveness of the presented control algorithm and better control performance when compared with an adaptive control scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the robust attitude synchronization issue in a multi-spacecraft formation system subjected to limited communication, space disturbances, modeling uncertainties, and actuator faults. To accommodate limited inter-spacecraft communication, a dynamic event-triggered mechanism is designed to reduce the communication trigger frequency by dynamically adjusting the trigger threshold. Moreover, an event-based distributed self-learning neural-network control (SLN2C) law is developed to guarantee robust attitude synchronization during multi-spacecraft formation. In the SLN2C scheme, a learning radial basis function neural network (RBFNN) model is proposed to online approximate and compensate for lumped disturbances, in which an iterative learning algorithm with a variable learning intensity is adopted to update the weight matrix of the RBFNN model. Compared with the traditional fixed learning intensity, a variable one can reduce initial oscillation and weaken the saturation response. Numerical simulations and comparisons are performed to illustrate the effectiveness and superiority of the proposed event-based spacecraft attitude synchronization control method. [ABSTRACT FROM AUTHOR]

This work develops a method for ascertaining the landing locations and thruster orientations of a formation of multiple spacecraft on an irregular asteroid for discrete time optimal detumbling control, as a prerequisite to asteroid redirection. Asteroid geometries are known to be extremely irregular, especially for small asteroids, which are the typical targets for redirection missions. The method entails the modelling of asteroids as convex polyhedra with triangular facets, and computing the mass and inertial properties through the divergence theorem and Green’s theorem. Given the asteroid geometry, mass, and inertial properties, the feasible lander locations and thruster orientations are determined. The model ensures full attitude control of the asteroid, using multiple spacecraft with fixed-orientation, low-thrust modules, through measures imposed on the location and orientation of each thruster. A linear control scheme is employed to assess the time and fuel requirements of the asteroid detumbling maneuver, given feasible spacecraft formation configurations and thruster orientations. The method then assesses the detumbling time performance of each formation configuration to determine the discrete optimal landed formation configuration for a given asteroid. Simulations are performed to demonstrate the method using an irregular asteroid with characteristics derived from available asteroid data. Extensions of the method are further discussed in light of the results. [ABSTRACT FROM AUTHOR]

A set of linearized relative motion equations of spacecraft flying on unperturbed elliptical orbits are specialized for particular cases, where the leader orbit is circular or equatorial. Based on these extended equations, we are able to analyze the relative motion regulation between a pair of spacecraft flying on arbitrary unperturbed orbits with the same semi-major axis in close formation. Given the initial orbital elements of the leader, this paper presents a simple way to design initial relative orbital elements of close spacecraft with the same semi-major axis, thus preventing collision under non-perturbed conditions. Considering the mean influence of J2 perturbation, namely secular J2 perturbation, we derive the mean derivatives of orbital element differences, and then expand them to first order. Thus the first order expansion of orbital element differences can be added to the relative motion equations for further analysis. For a pair of spacecraft that will never collide under non-perturbed situations, we present a simple method to determine whether a collision will occur when J2 perturbation is considered. Examples are given to prove the validity of the extended relative motion equations and to illustrate how the methods presented can be used. The simple method for designing initial relative orbital elements proposed here could be helpful to the preliminary design of the relative orbital elements between spacecraft in a close formation, when collision avoidance is necessary. [ABSTRACT FROM AUTHOR]

This article investigates the velocity-free attitude coordinated tracking control scheme for a group of spacecraft with the assumption that the angular velocities of the formation members are not available in control feedback. Initially, an angular velocity observer is constructed based on each individual's attitude quarternion. Then, the distributed attitude coordinated control law is designed by using the observed states, in which adaptive control method is adopted to handle the external disturbances. Stability of the overall closed-loop system is analyzed theoretically, which shows the system trajectory converges to a small set around origin with fast convergence rate. Numerical simulations are performed to demonstrate fast convergence and improved tracking performance of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Summary: In this paper, an adaptive fault‐tolerant attitude coordinated tracking problem for spacecraft formation is investigated under a directed communication topology containing a spanning tree with the leader as the root, where inertia matrices and external disturbances are unknown time‐varying. With no prior knowledge of faults and inertia, an adaptive approach is proposed to reject the influence of disturbances and uncertainties. Meanwhile, combining with a consensus algorithm and graph theory, an adaptive fault‐tolerant attitude synchronization tracking control law is presented to regulate the attitude to a common time‐varying reference state. Aiming at optimizing the control law, a dynamic adjustment function is introduced to adjust the control gain according to the attitude tracking error. The effectiveness of the proposed control approach is demonstrated through simulation results. [ABSTRACT FROM AUTHOR]