Optimal maneuver strategy to improve the observability of angles-only rendezvous

This paper proposes an optimal maneuver strategy to improve the observability of angles-only rendezvous from the perspective of relative navigation.A set of dimensionless relative orbital elements(ROEs)is used to parameterize the relative motion,and the objective function of the observability of anglesonly navigation is established.An analytical solution of the optimal maneuver strategy to improve the observability of anglesonly navigation is obtained by means of numerical analysis.A set of dedicated semi-physical simulation system is built to test the performances of the proposed optimal maneuver strategy.Finally,the effectiveness of the method proposed in this paper is verified through the comparative analysis of the objective function of the observability of angles-only navigation and the performances of the angles-only navigation filter under different maneuver schemes.Compared with the cases without orbital maneuver,it is concluded that the tangential filtering accuracy with the optimal orbital maneuver at the terminal time is increased by 35%on average,and the radial and normal filtering accuracy is increased by 30%on average.

Time-optimal rendezvous transfer trajectory for restricted cone-angle range solar sails

The advantage of solar sails in deep space exploration is that no fuel consumption is required. The heliocentric distance is one factor influencing the solar radiation pressure force exerted on solar sails. In addition, the solar radiation pressure force is also related to the solar sail orientation with respect to the sunlight direction. For an ideal flat solar sail, the cone angle between the sail normal and the sunlight direction determines the magnitude and direction of solar radiation pressure force. In general, the cone angle can change from 0° to 90°. However, in practical applications, a large cone angle may reduce the efficiency of solar radiation pressure force and there is a strict requirement on the attitude control. Usually, the cone angle range is restricted less more than an acute angle （for example, not more than 40°） in engineering practice. In this paper, the time-optimal transfer trajectory is designed over a restricted range of the cone angle, and an indirect method is used to solve the two point boundary value problem associated to the optimal control problem. Relevant numerical examples are provided to compare with the case of an unrestricted case, and the effects of different maximum restricted cone angles are discussed. The results indicate that （1） for the condition of a restricted cone-angle range the transfer time is longer than that for the unrestricted case and （2） the optimal transfer time increases as the maximum restricted cone angle decreases.

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.

Practical Optimization of Low-Thrust Minimum-Time Orbital Rendezvous in Sun-Synchronous Orbits

High-specific-impulse electric propulsion technology is promising for future space robotic debris removal in sun-synchronous orbits.Such a prospect involves solving a class of challenging problems of low-thrust orbital rendezvous between an active spacecraft and a free-flying debris.This study focuses on computing optimal low-thrust minimum-time many-revolution trajectories,considering the effects of the Earth oblateness perturbations and null thrust in Earth shadow.Firstly,a set of mean-element orbital dynamic equations of a chaser(spacecraft)and a target(debris)are derived by using the orbital averaging technique,and specifically a slow-changing state of the mean longitude difference is proposed to accommodate to the rendezvous problem.Subsequently,the corresponding optimal control problem is formulated based on the mean elements and their associated costate variables in terms of Pontryagin’s maximum principle,and a practical optimization procedure is adopted to find the specific initial costate variables,wherein the necessary conditions of the optimal solutions are all satisfied.Afterwards,the optimal control profile obtained in mean elements is then mapped into the counterpart that is employed by the osculating orbital dynamics.A simple correction strategy about the initialization of the mean elements,specifically the differential mean true longitude,is suggested,which is capable of minimizing the terminal orbital rendezvous errors for propagating orbital dynamics expressed by both mean and osculating elements.Finally,numerical examples are presented,and specifically,the terminal orbital rendezvous accuracy is verified by solving hundreds of rendezvous problems,demonstrating the effectiveness of the optimization method proposed in this article.

Optimizing Inter Cluster Ant Colony Optimization Data Aggregation Algorithm with Rendezvous Nodes and Mobile Sink

Energy conservation is becoming the main critical issue in wireless sensor network and also the main research area for most of the researchers. For improving the energy efficiency, sink mobility is used with constrain path in wireless sensor network. In order to solve these optimization problems, inter cluster Ant Colony Optimization Algorithm (ACO) is used with mobile sink (MS) and rendezvous nodes (RN). The proposed algorithm will improve 30% more network lifetime than the existing algorithm and prompts high accurate delivery of packets in highly dense network.

Optimal four-impulse rendezvous between coplanar elliptical orbits

Rendezvous in circular or near circular orbits has been investigated in great detail, while rendezvous in arbitrary eccentricity elliptical orbits is not sufficiently explored. Among the various optimization methods proposed for fuel optimal orbital rendezvous, Lawden＇s primer vector theory is favored by many researchers with its clear physical concept and simplicity in solu- tion. Prussing has applied the primer vector optimization theory to minimum-fuel, multiple-impulse, time-fixed orbital ren- dezvous in a near circular orbit and achieved great success. Extending Prussing＇s work, this paper will employ the primer vec- tor theory to study trajectory optimization problems of arbitrary eccentricity elliptical orbit rendezvous. Based on linearized equations of relative motion on elliptical reference orbit （referred to as T-H equations）, the primer vector theory is used to deal with time-fixed multiple-impulse optimal rendezvous between two coplanar, coaxial elliptical orbits with arbitrary large ec- centricity. A parameter adjustment method is developed for the prime vector to satisfy the Lawden＇s necessary condition for the optimal solution. Finally, the optimal multiple-impulse rendezvous solution including the time, direction and magnitudes of the impulse is obtained by solving the two-point boundary value problem. The rendezvous error of the linearized equation is also analyzed. The simulation results confirmed the analyzed results that the rendezvous error is small for the small eccentric- ity case and is large for the higher eccentricity. For better rendezvous accuracy of high eccentricity orbits, a combined method of multiplier penalty function with the simplex search method is used for local optimization. The simplex search method is sensitive to the initial values of optimization variables, but the simulation results show that initial values with the primer vector theory, and the local optimization algorithm can improve the rendezvous accuracy effectively with fast convergence, because the optimal results obtained by the primer vector theory are already very close to the actual optimal solution.

Optimal impulsive ellipse-to-circle coplanar rendezvous

The problem of ellipse-to-circle coplanar rendezvous with chaser spacecraft in low eccentricity was investigated in this paper.With reference frame established in the centroid of the target spacecraft,the process of ellipse-to-circle coplanar rendezvous was described by the relative equations based on cy-lindrical reference frame,and then the solutions and distributions of optimal rendezvous models of a kind of close ellipse-to-circle coplanar rendezvous were provided.The simulation results showed that the guidance law based on the optimal rendezvous model in this research has good performance,and that the distributions of optimal rendezvous models of ellipse-to-circle coplanar rendezvous with the chaser spacecraft in low eccentricity are similar,albeit with slight difference,to those of rendezvous between close circular orbits.The work in this paper is a useful extension to Prussing's optimal ren-dezvous theory between close circular orbits.

航天器多约束交会的仅测角导航最优多目标闭环制导

研究了航天器多约束交会的仅测角导航最优多目标闭环制导问题,优化目标包括交会时间、燃耗和仅测角导航可观性指标,并考虑了视觉传感器视场角、推力器推力幅度和最小安全距离等各种约束条件,建立了多约束、多目标优化下的仅测角导航和闭环制导问题的数学模型,分析了仅测角导航和闭环制导之间的耦合关系。最后,通过Matlab遗传算法工具箱中的多目标优化函数,求解得到了该多目标优化模型的Pareto最优解集,结果显示交会时间、燃耗和仅测角导航可观性指标不能同时达到最优,存在相互制约关系,即提高其中一种优化目标的性能会降低其他优化目标的性能。

基于安全强化学习的航天器交会制导方法

随着航天器交会对接任务越来越复杂,对其高效性、自主性和安全性的要求急剧增加。近年来,引入强化学习技术来解决航天器交会制导问题已经成为国际前沿热点。障碍物避撞对于确保航天器安全交会对接至关重要,而一般的强化学习算法没有对探索空间进行安全限制,这使得航天器交会制导策略设计面临挑战。为此,提出了基于安全强化学习的航天器交会制导方法。首先,设计避撞场景下航天器自主交会的马尔可夫模型,提出基于障碍预警与避撞约束的奖励机制,从而建立用于求解航天器交会制导策略的安全强化学习框架;其次,在该安全强化学习框架下,基于近端策略优化算法(PPO)和深度确定性策略梯度算法(DDPG)这两种深度强化学习算法生成了制导策略。实验结果表明,该方法能有效地进行障碍物避撞并以较高的精度完成交会。另外,通过分析两种算法的性能优劣和泛化能力,进一步证明了所提方法的有效性。

基于多智能体强化学习的无人艇集群集结方法

为解决数量不定的同构水面无人艇(USV)集群以期望队形协同集结的问题,提出一种基于多智能体强化学习(MARL)的分布式集群集结控制方法。针对USV通信感知能力约束,建立集群的动态交互图,通过引入二维网格状态特征编码的方法,构建维度不变的智能体观测空间;采用集中式训练和分布式执行的多智能体近端策略优化(MAPPO)强化学习架构,分别设计策略网络和价值网络的状态空间和动作空间,定义收益函数;构建编队集结仿真环境,经过训练,所提方法能有效收敛。仿真结果表明:所提方法在不同期望队形、不同集群数量和部分智能体失效等场景中,均能成功实现快速集结,其灵活性和鲁棒性得到验证。

采用注意力模型的多星交会序列优化方法

针对强化学习方法能够实现组合优化问题从无序输入到有序输出的离散决策特点,提出一种基于注意力模型的单航天器对多目标交会的序列优化方法,以快速估计转移成本较低的交会序列和时间。通过拓展注意力的时间维度使得策略网络能够同时选择目标和时间,并设计启发因子引导注意力有侧重地分布于不同的交会时刻,然后基于带基线的REINFORCE算法对网络参数进行更新。将所提方法应用于轨道分布较为集中的10目标交会任务,所得序列成本相对于蚁群算法优化结果的平均误差为9.7%,且强化学习方法的计算时间极短,可用于多目标对多航天器的分组指派全局规划的底层评价。

有人/无人机编队队形集结控制研究

针对有人/无人机(manned/unmanned aerial vehicle,MAV/UAV)编队队形集结控制问题,设计了一种基于航迹规划-跟踪的MAV/UAV编队集结控制策略。首先,考虑编队队形集结边界约束与防碰撞约束条件,设计了一种基于Dubins曲线与协同模拟退火粒子群优化相结合的编队集结航迹规划算法。然后,以规划得到的集结航迹作为期望航迹,设计了一种双回路结构的非线性路径跟踪控制方法。最后,利用Matlab软件对设计的航迹规划与跟踪控制方法进行了仿真对比实验,仿真结果验证了方法的有效性和优越性。

基于人工蜂群算法的固定时间多脉冲交会

在两航天器交会问题中,采用多脉冲变轨策略往往能取得更小的燃料消耗.利用人工蜂群算法优化了航天器固定时间多脉冲交会问题,提出一种改进的人工蜂群算法.该方法能够简化时间约束的处理,能获得满足地球半径约束的解.该方法易于编程,鲁棒性强,可以应用到不同的摄动模型.仿真结果表明,该算法不易陷入局部最优,相比于粒子群算法和传统人工蜂群算法具有更高的求解精度.

帕累托-有限推力航天器轨道机动问题中相对运动的最优控制

针对时间自由的两航天器交会问题,考虑了在轨道圆柱参考系中线性运动模型的相对运动轨迹的多准则优化。得到了描述相对运动的长期参数和周期参数方程。详细研究了具有有限横向推力的纵向运动控制变体的标称控制程序结构,并获得了解析解。开发了一种求解任意边界条件和推力控制加速度值的帕累托最优控制程序在标准空间(机动时间、总时间)中的算法。该算法中,使用帕累托最优方法,实现了多目标的优化(总时间最优,燃料最优),给出了地球静止轨道平面上参数校正变体的数值计算结果。

Lambert交会中转移时间的优化及应用

针对固定速度增量条件下Lambert交会中的转移时间,使用一种基于横向偏心率的Lambert交会求解算法,解决了经典普适变量法求解Lambert交会中的奇异点问题,并将转移时间表示为横向偏心率的函数;利用自适应粒子群优化算法对轨道转移中转移时间进行优化,采用自适应惯性权重和自适应变异机制优化转移时间,达到用最短的时间在固定速度增量的情况下实现Lambert交会。仿真校验新算法,结果表明新算法在固定速度增量条件下求解效率高,能得到最优转移时间,可应用于航天器空间交会。

Robust optimization of nonlinear impulsive rendezvous with uncertainty

The optimal rendezvous trajectory designs in many current research efforts do not incorporate the practical uncertainties into the closed loop of the design.A robust optimization design method for a nonlinear rendezvous trajectory with uncertainty is proposed in this paper.One performance index related to the variances of the terminal state error is termed the robustness performance index,and a two-objective optimization model(including the minimum characteristic velocity and the minimum robustness performance index)is formulated on the basis of the Lambert algorithm.A multi-objective,non-dominated sorting genetic algorithm is employed to obtain the Pareto optimal solution set.It is shown that the proposed approach can be used to quickly obtain several inherent principles of the rendezvous trajectory by taking practical errors into account.Furthermore,this approach can identify the most preferable design space in which a specific solution for the actual application of the rendezvous control should be chosen.

Target sequence optimization for multiple debris rendezvous using low thrust based on characteristics of SSO

A method is proposed to select the target sequence for a J 2-perturbed multiple debris rendezvous mission aimed at removing dozens of debris from several thousand debris candidates running on sun-synchronous orbits(SSO).The solving methodology proceeds in two steps:Firstly,the variance of the right ascension of ascending node(RAAN)of the debris group is used for narrowing down the potential debris candidate;secondly,the debris of the candidate group that has closest RAAN to the current debris is chosen as the next debris.The low thrust near-minimum-fuel trajectories of each rendezvous leg are obtained by the indirect optimization method.The proposed approach is demonstrated for the problem of the 8th China Trajectory Optimization Competition(CTOC).The radar cross section(RCS)of the debris is also considered in the first step since the primary performance index of the competition is to maximize the total RCS of the debris visited.The results show that the proposed approach achieves better performance within a competition period.Of the many rendezvous sequences found,the best one submitted for the competition obtained a total RCS of 184 by accomplishing rendezvous with 70 debris within a transfer duration of one year.

Fast optimization of impulsive perturbed orbit rendezvous using simplified parametric model

A novel simplified parametric model for long-duration impulsive orbit rendezvous is proposed.Based on an existing fast estimation method,the optimal impulses and trajectory can be expressed by only ten parameters whose initial values can be easily determined.Then,these parameters are used to predict orbital deviations with a target orbit.A simple correction process is designed to sequentially update the parameters based on the J_(2) perturbed analytical dynamic equations of circular orbits.Finally,an iteration loop is formed to obtain the precise parameters and optimal trajectory.The simulation results confirm that the simplified parametric optimization method can be applied to elliptical orbits of small eccentricity and adapts well to both analytical and high-precision dynamics.The deviations could always converge within five iterations and the calculation was more efficient than the existing methods.

空间交会寻的最优轨道机动

研究了交会寻的阶段的燃料优化问题。在经典Ｃ－Ｗ方法基础上，导出了考虑第一次脉冲位置的双脉冲寻的燃料优化方法。当寻的时间给定时，优化变量为第一次脉冲启动的时刻；当寻的时间不定时，优化变量为第一次脉冲启动的时刻和寻的时间。仿真结果表明，考虑和不考虑第一次脉冲位置，燃料消耗差别悬殊。对于地面站较少、要求寻的时间比较长的情况，该方法有重要意义。

用弹性绳系系统进行空间捕捉的最优控制

研究如何从空间平台上释放绳系捕捉系统与被捕捉负载相交会,给出了交会机动可行点的求解过程。计入系绳弹性,采用高斯伪谱算法计算交会机动涉及的非线性最优控制问题。结果表明,在满足相关约束的条件下,通过调节系绳张力和捕捉系统上的推进力即可实现精确的交会控制。