Shaping low-thrust trajectories with thrust-handling feature

Shape-based methods are becoming popular in low-thrust trajectory optimization due to their fast computation speeds. In existing shape-based methods constraints are treated at the acceleration level but not at the thrust level. These two constraint types are not equivalent since spacecraft mass decreases over time as fuel is expended. This paper develops a shape-based method based on a Fourier series approximation that is capable of representing trajectories defined in spherical coordinates and that enforces thrust constraints. An objective function can be incorporated to minimize overall mission cost, i.e., achieve minimum $\mathrm{\Delta }V$. A representative mission from Earth to Mars is studied. The proposed Fourier series technique is demonstrated capable of generating feasible and near-optimal trajectories. These attributes can facilitate future low-thrust mission designs where different trajectory alternatives must be rapidly constructed and evaluated.     

基于NFTET的高超声速飞行器再入容错制导

针对以X-33为对象的三自由度高超声速飞行器,采用相邻可行轨迹存在定理(NFTET)设计了容错制导律以解决再入段执行器发生故障的轨迹重构问题。在标称情况下采用预测校正算法生成满足再入过程约束和终端约束要求的再入轨迹;当执行器发生故障时,飞行器气动参数、结构和舵面力矩都可能发生不可预测的变化,原先的轨迹不再满足制导要求,因此需要设计新型容错制导律。针对实际再入制导模型,基于NFTET设计容错制导算法对轨迹进行重构,得到满足故障情况下制导任务的可行轨迹。从仿真结果中可以看出,容错制导算法生成的新轨迹重新回到了约束范围之内,轨迹呈收敛趋势,使得高超声速飞行器从故障恢复到正常飞行状态,提高了飞行器的自主容错能力。     

基于粒子群算法的电帆轨迹优化设计

电帆是一种利用太阳风动量的新颖的无工质空间推进系统,文章研究了以电帆为对象的行星际转移轨迹优化问题。以地球轨道转移到火星、金星轨道为任务对象,采用连续推力模型,研究极坐标系下最小时间转移轨迹优化设计问题。提出了两种基于粒子群算法(PSO)的直接优化方法,避免对协态变量初值敏感的两点边值问题（TPBVP）求解。方法一是通过打靶法直接离散化控制量输入,将最优控制问题转化为非线性规划参数优化问题,采用PSO算法寻优,获得近似最优的转移轨迹。方法二是针对任何连续控制律曲线都能以一定精度的多项式函数进行曲线拟合的特性,设计逼近最优转移轨迹控制律的多项式函数,通过PSO算法优化多项式函数参数获得逼近最优解的转移轨迹。仿真结果表明采用上述两种方法进行转移轨迹优化设计,具有随机猜测初值、全局收敛、鲁棒性强的特点。     

三维弹道有理Bezier曲线造型与优化方法

为有效克服传统弹道优化方法解的收敛性和最优性受搜索算法、初始猜测等影响大的问题,提出了基于有理Bezier曲线的三维弹道造型与优化计算方法。根据边界条件用光滑且只含少量造型变量的有理Bezier曲线形成待优化三维造型弹道,采用逆动力学方法计算造型弹道倾角、弹道角速度和法向加速度等,结合弹道其它动力学方程和约束计算造型弹道性能指标,通过对弹道造型变量寻优得到最优弹道。这种方法将无限维弹道优化问题转换为对很少造型变量的参数优化问题, 而且得到的最优弹道完全光滑可飞。与间接法相比,无需求解两点边值问题使用方便、鲁棒性强;与直接法相比,不需要对动力学方程离散化、寻优变量少、求解收敛性好,而且解的全局最优性和光滑性更高。仿真结果及与自适应伪谱法的比较校验了方法的实用性和有效性。     

姿态角幅值约束下的太阳帆Lissajous轨道保持控制

太阳帆航天器以两姿态角作为轨道控制输入时, 其轨道动力学方程具有非仿射非线性特性. 通过人工平动点处线性化获得的线性系统可完成太阳帆航天器轨道保持控制器的分析与设计. 由于线性近似模型为有误差模型, 存在近似有效范围约束, 表现为轨道高度约束和姿态角幅值约束. 本文研究了姿态角幅值约束对线性近似模型有效性的影响, 通过计算给出满足近似误差要求的姿态角幅值约束. 当控制输入存在幅值约束时, 控制器轨道修正能力受到束缚. 通过研究姿态角幅值约束下的最大允许入轨误差, 设计了最大允许入轨误差下线性二次型调节器(LQR)用于轨道保持控制, 并将控制器应用于太阳帆日地三体系统非线性模型中, 实现了日地人工L₁点Lissajous轨道最大允许入轨误差的控制收敛和良好精度下的轨道保持控制.      

Simple method for performance evaluation of multistage rockets

Multistage rockets are commonly employed to place spacecraft and satellites in their operational orbits. Performance evaluation of multistage rockets is aimed at defining the maximum payload mass at orbit injection, for specified structural, propulsive, and aerodynamic data of the launch vehicle. This work proposes a simple method for a fast performance evaluation of multistage rockets. The technique at hand is based on three steps: (i) the flight-path angle at each stage separation is guessed, (ii) the spacecraft velocity is maximized at the first and second stage separation, and (iii) for the last stage the thrust direction is obtained through the particle swarm optimization technique, in conjunction with the use of the Euler–Lagrange equations and the Pontryagin minimum principle. The coast duration at the second stage separation is optimized as well. The method at hand is extremely simple and easy-to-implement, but nevertheless it proves to be capable of yielding near-optimal ascending trajectories for a multistage launch vehicle with realistic structural, propulsive, and aerodynamic characteristics. The solutions found with the technique under consideration can be employed either for a rapid evaluation of the multistage rocket performance or as guesses for more refined optimization algorithms.     

Optimal nodal flyby with near-Earth asteroids using electric sail

The aim of this paper is to quantify the performance of an Electric Solar Wind Sail for accomplishing flyby missions toward one of the two orbital nodes of a near-Earth asteroid. Assuming a simplified, two-dimensional mission scenario, a preliminary mission analysis has been conducted involving the whole known population of those asteroids at the beginning of the 2013 year. The analysis of each mission scenario has been performed within an optimal framework, by calculating the minimum-time trajectory required to reach each orbital node of the target asteroid. A considerable amount of simulation data have been collected, using the spacecraft characteristic acceleration as a parameter to quantify the Electric Solar Wind Sail propulsive performance. The minimum time trajectory exhibits a different structure, which may or may not include a solar wind assist maneuver, depending both on the Sun-node distance and the value of the spacecraft characteristic acceleration. Simulations show that over 60% of near-Earth asteroids can be reached with a total mission time less than 100 days, whereas the entire population can be reached in less than 10 months with a spacecraft characteristic acceleration of 1 mm/s².     

一种新型火星定点着陆轨迹快速优化方法

针对火星定点着陆任务大气进入段的轨迹规划问题,给出了一种基于hp Radau伪谱法的快速优化算法。综合考虑大气进入段的动力学约束、边值约束、以及着陆器的机动能力约束和安全性约束,结合hp Radau伪谱法的配点特性,将轨迹优化问题转换成一个大规模多约束参数优化问题,给出了大气进入段轨迹优化问题的求解框架;为了提高算法的计算效率,给出了参数优化过程中雅克比矩阵的解析表达式;并通过数学仿真对本文算法进行了数值验证,结果表明：     

基于闭环解析解的可重复使用运载器轨迹在线生成方法

The relationships between path constraints such as heating rate, dynamic pressure and aerodynamic load and velocity during entry flight are analyzed in  r-V  plane for an entry vehicle with mediate high lift to drag ratio. Through derivation and integration, a unified formula for path constraints is obtained in  r-V  plane. Based on the unified formula and several characteristics an analytical solution is obtained,and an online trajectory generation method is developed. In the method, the coupled longitudinal and lateral motion is considered, and can make the best use of flight capability and satisfy path constraints. Trajectory generation cases with different flight mission and downranges are tested. Simulation results demonstrate the capability and efficiency of the trajectory planning method in dealing with path constraints.     

亚轨道飞行器返回轨迹快速优化

快速、准确、鲁棒的轨迹生成方法可以增加任务的安全性与可靠性,极大地降低成本。针对亚轨道飞行器返回段特点,引入"伪控制量"、"末端进场走廊"等概念,分别采用高斯伪谱法和向前拉道伪谱法进行了返回轨迹快速优化研究,比较了两种伪谱法在处理复杂问题时的能力。仿真结果表明,向前拉道伪谱法不适合处理含控制量约束的问题,而高斯伪谱法在满足各种约束条件下,能够快速准确地生成亚轨道飞行器返回轨迹,同时验证了结果的可行性与最优性。