Multiple Spacecraft Formation Flying Research Articles

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.

Collision avoidance control for formation flying of multiple spacecraft using artificial potential field

• Trajectory design/control for spacecraft formation flying with obstacle avoidance is presented. • Rotational potential function for obstacle avoidance in 3-dimensional space is newly proposed. • The controller is proven to be asymptotically stable in the sense of Lyapunov and successfully tested. This study presents trajectory design/control for spacecraft formation flying with obstacle avoidance. Based on the artificial potential field (APF), a formation potential is first defined to derive a formation control law for virtual structure, which enables multiple spacecraft to maintain polygonal or tetrahedral formation. As an efficient method to circumvent local minima which often occur in the APF-based approach, a newly proposed rotational potential is derived in a local coordinate frame to add in the APF framework. The synthesized formation and rotational potential function is used to develop a gradient-based control law to design/control the formation flying trajectory while avoiding collision with obstacles. Proven to be asymptotically stable in the sense of Lyapunov, the proposed continuous feedback control law is demonstrated via formation keeping/reconfiguration examples. The proposed approach successfully maintains the trajectory in the desired formation without colliding with obstacles and without falling into local minimum. These results are comparatively analysed with those of other APF-based approaches. The overall analysis shows that the proposed rotational potential, which has been newly derived in this research, enables a group of spacecraft in formation to efficiently avoid collision with obstacles without convergence to a local minimum.

Distributed Predefined-Time Attitude Consensus Control for Multiple Uncertain Spacecraft Formation Flying

This paper addresses the distributed predefined-time attitude consensus problem for multiple uncertain spacecraft systems in the presence of model uncertainties and external disturbances. Firstly, a new predefined-time terminal sliding surface (PTS) is proposed. Secondly, a distributed predefined-time consensus control (DPTC) based on the PTS is designed to solve the robust attitude consensus problem. It is proved that the proposed DPTC can ensure that the attitude consensus errors converge to an arbitrary small bound centered on equilibrium point within predefined time and then go to equilibrium point asymptotically. The appealing features of the proposed control are faster convergence, higher precision, stronger robustness and easy implementation. Simulations verify the effectiveness of the proposed approach.

Adaptive Fixed-Time 6-DOF Coordinated Control of Multiple Spacecraft Formation Flying with Input Quantization

This paper investigates the fixed-time coordinated control problem of six-degree-of-freedom (6-DOF) dynamic model for multiple spacecraft formation flying (SFF) with input quantization, where the communication topology is assumed directed. Firstly, a new multispacecraft nonsingular fixed-time terminal sliding mode vector is derived by using neighborhood state information. Secondly, a hysteretic quantizer is utilized to quantify control force and torque. Utilizing such a quantizer not only can reduce the required communication rate but also can eliminate the control chattering phenomenon induced by the logarithmic quantizer. Thirdly, a 6-DOF fixed-time coordinated control strategy with adaptive tuning laws is proposed, such that the practical fixed-time stability of the controlled system is ensured in the presence of both upper bounds of unknown external disturbances. It theoretically proves that the relative tracking errors of attitude and position can converge into the regions in a fixed time. Finally, a numerical example is exploited to show the usefulness of the theoretical results.

Distributed Game Strategy for Formation Flying of Multiple Spacecraft With Disturbance Rejection

This article investigates a distributed game strategy for formation control of multispacecraft subjected to nonlinear dynamics and J <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> perturbations. In the proposed problem, each spacecraft is devoted to minimize its own performance cost using only local information, whereas the overall formation system attempts to seek an optimized decision based on communication topology. Therefore, in our scheme, the formation control problem can be treated using a Nash strategy. A worst case Nash strategy is proposed against the disturbance defined as a player, and we prove rigorously that an open-loop Nash equilibrium exists in the underlying problem. Then, a distributed terminal state observer is introduced to facilitate the local implementation of the proposed Nash strategy. Simulation results verified the performance of the proposed scheme.

Finite‐time distributed cooperative attitude control for multiple spacecraft with actuator saturation

In this study, the distributed cooperative attitude tracking controller based on fast terminal sliding mode and Chebyshev neural network (CNN) is proposed for multiple spacecraft formation flying (SFF) system in the presence of external disturbance. Firstly, a new modified fast terminal sliding mode manifold, which has faster convergence rate than the existing terminal sliding modes, is proposed. Then, based on the proposed terminal sliding mode manifold, the distributed cooperative attitude tracking controller is designed for the SFF system, where the time varying reference attitude can be only accessed to a subset of the group member. To guarantee that the output of CNN used in the controller is bounded by the corresponding bound of the approximated unknown function, a modified adaptive law is proposed to revise the sliding mode manifold, meanwhile, the finite-time stability of SFF system can be also guaranteed. Finally, numerical simulations are presented to verify the validity and robustness of the proposed control algorithm.

Position/Velocity Consensus in Formation Flying of Multiple Spacecraft

This paper investigates the position/velocity consensus problem for multiple spacecraft agents subjected to nonlinear gravitational forces, where the interconnection graph among the agents is assumed to contain a spanning tree. We employ the linear position/velocity coupling control for attaining consensus of the spacecraft agents. With a similarity decomposition approach, the closed-loop networked system is decomposed into two subsystems, i.e., the group dynamics and the formation dynamics. First, we derive the boundedness of the formation errors relying on the input-output analysis of the formation dynamics, where a relatively aggressive sufficient condition is presented. Second, we present a sufficient condition to ensure the exponential convergence of the formation errors using the Lyapunov analysis.

A Memory/Immunology-Based Control Approach with Applications to Multiple Spacecraft Formation Flying

This paper addresses the problem of formation control for multiple spacecrafts in Planetary Orbital Environment (POE). Due to the presence of diverse interferences and uncertainties in the outer space, such as the changing spacecraft mass, unavailable space parameters, and varying gravity forces, traditional control methods encounter great difficulties in this area. A new control approach inspired by human memory and immune system is proposed, and this approach is shown to be capable of learning from past control experience and current behavior to improve its performance. It demands much less system dynamic information as compared with traditional controls. Both theoretic analysis and computer simulation verify its effectiveness.

Nonlinear Control of Formation Flying with State Constraints

Nonlinear Control of Formation Flying with State Constraints

Fault Tolerant Reconfigurable Satellite Formations Using Adaptive Variable Structure Techniques

This paper proposes two adaptive nonlinear control algorithms based on a variable-structure control design for multiple spacecraft formation flying. The nonlinear dynamics describing the motion of the follower spacecraft relative to the leader spacecraft are considered for the case in which the leader spacecraft is in an elliptical reference orbit, and the stability of such a formation in the presence of external perturbations is investigated. This paper presents fault-tolerant control schemes to account for accidental or degradation faults in spacecraft sensors and thrusters. The nonlinear analytical model describing the system is used to develop two adaptive fault-tolerant control laws (continuous sliding mode control and nonsingular terminal sliding mode control) that guarantee global asymptotic convergence of the position tracking error in the presence of unknown follower spacecraft mass and external disturbances. Several numerical examples are presented to demonstrate the efficacy of the proposed controllers to maintain the relative motion by correcting for initial offsets and external perturbation effects that tend to disperse the formation. Simulation results confirm that the suggested methodologies yield submillimeter formation, keeping precision and effectiveness in ensuring formation maneuvering. In addition, an abrupt blockage of the relative position sensors, thruster failure for a period of time, and thruster degradation (amidst formation keeping and reconfiguration maneuvers) are simulated to demonstrate the fault recovery capability of the controllers. The numerical results clearly establish the robustness of the proposed reconfigurable adaptive control scheme for precise formation keeping in the event of sensor and thruster faults.

Hardware-in-the-Loop Simulation for Spacecraft Formation Flying

This paper presents a hardware-in-the-loop (HITL) simulation approach for multiple spacecraft formation flying. Considering a leader-follower formation flying configuration, a Fuzzy Logic controller is developed first to maintain the desired formation shape under external perturbations and the initial position offsets. Cold-gas on/off thrusters are developed to be introduced to the simulation loop, and the HITL simulations are conducted to validate the effectiveness of the proposed simulation configuration and Fuzzy Logic control.

Formation flying of multiple spacecraft with autonomous rendezvous and docking capability

The idea of incorporating autonomous rendezvous and docking (ARVD) capability into spacecraft flying in formation is explored. The situations where it is advantageous to incorporate ARVD capability into spacecraft formations are identified. Attention is focused on various potential problems pertaining to the control of multiple spacecraft with ARVD capability. Multiple-model-based control laws for formation acquisition and ARVD are developed using generic spacecraft models. In particular, the use of such control laws for simultaneous docking of multiple spacecraft in formation acquisition and reconfiguration is studied. Various optimal formation reconfiguration problems are briefly discussed. The effectiveness of the developed control laws is studied via computer simulation using a six-spacecraft formation model.

Adaptive Synchronization Control of Multiple Spacecraft Formation Flying

An adaptive nonlinear synchronization control approach is developed for multiple spacecraft formation flying with elliptical reference orbits. It can guarantee that both the tracking errors and the synchronization errors of the relative positions converge to zero globally, even in the presence of uncertain parameters. The generalized synchronization concept allows us to design various synchronization errors so that different synchronization performance can be obtained. Simulation results of a leader-follower spacecraft pair and the maneuvering of multiple spacecraft in formation flying are presented to verify the effectiveness of the proposed control technique.

Formation Flying Control of Multiple Spacecraft via Graphs, Matrix Inequalities, and Switching

Ideas from elementary graph theory and linear matrix inequalities are combined with logic-based switching to shed light on the various control strategies which are feasible in the leader-following framework for the formation flying of multiple spacecraft.

Adaptive Nonlinear Control of Multiple Spacecraft Formation Flying

Thispaperconsiderstheproblemofrelativepositioncontrolformultiplespacecraftformatione ying.Specie cally, the full nonlinear dynamics describing the relative positioning of multiple spacecraft formation e ying are used to develop a Lyapunov-based, nonlinear, adaptive control law that guarantees global asymptotic convergence of the position tracking error in the presence of unknown, constant, or slow-varying spacecraft masses, disturbance forces, and gravity forces. Simulation results are included to illustrate the controller performance. that compensated for unknown, constant disturbances while pro- ducing globally asymptotically decaying position tracking errors. This controller, however, required exact knowledge of the space- craft parameters. In this paper we consider the full nonlinear dynamics describ- ing the relative positioning of MSFF for control design purposes. Using Lyapunov-based control design and stability analysis tech- niques, we develop a nonlinear adaptive control law that guarantees global asymptotic convergence of the spacecraft relative position to any sufe ciently smooth desired trajectory, despite the presence of unknown, constant, or slow-varying spacecraft masses, disturbance forces, and gravity forces. In the case when the parameters are ex- actlyknown,theproposedcontrolstrategyyieldsglobalexponential convergence of the tracking errors. In comparison to the work of Refs. 11 and 12, the proposed controller ensures stronger stability resultsandaccountsforawiderclassofparametricuncertainties.As inRefs.11-13, we will consider in this paper the idealized scenario where the spacecraft actuators are capable of providing continuous- time control efforts, as opposed to being of pulse type. 9 We note that the problem of pulse-type, nonlinear control design for MSFF constitutes an open research problem and is beyond the scope of this paper. The paper is organized as follows. Section II presents the non- linear dynamic model derivation. The control objective is stated in Sec. III. The control design and closed-loop stability analysis are presented in Sec. IV. Simulation results are provided in Sec. V, whereas some concluding remarks are given in Sec. VI.