Spin deployment of Hub-Spoke tethered satellite formation with sliding mode tether tension control

This work develops a tension control strategy for deploying an underactuated spin-stable tethered satellite formation in the hub-spoke configuration. First, the Lagrange equation is used to model the spin-deployment dynamics of the tethered satellite formation. The central spacecraft is modeled as a rigid body, and the tethered subsatellites are simplified as lumped masses. Second, a pure tension controller has been proposed to suppress the tether libration motion in the deployment without thrusting at the subsatellites. A nonlinear sliding mode control is introduced in the tension controller for the underactuated system to suppress the periodic gravitational perturbations caused by the spinning hub-spoke tethered satellite formation. The unknown upper bounds of the perturbations are estimated by adaptive control law. The bounded stability of the closed-loop tension controller has been proved by the Lyapunov theory. Finally, numerical simulations validate the effectiveness and robustness of the proposed controller, i.e., tethers are fully deployed stably to the desired hub-spoke configuration.     

Space-based line-of-sight tracking control of GEO target using nonsingular terminal sliding mode

This paper addresses the issue of high-precision line-of-sight (LOS) tracking of geosynchronous earth orbit target in highly dynamic conditions via spacecraft attitude maneuver. First, characteristics of the LOS motion are analyzed by a simplified linear relative motion model. Second, after transforming the quaternion-based attitude model into a double integrator system, a new nonsingular terminal sliding mode controller is proposed for spacecraft attitude tracking in a nominal case without parametric uncertainties and external disturbances. Third, an adaptive new nonsingular terminal mode controller is proposed for spacecraft attitude tracking in an uncertain case, which is done via constructing a pair of adaptive laws to estimate the parametric uncertainties and external disturbances online. The robust stability and finite time convergence property of the closed-loop system are demonstrated by Lyapunov theorem. Under control of the proposed controller, zero steady state error tracking of LOS with a smooth transition phase can be achieved in scheduled time, regardless of parametric uncertainties and external disturbances online. Finally, detailed numerical simulation results are presented to illustrate the effectiveness and performance of the proposed controllers. Contrasting simulation results shows that proposed controllers can track the desired trajectories effectively and have better performance against the controllers based on linear sliding mode and the existing fast nonsingular terminal sliding mode.     

Optimal spacecraft rendezvous using the combination of aerodynamic force and Lorentz force

This paper presents a propellantless spacecraft rendezvous method by using the optimal combination of aerodynamic force and Lorentz force. Aerodynamic force is provided by the rotations of the plates attached to the spacecraft, and Lorentz force is achieved by modulating spacecraft's electrostatic charge. Considering the limitation of the charging level of the spacecraft and physical constraints of the plates system, an optimal open-loop rendezvous trajectory is designed, which aims to minimize the energy consumed to actuate the hybrid system. The rotation rates of the plates and the electrostatic charge are constrained in the optimization problem, which is solved via the Gauss pseudospectral method. To track the open-loop trajectory in the presence of external perturbations, a novel adaptive nonsingular terminal sliding mode controller is designed. The stability of the closed-loop system is proved by the Lyapunov-based method. Several numerical examples are conducted to verify the validity of both the open-loop and closed-loop control strategy.     

Adaptive sliding mode control of spacecraft attitude-orbit dynamics on SE(3)

In this paper, to solve the problem of parameters uncertainty in spacecraft tracking control, an adaptive controller based on sliding mode is proposed for the relative spacecraft attitude-orbit dynamics on the Lie group SE(3). The dynamic equations of relative attitude orbit error for two spacecraft are established in the framework of Lie group SE(3). Considering the uncertainty of spacecraft parameters, a formal decomposition of known and unknown parameters, the state variables and control variables is firstly made in the original system. An online estimator is designed to evaluate the unknown parameters. A sliding mode controller is developed to actuate the spacecraft to track the target spacecraft. Then a Lyapunov function of tracking error and parameters estimated error is designed to prove the stability of the closed-loop system. Finally, the simulation results and analysis are presented to verify the effectiveness and feasibility of the proposed method.     

Nonlinear attitude tracking control for spacecraft formation with multiple delays

This paper addresses the attitude tracking control for spacecraft formation with delay free and communication delays. With help of the idea of sliding control, an adaptive attitude synchronization control architecture is established. Furthermore, by introducing a nonsmooth feedback function, a new class of nonlinear controllers for the attitude tracking of spacecraft is developed. Both parameter uncertainties and unknown external disturbances are dealt with via the kind of controllers. Finally, some simulation results are given to demonstrate the effectiveness and advantages of the proposed results.     

Automatic orbital docking with tumbling target using sliding mode control

The present study aimed to propose translational and rotational control of a chaser spacecraft in the close vicinity docking phase with a target subjected to external disturbances. For this purpose, two sliding mode controls (SMC) are developed to coordinate the relative position and attitude of two spacecraft. The chaser is guided to the tumbling target by the relative position control, approaching in the direction of the target docking port. At the same moment, the relative attitude control coordinates the chaser attitude so that it can be aligned with the target orientation. These control systems regulate the relative translational and rotational velocities to be zero when two spacecraft are docking. The robustness of the closed-loop system in the presence of external disturbances, measurement noises and uncertainties is guaranteed by analyzing and calculating the control gains via the Lyapunov function. The simulations in different scenarios indicated the effectiveness of the controller scheme and precise maneuver regarding the accuracy of docking conditions.     

Constant thrust fuel-optimal control for spacecraft rendezvous

In this paper, constant thrust rendezvous is studied and the optimal rendezvous time is calculated by using continuous genetic algorithm. Firstly, the relative position parameters of the target spacecraft are obtained by using the vision measurement and the target maneuver positions are calculated through the isochronous interpolation method. Then, the results of the calculation of constant thrust rendezvous is founded by processing with multivariate linear regression method. Next, a new switching control law is designed based on the thrust acceleration sequence and the on time of thrusters which can be computed by the time series analysis method. The perturbations and fuel consumptions are addressed during the computation of the on time of thrusters.     

Adaptive predefined-time control for liquid-filled flexible spacecraft attitude stabilization during orbit maneuver

A predefined-time attitude stabilization for complex structure spacecraft with liquid sloshing and flexible vibration is investigated under input saturation during orbital maneuver. First, the attitude dynamics model of liquid-filled flexible spacecraft is constructed. Meanwhile, the influence of solar panel vibration and liquid sloshing is treated as a disturbance in the controller design. Next, an adaptive predefined-time control scheme is proposed by applying sliding mode control theory. A predefined-time convergent sliding surface and reaching law are designed to ensure the predefined-time fast convergence rate. Furthermore, a novel adaptive algorithm is developed to handle the disturbances from liquid sloshing and flexible vibration, ensuring that the system converges to a small neighborhood of the equilibrium. Additionally, a new auxiliary system is constructed to deal with the effects of input saturation. At last, one simulation case is performed to verify the feasibility and advantages of the proposed algorithm.     

Libration point orbit rendezvous using PWPF modulated terminal sliding mode control

The near-range rendezvous problem of two libration point orbit spacecraft in the Earth–Moon system is studied using the terminal sliding mode control which enables a time-fixed process with the flight time prescribed a priori. The underlying dynamics are the full nonlinear equations of motion for a complete Solar System model. For practical purposes, two means of pulse-width pulse-frequency (PWPF) modulation are employed to realize the theoretical continuous control with a series of thrust pulses. Extensive simulations with major errors taken into account show that the sliding mode controller can successfully guide the chaser to a given staging node with the final position and velocity errors, on average, lower than 20 m and 1 mm/s, respectively. Compared with the glideslope guidance previously studied, the proposed approach outperforms the former by saving approximately 50–60% of total delta-v.     

Multi-agent Q-Learning control of spacecraft formation flying reconfiguration trajectories

This paper presents a novel approach based on multi-agent reinforcement learning for spacecraft formation flying reconfiguration tracking problems. In this scheme, spacecrafts learn the control strategy via transfer learning. For this matter, a new generalized discounted value function is introduced for the tracking problems. Due to the digital nature of spacecraft computer systems, local optimal controllers are developed for the spacecrafts in discrete-time. The stability of the controller is proven. Two Q-learning algorithms are proposed, in each of which the optimal control solution is learned on-line without knowledge about the system dynamics. In the first algorithm, each agent learns the optimal control independently. In the second one, each agent shares the learned information with other agents. Next, the collision avoidance capability is provided. The effectiveness of the presented schemes is verified through simulations and compared with each other.     

Command filtered sliding mode trajectory tracking control for unmanned airships based on RBFNN approximation

This paper presents two sliding mode controllers to address the trajectory tracking problem of unmanned airships in the presence of unknown wind disturbance. The sliding mode controller proposed first is designed by a fast power rate reaching law(FPRRL). The disturbance is compensated by a radial basis function neural network (RBFNN). To avoid the aggressive adaptation, the controller is augmented by a command filter. The controller provides good robustness and tracking performance with no chattering under the hypothesis of ideal wind field. However, serious chattering occurs when simulation is performed under discontinuous wind field. To simulate the wind in practice, the wind field employed in the simulation is generated by the combination of a constant field and white noise. The controller is improved subsequently with an extended model to suppress the chattering induced by the white noise. The enhanced controller manipulates the derivation of system input, thus attenuating the chattering. Stability analysis shows that both controllers drive the tracking error into a controllable small region near zero. Simulations are provided to validate the performance of the proposed controllers under different wind hypothesis.     

Energy-optimal reconfiguration of satellite formation flying in the presence of uncertainties

In this study, a two-step control methodology is developed for energy-optimal reconfiguration of satellites in formation in the presence of uncertainties or external disturbances. First, based on a linear deterministic system model, an optimal control law is analytically determined such that a satellite maneuvers from an initial state to a final state relative to another satellite. The structure of this optimal solution is predetermined and simply given by a linear combination of the fundamental matrix solutions associated with the original equations of relative motion. Only the coefficients are to be determined to satisfy given initial and final conditions. In the second step, an uncertain nonlinear formation system is considered and a robust adaptive controller is designed to compensate for the effects of uncertainties or disturbances that the formation system may encounter. Although the control strategy is inspired by sliding mode control, it produces smooth control signals, thereby avoiding chattering. Also, an adaptation law is added such that the uncertainty or disturbance effects are effectively and quickly eliminated without a priori information about them. The combination of these two controllers guarantees that the satellite accurately tracks the optimal path in the unknown environment. Numerical simulations demonstrate the effectiveness and accuracy of the proposed two-step control methodology, in which a satellite formation is optimally reconfigured under unknown environmental disturbances.     

Hardware-in-the-loop simulations of GPS-based navigation and control for satellite formation flying

A relative navigation and formation control algorithm for satellite formation flying was developed, and a hardware-in-the-loop (HIL) simulation testbed was established and configured to evaluate this algorithm. The algorithm presented is a relative navigation estimation algorithm using double-difference carrier-phase and single-difference code measurements based on the extended Kalman filter (EKF). In addition, a state-dependent Riccati equation (SDRE) technique is utilized as a nonlinear controller for the formation control problem. The state-dependent coefficient (SDC) form is formulated to include nonlinearities in the relative dynamics. To evaluate the relative navigation and control algorithms developed, a closed-loop HIL testbed is configured. To demonstrate the performance of the testbed, a test formation flying scenario comprising formation acquisition and keeping in a low earth orbit (LEO) has been established. The relative navigation results from the closed-loop simulations show that a 3D RMS of 0.07 m can be achieved for position accuracy. The targeted leader–follower formation flying in the along-track separation of 100 m was maintained with a mean position error of approximately 0.2 m and a standard deviation of 0.9 m. The simulation results show that the HIL testbed is capable of successful demonstration of the GPS-based satellite autonomous formation flying mission.     

基于终端滑模的卫星编队飞行有限时间控制

针对考虑参考星机动的编队飞行相对位置控制问题,给出了一种基于终端滑模的有限时间控制方法. 基于编队卫星相对运动动力学模型,设计了有限时间终端滑模控制器,同时证明了该控制器作用下系统状态误差可在有限时间内收敛. 以编队构型重构和考虑参考星机动时的构型保持控制为例,利用本文控制方法进行了仿真分析. 仿真结果表明,基于终端滑模的有限时间控制方法相比于传统的线性滑模控制方法,在保证编队飞行控制高精度的同时,有效提升了误差的收敛速度,验证了该方法的有效性和优越性.     

航天器编队飞行多目标姿态跟踪终端滑模控制

研究航天器编队飞行多目标姿态跟踪控制问题.为避免姿态大范围跟踪可能出现的奇点,采用欧拉参数描述航天器姿态.基于终端滑模技术,设计多目标姿态跟踪终端滑模控制器,并应用Lyapunov稳定性理论和扩展的Lyapunov有限时间稳定性理论证明控制系统稳定性和有限时间收敛性.该控制器参数方便调整,易于实现.由于没有对复杂多体航天器动力学进行线性化处理,从而保证了姿态跟踪控制精度.仿真结果表明,存在惯量参数摄动和外部干扰力矩的情况下,所设计的多目标姿态跟踪控制器具有良好鲁棒性和优越的跟踪性能.     

Optimal H∞ robust output feedback control for satellite formation in arbitrary elliptical reference orbits

A two degree-of-freedom signal-based optimal H_∞ robust output feedback controller is designed for satellite formation in an arbitrary elliptical reference orbit. Based on high-fidelity linearized dynamics of relative motion, uncertainties introduced by non-zero eccentricity and gravitational J2 perturbation are separated to construct a robust control model. Furthermore, a distributed robust control model is derived by modifying the perturbed robust control model of each satellite with the eigenvalues of the Laplacian matrix of the communication graph, which represent uncertainty in the communication topology. A signal-based optimal H_∞ robust controller is then designed primarily. Considering that the uncertainties involved in the distributed robust control model have a completely diagonal structure, the corresponding analyses are made through structured singular value theory to reduce the conservativeness. Based on simulation results, further designs including increasing the degrees of freedom of the controller, modifying the performance and control weighted functions, adding a post high-pass filter according to the dynamic characteristics, and reducing the control model are made to improve the control performance. Nonlinear simulations demonstrate that the resultant optimal H_∞ robust output feedback controller satisfies the robust performance requirements under uncertainties caused by non-zero eccentricity, J2 perturbation, and varying communication topology, and that 5 m accuracy in terms of stable desired formation configuration can be achieved by the presented optimal H_∞ robust controller. In addition to considering the widely discussed uncertainties caused by the orbit of each satellite in a formation, the optimal H_∞ robust output feedback control model presented in the current work considers the uncertainties caused by varying communication topology in the satellite formation that works in a cooperative way. Other new improvements include adopting a new method to more accurately describe and analyze the effects of the higher-order J2 perturbation, combining all the uncertainties into a diagonal structure, and utilizing a structured singular value to synthesize and analyze the controller.     

High precision dynamic model and control considering J2 perturbation for spacecraft hovering in low orbit

For spacecraft hovering in low orbit, a high precision spacecraft relative dynamics model without any simplification and considering J₂ perturbation is established in this paper. Using the derived model, open-loop control and closed-loop control are proposed respectively. Gauss's variation equations and the coordinate transformation method are combined to deal with the relative J₂ perturbation between the two spacecraft. The sliding mode controller is adopted as the closed-loop controller for spacecraft hovering. To improve the control accuracy, the relative J₂ perturbation is regarded as a known parameter term in the closed-loop controller. The external uncertainty perturbations except J₂ perturbation are estimated by numerical difference method, and the boundary layer method is used to weaken the impact of chattering on the sliding mode controller. The open-loop control of spacecraft hovering with the relative J₂ perturbation and without the relative J₂ perturbation are simulated and compared, and the results prove that the accuracy of open-loop control with relative J₂ perturbation has been significantly improved. Similarly, the simulation of the closed-loop control are presented to validate the effectiveness of the designed sliding mode controller, and the results demonstrate that the designed sliding mode controller including the derived relative J₂ perturbation can guarantee the high accuracy and robustness of spacecraft hovering in long-term mission.