Application of SDRE technique to orbital and attitude control of spacecraft formation flying

This paper proposes the application of a nonlinear control technique for coupled orbital and attitude relative motion of formation flying. Recently, mission concepts based on the formations of spacecraft that require an increased performance level for in-space maneuvers and operations, have been proposed. In order to guarantee the required performance level, those missions will be characterized by very low inter-satellite distance and demanding relative pointing requirements. Therefore, an autonomous control with high accuracy will be required, both for the control of relative distance and relative attitude. The control system proposed in this work is based on the solution of the State-Dependent Riccati Equation (SDRE), which is one of the more promising nonlinear techniques for regulating nonlinear systems in all the major branches of engineering. The coupling of the relative orbital and attitude motion is obtained considering the same set of thrusters for the control of both orbital and attitude relative dynamics. In addition, the SDRE algorithm is implemented with a timing update strategy both for the controller and the proposed nonlinear filter. The proposed control system approach has been applied to the design of a nonlinear controller for an up-to-date formation mission, which is ESA Proba-3. Numerical simulations considering a tracking signal for both orbital and attitude relative maneuver during an operative orbit of the mission are presented.     

A novel single thruster control strategy for spacecraft attitude stabilization

Feasibility of achieving three axis attitude stabilization using a single thruster is explored in this paper. Torques are generated using a thruster orientation mechanism with which the thrust vector can be tilted on a two axis gimbal. A robust nonlinear control scheme is developed based on the nonlinear kinematic and dynamic equations of motion of a rigid body spacecraft in the presence of gravity gradient torque and external disturbances. The spacecraft, controlled using the proposed concept, constitutes an underactuated system (a system with fewer independent control inputs than degrees of freedom) with nonlinear dynamics. Moreover, using thruster gimbal angles as control inputs make the system non-affine (control terms appear nonlinearly in the state equation). This necessitates the control algorithms to be developed based on nonlinear control theory since linear control methods are not directly applicable. The stability conditions for the spacecraft attitude motion for robustness against uncertainties and disturbances are derived to establish the regions of asymptotic 3-axis attitude stabilization. Several numerical simulations are presented to demonstrate the efficacy of the proposed controller and validate the theoretical results. The control algorithm is shown to compensate for time-varying external disturbances including solar radiation pressure, aerodynamic forces, and magnetic disturbances; and uncertainties in the spacecraft inertia parameters. The numerical results also establish the robustness of the proposed control scheme to negate disturbances caused by orbit eccentricity.     

光学稳像系统颤振抑制性能的分析与设计

光学稳定成像方法是一种用于隔离视轴颤振对成像质量影响的综合处理技术,它结合传统光学与反馈控制理论,通过闭环控制系统驱动在光成像通路内的动态校正机构补偿探测视轴与成像焦面间的相对运动,进而有效提升成像质量。文章首先建立了光学稳像系统的回路模型,并在此基础上,根据控制系统稳定性判据导出了颤振抑制函数的设计约束,分析了像移测量延时特性、测量精度特性及校正机构动态性能对颤振抑制带宽的影响。文章进一步给出了一种光学稳像系统颤振抑制带宽的设计方法,该方法针对视轴颤振的功率谱密度、像移探测性能和光机校正机构的动态性能完成了颤振抑制带宽的优化,从而可最小化颤振补偿残差。最后通过试验验证了文中分析结论和设计方法的有效性。     

解析求解非线性相对运动的最优重构问题

椭圆轨道相对运动模型的线性化导致其在大尺度相对运动应用中精度不能满足需求。针对任意椭圆轨道上的大尺度航天器编队最优重构问题,提出一种基于椭圆轨道非线性相对运动模型的近似解析求解方法。首先通过变分法建立了非线性最优重构问题的数学模型;然后采用摄动法,以偏近点角为积分变量求得了不含特殊积分的解析开环最优控制,有效地避免了真近点角域下最优控制解所含有的特殊积分。仿真验证了所求最优控制的有效性和优越性,结果表明在相对运动尺度较大时,相比基于椭圆轨道线性化模型的最优控制,在燃耗保持相近的情况下,所求非线性控制有效地降低了重构误差。     

基于EKF算法的单站无源定位跟踪研究

针对无源单站定位系统中观测方程非线性的特点,给出了一种适用于非线性的卡尔曼滤波估计改进算法——EKF算法。以方位角和方位角变化率为观测量,建立了EKF算法模型。仿真结果表明EKF算法具有收敛速度快,定位精度高的特点,可以提供较高精度的单站无源定位跟踪结果。     

基于滚动优化和微分Theta-D方法的快速绕飞航天器姿轨协同控制

针对近距离快速绕飞的视线保持要求和姿轨耦合特点,研究航天器姿轨协同最优控制方法。建立了六自由度相对运动耦合非线性模型,偏心推力矢量同时提供位置和姿态控制能力;考虑到近距离相对运动对动态性能的高精度要求,不同于无限时域经典Theta-D方法,提出了一种包含终端状态约束的滚动优化有限时域最优控制快速解算方法,推导了中间过程微分Riccati方程和微分Lyapunov方程的横截条件。控制器设计充分考虑了有限脉冲小推力器和有限力矩输出装置的约束。对近距离快速绕飞的仿真结果说明了方法的有效性,所提方法在保证相对运动稳定和动态性能的前提下控制输出幅值小,具有工程实际意义。     

远程自主交会改进制导算法

给出了一种适用于中、远程自主交会的改进制导算法。建立了交会两飞行器的相 对运动动力学模型;给出了可用于获取主、被动飞行器在惯性空间信息的轨道预报算法,并 且本预报算法是基于轨道要素描述的,同时考虑了J2项引力摄动,具有较高精度 。最后建立了用于优化制导指令速度的优化算法,和优化制导时间的燃料最优目标函数,优 化后的指令速度可使主动飞行器更精确地到达预定交会点。给出的数值仿真算例显示, 对于中、远程交会任务,单纯的C\|W制导算法所带来的终端误差较大,而改进的交会制导 算法可以十分明显地提高远程自主交会的制导精度。     

Analysis of a double gimbaled reaction wheel spacecraft attitude stabilization system

Three axis attitude stabilization of a satellite using a single spinning reaction wheel mounted on a two degree-of-freedom passively and actively torqued gimbal system is investigated. The passive control is assumed to be provided by a spring-loaded damper mounted on each of the gimbal axes, while active control results from both the wheel acceleration and the torque applied about the gimbal axes. The stability of the uncontrolled and passively controlled systems is investigated analytically. For constant wheel speed the pitch motion is decoupled from the roll-yaw and gimbal motions. Control laws for the roll-yaw motion are developed based on pole clustering and linear optimal control theory. For the pitch motion control laws are obtained based on classical second order system theory. Estimation techniques are applied to the roll-yaw system for the case when the complete state may not be directly observable (in the absence of a fine yaw position sensor).     

Lunar lander's three-dimensional translation and yaw rotation motion estimation during a descent phase using optical navigation

Optical navigation for a lunar lander consists of estimating a lander's 3-dimensional (3-D) relative dynamic motion with respect to a preselected landing site using a passive 2-dimensional (2-D) video image sequence. Lunar landing missions require a lander to perform an autonomous accurate landing with simple mechanical structure, easy operation and low cost. These requirements have motivated the need to develop an advanced navigation system. Existing navigation systems trade-off simplicity, accuracy and cost. High accuracy navigation systems typically imply complexity and high cost. In this paper, we consider a scenario where the descending phase starts from an initial altitude of 10 km with a time-of-descent of 100 s. The navigation camera is an off-the-shelf optical instrument used to take the video image sequence of the landing site during the landing phase. It is fed into the motion estimation algorithm to be processed. The continuous wavelet transform (CWT) is used to analyse each image frame of the input digital video image sequence. The output is a 2-D video image motion trajectory map, which represents the projection motion of the landing site. The 2-D video image motion is projected back to the 3-D lander's relative motion based on a geometric analysis. The outputs of this estimation algorithm are the 3-D attitude motion parameters of the lander at a time corresponding to an image being taken. The attitude determination and control system (ADCS) of the lander uses these data to perform the lander's attitude control task. In this article, we provide the motion modelling for a lunar lander during the descending phase. The projection of a 3-D planar to 2-D image plane is analysed which build the correspondence between the 3-D lander's motion and the 2-D image motion. This link provides the evidence for the geometry analysis. CWT is reviewed and CWT for video image sequence analysis is also introduced. Numerical simulation of the estimated 2-D video image sequence under the lander performing a 3-D translation and yaw rotation during the terminal descent are shown to verify the proposed concepts. The analysis of the results show that the proposed method achieves highly accurate 2-D video image motion estimation of less then 1% error with significant savings of cost, mass and volume. It leads to the accurate estimation of the lander's 3-D relative motion with respect to the landing site.     

航天飞行器相对运动动力学及其控制方法

采用本地轨道从标系对两邻飞船间相对运动动力学展开研究，指出在相对运动中也存在平衡状态，用相平面方法分析了其稳定性，基于此分析，综合出相对运动控制方法，即距离速率控制方法，受控运动轨迹是一条稳定的稳态直线，进而建立了全方位距离速率控制方法。最后以系绳卫星系统和飞船安全为例完成了计算机模拟。     

Spacecraft formation flying: A review and new results on state feedback control

This paper presents a review of previous work within the field of spacecraft formation flying, including modeling approaches and controller design. In addition, five new approaches for tracking control of relative translational motion between two spacecraft in a leader–follower formation are derived. One PD controller with feedback linearisation is derived and shown to result in an exponentially stable equilibrium point of the closed loop system. Four nonlinear controllers are derived and proved by using Lyapunov theory and Matrosov's theorem to leave the closed loop system uniformly globally asymptotically stable. Results from the simulation of the system with the derived controllers are presented, and compared with respect to power consumption and tracking performance.     

一种基于Star算法的多路视频稳像方法研究

目前,基于特征点匹配的稳像算法中存在特征点提取速度慢、误匹配率高,以及多目相机的多路视频稳像太过耗时、实时性不好的问题,提出了一种基于Star特征点提取算法的多路视频快速稳像方法。首先采用Star算法提取视频当前帧特征点,然后采用光流法结合当前帧特征点信息跟踪预测下一帧对应的特征点,以加快特征点提取速度,同时减少所提取的特征点错误匹配率。通过对匹配的特征点求取相应的仿射变换矩阵获取帧间运动矢量,进而采用卡尔曼滤波器对帧间运动矢量进行滤波处理,以滤除其中的相机随机抖动矢量并保留相机的主观运动矢量。最后依据滤波后的运动矢量进行图像补偿得到稳定的图像序列。针对复眼导引头存在的多路视频抖动情况,基于OpenMP并行开发库,利用多核处理器的优势,实现了多路抖动视频的并行实时稳像。所设计的数字稳像算法在PC平台下对4路抖动视频（OTB100的BlurCar系列视频,分辨率为640×480,帧率为30 FPS）并行稳像的结果参数为：峰值信噪比（Peak Signal-to-Noise Ratio,PPSNR）平均提升了4.62 dB,单帧耗时平均为14.51 ms。经仿真实验证实,算法的计算效率和特...     

J2项摄动条件下线性化的编队卫星动力学方程

考虑J2项摄动力对参考卫星轨道的绝对影响和对伴随卫星轨道的相对影响,应用拉格朗日方法,在笛卡尔坐标系下,给出了一组考虑J2项摄动的线性化的编队卫星相对动力学方程。该方程考虑了J2项摄动力带来的相对运动平面内外的耦合和短周期项的影响,有效地提高了相对动力学模型的精度。仿真结果表明,该方程组可有效地描述J2项摄动条件下编队卫星的相对运动,其误差只有二体非线性模型的10%,利用其设计的水平圆编队半径的相对误差不超过1%,并且由于是线性化的微分方程描述,可方便地应用到编队卫星导航、制导与控制系统的设计中。     

Analysis of the dynamics of the deployed aerodynamic space tether system

An analysis of the motion of a deployed space system that consists of two end bodies connected by a tether has been considered. One of the bodies has a relatively large ballistic coefficient that ensures aerodynamic braking or the stabilization of the motion of the entire system in relatively low near-Earth orbits. The deployment of this system mainly occurs due to the action of aerodynamic forces. Several ways of deploying the system have been analyzed, including (1) the uncontrolled release of the tether with hardly any braking; (2) deployment with constant braking force; (3) the dynamic control law without feedback, when the resistance force varies according to a set program; (4) a kinematic control law with feedback when programs are set for varying the velocity and length of the tether release. To analyze the dynamics of the system, a mathematical model of motion has been constructed in which the motion of the end bodies relative to their centers of mass is taken into account.     

Synthesis of a combined system for precise stabilization of the Spektr-UF observatory: II

The paper presents the second part of the results of search studies for the development of a combined system of high-precision stabilization of the optical telescope for the designed Spectr-UF international observatory [1]. A new modification of the strict method of the synthesis of nonlinear discrete-continuous stabilization systems with uncertainties is described, which is based on the minimization of the guaranteed accuracy estimate calculated using vector Lyapunov functions. Using this method, the synthesis of the feedback parameters in the mode of precise inertial stabilization of the optical telescope axis is performed taking the design nonrigidity, quantization of signals over time and level, and errors of orientation meters, as well as the errors and limitation of control moments of executive engine-flywheels into account. The results of numerical experiments that demonstrate the quality of the synthesized system are presented.     

基于遗传算法的空间自由漂浮机械臂系统运动规划

为了研究空间自由漂浮机械臂系统的运动规划问题,本文将其动力学模型转化为以关节角速度为控制输入变量的非线性控制系统状态方程,确定了以能耗最小为主要目标,同时满足一定约束条件的多种目标函数,提出了运用遗传算法求解最优控制变量的运动规划方法。同时,以机械臂从初始位形运动至指定终端位形的过程为仿真算例,对上述规划算法及其应用进行了分析和验证。仿真结果表明该算法有效可行,能够为机械臂系统的空间操作提供理论参考。     

无阻力双星串行编队相对位置有限时间控制

研究无阻力卫星构成的双星串行编队相对位置的有限时间控制问题。首先,选取两颗卫星位置连线中点为参考坐标系原点,考虑J2摄动项,建立了双星相对位置的动力学模型。与传统的主从式卫星编队模型中假设主星为理想运动不同,本文的建模方法同时考虑了两颗卫星受到扰动的情况。而后,为使无阻力卫星编队相对位置快速达到期望状态,采用自适应参数更新律和加幂积分技术设计控制律,实现了闭环系统的实际有限时间稳定。最后,通过数值仿真校验了本文控制器的有效性和鲁棒性。     

一种用于导弹姿态控制系统的直接力非线性控制法

为改善传统导弹姿控系统线性控制法的不足,用相平面法分析了直接力作用下导弹的姿态运动规律和气动力作用对直接力控制的影响,提出了一种综合控制精度、姿控发动机产品特性和推进剂消耗量等指标的直接力非线性控制方法,给出了控制模型。仿真结果表明,该法能在气动力作用或干扰无法忽略的条件下实现导弹姿控发动机的开关工作正常,保证精度及推进剂消耗最省,其控制精度与线性比例微分(PD)控制律相当。     

时变拓扑卫星集群分布式自主相对导航方法

针对时变拓扑卫星集群的相对导航需求,提出了基于图论的时变拓扑分布式一致性无迹卡尔曼滤波算法。首先给出了固定拓扑卫星集群的相对运动方程、测角测距测量模型和无迹卡尔曼滤波算法,然后考虑测角失效时相对导航系统不可观或弱可观的问题,结合矢量环一致性约束,构造了一致性无迹卡尔曼滤波算法,以提高系统的可观度;在此基础上,针对时变拓扑卫星集群,以滤波精度为优化指标,在图论的基础上利用Dijkstra算法对卫星集群的时变拓扑结构进行重构,并将重构后的拓扑结构应用于卫星集群相对导航。仿真结果表明所提算法能有效改善不完备测量带来的模糊轨道问题,并且能够实现实时的拓扑重构,以满足时变拓扑星群的相对导航精度要求。     

欠驱动冗余度机器人运动优化控制

研究了具有多个被动关节的欠驱动冗余机器人的运动优化控制问题。基于滑模变结构控制方法，首先实现了被动关节位置控制；进一步利用“虚拟模型引导控制”方法实现了欠驱动冗余度机器人的连续轨迹运动优化控制；通过平面三连杆机器人臂进行了避障运动仿真，仿真结果证明了提出的方法的有效性。