自适应Radau伪谱法自由漂浮空间机器人轨迹规划

为解决Gauss伪谱法(GPM)计算速度和求解精度之间的矛盾,在多段Radau伪谱法的基础上,提出了求解自由漂浮空间机器人(FFSM)最优路径规划问题的hp自适应Radau伪谱法(hp-RPM).与传统的Gauss伪谱法不同,该方法并不是单纯通过增加节点数量来提高精度,而是在每次迭代的过程中对整个路径分段个数和各个路径子区间的宽度进行合理的分配,并能配置每个子区间内节点的数量.通过增加分段个数可以减小子区间内所需节点个数,以此降低多项式阶数、提高计算速度.基于上述理论,首先建立了多臂FFSM系统动力学模型,并给出了运动过程中系统模型更新方法;然后将连续最优轨迹规划问题离散化,完成了hp自适应Radau伪谱法的设计;最后利用hp-RPM解决两连杆FFSM系统轨迹规划问题并进行了仿真实验.结果表明:在初始条件相同的情况下,两种方法得到的位置、速度规划曲线相似,但hp-RPM在各个节点处的误差明显低于GPM计算误差;在精度要求较高,初始节点较多的情况下,hp-RPM可以在保证精度的同时有效的提高计算速度.     

多引力场小推力引力借力轨道设计与优化

采用序贯法设计优化小推力引力借力轨道(low-thrust gravity-assist,LTGA)时,设计步骤复杂且优化结果最优性条件难以保证.本文提出一种多引力场LTGA问题联立求解框架.首先对多引力场环境和探测器动力学模型进行统一描述和处理.设计初始化策略,利用Radau伪谱法将发射窗口、借力顺序、初始轨道搜索以及轨道优化联立求解,简化设计步骤.利用hp自适应网格精细化策略保证优化结果最优性条件.该联立框架用于求解地木转移任务,得到地球–火星–地球–木星的转移方案.本文提出的联立求解框架,简化了设计步骤,保证了优化结果的最优性条件,得到比序贯求解更优的转移方案.     

基于Radau伪谱法的非线性最优控制问题的收敛性

在过去的10年里,伪谱方法(如Legendre伪谱法、Gauss伪谱法、Radau伪谱法)逐步成为求解不同领域中非线性最优控制问题的一种高效、灵活的数值解法.本文从最优控制问题解的存在性、收敛性以及解的可行性3个方面对采用Radau伪谱法求解一般非线性最优控制问题解的收敛性进行研究.证明了原最优控制问题的离散解存在、存在收敛到原最优控制问题解上的离散解和离散形式的收敛解是原最优控制问题的最优解.在此基础上,证明了Radau伪谱法的收敛性.本文结论与现有文献相比,去掉了一些必要条件,更适合一般的非线性时不变系统.     

基于伪谱法的编队卫星队形重构防碰撞轨迹优化

提出了基于伪谱法的编队卫星队形重构最优轨迹规划方法.首先,应用Legendre伪谱法将队形重构问题离散化为非线性规划问题;然后,通过庞特里亚金极小值原理计算出不考虑碰撞规避问题时各星最优轨迹的解析形式,并由此计算出各星间的碰撞点;最后,在碰撞点附近设置符合高斯分布的测试点,进一步避免各星在配置点间发生碰撞.仿真结果表明,应用所提出方法得到的队形重构的最优轨迹能够较好地满足各种约束条件,计算精度高、速度快,使得编队卫星自主重构成为可能.     

考虑导引头多约束的滑翔制导炮弹弹道规划

为提高制导炮弹在大着角情况下导引头捕捉目标的速度,减小末制导起始点角度偏差,在传统制导炮弹方案弹道规划方法(trajectory programming method, TPM)的基础上考虑末制导段,提出一种考虑导引头多约束的弹道规划方法(trajectory programming method-constraints of seeker, TPM-CS)。根据导引头最大探测距离建立末制导起始点约束,根据弹目几何关系和导引头视场角建立攻击路径约束,并建立最小化前置角和控制变量幅值的目标函数。为实现制导炮弹初始弹道倾角、偏角、火箭点火时间、滑翔启控时间、导引头开启时间等参数的最佳匹配,建立了5阶段弹道规划模型,并采用多阶段Radau伪谱法将该弹道规划问题转化为非线性规划问题,最后调用非线性规划求解器SNOPT进行求解。选取不同性能参数的导引头进行仿真,分析了导引头最大探测距离和导引头视场角对方案弹道的影响。将文中提出的弹道规划方法与传统弹道规划方法进行对比仿真,结果表明,相比于传统方法,文中所提方法规划方案弹道的末制导初始角度偏差缩小71.590%,导引头对目标保持照射状态的时间延长6...     

欠驱动刚性航天器时间最优轨迹规划设计

应用伪谱法解决欠驱动刚性航天器的时间最优轨迹规划问题.首先建立欠驱动刚性航天器的动力学和运动学模型,对于给定的初末姿态,选取机动时间最短为待优化的性能指标,并考虑到实际控制输入受限,将其转化为优化过程中的不等式约束条件;然后应用Legendre伪谱法,将优化问题离散化为非线性规划问题进行求解.仿真结果表明,应用伪谱法规划得到的欠驱动航天器最优轨迹,能够较好地满足各种约束条件,而且计算精度高、速度快,具有良好的实时性.     

New computational treatment of optical wave propagation in lossy waveguides

In this paper, the optical wave propagation in lossy waveguides is described by the Helmholtz equation with the complex refractive-index, and the Chebyshev pseudospectral method is used to discretize t...     

A MODEL OF THE VISCOUS WALL REGION OF TURBULENT SHEAR FLOWS

The viscous wall region of a fully developed turbulent pipe flow is investigated using a nonlinear, time-dependent, three-dimensional model. In the model, the velocity field is assumed to satisfy periodic boundary conditions in the longitudinal and spanwise directions, the velocity vanishes at the pipe wall, the velocity fluctuations are assumed to vanish at large distances from the wall, and a law of the wall profile is imposed on the longitudinal and spanwise average of the longitudinal component of velocity outside the viscous wall region. The model equations are solved using pseudospectral methods and the computed mean velocity profile, fluctuation intensities, and turbulence production rate are found to be in good agreement with experiment in the viscous wall region. It is found that the bulk of turbulence production is generated by length scales larger than 40 in the spanwise direction and 200 in the longitudinal direction.     

Propagation of Radar Pulses from a Horizontal Dipole in Variable Dielectric Ground: A Numerical Approach

We numerically investigate the propagation of radar type short pulses from a horizontal dipole in the presence of some simple models of inhomogeneous ground with a flat surface. We use 3-dimensional (3-D) pseudospectral time domain (PSTD) and 2-D finite difference time domain forward modeling to determine the range and azimuth dependence of electric field components and to simulate events in a moveout profile. The models are: (i) a uniform half space with either high or low conductivity; (ii) a vertical dielectric wedge; (iii) a surface thin layer with a monocline wedge overlaid on the dielectric half space. Our homogeneous results agree with the analytical solutions, and more clearly show the significant vertical electric field component, which occurs for all models. The incorporation of an anomalous dielectric quadrant does not affect the air wave and only complicates ground wave propagation near the boundary. Modeling of a monocline dielectric wedge shows predictable subsurface reflections and refractions, some of which are highly dispersive events, depending on the direction of propagation. We present two field examples that appear to demonstrate some of our findings. We conclude that air waves make suitable references for moveout profiles regardless of dielectric complications, and that our results provide some insight into the interpretation of unique events seen in moveout profiles.     

A Hermite‐Lobatto Pseudospectral Method for Optimal Control

A pseudospectral (PS) method based on Hermite interpolation and collocation at the Legendre‐Gauss‐Lobatto (LGL) points is presented for direct trajectory optimization and costate estimation of optimal control problems. A major characteristic of this method is that the state is approximated by the Hermite interpolation instead of the commonly used Lagrange interpolation. The derivatives of the state and its approximation at the terminal time are set to match up by using a Hermite interpolation. Since the terminal state derivative is determined from the dynamic, the state approximation can automatically satisfy the dynamic at the terminal time. When collocating the dynamic at the LGL points, the collocation equation for the terminal point can be omitted because it is constantly satisfied. By this approach, the proposed method avoids the issue of the Legendre PS method where the discrete state variables are over‐constrained by the collocation equations, hence achieving the same level of solution accuracy as the Gauss PS method and the Radau PS method, while retaining the ability to explicitly generate the control solution at the endpoints. A mapping relationship between the Karush‐Kuhn‐Tucker multipliers of the nonlinear programming problem and the costate of the optimal control problem is developed for this method. The numerical example illustrates that the use of the Hermite interpolation as described leads to the ability to produce both highly accurate primal and dual solutions for optimal control problems.