Follower Spacecraft Research Articles

Distributed Attitude Consensus for Multiple Rigid Spacecraft under Jointly Connected Switching Topologies

We study the distributed leader-following attitude consensus problem for multiple rigid spacecraft with a single leader under jointly connected switching topologies. Two cases are considered, where the first case is with a static leader and the second case is with a dynamic leader. By constructing an auxiliary vector and a distributed observer for each follower spacecraft, the controllers are designed to drive all the attitudes of the follower spacecraft to the leader’s, respectively, for both of the two cases, though there are some time intervals in which the communication topology is not connected. The whole system is proved to be stable by using common Lyapunov function method. Finally, the theoretical result is illustrated by numerical simulations.

Distributed fault‐tolerant control design for spacecraft finite‐time attitude synchronization

SummaryThis paper develops two distributed finite‐time fault‐tolerant control algorithms for attitude synchronization of multiple spacecraft with a dynamic virtual leader in the presence of modeling uncertainties, external disturbances, and actuator faults. The leader gives commands only to a subset of the followers, and the communication flow between followers is directed. By employing a novel distributed nonsingular fast terminal sliding mode and adaptive mechanism, a distributed finite‐time fault‐tolerant control law is proposed to guarantee all the follower spacecraft that finite‐time track a dynamic virtual leader. Then utilizing three distributed finite‐time sliding mode estimators, an estimator‐based distributed finite‐time fault‐tolerant control law is proposed using only the followers' estimates of the virtual leader. Both of them do not require online identification of the actuator faults and provide robustness, finite‐time convergence, fault‐tolerant, disturbance rejection, and high control precision. Finally, numerical simulations are presented to evaluate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.

Robust adaptive terminal sliding mode control on SE(3) for autonomous spacecraft rendezvous and docking

This paper addresses the relative position and attitude tracking control in the framework of geometric mechanics for autonomous rendezvous and docking of two spacecraft where the relative motion of the leader and follower spacecraft tracks a desired time-varying trajectory. Using exponential coordinates on the Lie group \(\mathrm {SE(3)}\), which is the set of positions and orientations in three-dimensional Euclidean space, and the adjoint operator on the Lie algebra \(\mathfrak {se}(3)\), the relative coupled translational and rotational dynamics is modeled. Based on the terminal sliding mode, a robust adaptive terminal sliding mode control scheme on \(\mathrm {SE(3)}\) is proposed to ensure the finite-time convergence of the relative motion tracking errors using limited control inputs despite the presence of unknown disturbances and moment of inertia uncertainty. The control scheme is then applied to a situation where the follower spacecraft synchronizes its attitude motion with the leader, while maintaining a constant relative position with respect to the leader. The robustness of the controller is established using Lyapunov stability theory. Simulation results of close range rendezvous and docking verify that the proposed control scheme can achieve faster and more accurate tracking performance while consuming less control energy than the conventional terminal sliding mode control method.

Distributed cooperative control design for finite‐time attitude synchronisation of rigid spacecraft

Two finite-time control algorithms are developed for distributed cooperative attitude synchronization of multiple spacecraft with a dynamic virtual leader. Each spacecraft is modeled as a rigid body incorporating with model uncertainty and unknown external disturbance. The virtual leader gives commands to some of the follower spacecraft, and the communication network between followers can be an undirected or a directed graph. By using two neighborhood synchronization error signals, a finite-time control algorithm is designed associated with adaptive mechanism such that all follower spacecraft synchronize to the virtual leader in finite time. Then, a novel estimator-based finite-time distributed cooperative control algorithm is developed by using the followers estimates of the virtual leader, and the convergence of the attitude and angular velocity errors can be guaranteed in finite time. Moreover, both of the control strategies are chattering-free for their continuous design. Simulation examples are illustrated to demonstrate the validity of the two algorithms.

Nonlinear suboptimal synchronized control for relative position and relative attitude tracking of spacecraft formation flying

This paper deals with the optimal tracking and synchronized control of leader–follower spacecraft formation flying, considering motion with 6 degree-of-freedom (6-DOF). The relative position and relative attitude between spacecrafts are required to track a desired time-dependent trajectory. Modeling of 6-DOF formation spacecraft is introduced firstly, applying dual quaternion in describing the coupled relative motion. A nonlinear suboptimal synchronized tracking controller is then proposed to perform two tasks: (1) to ensure globally asymptotic convergence of the translational and rotational tracking errors with parametric uncertainties and external disturbances considered, and (2) to minimize the predefined performance indices. In the proposed controller, the optimal control and the sliding mode control (SMC) operate in a complementary manner. A control Lyapunov function (CLF) is constructed to solve the nonlinear optimal control problem, whereas SMC is established to ensure robustness and achieve accurate control. A detailed stability analysis and proofs of the resulting closed-loop system using a Lyapunov framework are also included. Finally, illustrative numerical simulations and comparisons are presented to demonstrate the validity and advantages of the proposed controller.

Finite-Time Control for 6DOF Spacecraft Formation Flying Systems

AbstractThis paper considers the finite-time control problem of 6DOF spacecraft formation flying (SFF) systems in the presence of external disturbances. First of all, based on nonsingular terminal sliding mode (NTSM) method, a local finite-time control law is proposed. Then a finite-time disturbance observer (FTDOB) is introduced to estimate the disturbances, and a composite control law which consists of a feedback control law based on NTSM method and a feed-forward compensation term based on FTDOB technique is constructed such that the follower spacecraft can track the desired trajectory in finite time. The major merit of the proposed method is that chattering is substantially reduced because the switching gain of the discontinuous control law is only required to be greater than the bound of disturbance estimation error rather than that of the disturbances. Furthermore, based on switching control method, continuous NTSM and FTDOB technique, a global finite-time control law is developed for 6DOF SFF syste...

Multiple spacecraft formation reconfiguration using solar radiation pressure

In this paper the use of solar radiation pressure for spacecraft formation reconfiguration at the L2 Sun–Earth/Moon collinear libration point is presented. The system consisting of a leader and three follower spacecraft is considered. The leader spacecraft is assumed to be in a fixed halo trajectory and the follower spacecraft position relative to the leader satellite is controlled using two angles and area; these are varied based on a variable structure model reference adaptive control technique to achieve the desired formation reconfiguration. This approach ensures that all follower spacecraft complete the required maneuver in the same time. An intertially fixed circular trajectory, which is suitable for interferometer missions, is used in this paper. The stability of the proposed controller is established using Lyapunov theory. The performance of the proposed controller is tested through numerical simulation of the governing nonlinear equations of motion and is applied for formation initialization, resizing, retargeting, and rotation. The numerical results demonstrate the effectiveness of the proposed control technique for spacecraft formation reconfiguration using solar radiation pressure at the L2 libration point. Furthermore, control inputs on the order of 15degrees and 2m2 for area change are sufficient to execute the maneuvers.

Fault detection and recovery of spacecraft formation flying using nonlinear observer and reconfigurable controller

This paper addresses fault tolerant spacecraft leader–follower formation control through the development of a fault observer and a re-configurable control law. Using carrier-phase differential GPS measurements for relative position and velocity, an estimate of the true thrust output on all three axes of the follower spacecraft is accomplished using a pair of super twisting sliding mode observers. Modifications on the ‘broken’ super twisting observer are applied in order to accommodate additional sensor feedback inputs for relative position and velocity between the leader and the follower spacecraft. A fault observer estimating the true thrust output of the follower spacecraft is developed which functions in parallel with a re-configurable control law capable of formation maintenance in the event thrust in the along-track and radial axes are no longer available. Simulation results show fault reconstruction and recovery with formation stabilization even in the presence of external disturbances which are unknown to both the controller and the observer.

Conceptual design of a hypervelocity asteroid intercept vehicle (HAIV) and its flight validation mission

An intercept mission with nuclear explosives is the most effective of the practical mitigation options against the impact threat of near-Earth objects (NEOs) with a short warning time (e.g., much less than 10 years). The existing penetrated subsurface nuclear explosion technology limits the intercept velocity to less than approximately 300m/s. Consequently, an innovative concept of blending a hypervelocity kinetic impactor with a subsurface nuclear explosion has been developed for optimal penetration, fragmentation, and dispersion of the target NEO. A proposed hypervelocity asteroid intercept vehicle (HAIV) consists of a kinetic-impact leader spacecraft and a follower spacecraft carrying nuclear explosives. This paper describes the conceptual development and design of a baseline HAIV system and its flight validation mission architecture for three mission cost classifications (e.g., $500M, $1B, and $1.5B).

Spacecraft Formation Reconfiguration using Impulsive Control Input

This paper presents formation reconfiguration using impulsive control input for spacecraft formation flying. Spacecraft in a formation should change the formation size and/or geometry according to the mission requirements and space environment. To modify the formation radius and geometry with respect to the leader spacecraft, the follower spacecraft generates additional control inputs; the two impulsive control inputs are general control type of the spacecraft system. For the impulsive control input, Lambert's problem is modified to construct the transfer orbit in relative motion, given two position vectors at the initial and final time. Moreover, the numerical simulation results show the transfer trajectories to resize the formation radius in the radial/along-track plane formation and in the along-track/cross-track plane formation. In addition, the maneuver characteristics are described by comparing the differential orbital elements between the reference orbit and transfer orbit in the radial/along-track plane formation and along-track/cross-track plane formation.

Formation Pattern Analysis of Follower Spacecraft for Elliptic Reference Orbits

Formation analysis is performed for the periodic relative motion between two spacecraft in Keplerian elliptic orbits. For a leader spacecraft moving in a circular orbit around the Earth, the relative motion of a follower spacecraft has an ellipse in the radial/along-track plane. On the other hand, when a leader spacecraft flies in an elliptical orbit, the follower spacecraft does not have an ellipse of fixed eccentricity in the relative motion plane due to the eccentricity of the reference orbit. In this study, the spacecraft formation flying is analyzed to describe the natural periodic relative motion. The instantaneous eccentricity of the relative motion is derived in the radial/along-track (R/AT) plane (x−y plane) formation and the along-track/cross-track (AT/CT) plane (y−z plane) formation. Numerical simulations are performed to yield the periodic relative motion and the formation trajectories in the elliptical reference orbit. The variation of the formation radius according to the eccentricity of the reference orbit is analyzed for R/AT plane and AT/CT plane formations. In addition, the range of the angle difference between two follower spacecraft is described with respect to the eccentricity of the leader spacecraft. Using these results, the desired constraints can be provided for a designer to choose the formation pattern in accordance with the mission requirements.

Optimal sliding mode control for spacecraft formation flying in eccentric orbits

In order to control the relative motion for spacecraft formation flying in eccentric orbits, an optimal sliding mode controller is presented. This controller is designed based on the linearized two-body relative motion dynamics and is applied to the nonlinear system that includes the effects of external disturbances. The optimal control design is based on a linear quadratic method that is supplemented by an integral sliding mode control technique to robustify the controller. It is assumed that the leader and follower spacecraft are in a low Earth orbit and subject to the perturbing effects of J2 and atmospheric drag. Using the Lyapunov second method, the stability of the closed-loop system is guaranteed. The performance of the proposed controller in tracking the desired reference trajectory is compared to a sliding mode controller, and simulation results show the effectiveness of the proposed controller.

Network-Based Tracking Control of Spacecraft Formation Flying with Communication Delays

The formation tracking problem for multiple spacecraft in the framework of networked control systems (NCSs) is investigated. A reference trajectory is generated by the force-free linearized equations of the relative motion (known as Hill's equations). A sampled-data representation of the NCS is considered for the tracking control of relative motion between the leader and follower spacecraft in the presence of variable communication delays and bounded external disturbances. By adding a buffer which is longer than the worst case delay and augmenting the system model to include past values of system input as additional states, a new discrete time-invariant model is formulated, and a digital controller is developed to guarantee the exponentially uniformly ultimate boundedness (UUB) of the tracking errors and to ensure desired formation objectives. Numerical simulations are presented to demonstrate the effectiveness of the controller. The proposed controller is successful in establishing projected circular formation with the maximum magnitude of the steady-state tracking error 0.056 and the control forces remain bounded within 50 mN.

Dual-quaternion-based finite-time control for spacecraft tracking in six degrees of freedom

This article investigates the tracking control problem for the six-degree-of-freedom motion of a follower spacecraft relative to a leader spacecraft. Employing dual quaternion representation, the model of the six-degree-of-freedom relative motion between the two spacecraft is derived. Taking into account the model uncertainties and external disturbances, two robust fast sliding mode control laws are proposed to guarantee the finite-time convergence of the tracking errors, where the second control law can solve the dual-equilibrium problem that exists in the first one. In order to alleviate chattering phenomenon, continuous saturation function is introduced into the controller and a softening control strategy is developed. It is worth pointing out that the convergence rate of the proposed fast sliding mode control is faster than that of the linear sliding mode control and terminal sliding mode control. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed approaches.

6-DOF robust adaptive terminal sliding mode control for spacecraft formation flying

This paper addresses the tracking control problem of the leader–follower spacecraft formation, by which we mean that the relative motion between the leader and the follower is required to track a desired time-varying trajectory given in advance. Using dual number, the six-degree-of-freedom motion of the follower spacecraft relative to the leader spacecraft is modeled, where the coupling effect between the translational motion and the rotational one is accounted. A robust adaptive terminal sliding mode control law, including the adaptive algorithms, is proposed to ensure the finite time convergence of the relative motion tracking errors despite the presence of model uncertainties and external disturbances, based on which a modified controller is furthermore developed to solve the dual-equilibrium problem caused by dual quaternion representation. In addition, to alleviate the chattering, hyperbolic tangent function is adopted to substitute for the sign function. And by theoretical analysis, it is proved that the tracking error in such case will converge to a neighborhood of the origin in finite time. Finally, numerical simulations are performed to demonstrate the validity of the proposed approaches.

Tuning functions-based output feedback adaptive spacecraft formation flying despite disturbances

This article presents a non-linear adaptive satellite formation control system based on the tuning functions design method using output feedback. A leader spacecraft is orbiting in an elliptic orbit, and a follower satellite is in motion around it. It is assumed that unknown periodic disturbance forces as well as random disturbances are acting on the follower spacecraft, and its mass is not known. Furthermore, only the relative position of the follower satellite, with respect to the leader satellite, is measured for feedback. The objective is to design an adaptive controller so that the follower spacecraft remains in a specific formation with respect to the leader spacecraft. For the purpose of design, first a simplified model including only periodic disturbance inputs is considered, and a canonical representation of the non-linear relative dynamics is obtained. Based on this canonical form, filters are designed to obtain the estimate of the relative velocity of the follower spacecraft and an output feedback adaptive law is derived for the relative position trajectory control. Based on the Lyapunov approach, it is shown that the closed-loop system is globally uniformly stable, and that the adaptive law accomplishes global asymptotic tracking of the reference trajectory in the presence of periodic disturbances. For robustness with respect to random forces in the model, a modified form of the adaptation law using σ-modification is synthesized. Simulation results are presented, which show that the designed output feedback control system achieves precise formation control, despite the periodic and random disturbance forces and parameter uncertainty in the model.

Adaptive controller design for spacecraft formation flying using sliding mode controller and neural networks

A spacecraft formation flying controller is designed using a sliding mode control scheme with the adaptive gain and neural networks. Six-degree-of-freedom spacecraft nonlinear dynamic model is considered, and a leader–follower approach is adopted for efficient spacecraft formation flying. Uncertainties and external disturbances have effects on controlling the relative position and attitude of the spacecrafts in the formation. The main benefit of the sliding mode control is the robust stability of the closed-loop system. To improve the performance of the sliding mode control, an adaptive controller based on neural networks is used to compensate for the effects of the modeling error, external disturbance, and nonlinearities. The stability analysis of the closed-loop system is performed using the Lyapunov stability theorem. A spacecraft model with 12 thrusts as actuators is considered for controlling the relative position and attitude of the follower spacecraft. Numerical simulation results are presented to show the effectiveness of the proposed controller.

Optimal periodic controller for formation flying on libration point orbits

An optimal periodic controller based on continuous low-thrust is proposed for the stabilization missions of spacecraft station-keeping and formation-keeping along periodic Libration point orbits of the Sun–Earth system. Additionally, a new numerical algorithm is proposed for solving the periodic Riccati differential equation in the design of the optimal periodic controller. Practical missions show that the optimal periodic controller (which is designed with the linear periodic time-varying equation of the relative dynamical model) overcomes the problems and limitations of the time-variant LQR controller. Furthermore, nonlinear numerical simulations are presented for the missions of a leader spacecraft station-keeping and three follower spacecraft formation-keeping. Numerical simulations show that the velocity increments for spacecraft control and relative position errors vary little with changes in the altitude of periodic orbits. In addition, the actual trajectories of the leader and the follower spacecraft track the periodic reference orbit with high accuracy under the perturbation of the eccentric nature of the Earth's orbit and the initial injection errors. In particular, the relative position errors obtained by the optimal periodic controller for spacecraft formation-keeping are all in the range of millimeters.

Cascade-Based Controlled Attitude Synchronization and Tracking of Spacecraft in Leader-Follower Formation

We propose controllers for leader-follower attitude synchronization of spacecraft formations in the presence of disturbances, that is, the leader spacecraft is controlled to follow a given reference, while a follower spacecraft is controlled to synchronize its motion with the leader's. In the ideal disturbance-free scenario, we show that synchronization takes place asymptotically. Moreover, we show the property of uniform practical asymptotic stability which implies that the synchronization is robust to bounded disturbances.

Fault Tolerant Attitude Synchronization Control during Formation Flying

It is necessary for precise satellite formations to keep each satellite in accurate relative attitude synchronization and to maintain relative angular velocity synchronization. An adaptive fuzzy terminal sliding mode control is proposed for a formation flying tracking system which includes acquisition, tracking, and pointing. The relative attitude of the leader and follower spacecraft under gravity gradient torque and external periodic disturbances is controlled by four reaction wheels. First, a terminal sliding mode controller is used to obtain stable and fast tracking. Then, the adaptive fuzzy logic system is used to approximate and learn the system uncertainty with the online fault and time-varied external disturbances. The system is proved to be stable, and the parameters are proved to be bounded under the control scheme, using a Lyapunov methodology. Finally, simulation results (under actuator faults like wheel failure and wheel degradation) show that the proposed control method has the advantages of...