Reentry trajectory optimization for hypersonic vehicle satisfying complex constraints

The reentry trajectory optimization for hypersonic vehicle（HV）is a current problem of great interest.Some complex constraints,such as waypoints for reconnaissance and no-fly zones for threat avoidance,are inevitably involved in a global strike mission.Of the many direct methods,Gauss pseudospectral method（GPM）has been demonstrated as an effective tool to solve the trajectory optimization problem with typical constraints.However,a series of diffculties arises for complex constraints,such as the uncertainty of passage time for waypoints and the inaccuracy of approximate trajectory near no-fly zones.The research herein proposes a multi-phase technique based on the GPM to generate an optimal reentry trajectory for HV satisfying waypoint and nofly zone constraints.Three kinds of specifc breaks are introduced to divide the full trajectory into multiple phases.The continuity conditions are presented to ensure a smooth connection between each pair of phases.Numerical examples for reentry trajectory optimization in free-space flight and with complex constraints are used to demonstrate the proposed technique.Simulation results show the feasible application of multi-phase technique in reentry trajectory optimization with waypoint and no-fly zone constraints.     

基于样条曲线的机动弹头再入轨迹优化研究

使用三次样条函数拟合再入飞行器纵向运动轨迹,以样条曲线上的控制节点为优化参数,将再入轨迹优化问题转化为静态参数优化问题.最后以纵向平面内的最优轨迹为例,以终点速度最大和飞行时间最短为优化目标,采用基于Pareto定级排序遗传算法求解了在末端状态受约束的最优再入轨迹问题,验证了该方法的有效性.     

基于高斯伪谱法的翼伞系统复杂多约束轨迹规划

翼伞系统在实际环境中飞行时易受到风场以及地形环境等复杂干扰的影响,无法精确归航,控制难度较大。针对该问题,提出了一种针对复杂多约束条件的翼伞系统的最优控制轨迹规划方法,可同时实现翼伞系统在复杂环境下逆风对准、精确着陆以及控制量全局最优的控制目标。首先,建立了风场干扰下的翼伞系统模型;然后,通过引入地形环境曲面,将复杂环境转化为实时路径约束,将轨迹着陆偏差以及逆风雀降转化为终端约束,并考虑控制量消耗最小为目标函数,以此将复杂环境下的翼伞系统的轨迹优化转化为一系列非线性的带有复杂约束的最优控制问题;最后,采用高斯伪谱法将多约束最优控制问题转化为易于求解的非线性规划问题。通过设立3组复杂环境仿真实例和实验验证,表明本文方法使翼伞系统在多种较恶劣的复杂环境中有效应对多类约束条件,规划出控制量全局最优的可行轨迹。与已有的混沌粒子群优化算法相比,本文方法具有较好的最优性和较高的精度。     

基于Proximal-Newton-Kantorovich凸规划的空天飞行器实时轨迹优化

针对空天飞行器大气层内上升段实时轨迹优化问题，提出一种基于Proximal-Newton-Kantorovich凸规划的轨迹优化方法。首先，应用Newton-Kantorovich迭代方法将轨迹优化问题转化为一系列的子问题，每个子问题都是一个线性最优控制问题；其次，针对Newton-Kantorovich迭代方法忽略运动方程中的高阶信息，导致难以收敛这一问题，提出Proximal-Newton-Kantorovich迭代方法，在子问题的性能指标中加入邻近规则化项，改善了Newton-Kantorovich迭代方法的收敛性；最后，将子问题离散为二阶锥规划问题，并应用内点法进行求解。提出的Proximal-Newton-Kantorovich凸规划方法是一种求解非线性轨迹规划问题的可行途径。理论分析表明，Proximal-Newton-Kantorovich迭代方法的收敛结果一定是轨迹优化问题的局部最优解。数值实验表明，此方法的计算时间在毫秒级。     

Real-time trajectory planning for UCAV air-to-surface attack using inverse dynamics optimization method and receding horizon control

This paper presents a computationally efficient real-time trajectory planning framework for typical unmanned combat aerial vehicle (UCAV) performing autonomous air-to-surface (A/S) attack. It combines the benefits of inverse dynamics optimization method and receding horizon optimal control technique. Firstly, the ground attack trajectory planning problem is mathematically formulated as a receding horizon optimal control problem (RHC-OCP). In particular, an approximate elliptic launch acceptable region (LAR) model is proposed to model the critical weapon delivery constraints. Secondly, a planning algorithm based on inverse dynamics optimization, which has high computational efficiency and good convergence properties, is developed to solve the RHCOCP in real-time. Thirdly, in order to improve robustness and adaptivity in a dynamic and uncer- tain environment, a two-degree-of-freedom (2-DOF) receding horizon control architecture is introduced and a regular real-time update strategy is proposed as well, and the real-time feedback can be achieved and the not-converged situations can be handled. Finally, numerical simulations demon- strate the efficiency of this framework, and the results also show that the presented technique is well suited for real-time implementation in dynamic and uncertain environment.     

Optimal trajectory design accounting for the stabilization of linear time-varying error dynamics

This study is dedicated to the development of a direct optimal control-based algorithm for trajectory optimization problems that accounts for the closed-loop stability of the trajectory tracking error dynamics already during the optimization. Consequently, the trajectory is designed such that the Linear Time-Varying(LTV) dynamic system, describing the controller’s error dynamics, is stable, while additionally the desired optimality criterion is optimized and all enforced constraints on the traje...     

Earth-moon Trajectory Optimization Using Solar Electric Propulsion

The optimization of the Earth-moon trajectory using solar electric propulsion is presented. A feasible method is proposed to optimize the transfer trajectory starting from a low Earth circular orbit (500 km altitude) to a low lunar circular orbit (200 km altitude). Due to the use of low-thrust solar electric propulsion, the entire transfer trajectory consists of hundreds or even thousands of orbital revolutions around the Earth and the moon. The Earth-orbit ascending (from low Earth orbit to high Earth orbit) and lunar descending (from high lunar orbit to low lunar orbit) trajectories in the presence of J2 perturbations and shadowing effect are computed by an analytic orbital averaging technique. A direct/indirect method is used to optimize the control steering for the trans-lunar trajectory segment, a segment from a high Earth orbit to a high lunar orbit, with a fixed thrust-coast-thrust engine sequence. For the trans-lunar trajectory segment, the equations of motion are expressed in the inertial coordinates about the Earth and the moon using a set of nonsingular equinoctial elements inclusive of the gravitational forces of the sun, the Earth, and the moon. By way of the analytic orbital averaging technique and the direct/indirect method, the Earth-moon transfer problem is converted to a parameter optimization problem, and the entire transfer trajectory is formulated and optimized in the form of a single nonlinear optimization problem with a small number of variables and constraints. Finally, an example of an Earth-moon transfer trajectory using solar electric propulsion is demonstrated.     

基于协同进化粒子群和Pareto最优解的卫星编队队形重构方法

针对卫星编队自主队形重构问题,提出了基于协同进化粒子群优化(CPSO)和Pareto最优解的求解方法.首先,使用Legendre伪谱法(LPM)将队形重构问题离散化为非线性规划(NLP)问题;其次,根据卫星编队的特点及碰撞规避的需要,使用CPSO算法对重构问题采用既独立又集中的求解方式,避免了传统优化方法对梯度的求解;...     

基于非线性规划的空空导弹水平转弯轨迹优化

基于空空导弹的质点动力学方程建立了轨迹优化模型,并根据非线性规划优化算法的特点,对优化模型中的积分变量进行替换。采用一种改进的多重打靶法将轨迹优化问题转化为约束非线性规划问题,在此基础上采用广义乘子法和变尺度法求解满足各种约束条件的最优转弯轨迹。仿真结果表明,该轨迹优化方法实现了导弹在约束条件下的最短时间转弯,且所得结果符合运动学规律,对于离轴发射以及越肩发射的转弯问题具有一定意义。     

用参数最优化方法计算最优飞行轨迹

介绍了如何应用参数最优化方法将具有状态变量不等式约束和控制变量不等式约束以及终端等式约束的最优控制问题转化为静态非线性规划问题,并提出了将求解静态约束最优化问题的系贯加权因子法,即ＳＷＩＦＴ(ＳｅｑｕｅｎｔｉａｌＷｅｉｇｈｔ－ＩｎｃｒｅａｓｉｎｇＦａｃｔｏｒＴｅｃｈｎｉｑｕｅ)法推广为求解动态约束最优化问题的增广ＳＷＩＦＴ法。最后用计算美国航天飞机的返回最优轨迹说明了该法的可行性。     

编队卫星队形重构防碰撞最优轨迹规划

 针对编队卫星队形重构的轨迹规划问题,提出了直接配置混合整数线性规划(DCMILP)方法。首先将卫星编队飞行问题进行简化,整个过程使用线性化描述;继而将三阶Simpson方法扩展至编队卫星的队形重构过程中,将各卫星的状态量和控制量在各节点处离散化;然后根据目标函数及碰撞规避问题等各种约束条件,将整个过程转化为混合整数线性规划问题,从而可以找到该非凸问题的全局最优解。最后,通过对三维和二维两组编队卫星队形重构进行仿真,由结果可以看出,与传统方法相比该方法快速有效,能够满足实时性的要求,使得卫星编队的自主运行成为可能。     

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.     

基于HP-RPM的高超声速滑翔飞行器轨迹优化

针对含有航路点、禁飞区约束的再入突防轨迹优化问题,提出了基于HP自适应Radau伪谱法(HP-RPM)的分段轨迹优化策略,给出了在含有热流密度、过载、动压、航路点和禁飞区等约束条件下的再入轨迹优化模型;利用HP-RPM对含有再入的最优控制问题进行离散化,将其转为非线性规划问题,并根据航路点所在的位置,对再入轨迹进行分段,以再入滑翔飞行的时间最短为仿真目标函数进行仿真计算。仿真结果表明,此方法可以生成一条满足多种约束条件的高精度优化轨迹,并且用时较短。     

垂直起降运载火箭返回轨迹不确定性优化

针对垂直起降运载火箭一子级在返回着陆的过程中存在的参数不确定性,提出了一种基于非侵入式多项式混沌展开的序列优化和可靠度评估的返回轨迹不确定性优化方法。首先,建立了返回多飞行段轨迹在确定性条件下的优化模型。然后,为同时兼顾轨迹的鲁棒性和可靠性,建立了由鲁棒最优目标函数、基于可靠度的路径约束和鲁棒等式约束组成的不确定性返回轨迹优化模型。最后,基于非侵入式多项式混沌展开方法对鲁棒目标函数和等式约束进行量化处理,将原随机鲁棒优化问题转化为高维状态空间中的等价确定性优化问题;为提高路径约束的可靠度评估效率,基于非侵入式多项式混沌展开方法对最可能点法进行改进,进一步发展了序列优化和可靠度评估策略。数值仿真结果表明,所提出的不确定性优化方法具有较好的鲁棒性,可以满足工程可靠性指标要求,同时还具有较高的精度和计算效率。     

Robust optimization of control command for aerospace vehicles with aerodynamic uncertainty

To reduce the design burden of Aerospace Vehicles (ASVs) control systems, this paper proposes a multi-constrained robust trajectory optimization method, which provides a good front-end input for the control system. Differ from the conventional aircraft, some control performance of ASVs is not only related to the model parameters, but also affected by the flight status. Therefore, the robust optimization method combines this characteristic of ASVs, sets the control performance as one of the optimization objectives, and considers the influence of parameter uncertainty. In this method, the polynomial chaos expansion algorithm is used to transform the trajectory optimization problem with uncertain parameters into the equivalent deterministic robust trajectory optimization problem. Finally, compared with traditional deterministic trajectory optimization methods to illustrate the effectiveness of proposed control optimization method.     

基于罚函数序列凸规划的多无人机轨迹规划

多无人机（UAVs）轨迹规划是具有非线性运动约束和非凸路径约束的最优控制问题。引入序列凸规划思想,将非凸最优控制问题近似为一系列凸优化子问题,并利用成熟的凸优化算法进行求解,以更好地权衡最优性和时效性。首先,建立了多无人机协同轨迹规划的非凸最优控制模型。然后,利用离散化和凸近似方法将其转换为凸优化问题,包括对无人机运动模型的线性化,以及对威胁规避约束和无人机碰撞约束的凸化。同时,提出了一种离散点间的威胁规避方法,保证无人机在离散轨迹点间的飞行安全。在凸优化模型的基础上,给出了基于罚函数序列凸规划求解多无人机轨迹规划的具体框架。最后,通过数值仿真验证了方法的有效性,结果表明该方法在多机轨迹规划结果的最优性和时效性都要优于伪谱法,而且优势随编队数量的增加而增大。     

基于配点法的轨道在线优化方法研究

针对传统轨道优化方法无法应用于轨道在线优化的问题,提出了三阶辛普森配点法结合乘子法求解轨道在线优化问题的方法.首先建立变轨的最优化模型;然后,用三阶辛普森配点法将该最优控制问题转化为受约束的非线性规划问题;最后,采用增广拉格朗日乘子法对转化得来的受约束的非线性规划问题进行求解.仿真结果表明,所提出的方法可以得到高精度的轨道优化结果,并且对状态量和控制量的初值选取不敏感,且仿真具有实时性,计算速度快,可以达到在线进行轨道优化的要求.     

空天飞行器弹道/轨道一体化设计

弹道/轨道一体化设计是解决空天飞行器发射入轨和轨道转移问题的一种全新思路。针对目前存在的空天飞行器弹道/轨道一体化设计问题,通过改进非开普勒轨道方程的方法建立飞行器在连续推力、气动力、引力以及摄动力等多种力作用下的弹道/轨道一体化设计动力学模型;提出基于轨道设计反方法的弹道/轨道一体化设计方法。其创新点主要体现在：通过整合连续推力、气动力、引力以及摄动力等多种作用力达到了统一弹道/轨道模型的目的;提出了基于傅里叶级数形状方法的轨道设计方法,该方法相比于之前的逆多项式法,可以处理带推力约束的轨道设计问题;由于在弹道段采用类似于轨道设计反方法的设计思想设计弹道,使得弹道和轨道两段轨迹的设计方法也达到了统一,致使从模型和设计方法的角度都体现了弹道/轨道设计的统一性,解决了传统分段设计方法是在不同段采用不同的模型和方法,很难体现出一体化设计思想的问题。仿真分析表明本文提出的弹道/轨道一体化设计方法是可行和有效的。     

基于凸优化的再入轨迹三维剖面规划方法

可重复使用飞行器一般采用大升阻比气动外形，再入轨迹三维剖面规划方法可充分发挥这类飞行器固有的机动能力。计算量大是制约三维剖面规划应用的难题，为提高计算效率，提出了一种基于凸优化的再入轨迹三维剖面规划方法。首先，分析运动方程特性，利用定义新的控制变量、约束松弛、连续线性化等技术，将原始非凸的三维剖面规划问题转化为一个凸优化问题。其次，将指令反解步骤嵌入至序列凸化算法中，通过迭代求解凸优化子问题，获得原问题的可行解。数值仿真结果表明所提方法具有较高的求解精度和确定的收敛性质，飞行器的机动能力得到充分发挥；与伪谱法的结果对比表明凸优化方法在轨迹规划问题上具有更高的求解效率。     

基于直接配点法的绳系卫星系统变轨控制

讨论了不必回收子星的二体绳系卫星系统(TSS)的变轨方案。假设TSS质心运动满足经典的二脉冲Hohmann变轨,用未变形绳长加速率控制两次脉冲期间的TSS运动。利用直接配点法中的Hermite-Simpson方法将控制消耗最小的最优问题离散为大型非线性规划问题,然后用MATLAB的SNOPT软件包求解;针对初始偏差较大的实际情况,又结合直接配点法和滚动时域控制得到了解析的反馈控制律。仿真算例表明,得到的TSS变轨过程状态变化平滑,控制消耗较小,而且变轨之后TSS接近平衡状态;此外,反馈控制律对最优路径的跟踪效果较好,能够消除初始偏差的影响。