J_2 invariant relative orbits via differential correction algorithm

This paper describes a practical method for finding the invariant orbits in Ja relative dynamics. Working with the Hamiltonian model of the relative motion including the J2 perturbation, the effective differential correction algorithm for finding periodic orbits in three-body problem is extended to formation flying of Earth＇s orbiters. Rather than using orbital elements, the analysis is done directly in physical space, which makes a direct connection with physical requirements. The asymptotic behavior of the invariant orbit is indicated by its stable and unstable manifolds. The period of the relative orbits is proved numerically to be slightly different from the ascending node period of the leader satellite, and a preliminary explanation for this phenomenon is presented. Then the compatibility between J2 invariant orbit and desired relative geometry is considered, and the design procedure for the initial values of the compatible configuration is proposed. The influences of measure errors on the invariant orbit are also investigated by the Monte-Carlo simulation.

The J_2 invariant relative configuration of spaceborne SAR interferometer for digital elevation measurement

A 3-craft formation configuration is proposed to perform the digital elevation model （DEM） for the distributed spacebome interferometric synthetic aperture radar （InSAR）, and it is optimized by the modified ant colony algorithm to have the best compatibility with J2 invariant orbits created by differential correction algorithm. The configuration has succeeded in assigning the across-track baseline to vary periodically and with its mean value equal to the optimal baseline determined by the relative height measurement accuracy. The required relationship between crafts＇ magnitudes and phases is formulated for the general case of interferometry measure from non-orthographic and non-lateral view. The J2 invariant configurations created by differential correction algorithm are employed to investigate their compatibility with the required configuration. The colony algorithm is applied to search the optimal configuration holding the near-constant across-track baseline under the J2 perturbation, and the absolute height measurement accuracy is preferable as expected.

考虑J_2项摄动的卫星编队飞行

针对参考卫星运行于圆轨道的编队飞行 ,分析了J2 项摄动的影响。在此基础上提出了一种方法 ,通过调整环绕卫星的半长轴 ,大大减小了J2 项摄动对编队飞行的破坏作用。此外 ,基于冲量假设估计了编队保持的代价。数值结果表明 ,调整长半轴的卫星编队可以长期保持 ,节省了大量的控制燃料。

Short-Term Orbit Prediction with J₂and Mean Orbital Elements

An analytical theory for calculating perturbations of the orbital elements of a satellite due to J2 to accuracy up to fourth power in eccentricity is developed. It is observed that there is significant improvement in all the orbital elements with the present theory over second-order theory. The theory is used for computing the mean orbital elements, which are found to be more accurate than provided by Bhatnagar and taqvi’s theory (up to second power in eccentricity). Mean elements have a large number of practical applications.

卫星编队脉冲机动维持控制与策略

针对近地圆轨道卫星编队维持问题,开展了脉冲控制方案与维持控制策略研究,并搭建了仿真环境进行验证。根据相对轨道根数(relative orbital elements,ROEs)的状态转移方程,推导了各ROEs元素在J 2摄动下的漂移速率,并针对编队构型受到空间摄动的破坏问题,提出了两种不同的编队脉冲控制方案和维持策略。基于空间圆编队长期维持需求,建立了包括高精度轨道递推算法的任务仿真环境,从脉冲消耗与控制误差对提出的方案策略进行了分析讨论,验证了脉冲方案与维持策略的可行性。仿真结果表明,所提出的脉冲控制方案与维持策略具有较高的有效性及可靠性,可用于未来空间编队飞行任务。

编队飞行卫星相对运动的零J_2摄动条件

地球形状摄动对卫星编队飞行的相对运动有很大影响,会使卫星的相对轨道发生转动或漂移。该文推导了主、从星沿小偏心率轨道运行情况下的相对轨道的零J2摄动条件。如果编队卫星的交点周期和节线的进动速率相等,那么J2摄动对相对运动没有影响,卫星可长期保持编队飞行。在选取的主、从星轨道根数之差为小量的前提下,给出了零J2摄动的一阶近似条件的解析表达式。仿真结果表明,当编队卫星的相对运动满足零J2摄动的一阶近似条件时,卫星相对运动轨道构形的漂移明显减少。

J_2摄动对编队飞行卫星相对轨道构形的影响

利用相对轨道根数法研究J2摄动对卫星编队飞行的相对轨道构形的影响,并利用高精度的算法进行数值仿真。结果表明:摄动可以使相对轨道构形发生转动与漂移两种变化。摄动引起相对轨道构形变化的形式,取决于参加编队卫星的轨道根数。当主、从星的轨道参数中只有升交点赤径不相同时,摄动对相对轨道构形几乎没有影响;当主、从星偏心率不相同时,摄动将引起相对轨道构形的转动;而当主、从星之间轨道倾角、近地点幅角和近地点时刻各不相同时,摄动将引起相对轨道构形的漂移。

Optimal Rendezvous Sequence for LEO Debris Capture

The primary purpose of this study is to exploit the effect of Earth＇s non-sphericity perturbation, particularly due to the J2 term, in order to optimize the capture sequence of potential orbital debris, that is the cumulative AV associated to the transfers between one object and the others. As results of several researches and model predictions, many international agencies agree that the growing population of objects and debris in LEO （low earth orbits）, will follow a diverging trend in the future. This, in turn, would constitute a serious threat to circum-terrestrial space safety and sustainability. In LEO, the ,J disturbance is prevailing over the others, and it acts by affecting the longitude of the ascending node （Ω）, the argument of perigee （ω） and, accordingly, the true anomaly （v）. Therefore, the goal of optimizing the AV is achieved by taking advantage of the rate of variation of Ω and ω, thereby compensating for the △Ω and △ω, present between the orbital transfer vehicle （chaser） and the debris to be captured （target）. Obviously, the perturbation will lead to favourable variations of the orbital parameters only for some combinations of Ω and ω. Yet the presence of a debris population with random distribution of Ω and ω, makes this application particularly suited to the problem. The single maneuver has been modelled with a 4-impulse time fixed rendezvous and the optimization problem has been addressed by implementing a hybrid evolutionary algorithm, which adopts, in parallel, three different strategies, namely, genetic algorithm, differential evolution and particle swarm optimization.

Decay parameter and related properties of 2-type branching processes

We consider the decay parameter, invariant measures/vectors and quasi-stationary dis- tributions for 2-type Markov branching processes. Investigating such properties is crucial in realizing life period of branching models. In this paper, some important properties of the generating functions for 2-type Markov branching q-matrix are firstly investigated in detail. The exact value of the decay parameter λC of such model is given for the communicating class C = Z+2 \ 0. It is shown that this λC can be directly obtained from the generating functions of the corresponding q-matrix. Moreover, the λC-invariant measures/vectors and quasi-distributions of such processes are deeply considered. A λC-invariant vector for the q-matrix (or for the process) on C is given and the generating functions of λC-invariant measures and quasi-stationary distributions for the process on C are presented.

Hybrid planning for LEO long-duration multi-spacecraft rendezvous mission

For the low-earth-orbit （LEO） long-duration multi-spacecraft rendezvous mission, a mixed integer nonlinear programming （MINLP） model is built with consideration of the , perturbation and the time window constraints based on lighting condition. A two-level hybrid optimization approach is proposed. The up-level problem uses the visiting sequence, the orbital transfer duration and the service time after each rendezvous as design variables, and employs the mix-coded genetic algorithm to search the optimal solution; the low-level problem uses the maneuver time and impulses in each rendezvous as design vari- ables, and employs the downhill simplex method to search the optimal solution. To improve the solving efficiency of the low-level problem, a linear dynamic model with J~ perturbation is derived, and the approximate strategy of the low-level prob- lem is then proposed. The proposed method has been applied to several numerical problems. The results lead to three major conclusions： （1） The MINLP model for LEO long-duration multi-spacecraft rendezvous mission is effective, and the proposed hybrid optimization strategy can obtain good solutions that satisfy time window constraints; （2） The derived linear dynamic equations are good first-order approximation to the long-duration rendezvous trajectory under ,J2 perturbation; （3） Under J2 perturbation, the long-duration rendezvous problem has multiple local minimums either in the duration of multiple orbits or in a single orbit, and it agrees with the problem＇s characteristic to use the mix-coded genetic algorithm.

Planning for space station long-duration orbital mission under multi-constraints

An integrated nonlinear planning(NLP) model is built for space station long-duration orbital missions considering both the vehicle visiting schedules and the interaction effects between target phasing,vehicle return adjusting and Earth observation aiming.A two-level optimization approach is proposed to solve this complicated problem.The up-level problem employs the launch times of visiting vehicles as design variables,considers the constraints of crew rotations,resource resupplies and rendezvous launch windows,and is solved by a genetic algorithm.The low-level problems employ the maneuver impulses and burn times within each orbital mission as design variables,and a high-efficient shooting iteration method is proposed based on an analytical equation for the phase angle correction considering the J 2 perturbation.The results indicate that the integrated NLP model for space station long-duration orbital missions is effective,and the proposed optimization approach can obtain the optimal solutions that satisfy the multiple constraints and reduce the total propellant consumption.