Adaptive control for autonomous rendezvous of spacecraft on elliptical orbit

A strategy for spacecraft autonomous rendezvous on an elliptical orbit in situation of no orbit information is developed. Lawden equation is used to describe relative motion of two spacecraft. Then an adaptive gain factor is introduced, and an adaptive control law for auton- omous rendezvous on the elliptical orbit is designed using Lyapunov approach. The relative motion is proved to be ultimately bounded under this control law, and the final relative position error can achieve the expected magnitude. Simulation results indicate that the adaptive control law can realize autonomous rendezvous on the elliptical orbit with relative state information only.

An ergodic algorithm for long-term coverage of elliptical orbits

This paper deals with the coverage analysis problem of elliptical orbits. An algorithm based on ergodic theory, for long-term coverage of elliptical orbits, is proposed. The differential form of the invariant measure is constructed via the perturbation on mean orbital elements resulted from the J2 term of non-spherical shape of the earth. A rigorous proof for this is then given. Different from the case of circular orbits, here the flow and its space of the dynamical system are defined on a physical space, and the real-value function is defined as the characteristic function on station mask. Therefore, the long-term coverage is reduced to a double integral via Birkhoff-Khinchin theorem. The numerical implementation indicates that the ergodic algorithm developed is available for a wide range of eccentricities.

Simulation for MSS-2 low-perigee elliptical orbit satellites:an example of lithospheric magnetic field modelling

A future constellation of at least four geomagnetic satellites(designated Macao Scientific Satellite-1(MSS-1)and Macao Scientific Satellite-2(MSS-2))was recently proposed,to continue high-quality geomagnetic observations in the post-Swarm period,focusing especially on collecting data that will provide a global,three-dimensional survey of the geomagnetic field.In this paper,we present a simulation of two years of orbits(2020.01.01-2022.01.01)of two satellites(tentatively denoted as MSS-2)that are constellated in elliptical(200×5,300 km)low-perigee orbits.By comparing error variances of Gauss coefficients,we investigate the sensitivity of lithospheric magnetic field modelling to data collected from various satellite orbits,including a near circular reference orbit of 300×350km,and elliptical orbit of 180×5,300 km,220×5,300 km,200×3,000 km and 200×1,500 km.We find that in two years the two MSS-2 satellites can collect 35,000 observations at altitude below 250 km,data that will be useful in advancing the quality of lithospheric magnetic field modelling;this number of observations reflects the fact that only 4.5%of the flight time of these satellites will be below250 km(just 6.4%of their flight time below 300 km).By combining observations from the MSS-2 satellites’elliptical orbits of 200×5,300km with observations from a circular reference orbit,the variance of the geomagnetic model can be reduced by a factor of 285 at spherical harmonic degree n=200 and by a factor of 1,300 at n=250.The planned lower perigee of their orbits allows the new satellites to collect data at unprecedentedly lower altitudes,thus dramatically improving the spatial resolution of satellite-derived lithospheric field models,(up to 80%at n=150).In addition,lowering the apogee increases the time interval during which the satellites fly at near-Earth altitudes,thus improving the model predictions at all spherical harmonic degrees(around 52%-62%at n=150).The upper limit of the expected improvement to the field model at the orbital apogee is not as good as at the perigee.However,data from the MSS-1 orbit can help fill the gap between data from the MSS-2 orbits and from the circular reference orbit for the low-degree part of the model.The feasibility of even lower-altitude flight requires further discussion with satellite engineers.

Angles-only relative navigation in highly elliptical orbits

For angles-only relative navigation system only measures line-of-sight information,there are inherent problems in the ability to determine the range between Chaser and Target. Angles-only relative navigation is an attractive alternative for inspecting or rendezvous with noncooperative target,if adequate accuracy can be achieved. Angles-only relative navigation model considering J2 perturbation is presented for tracking and rendezvous with noncooperative target in highly elliptical orbit. Impulsive out-of-plane maneuvers of the Chaser are used to improve the navigation accuracy. The first impulse burns in cross-track directions to change the orbit inclination of the Chaser. The second impulse burns after one orbit period to change the orbit of the Chaser back. The simulation results show that the relative navigation system without maneuvers can't correct the initial state errors,while impulsive out-ofplane maneuvers of the Chaser improves the navigation accuracy. Angles-only relative navigation with chaser vehicle maneuvers to improve observability is effective when the spacecrafts are in highly elliptical orbits.

Randomization-based algorithms for servicing spacecraft motion planning on elliptical orbit

Randomization-based motion planning algorithms are presented to solve problems of servicing spacecraft maneuvering in proximity to servicing targets on an elliptical orbit.The feasible trajectories of position and attitude for spacecraft are obtained by these algorithms under a variety of constraints.The state transition matrix is applied to computation of relative motion on elliptical orbits without performing numerical integration.The pseudo body coordinate system is built for identifying the planners on three coordinate axes with different functions.Finally,motion planning algorithm for translation and attitude taking account of the dependent variable (i.e.time) is used to obtain feasible trajectories.As the simulation examples indicate,the effectiveness of these methods is verified for relative motion while getting close to large structures,and the paper concludes with a detailed analysis of the results.

The Solution of Optimal Two-Impulse Transfer between Elliptical Orbits with Plane Change

The optimizing total velocity increment Δv needed for orbital maneuver between two elliptic orbits with plane change is investigated. Two-impulse orbital transfer is used based on a changing of transfer velocities concept due to the changing in the energy. The transferring has been made between two elliptic orbits having a common centre of attraction with changing in their planes in standard Hohmann transfer with the terminal orbit which is elliptic orbit and not circular. We develop a treatment based on the elements of elliptic orbits a1,e1, a2,e2, and?aT,eT of the initial orbit, final orbit and transferred orbit respectively. The first impulse Δv1 at the perigee induces a rotation of the orbital plane by ?which will be minimized. The second impulse Δv2 at apogee is induced an angle ?to product the final elliptic orbit. The total plane change required . We calculate the total impulse Δv and minimize by optimizing angle of plane’s variation . We obtain a polynomial equation of six degrees on the two transfer angles between neither two elliptic orbits ?and . The solution obtained numerically, using programming code of MATHEMATICA V10, with no condition on the eccentricity or the semi-major axis of the initial, transformed, and the final orbits. We find that there are constrains on the transfer angles and α. For αit must be between 40°and 160°, and there is no solution if αis less than 40°and bigger than 160°and ?takes the values less than 40°. The minimum total velocity increments obtained at the value of ?less than 25°and& alpha;equal to 160°. This is an interesting result in orbital transfer problem in which the change of orbital plane is necessary for the transferring.

Design and control of multiple spacecraft formation flying in elliptical orbits

Spacecraft formation flying is an attractive new concept in international aeronautic fields because of its powerful functions and low cost. In this paper, the formation design and PD closed-loop control of spacecraft formation flying in elliptical orbits are discussed. Based on two-body relative dynamics, the true anomaly is applied as independent variable instead of the variable of time. Since the apogee is considered as the starting point, the six integrating constants are calculated. Therefore, the algebraic solution is obtained for the relative motion in elliptical orbits. Moreover, the formation design is presented and both circular formation and line formation are provided in terms of an algebraic solution. This paper also discusses the PD-closed loop control for precise formation control in elliptical orbits. In this part, the error-type state equation is put forward and the linear quadratic regulator （LQR） method is used to calculate PD parameters. Though the gain matrix calculated from LQR is time-variable because the error-type state equation is time variable, the PD parameters are also considered as constants because of their small changes in simulation. Finally, taking circular formation as an example, the initial orbital elements are achieved for three secondary spacecraft. And the numerical simulation is analyzed under PD formation control with initial errors and J2 perturbation. The simulation results demonstrate the validity of PD closed-loop control scheme.

Resolving multi-orbital effects on high harmonic generation from aligned N2 molecules in linearly and elliptically polarized intense laser fields

We perform an experimental study of the multi-orbital effect on the high-order harmonic generation(HHG) from aligned N_2 molecules in both linearly and elliptically polarized intense laser fields.Measured by a home-built extreme ultraviolet(XUV) flat grating spectrometer with the pump-probe method, the angular distributions of different orders of HHG are obtained, which show distinctive behaviors for harmonics in the plateau and the cut-off regions.The ellipticity dependence of HHG is investigated by aligning the molecular axis parallel or perpendicular to the laser polarization.Our results indicate that both the highest occupied molecular orbital(HOMO) as well as the lower one(HOMO-1) contribute to the HHG of N2 molecules, in either linearly or elliptically polarized intense laser field.The study paves the way for understanding the ultrafast electron dynamics of molecules exposed to an intense laser field.

产生多OAM模态的单馈椭圆天线

阵列天线可以有效地辐射涡旋电磁波,但该方法难以实时辐射多种模态,且其尺寸较大,馈电网络也非常复杂。涡旋天线的单贴片结构设计可以有效地简化馈电,减小天线尺寸。通过将不同模态的贴片集成到同一个介质板上,可以实现实时多模态传输。然而,目前贴片涡旋天线仍采用2个或2个以上的馈电点进行馈电,形成阵列后仍有庞大的馈电系统。本文提出了一种单点馈电的椭圆环形天线,并利用这种结构设计了8种模态的涡旋天线。天线的最大尺寸为8 mm。通过在微波暗室测试,证明了提出的椭圆天线成功地产生8种模态的涡旋电磁波。该结构的实现使得以不同模态贴片天线为阵元的涡旋阵列天线的设计更加容易。

“球槽模型”中临界质量比的拓展研究

在“球槽模型”中,以凹槽为椭圆形为例,给出一种相对简洁的推导临界质量比的处理方法.

Mathematical Rotordynamic Model Regarding Excitation Due to Elliptical Shaft Journals in Electrical Motors Considering the Gyroscopic Effect

The paper presents a mathematical rotordynamic model regarding excitation due to elliptical shaft journals in sleeve bearings of electrical motors also considering the gyroscopic effect. For this kind of excitation, a mathematical rotordynamic model was developed considering the influence of the oil film stiffness and damping of the sleeve bearings, the stiffness of the end-shields and bearing housings, the stiffness of the rotor, the electromagnetic stiffness in the air gap of the electrical motor and the mass moment of inertia of the rotor and therefore also considering the gyroscopic effect. The solution of the linear differential equation system leads to the mathematical description of the absolute orbits of the shaft centre, the shaft journals and the bearing housings and to the relative orbits between the shaft journals and the bearing housings. Additionally, the bearing housing velocities can also be derived with this mathematical rotordynamic model.

Solution set on the natural satellite formation orbits under first-order earth's non-spherical perturbation

Using the reference orbital element approach, the precise governing equations for the relative motion of formation flight are formulated. A number of ideal formations with respect to an elliptic orbit can be designed based on the relative motion analysis from the equations. The features of the oscillating reference orbital elements are studied by using the perturbation theory. The changes in the relative orbit under perturbation are divided into three categories, termed scale enlargement, drift and distortion respectively. By properly choosing the initial mean orbital elements for the leader and follower satellites, the deviations from originally regular formation orbit caused by the perturbation can be suppressed. Thereby the natural formation is set up. It behaves either like non-disturbed or need little control to maintain. The presented reference orbital element approach highlights the kinematics properties of the relative motion and is convenient to incorporate the results of perturbation analysis on orbital elements. This method of formation design has advantages over other methods in seeking natural formation and in initializing formation.

Inverse Transformation of Elliptical Relative State Transition Matrix

A new set of relative orbit elements (ROEs) is used to derive a new elliptical formation flying model in previous work. In-plane and out-of-plane relative motions can be completely decoupled, which benefits elliptical formation design. In order to study the elliptical control strategy and perturbation effects, it is necessary to derive the inverse transformation of the relative state transition matrix based on relative orbit elements. Poisson bracket theory is used to obtain the linear transformations between the two representations: the relative orbit elements and the geocentric orbital frame. In this paper, the details of these transformations are presented.

Approximate Kepler’s Elliptic Orbits with the Relativistic Effects

Beginning with a Lagrangian, we derived an approximate relativistic orbit equation which describes relativistic corrections to Keplerian orbits. The critical angular moment to guarantee the existence of periodic orbits is determined. An approximate relativistic Kepler’s elliptic orbit is illustrated by numerical simulation via a second-order perturbation method of averaging.

鹊桥二号轨道与嫦娥六号任务匹配性设计和飞行实践

鹊桥二号整个寿命期间提供中继服务的任务有嫦娥六号、嫦娥七号、嫦娥八号、嫦娥四号,以及国际合作的月球探测任务。为了满足嫦娥六号多发射窗口下各飞行阶段的中继要求,首先从任务分析的角度介绍鹊桥二号中继星为匹配嫦娥六号任务的轨道设计过程和方法,采用环月大椭圆太阳同步冻结轨道满足了嫦娥六号通信距离、通信覆盖、发射窗口和轨道相位的需求;然后在最省燃料约束下,对各阶段轨道的运行方式和轨控策略进行优化,采用四脉冲联合优化的轨控策略,以较少的速度增量大幅改变轨道升交点、倾角和近月点幅角;最后给出了在轨飞行和对嫦娥六号中继支持等情况。鹊桥二号卫星在国际上首次采用月球低能捕获轨道,实现了环月轨道升交点赤经的大幅更改;也是国际上首次采用环月大椭圆太阳同步冻结轨道,实现了对月背南极目标的近距离、长弧段的中继。鹊桥二号飞行结果和轨道设计结果一致,保证了嫦娥六号世界首次月背采样返回任务的成功实施,设计方法可为后续深空探测任务轨道设计提供参考。

利用径向力平衡飞行控制的航天器高精度轨道捕获方法

为实现对探测器轨道形状与高度的精准调整,提出一种径向力平衡飞行的航天器连续推力控制新方法。建立连续推力平衡飞行的动力学极坐标模型,并推导出特殊条件下的解析轨道解,进一步分析边值条件,给出连续推力的控制律。利用这一平衡飞行控制理论,构建轨道捕获的最优控制策略。考虑推力器的推力水平,通过一次或多次的控制过程,实现对轨道形状、轨道高度及轨道相位的综合调整。数值仿真表明:利用平衡飞行的轨道控制方法,配置微小推力器的空间引力波探测器可以实现高精度的轨道捕获;该方法具有控制过程可解析、计算量小、简便、实用等特点。

机载水平后向弹射同时离轨动力学响应研究

为解决小型火箭自力发射消耗燃料较大、运载能力较弱的不足,进一步提高小型火箭运载能力,在现有冷弹射技术的基础上提出一种机载水平后向弹射方法,实现小型火箭机载平台冷弹射发射,以减小发射所需燃料、提高火箭运载能力。基于发射动力学理论,建立火箭机载水平后向弹射动力学模型,实现多工况机载水平后向弹射有限元数值仿真,研究机载平台后向弹射的弹射机理和规律。研究结果表明,以梁单元和壳单元为主的有限元模型模态振型一致,特征频率相近,各阶频率相差在10%以内;进一步研究表明,飞机攻角对弹射速度和加速度影响较小,但对角位移、角速度影响较大,飞行攻角不会影响火箭分离过程的安全性;载机振动对弹射动力学响应影响较小,且不会影响分离过程的安全性。

HEO轨道卫星相对运动建模与编队构形设计

随着全球卫星组网编队飞行技术成熟应用,通过卫星之间基本运动方程进行相对运动求解,各种编队构型设计已经成为一种发展趋势.建立了基于相对轨道根数偏差的相对运动模型,理论推导了二阶近似条件下的适用于大偏心率椭圆轨道的相对运动方程,并进一步分析了二阶项的精度.在二体假设下,使用近地点真近点角差取代平近点角差作为编队构型设计输入,对多种不同初始轨道根数差条件下的典型编队构型进行了设计以及构型特征分析.对编队构型设计的正确性进行了仿真验证,并分析了从二体假设推广到含摄动情况的适用性,结果表明本文推导的椭圆轨道相对运动方程和编队构型设计正确有效.

空间引力波探测无拖曳技术现状与趋势

航天器无拖曳控制是实现引力波空间探测科学平台超静超稳运行的核心关键技术之一。目前,国内外各研究机构对航天器系统的动力学与控制进行了深入研究,并针对不同的探测频段需求提出了不同的探测任务。根据探测任务进行了航天器编队设计与控制的详细介绍和分析,对涉及的无拖曳与姿态控制、高精度惯性传感器与执行机构等原理和理论方法进行了深入的剖析。针对现已开展的空间引力波探测无拖曳航天器在轨飞行的演示验证整体情况进行详述和分析。在此基础上,提出后续开展相关研究中亟待解决的关键问题,指出未来无拖曳航天器系统动力学与控制的研究热点和趋势。

基于轨道动力学的椭圆轨道悬停方法

连续有限推力条件下,基于动力学原理设计了伴随卫星相对于椭圆轨道的参考卫星在任意位置实现悬停的方法。给出了对任意椭圆参考轨道实现悬停的开环控制律,推导了一个周期内的速度增量计算公式。特别分析了参考卫星为"Molniya"轨道时,实现悬停需要的控制推力及速度增量。仿真结果表明,"Molniya"轨道正下方1km的悬停伴飞,一个轨道周期时间内连续有限推力发动机需要产生的速度增量为10.317m/s。文章提出的方法也可用于椭圆轨道的空间圆或水平圆等非自然编队构型设计。