Low-thrust trajectory optimization in a full ephemeris model

The low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject to the gravitational force at the center of mass and the spacecraft＇s own electric propulsion only, and the gravity assist （GA） is modeled as an instantaneous velocity increment. This paper presents a method to solve the fuel-optimal problem of low-thrust trajectory with complicated constraints in a full ephemeris model, which is closer to practical engineering conditions. First, it introduces various perturbations, including a third body＇s gravity, the nonspherical perturbation and the solar radiation pressure in a dynamic equation. Second, it builds two types of equivalent inner constraints to describe the GA. At the same time, the present paper applies a series of techniques, such as a homotopic approach, to enhance the possibility of convergence of the global optimal solution.

Low-thrust trajectory optimization for multiple target bodies tour mission

Spacecraft science missions to planets or asteroids have historically visited only one or several celestial bodies per mission.The research goal of this paper is to create a trajectory design algorithm that generates trajectory allowing a spacecraft to visit a significant number of asteroids during a single mission.For the problem of global trajectory optimization,even with recent advances in low-thrust trajectory optimization,a full enumeration of this problem is not possible.This work presents an algorithm to traverse the searching space in a practical fashion and generate solutions.The flight sequence is determined in ballistic scenario,and a differential evolution method is used with constructing a three-impulse transfer problem,then the local optimization is implemented with low-thrust propulsion on the basis of the solutions of impulsive trajectories.The proposed method enables trajectory design for multiple asteroids tour by using available low thrust propulsion technology within fuel and time duration constraints.

Optimization of multi-revolution low-thrust transfer based on modified direct method

A modified direct optimization method is proposed to solve the optimal multi-revolution transfer with low-thrust between Earth-orbits. First, through parameterizing the control steering angles by costate variables, the search space of free parameters has been decreased. Then, in order to obtain the global optimal solution effectively and robustly, the simulated annealing and penalty function strategies were used to handle the constraints, and a GA/SQP hybrid optimization algorithm was utilized to solve the parameter optimization problem, in which, a feasible suboptimal solution obtained by GA was submitted as an initial parameter set to SQP for refinement. Comparing to the classical direct method, this novel method has fewer free parameters, needs not initial guesses, and has higher computation precision. An optimal-fuel transfer problem from LEO to GEO was taken as an example to validate the proposed approach. The results of simulation indicate that our approach is available to solve the problem of optimal muhi-revolution transfer between Earth-orbits.

Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem When Both the Primaries Are Oblate Spheroids

This paper studies the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem when both the primaries are oblate spheroids. The artificial equilibrium points (AEPs) are generated by canceling the gravitational and centrifugal forces with continuous low-thrust at a non-equilibrium point. Some graphical investigations are shown for the effects of the relative parameters which characterized the locations of the AEPs. Also, the numerical values of AEPs have been calculated. The positions of these AEPs will depend not only also on magnitude and directions of low-thrust acceleration. The linear stability of the AEPs has been investigated. We have determined the stability regions in the xy, xz and yz-planes and studied the effect of oblateness parameters A1(0A1?and ?A2(0A2<1) on the motion of the spacecraft. We have found that the stability regions reduce around both the primaries for the increasing values of oblateness of the primaries. Finally, we have plotted the zero velocity curves to determine the possible regions of motion of the spacecraft.

Multi-revolution low-thrust trajectory optimization using symplectic methods

Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered as a challenging problem.This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy low-thrust multi-revolution orbit transfer problem. First, the optimal orbit transfer problem is posed as a constrained nonlinear optimal control problem. Then, the constrained nonlinear optimal control problem is converted into an equivalent linear quadratic form near a reference solution. The reference solution is updated iteratively by solving a sequence of linear-quadratic optimal control sub-problems, until convergence. Each sub-problem is solved via a symplectic method in discrete form. To facilitate the convergence of the algorithm, the spacecraft dynamics are expressed via modified equinoctial elements. Interpolating the non-singular equinoctial orbital elements and the spacecraft mass between the initial point and end point is proven beneficial to accelerate the convergence process. Numerical examples reveal that the proposed method displays high accuracy and efficiency.

High-precision shape approximation low-thrust trajectory optimization method satisfying bi-objective index

The shape approximation method has been proven to be rapid and practicable in resolving low-thrust trajectory;however,it still faces the challenges of large deviation from the optimal solution and inability to satisfy the specific flight time and fuel mass constraints.In this paper,a modified shape approximation low-thrust model is presented,and a novel constrained optimization algorithm is developed to solve this problem.The proposed method aims at settling the bi-objective optimization orbit involving the twin objectives of minimum flight time and low fuel consumption and enhancing the accuracy of optimized orbit.In particular,a transformed high-order polynomial model based on finite Fourier series is proposed,which can be characterized as a multi-constraint optimization problem.Then,a novel optimization algorithm is specifically developed to optimize the large-scale multi-constraint dynamical equations of shape trajectory.The key performance indicators of the index include minimum flight time,low fuel consumption and bi-objective optimization of the two.Simulation results prove that this approach possesses both the high precision achievable by numerical methods and low computational complexity offered by shape approximation techniques.Besides,the Pareto front of the fuel-time bi-objective optimization orbit is firstly introduced to analyze an intact optimal solution set.Furthermore,we have demonstrated that our proposed approach is appropriate to generate the preliminary orbit for pseudo-spectral method.

Target selection for a small low-thrust mission to near-Earth asteroids

The preliminary mission design of spacecraft missions to asteroids often involves,in the early phases,the selection of candidate target asteroids.The final result of such an analysis is a list of asteroids,ranked with respect to the necessary propellant to be used,that the spacecraft could potentially reach.In this paper we investigate the sensitivity of the produced asteroids rank to the employed trajectory model in the specific case of a small low-thrust propelled spacecraft beginning its journey from the Sun–Earth L2 Lagrangian point and heading to a rendezvous with some near-Earth asteroid.We consider five increasingly complex trajectory models:impulsive,Lambert,nuclear electric propulsion,nuclear electric propulsion including the Earth’s gravity,solar electric propulsion including the Earth’s gravity and we study the final correlation between the obtained target rankings.We find that the use of a lowthrust trajectory model is of great importance for target selection,since the use of chemical propulsion surrogates leads to favouring less attractive options 19%of times,a percentage that drops to 8%already using a simple nuclear electric propulsion model that neglects the Earth’s gravity effects and thrust dependence on the solar distance.We also find that for the study case considered,a small interplanetary CubeSat named M-ARGO,the inclusion of the Earth’s gravity in the considered dynamics does not affect the target selection significantly.

Efficient optimization method for variable-specific-impulse low-thrust trajectories with shutdown constraint

This paper develops a sequential convex programming(SCP)-based method to solve the minimum-fuel variable-specific-impulse low-thrust transfer problem considering shutdown constraint,with emphasize on improving the computational efficiency.The variable parameter engine is more applicable for many low-thrust scenarios,therefore,both a continuously variable model and a ladder variable model are adopted.First,the original problem is convexified by processing the constraint feasible domain,which is composed of the nonlinear dynamic equations and second-order equality constraint,into convex sets.Then,the approximation is generated to close the optimal solution of the low-thrust problem by iteratively solving the convexified subproblem.Moreover,the switching self-detection and adaptive node refinement methods are presented,which can improve the accuracy of the solution and accelerate the convergence during the approximation process and is especially necessary and effective in the scenarios with shutdown constraint.In numerical simulations,the comparison with the homotopic approach shows that the proposed method only needs 4%computational time as that of the homotopic approach,and two variable-specificimpulse examples further demonstrate the effectiveness and efficiency of the proposed method.

Direct Optimization of Low-thrust Many-revolution Earth-orbit Transfers

Low-thrust Earth-orbit transfers with 10^- 5-order thrust-to-weight ratios involve a large number of orbital revolutions which poses a real challenge to trajectory optimization. This article develops a direct method to optimize minimum-time low-thrust many-revolution Earth-orbit transfers. A parameterized control law in each orbit, in the form of the true optimal control, is proposed, and the time history of the parameters governing the control law is interpolated through a finite number of nodal values. The orbital averaging method is used to significantly reduce the computational workload and the trajectory optimization is conducted based on the orbital averaging dynamics expressed by nonsingular equinoctial elements. Furthermore, Earth＇s shadowing and perturbation effects are taken into account. The optimal transfer problem is thus converted to the parameter optimization problem that can be solved by nonlinear programming. Taking advantage of the mapping between the parameterized control law and the Lyapunov control law, a technique is proposed to acquire good initial guesses for optimization variables, which results in enlarged convergence domain of the direct optimization method. Numerical examples of optimal Earth-orbit transfers are presented.

双机械臂布局下的电推进位保策略

对于地球同步轨道的电推进卫星,可采用双机械臂式电推布局进行轨道维持控制.本文研究了双机械臂式电推布局的自主位保控制策略,针对南北各一台机械臂,每台机械臂分别配置一台电推力器的布局方式,通过每天1~2次点火,以尽量少的点火指向变动实现东西/南北联合位保控制.在双侧机械臂、电推力器正常情况下研究具有解析形式的在轨位保算法.研究基于单侧矢量调节机构和该侧电推力器的故障位保策略,给出衡量不同矢量机构能力和推力比冲下的位保效率衡量方法.仿真结果表明,正常/故障情况下的位保控制精度均能够满足同步轨道位保控制要求.本算法为解析形式,计算量较小,可以实现多星共轨和定点捕获/轨位漂移,便于量上自主实施.

小推力航天器逃离太阳系的引力辅助轨迹设计

针对太阳系边界探测,利用形函数轨迹优化算法快速生成连续小推力航天器引力辅助逃离太阳系的三维轨迹,实现在有限燃料条件下的超远距离探测。通过对比有无引力辅助设计的仿真结果,证明了引力辅助技术在逃离太阳系过程中的有效性。仿真结果表明,基于贝塞尔形函数方法的连续小推力轨迹优化算法可以高效地设计出引力辅助逃离太阳系的合理三维初始轨迹,对于初始探测任务的快速设计和分析具有重要意义。

多星机动接近威胁下航天器反包围规避方法

针对多个来袭航天器连续机动接近的威胁,提出一种基于轨道根数可达集的航天器反包围威胁规避方法。首先,给出航天器小推力机动轨道根数可达集的求解方法。其次,在轨道根数相平面中计算来袭航天器威胁在轨航天器的最小机动飞行时间,进而得到威胁“势场”与威胁区。然后,根据来袭航天器威胁在轨航天器的方位特征定义了包围威胁场景。最后,建立反包围约束条件及规避机动效能评价指标,给出了在轨航天器反包围威胁规避最优机动策略。仿真结果表明,所定义的包围威胁场景是合理的,提出的方法能够使在轨航天器对多个来袭航天器所带来的包围威胁实现机动规避,并节省燃料消耗。

基于调相机制的航天器碰撞规避策略设计

针对携带电推进等小推力推进系统工作的航天器,提出一种利用连续推力调相机制的在轨碰撞规避机动策略。首先,采用混沌多项式展开方法对初始状态不确定性的航天器碰撞概率进行分析,并以此作为碰撞规避策略的评价指标;进而推导了一种适用于小推力的轨道机动的解析解。利用这一解析结果可以提出一种新的避碰方法,即通过航天器轨道相位的微调减小航天器碰撞概率,并且在机动后能够迅速恢复原轨道相位。数值仿真表明:基于所提出的避碰机动策略,可以在较短时间内减小碰撞概率。数值仿真还揭示了避碰时间、燃耗和推力加速度之间的关系。

低温热年代学和构造模拟约束下逆冲推覆带的构造-热演化及剥露历史恢复

利用古温标进行热史模拟时,需要设置时间域和温度域的地质约束,其中时间域约束条件的设置限制了热史结果的准确性。逆冲推覆带发生逆冲推覆时,地层抬升和冷却的同时也发生差异水平滑移,使得同一逆冲席的构造抬升过程存在差异,但古温标模拟热史仅揭示样品的冷却过程,无法获得水平位移的信息,因此如何设置合适的时间域约束模拟热史并准确揭示逆冲推覆带的构造-热演化过程是低温热年代学领域探索研究的科学难题。本文以华南地区川东逆冲推覆带为示例,介绍了一种联合构造模拟、平衡剖面解析和低温热年代学、镜质组反射率等多种古温标的热运动学方法,实现“点-面”结合和整体-局部定量耦合,精细剖析逆冲推覆过程抬升剥露的起始时间、方式、速率、期次和幅度,为逆冲推覆带构造-热演化研究提供思路参考。

基于EKF/PI滤波的小推力轨控期间自主导航算法

研究了以电推小推力作为主要的轨控推力来源的高轨卫星在轨控期间的自主导航算法。针对GNSS接收机在高轨的测速精度相对较差,以及轨控期间电推产生的推力较小,常规加速度计无法准确测量,从而导致在轨控期间自主导航精度下降的问题,提出了基于EKF+PI滤波的一体化自主导航算法。通过结合EKF滤波和PI滤波算法,经EKF滤波抑制GNSS接收机定位数据的测量白噪声,然后通过PI滤波估计电推加速度并反馈给EKF滤波算法,提高电推工作期间EKF算法的导航精度。仿真结果表明,基于EKF+PI滤波的一体化自主导航算法可以准确估计出电推加速度大小,同时可有效提高连续小推力轨控期间的自主导航精度。

相继增压系统切换过程对增压器辅推轴承轴向力影响与轴承优化研究

采用数值仿真方法研究基本增压器在系统切换过程中的轴向力变化规律,并提出了辅助推力轴承的改进设计方法。首先数值仿真研究了基本增压器的转子系统在切换时的压气机/涡轮关键典型截面气动参数分布情况,分析了在柴油机增压模式切换过程中基本增压器转子轴向力大小和方向变化规律,然后提出了增加轴承承力面及改变承力面材料的优化方案。结果表明:基本增压器辅助推力轴承在切换的5 s时间内轴向力发生翻转,最大约承受2273 N的反向轴向力,是造成切换过程辅助推力轴承磨损的关键原因;优化方案最大承载能力为优化前的4.8倍,显著提升了辅助推力轴承承载力。经增压器平台可靠性验证,改进后的增压器辅助推力轴承在相同时间内未出现碰磨现象。

基于高斯伪光谱的星际小推力转移轨道快速优化

针对星际小推力转移轨道优化问题,给出了一种基于高斯伪光谱配点的快速优化算法。首先,基于归一化的改进春分点根数建立了星际小推力转移轨道的优化模型;然后,采用高斯伪光谱配点策略对优化模型进行离散化处理,推力方向限制和天体星历分别作为路径约束和事件约束,将轨道优化问题转化为一个大规模多约束参数优化问题;在此基础上,基于高斯伪光谱的配点特性,推导出性能指标和约束方程的解析雅可比矩阵,保证了雅可比矩阵计算的准确性和效率;最后,以利用太阳能电推进探测火星和水星为例,对所给算法进行了数值验证。数值结果表明:高斯伪光谱方法可有效用于星际小推力轨道的优化问题,并且与数值差分相比,解析的雅可比矩阵算法可提高计算效率67.78%。

快速绕飞卫星空间圆编队设计方法

连续小推力条件下,针对圆参考轨道卫星,推导了满足快速绕飞条件的空间圆编队动力学模型。分析了一个绕飞周期内的燃耗情况。在绕飞周期确定的条件下,给出了最小燃耗的计算方法,并利用数值方法验证了所推导公式的正确性。计算结果表明,在高度为500km的圆轨参考道卫星实现周期为10分钟、半径100m的空间圆绕飞,一个绕飞周期所需最小速度增量约为4.77m/s。文章提出的基本设计原理并不局限于空间圆编队,也可用于其它快速绕飞编队的设计工作。

结合行星借力飞行技术的小推力转移轨道初始设计

针对结合行星借力和小推力技术的行星际转移轨道设计问题,提出一种基于形状逼近策略的初始设计方法。采用改进的逆六次多项式策略计算小推力弧段,通过引入B平面参数和推进器开关点时间系数实现行星借力和推滑混合轨道的拼接,将初始设计问题转化为求解混合整数非线性规划问题。为降低规划模型求解难度,通过参数变换对模型进行简化处理,并采用具有全局大范围搜索能力的改进微分进化算法求解最优设计参数。数值结果表明:相比正弦指数曲线设计方法,本文方法可以有效对交会型转移轨道进行设计,并且可以提供更少燃料消耗的探测机会。

面向小推力变轨的天文组合自主导航方法

针对小行星探测任务对导航系统自主性强、实时性高的需求,研究了一种面向小推力变轨的天文组合自主导航方法。根据工程实践分析并建立了电推进变轨过程中的动力学模型,给出了天文测角测速组合的小行星探测自主导航方案。为克服小行星探测器推力的不确定性,提出了采用自适应交互式多模型无迹卡尔曼滤波(AIMM-UKF)算法,以较少的模型个数实现对导航系统状态的覆盖,克服了模型集合先验信息不准确对导航精度的影响,提高了组合导航系统的鲁棒性和抗干扰能力。最后,通过数学仿真对组合导航算法的性能进行了验证,结果表明本文提出的组合导航方法估计精度更高、计算消耗更小,可满足小行星探测工程任务对导航系统自主性、实时性和高精度的需求。