综合热力学模型的平流层飞艇上升轨迹优化

针对平流层飞艇的上升轨迹优化问题,综合热力学模型进行了研究.主要分析了飞艇基本热力学行为,研究了蒙皮及内部气体的能量方程并建立了详细的飞艇动力学和运动学模型.在热力学、动力学和运动学分析的基础上,建立了以飞行时间为优化目标的平流层飞艇的轨迹优化模型.利用直接配点法将轨迹优化问题转化为非线性优化问题,再通过非线性求解器SNOPT(Sparse Nonlinear Optimizer)对不同场景的问题进行最优化轨迹求解.优化结果表明:热力学效应对优化轨迹有较大影响,在上升过程中,太阳能辐射为主要影响因素,另外风场也对换热量有一定影响.     

Matching trajectory optimization and nonlinear tracking control for HALE

This paper concerns optimal trajectory generation and nonlinear tracking control for stratospheric airship platform of VIA-200. To compensate for the mismatch between the point-mass model of optimal trajectory and the 6-DOF model of the nonlinear tracking problem, a new matching trajectory optimization approach is proposed. The proposed idea reduces the dissimilarity of both problems and reduces the uncertainties in the nonlinear equations of motion for stratospheric airship. In addition, its refined optimal trajectories yield better results under jet stream conditions during flight. The resultant optimal trajectories of VIA-200 are full three-dimensional ascent flight trajectories reflecting the realistic constraints of flight conditions and airship performance with and without a jet stream. Finally, 6-DOF nonlinear equations of motion are derived, including a moving wind field, and the vectorial backstepping approach is applied. The desirable tracking performance is demonstrated that application of the proposed matching optimization method enables the smooth linkage of trajectory optimization to tracking control problems.     

基于高斯伪谱法的空天飞机上升段最优轨迹设计

针对复杂多约束条件下空天飞机上升段燃料最优轨迹优化问题,提出一种基于高斯伪谱法的上升段轨迹优化策略.依据发动机的推力特性将上升轨迹合理分段,使原最优控制问题转化为多段最优控制问题后,采用高斯伪谱法进行并行优化计算.数值仿真结果表明采用这种轨迹优化策略能够满足组合动力系统工作模态转换时对飞行状态的约束条件,可以在较短的时间内完成高精度的上升段轨迹优化任务,从而验证了该方法的有效性.     

基于分段常值的全电推进GEO卫星制导策略

电推进技术因其比冲高的技术特点在GEO轨道转移中应用可大大减少燃料质量,提高有效载荷质量比,延长任务寿命等。针对全电推进GEO卫星入轨的轨迹优化和制导问题,首先利用间接法获得小推力燃料最优GEO轨道转移的数值解,提出一种多项式曲线拟合最优轨迹的方法,多项式曲线形式简单,可作为参考轨道在星上存储和使用。在多项式参考轨道的基础上,建立了一种分段常值推力跟踪参考轨道的闭环制导策略,在常值推力条件下,轨道要素控制量与控制力有解析关系,简化了制导律设计;将多圈轨道转移问题分解为多个单圈轨道优化问题。结果显示,本文提出的分段常值跟踪制导策略跟踪精度高,和最优轨道相比多消耗7%的燃料。本制导策略控制结构简单,易于工程实施。     

高超末段机动突防/精确打击弹道建模与优化

针对高超声速飞行器再入末段机动突防、精确打击问题,从最优控制角度出发,提出了一种考虑拦截弹动力学特性的最优机动突防弹道优化方法,获得了高超声速飞行器的最大机动能力。该方法将拦截弹运动模型引入突防弹道优化的模型中,通过施加约束限制拦截弹按照比例导引律飞行。根据飞行任务和交战双方的弹道特点分段,结合各段的任务和特性,分别提出了突防性能指标和精确打击性能指标等,并通过加权函数将各个独立、矛盾的性能指标统一,建立了多对象、多段、多约束机动突防弹道优化模型,采用Radau多段伪谱法（MRPM）进行求解。针对该问题求解的初值敏感、可行域窄等问题,提出了一系列弹道优化策略,提高了收敛速度和求解精度,最终获得了最优机动弹道,并通过协态映射原理对其最优性进行了验证。结果表明,该方法能充分发挥高超声速飞行器的机动能力,获得满足落点精度要求的突防弹道,相对已有方法,将脱靶量提高了1~2个量级。灵敏度分析表明,该弹道对拦截弹的发射时间不敏感。      

快速爬升的奇异摄动中制导律设计

为满足实际作战的要求,基于最优控制理论和奇异摄动方法,提出了一种可保证中远程空地导弹快速爬升到最优高度的中制导律.它由变系数最优爬升控制,最小能量巡航控制和最小能量下滑控制组成.为了减小爬升段控制对下滑段的影响,提出了一种新的控制逻辑.最后针对某型空地导弹进行了仿真.结果表明,该中制导律较好地满足了中远程空地导弹在中制导段的要求.本文的研究结果具有较好地工程参考价值.     

基于虚拟目标的导弹越肩发射初制导轨迹优化

摘要： 对具有攻角约束的空空导弹越肩发射轨迹优化问题做出研究.针对空空导弹越肩发射初制导段拐弯问题,设计了基于虚拟目标的程序指令. 基于最优控制的思想,利用高斯伪谱法求解最优程序指令,并根据所得指令的特点提出了三段式指令计算方法.在此基础上,比较了不同空域、速度以及虚拟目标位置条件对程序指令的影响.同时基于预测控制的思想,对程序指令进行在线修正,提高了导引指令的鲁棒性.三通道仿真结果表明,指令可以使导弹快速转弯并在转弯完成时指向虚拟目标.     

一种月球表面飞跃转移轨迹设计方法

针对飞跃器在月球表面飞跃转移轨迹设计问题,提出了基于凸优化方法的整个飞跃过程燃料最优轨迹设计方法.与经典凸优化方法对轨迹分段求解后再拼接得到全轨迹设计的方法不同,在假设垂直上升、着陆时间固定条件下,根据实际工程需要对轨迹进行了分段设计约束,利用黄金分割法搜索上升着陆时间,通过将原问题转化为求解一个二阶锥问题得到了全飞行...     

基于解析解的小范围高频率机动飞行器制导律设计

针对机动飞行器的小范围高频率侧向机动飞行问题,结合飞行器的运动学和动力学方程,通过解析方法给出了机动幅值和飞行器最大可用过载下的最大机动频率,同时利用粒子群优化方法进行了制导律最优频率的优化。基于解析规划算法给出了正弦机动制导律的解析形式以实现飞行器在侧向方向的机动导引飞行。仿真结果表明：解析算法能够精确得出制导律频率,而粒子群优化方法的精度也能很好的满足要求,误差在5%以内。正弦机动制导律在大速度下可以较好的完成任务目标;在小速度下,幅值误差会有小幅度的增加。     

月面上升的轨迹优化与参数分析

面向月球采样返回任务分析需求,对月面上升段的轨迹优化及燃料消耗影响因素进行了研究。基于上升器运动模型,建立以燃料消耗最优为目标考虑入轨约束的轨迹优化模型,通过Gauss伪谱法和序列二次规划求解上升过程最优推力方向。改变运动模型中的初始推重比、入轨约束中的目标轨道参数,根据轨迹优化结果得到对应的燃料消耗,分析了这些因素对上升器燃料消耗的影响。针对上升器非共面起飞的问题,提出了上升偏航、升交点调整、倾角调整3种方案,从燃料消耗的角度分析了各方案的适用情况,为未来工程应用提供参考。     

月地转移轨道快速设计与特性分析

对采用直接大气再入方式的月地转移轨道,考虑大气再入界面参数和地面落点位置约束,提出了一种基于双二体模型的快速设计方法。该方法分为内外两层迭代循环,内层循环使月心段轨道和地心段轨道在月球影响球边界处连续,并采用Lambert问题与Newton-Raphson法相集合的方法求解满足再入角约束的地心段轨道参数;外层循环通过调整地心段轨道倾角和轨道置入时间使月地转移轨道满足地面落点位置约束。分析表明,存在四种类型的月地转移轨道满足大气再入界面约束,分别为降 降型、降 升型、升 降型和升 升型。在此基础上,对四种类型月地转移轨道的近地点地心距、置入分布点、再入点分布等特性进行了分析。仿真结果验证了所提出方法的有效性。     

Ascent trajectory optimization for stratospheric airship with thermal effects

Ascent trajectory optimization with thermal effects is addressed for a stratospheric airship. Basic thermal characteristics of the stratospheric airship are introduced. Besides, the airship’s equations of motion are constructed by including the factors about aerodynamic force, added mass and wind profiles which are developed based on horizontal-wind model. For both minimum-time and minimum-energy flights during ascent, the trajectory optimization problem is described with the path and terminal constraints in different scenarios and then, is converted into a parameter optimization problem by a direct collocation method. Sparse Nonlinear OPTimizer(SNOPT) is employed as a nonlinear programming solver and two scenarios are adopted. The solutions obtained illustrate that the trajectories are greatly affected by the thermal behaviors which prolong the daytime minimum-time flights of about 20.8% compared with that of nighttime in scenario 1 and of about 10.5% in scenario 2. And there is the same trend for minimum-energy flights. For the energy consumption of minimum-time flights, 6% decrease is abstained in scenario 1 and 5% decrease in scenario 2. However, a few energy consumption reduction is achieved for minimum-energy flights. Solar radiation is the principal component and the natural wind also affects the thermal behaviors of stratospheric airship during ascent. The relationship between take-off time and performance of airship during ascent is discussed. it is found that the take-off time at dusk is best choice for stratospheric airship. And in addition, for saving energy, airship prefers to fly downwind.     

Optimal guidance based on receding horizon control for low-thrust transfer to libration point orbits

This paper addresses the design and computation of a guidance law for a transfer mission from an orbit near the Earth to a halo orbit around the libration point L₂ in the Sun–Earth system. The guidance law, which is designed based on receding horizon control and compensates for launch velocity errors that are introduced by inaccuracies of the launch vehicle, is solved using the generating function method. During the design of the closed-loop guidance law, the entire transfer mission, which is considered a nonlinear optimal control problem, is evaluated to obtain a nominal reference trajectory. Using the launch velocity errors and the uncertainty of the model, a spacecraft controlled by the proposed guidance law tracks the reference trajectory. Furthermore, the original Riccati differential equation in the receding horizon control algorithm is replaced by an equivalent convenient form of the Riccati differential equation that is based on the generating function. The high-efficiency solution of the equivalent equation avoids the online direct integration of the original Riccati differential equation, which significantly increases the computational efficiency for the receding horizon control problem. Numerical simulations using a nonlinear bicircular four-body model demonstrate the capabilities of the proposed receding horizon guidance law for the transfer mission. In addition, the generating function method improves the computational efficiency by at least one order of magnitude over the backward sweep method in solving the receding horizon control problem.     

Earth–Moon low energy trajectory optimization in the real system

The problem of the Earth–Moon low energy trajectory optimization in the real system (the model defined by the JPL ephemeris DE405) is considered in this paper. First, this problem is investigated in the model of circular restricted three-body problem, since the fuel consumption is closely related to the Jacobi integral of the transfer trajectory, a method based on Jacobi integral is proposed and eight optimal trajectories are obtained. These optimal trajectories provide initial information (the flight time and the braking velocity impulse) to search the optimal low energy trajectories in the real system through optimization techniques. Considering the merit and drawback of particle swarm optimization and differential evolution algorithm in solving the space trajectory problem, an improved cooperative evolutionary algorithm is put forward. Result shows that the low energy trajectories in the real system are more fuel-efficient than the corresponding ones under the circular restricted three-body problem.     

A lunar cargo mission design strategy using variable low thrust

A design technique for a near optimal, Earth–Moon transfer trajectory using continuous variable low thrust is proposed. For the Earth–Moon transfer trajectory, analytical and numerical methods are combined to formulate the trajectory optimization problem. The basic concept of the proposed technique is to utilize analytically optimized solutions when the spacecraft is flying near a central body where the transfer trajectories are nearly circular shaped, and to use a numerical optimization method to match the spacecraft’s states to establish a final near optimal trajectory. The plasma thruster is considered as the main propulsion system which is currently being developed for crewed/cargo missions for interplanetary flight. The gravitational effects of the 3rd body and geopotential effects are included during the trajectory optimization process. With the proposed design technique, Earth–Moon transfer trajectory is successfully designed with the plasma thruster having a thrust direction sequence of “fixed-varied-fixed” and a thrust acceleration sequence of “constant-variable-constant”. As this strategy has the characteristics of a lesser computational load, little sensitivity to initial conditions, and obtaining solutions quickly, this method can be utilized in the initial scoping studies for mission design and analysis. Additionally, derived near optimal trajectory solution can be used as for initial trajectory solution for further detailed optimization problem. The demonstrated results will give various insights into future lunar cargo trajectories using plasma thrusters with continuous variable low thrust, establishing approximate costs as well as trajectory characteristics.     

Multiobjective genetic optimization of Earth–Moon trajectories in the restricted four-body problem

In this paper, optimal trajectories of a spacecraft traveling from Earth to Moon using impulsive maneuvers (ΔV maneuvers) are investigated. The total flight time and the summation of impulsive maneuvers ΔV are the objective functions to be minimized. The main celestial bodies influencing the motion of the spacecraft in this journey are Sun, Earth and Moon. Therefore, a three-dimensional restricted four-body problem (R4BP) model is utilized to represent the motion of the spacecraft in the gravitational field of these celestial bodies. The total ΔV of the maneuvers is minimized by eliminating the ΔV required for capturing the spacecraft by Moon. In this regard, only a mid-course impulsive maneuver is utilized for Moon ballistic capture. To achieve such trajectories, the optimization problem is parameterized with respect to the orbital elements of the ballistic capture orbits around Moon, the arrival date and a mid-course maneuver time. The equations of motion are solved backward in time with three impulsive maneuvers up to a specified low Earth parking orbit. The results show high potential and capability of this type of parameterization in finding several Pareto-optimal trajectories. Using the non-dominated sorting genetic algorithm with crowding distance sorting (NSGA-II) for the resulting multiobjective optimization problem, several trajectories are discovered. The resulting trajectories of the presented scheme permit alternative trade-off studies by designers incorporating higher level information and mission priorities.     

基于轨迹在线规划与跟踪律在线计算的自适应再入制导方法

针对高超声速飞行器非标称再入飞行任务的高精度自主制导问题,研究了一种基于轨迹在线规划与跟踪律在线计算的全自主自适应制导方法.该方法基于拟平衡滑翔条件与高精度的规划模型在线生成满足多路径约束的参考轨迹,在跟踪参考轨迹时引入符号函数法在线计算线性二次调节器的反馈增益矩阵,以获得高精度的自适应跟踪律.最后通过远程、近程两种工...     

Rapid design and optimization of low-thrust rendezvous/interception trajectory for asteroid deflection missions

Asteroid deflection techniques are essential in order to protect the Earth from catastrophic impacts by hazardous asteroids. Rapid design and optimization of low-thrust rendezvous/interception trajectories is considered as one of the key technologies to successfully deflect potentially hazardous asteroids. In this paper, we address a general framework for the rapid design and optimization of low-thrust rendezvous/interception trajectories for future asteroid deflection missions. The design and optimization process includes three closely associated steps. Firstly, shape-based approaches and genetic algorithm (GA) are adopted to perform preliminary design, which provides a reasonable initial guess for subsequent accurate optimization. Secondly, Radau pseudospectral method is utilized to transcribe the low-thrust trajectory optimization problem into a discrete nonlinear programming (NLP) problem. Finally, sequential quadratic programming (SQP) is used to efficiently solve the nonlinear programming problem and obtain the optimal low-thrust rendezvous/interception trajectories. The rapid design and optimization algorithms developed in this paper are validated by three simulation cases with different performance indexes and boundary constraints.     

基于在线约束限制的飞行器预测校正制导

针对传统预测校正算法在再入过程中弹道性能与约束无法保障等问题,提出了一种基于倾侧角参数化的离线弹道优化与在线预测校正相结合的再入制导方法。基于平衡滑翔条件对过程约束进行分析,并证明了倾侧角剖面对射程的单调性。离线部分通过控制量参数化(CVP)方法构建控制模型,并使用序列二次规划(SQP)方法对弹道进行优化,从而大幅度提高弹道性能。在线部分利用Gauss-Newton法实时对弹道进行迭代求解,得出满足终端约束的倾侧角剖面,引导飞行器平稳、精确地飞向末端能量段并满足射程约束,Gauss-Newton法求解弹道具有收敛速度快、精度高的特点。针对高升阻比飞行器导致平衡滑翔条件难以成立以及飞行过程中的强干扰使约束超出的问题,提出了一种约束限制方法,对再入时的过程约束进行了有效的保障。仿真结果表明,本文方法对投放偏差、飞行器参数与大气模型等不确定因素具有良好的鲁棒性,对弹道性能的保障具有工程应用价值。     

A faster optimization method based on support vector regression for aerodynamic problems

In this paper, a new strategy for optimal design of complex aerodynamic configuration with a reasonable low computational effort is proposed. In order to solve the formulated aerodynamic optimization problem with heavy computation complexity, two steps are taken: (1) a sequential approximation method based on support vector regression (SVR) and hybrid cross validation strategy, is proposed to predict aerodynamic coefficients, and thus approximates the objective function and constraint conditions of the originally formulated optimization problem with given limited sample points; (2) a sequential optimization algorithm is proposed to ensure the obtained optimal solution by solving the approximation optimization problem in step (1) is very close to the optimal solution of the originally formulated optimization problem. In the end, we adopt a complex aerodynamic design problem, that is optimal aerodynamic design of a flight vehicle with grid fins, to demonstrate our proposed optimization methods, and numerical results show that better results can be obtained with a significantly lower computational effort than using classical optimization techniques.