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.     

Multi-objective optimal formation reconfiguration with scalarization and stochastic boundaries

A new method is proposed for multi-objective optimal control of satellite formation reconfiguration. First, necessary optimality conditions of single-objective fuel-optimal reconfiguration are studied. Problem of initial guess of the costate and control discontinuity are addressed by using a new developed stochastic based method. Terminal conditions of Two Point Boundary Value Problem (TPBVP) of the optimal control equations are relaxed using augmented Gaussian. Variances or bandwidths of the terminal conditions are set to decision variables to be optimized. Responses of varied initial costate are modeled and propagated using Riccati equation. Using quadratic convolution of relaxed terminal conditions, objective function of the fuel-optimal problem is reformulated into a quadratic equation, and a gradient based optimizer is used to search the optimal initial guess. In the second part of the paper, optimal control of format flying reconfiguration with two competitive objectives:fuel and time of flight (ToF) is studied. With Pascoletti-Serafini scalarization, the Multi-objective Optimal Control Problem (MOCP) is scalarized into a set of weighted Single-objective Optimal Control Problems (SOCP). Hamiltonian and switch function for the weighted SOCP are developed and constructed. New developed stochastic based approach is then used to search the optimal Pareto solutions. Verification and performances of proposed algorithms are demonstrated through numerical simulations of single-objective and multi-objective optimal control of low-thrust elliptical orbit formation reconfiguration. Potential applications of the algorithms to some other preliminary space mission designs are also discussed.     

近地轨道集群航天器电磁编队飞行非线性反馈控制方法

针对近地轨道集群航天器电磁编队飞行的动力学和控制问题, 提出了一种非线性反馈控制方法. 基于电磁力模型和地磁场模型, 分析了地磁场对近地轨道电磁编队的影响; 建立了集群航天器电磁编队高精度相对轨道动力学模型; 基于Lyapunov稳定性理论设计了一种非线性反馈控制律, 利用该方法对两星电磁编队维持控制进行了仿真验证. 仿真结果表明, 地磁场引起的电磁干扰力可以忽略, 但是电磁干扰力矩的影响必须考虑; 近地轨道集群航天器电磁编队是可控的, 所设计的控制方法是可行的.      

基于对偶四元数的编队飞行卫星相对位姿描述

为统一描述编队飞行卫星中主从星的相对位置和姿态参数,利用对偶四元数,建立编队飞行卫星运动学模型,分析其物理意义,提出了基于对偶四元数的编队飞行卫星相对位姿描述的划船算法,并利用这一算法解算出相对位置和姿态参数,突破了传统方法中将卫星轨道和姿态分而治之的方式。仿真结果表明该算法科学合理,能够有效描述编队飞行卫星间的相对位置和姿态。     

Spacecraft formation flying for Earth-crossing object deflections using a power limited laser ablating

A formation flying strategy with an Earth-crossing object (ECO) is proposed to avoid the Earth collision. Assuming that a future conceptual spacecraft equipped with a powerful laser ablation tool already rendezvoused with a fictitious Earth collision object, the optimal required laser operating duration and direction histories are accurately derived to miss the Earth. Based on these results, the concept of formation flying between the object and the spacecraft is applied and analyzed as to establish the spacecraft’s orbital motion design strategy. A fictitious “Apophis”-like object is established to impact with the Earth and two major deflection scenarios are designed and analyzed. These scenarios include the cases for the both short and long laser operating duration to avoid the Earth impact. Also, requirement of onboard laser tool’s for both cases are discussed. As a result, the optimal initial conditions for the spacecraft to maintain its relative trajectory to the object are discovered. Additionally, the discovered optimal initial conditions also satisfied the optimal required laser operating conditions with no additional spacecraft’s own fuel expenditure to achieve the spacecraft formation flying with the ECO. The initial conditions founded in the current research can be used as a spacecraft’s initial rendezvous points with the ECO when designing the future deflection missions with laser ablation tools. The results with proposed strategy are expected to make more advances in the fields of the conceptual studies, especially for the future deflection missions using powerful laser ablation tools.     

Spacecraft formation flying control around L2 sun-earth libration point using on–off SDRE approach

In this paper, on–off SDRE control approach is presented for spacecraft formation flying control around sun-earth L2 libration point. Orbits around libration points are significant targets for many space missions mainly because of efficient fuel consumption. Furthermore, less propellant usage can be achieved by considering optimal control approaches in spacecraft formation flying control design. Among various nonlinear and optimal control methods, SDRE has shown to be a popular controller in various missions due to the privileges including efficiency, accuracy and robustness. The spacecraft are assumed to have on–off thrusters as actuators. It requires them to be fed with a sequence of on–off pulses which is regarded as a challenge for spacecraft designers. Hence, the main contribution of this paper is designing an on–off SDRE approach for the formation flight around sun-earth L2 point with uncertainty with energy and accuracy considerations. Including on–off input as a constraint is not feasible for SDRE implementation because it makes the system non-affine. An alternative is utilizing an integral action technique and an auxiliary control to make the system affine which leads to on–off SDRE approach. It has also been shown that the proposed method is robust against parametric uncertainties of the states. Present study aims to design an energy-beneficial, simple and attractive controller for a complex nonlinear system with on–off inputs and uncertainty in CRTBP. Simulation results show that the on–off SDRE control could provide the formation flight around L2 point with high accuracy using less energy consumption.     

Formation control using μ-synthesis for Inner-Formation Gravity Measurement Satellite System

Inner-Formation Gravity Measurement Satellite System (IFGMSS) is used to map the gravity field of Earth. The IFGMSS consists of two satellites in which one is called “inner satellite” and the other one is named as “outer satellite”. To measure the pure Earth gravity, the inner satellite is located in the cavity of the outer satellite. Because of the shield effect of the cavity, the inner satellite is affected only by the gravitational force, so it can sense Earth gravity precisely. To avoid the collision between the inner satellite and the outer satellite, it is best to perform a real-time control on the outer satellite. In orbit, the mass of the outer satellite decreases with the consumption of its propellant. The orbit angular rate of the inner satellite varies with time due to various disturbing forces. These two parameters’ uncertainties make the C–W function be not so accurate to describe the formation behavior of these two satellites. Furthermore, the thrusters also have some uncertainties due to the unmodelled dynamics. To cancel the effects caused by the above uncertainties, we have studied the robust control method based on the μ-synthesis. This μ-synthesis eliminates the conservativeness and improves the control efficiency comparing with the H_∞ method. Finally, to test the control method, we simulate an IFGMSS mission in which the satellite runs in a sun synchronous circular orbit with an altitude of 300 km. The simulation results show the effectiveness of the robust control method. The performances of the closed-loop system with the μ-controller are tested by the μ-analysis. It has found that the nominal performance, the robust stability and the robust performance are all achieved. The transient simulation results further prove the control response is fast and the accuracy of the relative position meets the demand of the gravity measurement.     

基于InSAR任务性能要求的编队轨道构型设计

为使卫星在飞过特定经纬度地面上空时对应特定的空间基线形式,系统的其他参数常受制于诸多限制,只有编队构型可以进行更为自由的设计。以双星编队为例,研究了基于轨道摄动理论的编队飞行模型;分析了编队飞行InSAR卫星的轨道设计约束条件与设计目标;提出了四种轨道构型方案并对其测高性能进行比较;并分析了地球扁率摄动因素对编队构型及InSAR测高性能的影响。     

航天器相对导航与控制技术的典型任务

在空间交会对接、在轨服务、近距离目标监视以及航天器编队飞行任务中,通常需要通过相对导航与控制技术对相互邻近的航天器进行控制.回顾了该领域典型的空间任务,特别关注任务、相对导航与控制方法、相对测量设备、推进系统等主要特征,并总结了该项技术的发展趋势.     

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.     

Finite-time relative orbit-attitude tracking control for multi-spacecraft with collision avoidance and changing network topologies

This paper addresses the relative position tracking and attitude synchronization control problem for spacecraft formation flying (SFF). Based on the derived relative coupled six-degree-of-freedom dynamics, a robust adaptive finite-time fast terminal sliding mode controller is proposed to achieve the desired formation in the presence of model uncertainties and external disturbances. It is shown that the designed controller is effective for changing information exchange topology making it robust to node failure. Then, the artificial potential function method is employed to generate collision avoidance schemes to modify the controller such that inter-agent collision avoidance can be ensured during the formation maneuver, which is critical for practical missions. The stability of the overall closed-loop system is proved by using Lyapunov theory. Finally, numerical examples for a given SFF scenario are presented to illustrate the performance of the controller.     

基于预设性能控制的超紧密航天器编队防避撞协同控制

研究了考虑具有外界干扰和防避撞约束的近地轨道超紧密航天器构型控制问题,将反步控制技术、预设性能控制相结合,提出了一种基于预设性能鲁棒控制的六自由度编队协同鲁棒控制方法。首先,给出了近地轨道完整的编队航天器相对位置和相对姿态非线性动力学方程,并根据状态约束条件转换了相对位置动力学模型。其次,设计了预设性能函数,通过误差转换,建立系统等效误差模型,基于反步法设计了预设性能鲁棒控制器,进一步应用Lyapunov稳定性定理证明了其闭环系统的一致最终有界性。最后在MATLAB/Simulink平台上进行了仿真验证,结果表明了方法的有效性。     

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.     

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.     

A lunar L2-Farside exploration and science mission concept with the Orion Multi-Purpose Crew Vehicle and a teleoperated lander/rover

A novel concept is presented in this paper for a human mission to the lunar L2 (Lagrange) point that would be a proving ground for future exploration missions to deep space while also overseeing scientifically important investigations. In an L2 halo orbit above the lunar farside, the astronauts aboard the Orion Crew Vehicle would travel 15% farther from Earth than did the Apollo astronauts and spend almost three times longer in deep space. Such a mission would serve as a first step beyond low Earth orbit and prove out operational spaceflight capabilities such as life support, communication, high speed re-entry, and radiation protection prior to more difficult human exploration missions. On this proposed mission, the crew would teleoperate landers/rovers on the unexplored lunar farside, which would obtain samples from the geologically interesting farside and deploy a low radio frequency telescope. Sampling the South Pole-Aitken basin, one of the oldest impact basins in the solar system, is a key science objective of the 2011 Planetary Science Decadal Survey. Observations at low radio frequencies to track the effects of the Universe’s first stars/galaxies on the intergalactic medium are a priority of the 2010 Astronomy and Astrophysics Decadal Survey. Such telerobotic oversight would also demonstrate capability for human and robotic cooperation on future, more complex deep space missions such as exploring Mars.     

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.      

连续小推力非开普勒悬浮轨道研究综述

连续小推力非开普勒悬浮轨道在深空探测与地球极地观测任务中有着重要的应用前景。归纳了电推进、太阳帆推进等连续小推力技术的发展历程与现状;阐述了日心、行星悬浮轨道的动力学特性、稳定性、轨道保持策略;分析了三体问题下人工拉格朗日点的优势及其在深空探测方面的应用;讨论了悬浮轨道编队飞行的研究方法与控制策略。最后针对小推力悬浮轨道研究发展面临的难题,提出了研究新思路和应用新方向。     

PROBA-3 mission and the Shadow Position Sensors: Metrology measurement concept and budget

PROBA-3 is a space mission of the European Space Agency that will test, and validate metrology and control systems for autonomous formation flying of two independent satellites. PROBA-3 will operate in a High Elliptic Orbit and when approaching the apogee at 6·10⁴ Km, the two spacecraft will align to realize a giant externally occulted coronagraph named ASPIICS, with the telescope on one satellite and the external occulter on the other one, at inter-satellite distance of 144.3 m. The formation will be maintained over 6 hrs across the apogee transit and during this time different validation operations will be performed to confirm the effectiveness of the formation flying metrology concept, the metrology control systems and algorithms, and the spacecraft manoeuvring. The observation of the Sun’s Corona in the field of view [1.08;3.0]R_Sun will represent the scientific tool to confirm the formation flying alignment. In this paper, we review the mission concept and we describe the Shadow Position Sensors (SPS), one of the metrological systems designed to provide high accuracy (sub-millimetre level) absolute and relative alignment measurement of the formation flying. The metrology algorithm developed to convert the SPS measurements in lateral and longitudinal movement estimation is also described and the measurement budget summarized.     

Optimal guidance based on receding horizon control for low-thrust transfer to libration point orbits

This paper addresses the design and computation of a guidance law for a transfer mission from an orbit near the Earth to a halo orbit around the libration point L₂ in the Sun–Earth system. The guidance law, which is designed based on receding horizon control and compensates for launch velocity errors that are introduced by inaccuracies of the launch vehicle, is solved using the generating function method. During the design of the closed-loop guidance law, the entire transfer mission, which is considered a nonlinear optimal control problem, is evaluated to obtain a nominal reference trajectory. Using the launch velocity errors and the uncertainty of the model, a spacecraft controlled by the proposed guidance law tracks the reference trajectory. Furthermore, the original Riccati differential equation in the receding horizon control algorithm is replaced by an equivalent convenient form of the Riccati differential equation that is based on the generating function. The high-efficiency solution of the equivalent equation avoids the online direct integration of the original Riccati differential equation, which significantly increases the computational efficiency for the receding horizon control problem. Numerical simulations using a nonlinear bicircular four-body model demonstrate the capabilities of the proposed receding horizon guidance law for the transfer mission. In addition, the generating function method improves the computational efficiency by at least one order of magnitude over the backward sweep method in solving the receding horizon control problem.     

资源约束突变的航天器观测快速重调度优化算法

针对航天器对地观测调度中资源约束发生突变的情况,提出了一种基于蚁群算法的启发式重调度算法。首先对重调度过程中的资源约束进行分析,给出了资源约束发生变化的重调度模型。然后,结合原调度优化结果,给出重调度任务集合更新方法,对任务集合进行剪裁。最终,基于最大限度利用原调度方案信息的思想,结合任务集合更新及优先级等启发式信息,给出了一种改进的重调度优化算法。数值计算结果表明,所设计的算法可以快速有效的提高重调度过程的收益。