Hybrid optimization for multiple-impulse reconfiguration trajectories of satellite formation flying

A hybrid optimization method is developed for fuel-optimal reconfigurations of a group of satellites flying in formation. The genetic algorithm performs a global search to find two-impulse trajectories, and primer vector analysis finds multiple-impulsive local optimal trajectories with the two-impulse trajectories as initial guesses. Hybrid optimization finds globally optimal trajectories for formation reconfigurations, including formation resizing, reassignment and reorientation maneuvers. Multiple-impulse trajectories reduce the fuel consumption from the two-impulse trajectories by up to 4.4% for those maneuvers. In real missions, satellites can follow two-impulse trajectories to gain the advantage of a smaller number of impulses, with the cost of slightly more propellant. The qualitative characteristics of the optimal trajectories are analyzed from the number of optimal trajectories found by hybrid optimization.     

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.     

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.     

Robust optimal sliding mode control for the deployment of Coulomb spacecraft formation flying

Inter-spacecraft electrostatic force (Coulomb force) is desirable for close formation flying control because of its propellant-less and free contaminate characteristics attributed to the propellant exhaust emission. This paper presents robust optimal sliding mode control to deal with the problem of thruster saturation in tracking the formation trajectory for Coulomb spacecraft formation flying. The robust controller design is based on optimal control theory as a linear quadratic system, and it is augmented with an integral sliding mode control technique. The stability of the closed-loop system is guaranteed using the second Lyapunov method. The developed controller outperforms the existing ones, because it has a higher degree of fine-tuning to cope with the uncertainty. Numerical simulations are employed to confirm the efficiency of the developed controller.     

Optimal spacecraft formation establishment and reconfiguration propelled by the geomagnetic Lorentz force

The Lorentz force acting on an electrostatically charged spacecraft as it moves through the planetary magnetic field could be utilized as propellantless electromagnetic propulsion for orbital maneuvering, such as spacecraft formation establishment and formation reconfiguration. By assuming that the Earth’s magnetic field could be modeled as a tilted dipole located at the center of Earth that corotates with Earth, a dynamical model that describes the relative orbital motion of Lorentz spacecraft is developed. Based on the proposed dynamical model, the energy-optimal open-loop trajectories of control inputs, namely, the required specific charges of Lorentz spacecraft, for Lorentz-propelled spacecraft formation establishment or reconfiguration problems with both fixed and free final conditions constraints are derived via Gauss pseudospectral method. The effect of the magnetic dipole tilt angle on the optimal control inputs and the relative transfer trajectories for formation establishment or reconfiguration is also investigated by comparisons with the results derived from a nontilted dipole model. Furthermore, a closed-loop integral sliding mode controller is designed to guarantee the trajectory tracking in the presence of external disturbances and modeling errors. The stability of the closed-loop system is proved by a Lyapunov-based approach. Numerical simulations are presented to verify the validity of the proposed open-loop control methods and demonstrate the performance of the closed-loop controller. Also, the results indicate the dipole tilt angle should be considered when designing control strategies for Lorentz-propelled spacecraft formation establishment or reconfiguration.     

Connectivity preservation and collision avoidance control for spacecraft formation flying in the presence of multiple obstacles

This paper addresses connectivity preservation and collision avoidance problem of spacecraft formation flying with multiple obstacles and parametric uncertainties under a proximity graph. In the proximity graph, each spacecraft can only get the states of the neighbor spacecraft within its sensing region. Connectivity preservation of a graph means that the connectivity of the graph should be preserved at all times during spacecraft formation flying. We consider two cases: (i) the obstacles are static, and (ii) the obstacles are dynamic. In the first case, a distributed continuous control algorithm based on artificial potential function and equivalent certainty principle is proposed to account for the unknown parameters and the static obstacles. In the second case, a sliding surface combined with a distributed adaptive control algorithm is proposed to tackle the influence of the dynamic obstacles and the unknown parameters at the same time. With the distributed control algorithms, the desired formation configuration can be achieved while the connectivity of the graph is preserved and the collisions between the spacecraft and the obstacles are avoided. Numerical simulations are presented to illustrate the theoretical results.     

Integrated orbit and attitude hardware-in-the-loop simulations for autonomous satellite formation flying

Development and experiment of an integrated orbit and attitude hardware-in-the-loop (HIL) simulator for autonomous satellite formation flying are presented. The integrated simulator system consists of an orbit HIL simulator for orbit determination and control, and an attitude HIL simulator for attitude determination and control. The integrated simulator involves four processes (orbit determination, orbit control, attitude determination, and attitude control), which interact with each other in the same way as actual flight processes do. Orbit determination is conducted by a relative navigation algorithm using double-difference GPS measurements based on the extended Kalman filter (EKF). Orbit control is performed by a state-dependent Riccati equation (SDRE) technique that is utilized as a nonlinear controller for the formation control problem. Attitude is determined from an attitude heading reference system (AHRS) sensor, and a proportional-derivative (PD) feedback controller is used to control the attitude HIL simulator using three momentum wheel assemblies. Integrated orbit and attitude simulations are performed for a formation reconfiguration scenario. By performing the four processes adequately, the desired formation reconfiguration from a baseline of 500–1000 m was achieved with meter-level position error and millimeter-level relative position navigation. This HIL simulation demonstrates the performance of the integrated HIL simulator and the feasibility of the applied algorithms in a real-time environment. Furthermore, the integrated HIL simulator system developed in the current study can be used as a ground-based testing environment to reproduce possible actual satellite formation operations.     

椭圆轨道卫星编队飞行的最优控制研究

研究了椭圆轨道卫星编队飞行的队形保持问题,设计了李雅普诺夫(Lyapunov)控制律,并用遗传算法对控制律进行了优化。为克服遗传算法局部寻优能力差的缺点,对遗传算法进行了改进,设计了自适应模拟退火遗传算法。仿真结果表明,采用Lyapunov方法进行队形保持能提高位置保持的精度,且在经过遗传算法优化后,所消耗的燃料基本与线性二次型(LQR)方法一致;同时,减少了计算时间,有利于星上计算机的实现。     

飞翼布局飞行器副翼性能及重构分析

针对飞翼布局飞行器副翼在偏转过程中引起的纵横航向运动耦合的问题,应用升降舵、副翼和阻力舵协调偏转的方法进行控制.为提高飞翼飞行器的生存性,对舵面故障时的重构方法进行了研究.升降舵故障时,直接应用伪逆法即可应用副翼完成重构;阻力舵故障时,为解决伪逆法带来的系统不稳定及重构后系统稳态精度差的问题,将一种基于劳斯稳定判据的、加入了比例-积分控制器的改进伪逆法引入重构.仿真结果表明:该方法在保证系统稳定的基础上能够使系统性能得到最大程度的恢复.     

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.     

A guidance approach to satellite formation reconfiguration based on convex optimization and genetic algorithms

This paper presents a new approach for autonomous reconfiguration of distributed space systems, which ensures safe guidance of spacecraft formations towards the desired patterns while optimizing the total propellant consumption. The orbital transfer is reduced to the form of a convex optimization problem to guarantee rapid computation of control laws. Hence, tasks are iteratively assigned to the component platforms to detect the best reconfiguration strategy. The path-planning is entrusted to a reference satellite of the cluster, that coordinates the remaining ones by means of a procedure based on genetic algorithms. Two methods are proposed, depending on the organizational architecture of the spacecraft formation. In the first one, the maneuver is completely planned by the reference satellite, that determines final tasks and control actions for the whole cluster. As an alternative to such a fully-centralized approach, a distributed version of the algorithm is proposed: tasks are sorted by the reference satellite and transfer orbits are computed by exploiting the computational resources of the whole cluster. Whatever the considered framework, both the planners ensure a safe transition of the formation towards the target geometry. Simulation results show that, when relative distances are of the order of hundreds of meters, a mean delta-v per satellite of the order of 0.1 m/s is required to reconfigure LEO clusters within one orbital period.     

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.     

两步法快速解算编队卫星GPS模糊度

为克服卫星编队飞行实时相对定位中双频模糊度解算速度慢的缺点,结合扩展Kalman滤波(EKF,Extended Kalman Filter),首先采用少数个历元(如10个)相位平滑伪距相对定位结果与 L₆的平均值对滤波初始化,再根据两步法解算双频模糊度,即先解算并正确固定宽巷模糊度,获得较准确的基线分量估值,然后采用选权拟合方法,将基线分量作为约束条件解算并固定双频模糊度.仿真算例计算结果表明,当宽巷模糊度正确固定后,编队卫星间相对定位误差在5cm以内,两步法可以在较短时间(约3min)内固定双频模糊度,为精确解算编队卫星的相对状态提供保障.     

Optimal mission planning of the reconfiguration process of satellite constellations through orbital maneuvers: A novel technical framework

In this paper, a general new methodology is presented for the orbital reconfiguration of satellite constellations on the basis of Lambert targeting theorem. In view of the cost and risk reduction, it is very important to consider the problem of satellite constellation reconfiguration with the two constraints of overall mission cost minimization and the desired final configuration. Hence, the dependent non-simultaneous deployment approach is proposed to minimize overall fuel cost. Despite the fact that the satellites deploy in a non-simultaneous manner, supplementary phasing maneuvers on the target orbital pattern to achieve the desired orbital configuration are avoided. Moreover, a novel idea is presented to optimize the flight of satellites, which plays an important role in complying with the constraint of overall fuel cost minimization as much as possible. In order to achieve the global optimal solution of the satellite constellation reconfiguration problem, the efficient hybrid Particle Swarm Optimization/Genetic Algorithm (PSO/GA) technique, is implemented. Finally, to indicate the superiority of the presented method, a comparison to the simultaneous maneuver viewpoint is made on a number of representative cases. The obtained results imply significant reduction of reconfiguration costs by employing the proposed method.     

Robust model predictive control for satellite formation keeping with eccentricity/inclination vector separation

This study presents model predictive formation control based on an eccentricity/inclination vector separation strategy. Alternative collision avoidance can be accomplished by using eccentricity/inclination vectors and adding a simple goal function term for optimization process. Real-time control is also achievable with model predictive controller based on convex formulation. Constraint-tightening approach is address as well improve robustness of the controller, and simulation results are presented to verify performance enhancement for the proposed approach.     

Neural network-based sliding mode control for atmospheric-actuated spacecraft formation using switching strategy

This paper presents an adaptive neural networks-based control method for spacecraft formation with coupled translational and rotational dynamics using only aerodynamic forces. It is assumed that each spacecraft is equipped with several large flat plates. A coupled orbit-attitude dynamic model is considered based on the specific configuration of atmospheric-based actuators. For this model, a neural network-based adaptive sliding mode controller is implemented, accounting for system uncertainties and external perturbations. To avoid invalidation of the neural networks destroying stability of the system, a switching control strategy is proposed which combines an adaptive neural networks controller dominating in its active region and an adaptive sliding mode controller outside the neural active region. An optimal process is developed to determine the control commands for the plates system. The stability of the closed-loop system is proved by a Lyapunov-based method. Comparative results through numerical simulations illustrate the effectiveness of executing attitude control while maintaining the relative motion, and higher control accuracy can be achieved by using the proposed neural-based switching control scheme than using only adaptive sliding mode controller.     

基于分数阶滑模的航天器姿态鲁棒控制

针对存在外部扰动及转动惯量不确定性的高精度高稳定度的航天器姿态控制问题,提出了一种具有强鲁棒性的分数阶滑模控制器。首先,在修正罗德里格参数描述的航天器数学模型基础上,导出了便于分数阶滑模控制器设计的等效数学模型。其次,在传统滑模控制的滑模面与控制律中均引入分数阶微分算子,利用分数阶微分算子的快速收敛性与信息记忆性,设计了分数阶滑模控制器,并使用Lyapunov理论与分数阶稳定性理论证明了整个系统的稳定性。最后,仿真试验表明,分数阶滑模控制器具有高精度、强鲁棒性和良好的抗干扰性。     

编队卫星防碰撞规避路径规划方法与控制研究

针对编队卫星在构型重构和构型失效重组时发生碰撞可能性最大的两种机动工况,采用数学规划的方法对其进行防碰撞规避准则、规避策略和控制方面的研究;并通过系统可控性证明出无径向推力相对于全向推力,也可以达到目标相位点只是燃料消耗得多。对编队构型失效重组工况中备份星机动前停泊位置,进入编队位置选择和启动时刻选择以及故障星离开编队后,目标轨道确定等问题通过数学仿真的形式予以解答。仿真结果表明,该研究方法真实可信、简便有效。     

电磁航天器编队悬停鲁棒协同控制方法

针对电磁航天器编队近地轨道悬停问题,提出一种在缺少参考轨道准确信息时的协同控制方法。用TH方程描述航天器间的相对运动,选择与参考轨道同周期的圆轨道为标称轨道。将参考轨道相对于标称圆轨道的偏差、地球非球形引力、大气阻力及其他天体引力等参数单独归类,视其为不确定量,构成不确定系统。通过引入一致性理论,在电磁作用模型和动力学方程均存在不确定性的条件下,针对航天器编队悬停的目标设计了鲁棒协同控制律。考虑能量消耗最优和均衡以及轨道姿态解耦,给出了通过优化进行磁矩配置的方案。仿真结果表明,所设计的鲁棒协同控制律能够实现编队电磁航天器高精度悬停,所给出的磁矩配置方案能够实现磁矩的合理分配。