最优轨迹规划方法及其平动点航天器编队均衡耗能重构应用

由于均衡耗能航天器编队能够提高整体航天器编队服役时间,针对平动点航天器编队重构的均衡耗能最优轨迹规划问题,提出一种以状态、协态和控制三类变量插值为核心的求解非线性最优控制问题的新方法。基于连续时间表达的非线性最优控制问题通过变分原理转化为非线性方程组的求解,并进一步推导非线性方程组显示格式的Jacobi矩阵提高非线性方程组的计算效率。本文方法既满足最优控制理论的一阶必要条件又具有较大的收敛域;同时,不需要对协态初值准确猜测,避免了大规模非线性规划问题的求解。通过对中心航天器位置固定和无中心航天器两种情况的数值模拟,结果表明,本文方法对航天器编队重构轨迹规划问题能够达到均衡耗能的目标,具有一定的应用价值。     

一维定常对流——扩散方程的弧长参数法

为了求解大Peclet数下的一维定常对流—扩散方程的两点边值问题,本文提出了一种以解曲线的弧长为参数的数值解法,成功地应用初值问题的打靶方法(单段或多段)解决了边界层型、激波型和气袋型等困难问题的数值计算问题.所得到的数值结果与精确解符合得相当满意,从而为奇摄动型常微分方程的两点边值问题的数值解提供了一种新的方法.     

连续小推力航天器的深空探测轨道优化方法综述

连续小推力作用下航天器的深空探测轨道的优化设计是一个存在大量局部最优解的全局优化问题. 轨道设计流程总体上分为全局优化和局部优化. 全局优化为粗略设计, 通常在对航天器受连续推力作用下的轨道作近似处理的前提下大致确定探测序列和时间节点. 局部优化方法可分为直接法、间接法和混合法. 直接法是将连续的问题离散成一个参数优化问题. 间接法是求解由变分法和极大值原理推导的满足一阶最优必要条件的两点或多点边值问题. 混合法利用间接法推导的方程, 再离散后优化求解. 本文综述当前轨道优化设计领域最新和最常用的方法, 分析各种方法的优缺点.     

弹性动力学轴对称问题的理论解

本文给出了弹性动力学轴对称问题基本方程的一种理论解。它由满足非齐次边界条件的准静态解和满足齐次边界条件的动态解的叠加构成。在求得准静态解后,代入基本方程,得到动态解所需满足的非齐次方程。由相应的齐次方程的特征值问题,定义了有限Hankel变换。通过这种变换及Laplace变换,求得动态解,从而得到了一个完整的理论解。文中通过对一个实例求解,表明该方法求解过程简便,实用,求解结果精确。     

不定边界问题中的打靶方法

本文讨论一维相变过程中不定边界问题的解。应用平行四边形公式消去时间变量后，转化为一系列离散时刻的两点边值问题和一个代数方程，再对这些两点边值问题采取改进打靶方法求解。这种算法的突出优点是求解的精度可随意提高，并不受计算规模的限制，文中算例表明，该方法是有效的。     

带滑移铰空间机器人运动规划的混合优化策略

研究了自由漂浮带滑移铰空间机器人非完整运动规划的最优控制问题,提出一种由高斯伪谱法求解可行解与直接打靶法求解最优解相结合的混合优化策略.首先,根据多体系统动力学理论建立空间机器人的动力学模型,给定系统的初始和目标位形,将空间机器人运动规划问题描述成博尔察（Bolza）型最优控制问题;然后,利用高斯伪谱法将最优控制问题离散为非线性规划问题,求解在较少勒让德-高斯（Legendre-Gauss,LG）点时状态变量和控制变量对应的可行解;最后,在LG点处离散控制变量,作为直接打靶法的初值,利用序列二次规划算法求解空间机器人系统的优化运动轨迹和最优控制输入.通过数值仿真,系统优化运动轨迹光滑平稳,最优控制输入也能很好地满足各种约束条件,仿真结果验证了该混合优化策略的鲁棒性和有效性.     

含间隙铰接的柔性航天器刚柔耦合动力学与控制研究

大型柔性航天器展开锁定后,运动副中仍存在大量无法消除的间隙.铰链间隙直接影响柔性航天器的姿态运动和有效载荷的指向精度及稳定度,会对航天器的动力学特性造成较大的影响.针对这一问题,提出一种含间隙铰接的航天器刚柔耦合动力学建模与控制方法.首先建立含间隙的铰链精确动力学模型,从而构建含间隙铰接的柔性结构动力学模型.然后利用哈密顿原理和模态离散方法,建立含间隙铰接柔性航天器离散形式的刚柔耦合非线性动力学模型,采用Newmark算法对非线性动力学方程进行求解.基于压电纤维复合材料(macro fiber composite, MFC)驱动器构建航天器的刚-柔-电耦合动力学方程,采用最优控制设计控制律.分析了铰链参数、中心刚体转动惯量、间隙尺寸和间隙数目对航天器动力学特性的影响,着重研究了铰链间隙对航天器姿态运动和结构振动的影响作用.最后采用MFC驱动器对航天器施加主动控制.结果表明,铰链参数和中心刚体转动惯量影响航天器的固有频率;随着铰链间隙尺寸的增大及间隙数目的增多,航天器的整体刚度逐渐减小,而航天器的姿态角和振动位移响应不断增大;通过基于MFC的主动控制,能够实现含间隙铰接航天器姿态运动与结...     

最优轨迹规划方法及其平动点航天器编队均衡耗能重构应用

由于均衡耗能航天器编队能够提高整体航天器编队服役时间,针对平动点航天器编队重构的均衡耗能最优轨迹规划问题,提出一种以状态、协态和控制三类变量插值为核心的求解非线性最优控制问题的新方法。基于连续时间表达的非线性最优控制问题通过变分原理转化为非线性方程组的求解,并进一步推导非线性方程组显示格式的Jacobi矩阵提高非线性方程组的计算效率。本文方法既满足最优控制理论的一阶必要条件又具有较大的收敛域;同时,不需要对协态初值准确猜测,避免了大规模非线性规划问题的求解。通过对中心航天器位置固定和无中心航天器两种情况的数值模拟,结果表明,本文方法对航天器编队重构轨迹规划问题能够达到均衡耗能的目标,具有一定的应用价值。     

HYBRID OPTIMIZATION STRATEGY FOR MOTION PLANNING OF SPACE ROBOT SYSTEM WITH PRISMATIC JOINT

研究了自由漂浮带滑移铰空间机器人非完整运动规划的最优控制问题,提出一种由高斯伪谱法求解可行解与直接打靶法求解最优解相结合的混合优化策略.首先,根据多体系统动力学理论建立空间机器人的动力学模型,给定系统的初始和目标位形,将空间机器人运动规划问题描述成博尔察（Bolza）型最优控制问题;然后,利用高斯伪谱法将最优控制问题离散为非线性规划问题,求解在较少勒让德-高斯（Legendre-Gauss,LG）点时状态变量和控制变量对应的可行解;最后,在LG点处离散控制变量,作为直接打靶法的初值,利用序列二次规划算法求解空间机器人系统的优化运动轨迹和最优控制输入.通过数值仿真,系统优化运动轨迹光滑平稳,最优控制输入也能很好地满足各种约束条件,仿真结果验证了该混合优化策略的鲁棒性和有效性.     

轴对称von Korman位移型方程的打靶法求解

本文采用常微分方程两点边值问题的打靶法，建立了圆薄板轴对称大挠度弯曲ｖｏｎＫáｒｍáｎ位移型方程的自动求解过程．作为例子，分析了圆薄板在均布横向截荷作用下的非线性弯曲问题，给出了载荷参数大范围变化的解曲线     

Optimal nonlinear feedback control of spacecraft rendezvous with finite low thrust between libration orbits

This paper presents the nonlinear closed-loop feedback control strategy for the spacecraft rendezvous problem with finite low thrust between libration orbits in the Sun–Earth system. The model of spacecraft rendezvous takes the perturbations in initial states, the actuator saturation limits, the measurement errors, and the external disturbance forces into consideration from an engineering point of view. The proposed nonlinear closed-loop feedback control strategy is not analytically explicit; rather, it is implemented by a rapid re-computation of the open-loop optimal control at each update instant. To guarantee the computational efficiency, a novel numerical algorithm for solving the open-loop optimal control is given. With the aid of the quasilinearization method, the open-loop optimal control problem is replaced successfully by a series of sparse symmetrical linear equations coupled with linear complementary problem, and the computational efficiency can be significantly increased. The numerical simulations of spacecraft rendezvous problems in the paper well demonstrate the robustness, high precision, and dominant real-time merits of the proposed closed-loop feedback control strategy.     

Optimal control of stretching process of flexible solar arrays on spacecraft based on a hybrid optimization strategy

The optimal control of multibody spacecraft during the stretching process of solar arrays is investigated,and a hybrid optimization strategy based on Gauss pseudospectral method(GPM) and direct shooting method(DSM) is presented. First, the elastic deformation of flexible solar arrays was described approximately by the assumed mode method, and a dynamic model was established by the second Lagrangian equation. Then, the nonholonomic motion planning problem is transformed into a nonlinear programming problem by using GPM. By giving fewer LG points, initial values of the state variables and control variables were obtained. A serial optimization framework was adopted to obtain the approximate optimal solution from a feasible solution. Finally, the control variables were discretized at LG points, and the precise optimal control inputs were obtained by DSM. The optimal trajectory of the system can be obtained through numerical integration. Through numerical simulation, the stretching process of solar arrays is stable with no detours, and the control inputs match the various constraints of actual conditions.The results indicate that the method is effective with good robustness.     

Control strategy of optimal deployment for spacecraft solar array system with initial state uncertainty

A control strategy combining feedforward control and feedback control is presented for the optimal deployment of a spacecraft solar array system with the initial state uncertainty. A dynamic equation of the spacecraft solar array system is established under the assumption that the initial linear momentum and angular momentum of the system are zero. In the design of feedforward control, the dissipation energy of each revolute joint is selected as the performance index of the system. A Legendre pseudospectral method (LPM) is used to transform the optimal control problem into a nonlinear programming problem. Then, a sequential quadratic programming algorithm is used to solve the nonlinear programming problem and offline generate the optimal reference trajectory of the system. In the design of feedback control, the dynamic equation is linearized along the reference trajectory in the presence of initial state errors. A trajectory tracking problem is converted to a two-point boundary value problem based on Pontryagin’s minimum principle. The LPM is used to discretize the two-point boundary value problem and transform it into a set of linear algebraic equations which can be easily calculated. Then, the closed-loop state feedback control law is designed based on the resulting optimal feedback control and achieves good performance in real time. Numerical simulations demonstrate the feasibility and effectiveness of the proposed control strategy.     

Use of the energy integral in optimal control of the spacecraft spatial attitude

In this paper, we study the problem of spacecraft optimal rotation into the position with given attitude. The rotation takes a fixed time. The control program is optimized by minimizing the energy integral. We present the analytic solution of this problem and obtain formalized equations and computational expressions for constructing the optimal rotation program. We also present an example and the results of mathematical simulation of the spacecraft motion dynamics under optimal control, which demonstrate the practical realizability of our method for the spacecraft spatial attitude control.     

Optimal spacecraft terminal attitude control synthesis by the quaternion method

We consider an optimal control problem of spacecraft retargeting from an arbitrary initial position to a given terminal angular position. The objective is to minimize a path functional. Using the quaternion method, we obtain an analytic solution of this problem and present formalized equations and computational expressions for synthesizing an optimal manoeuvre program. We also present an example and the results of mathematical simulation of the spacecraft motion dynamics under an optimal control, which demonstrate the practical implementability of the control method developed in the present paper.     

Mixed testing strategies in the quality check problem for stabilization algorithms

The maximin testing problem for the stabilization quality of linear systems with discrete initial and parametric disturbances is considered. A testing procedure is implemented by reducing the original dynamic game to a geometric game. The transition to a mixed expansion of the geometric game is proposed in the absence of saddle points. An optimal mixed disturbance strategy is shown to be applicable.     

Optimal control of drainage basin considering moving boundary

The purpose of this article is to present a technique to optimally control river flood using a drainage basin considering a moving boundary. The main theme of this article is to obtain outflow discharge from the drainage basin that maintains the water level at a downstream point and empties the drainage basin as soon as possible. The water flow phenomenon inside the drainage basin when a river flood occurs is considered. This phenomenon can be analysed by the finite element method considering a moving boundary. The optimal control theory can be implemented to obtain the optimal control discharge. The finite element analysis with a moving boundary is introduced in the optimal control theory. A new boundary condition on the downstream side of the river is proposed. This condition is formulated by the solitary wave condition based on the basic water level being capable of representing natural water surface. As a numerical study, optimal control of shallow water flow is carried out for the Tsurumi River and its drainage basin model.     

Nonlinear robust and optimal control of robot manipulators

In this paper, we propose a new optimal control method for robust control of nonlinear robot manipulators. Many industrial robot systems are required to perform relatively large angular movement with sufficient accuracy. In real circumstances, highly nonlinear manipulator dynamics and uncertainties such as unknown load placed on the manipulator, external disturbance, and joint friction make the precise control of manipulators a very challenging task. The main contribution of this work is to develop a new robust control strategy to accomplish the precise control of robot manipulators under load uncertainty using a nonlinear optimal control formulation and solution. This methodology is based on the underlying relation between the robust stability and performance optimality. A class of robust control problems can be transformed to an equivalent optimal control problem by incorporating the uncertainty bounds into the cost functional. The θ-D optimal control approach is utilized to find an approximate closed-form feedback solution to the resultant nonlinear optimal control problem via a perturbation process. Numerical simulations show that the proposed robust controller is able to control the robot manipulator precisely under large load variations.     

黏性边界层网格自动生成

高雷诺数黏性流动在壁面附近存在边界层,在计算模拟中自动生成可靠且有效的计算网格仍然是计算流体力学存在的瓶颈.三棱柱/四面体混合网格技术在一定程度上缓解了这个困难.然而,对于复杂外形的情况,在边界层内自动高效生成高质量的三棱柱单元仍然十分困难.常用的层推进法在凹凸区域及角点处生成的边界层网格单元质量较差,边界层网格最外层尺寸不均匀.针对这些问题,发展了一种黏性边界层网格自动生成方法,通过顶点周围边的二面角识别物面网格特征确定多生长方向,预估并调整生长高度处理相交情况.同时提出一种三维前沿尺寸调节方式,提高了边界层网格单元的正交性,保证了边界层网格与远场网格尺寸的光滑过渡.通过ONERA M6翼型以及带发动机短舱的DLR-F6翼身组合体等外形的网格生成实例及绕流数值模拟,将计算值与标准实验值进行对比,结果表明:该方法能够自动高效地生成满足数值计算需求的混合网格.