基于Radau伪谱法的重复使用运载器再入轨迹优化

为了提高数值解法的收敛速度,本文利用Radau伪谱法求解重复使用运载器的再入轨迹优化问题.该方法在一组Legendre-Gauss-Radau点上构造全局Lagrange插值多项式对状态变量和控制变量进行逼近,在动力学方程中状态变量对时间的导数可由插值多项式的导数来近似,故可将动力学方程约束转化为在Legendre-Gauss-Radau点上的代数微分方程约束.因此,可将连续时间的最优控制问题转化为有限维的非线性规划(NLP)问题,之后通过稀疏NLP求解器SNOPT即可对其进行求解.最后的仿真结果显示,通过该方法优化后的再入轨迹成功满足过程约束与边界约束.由于该方法的高效率和高精度特性,可将其应用于轨迹快速优化工程实际问题中.     

计算机数控系统光滑时间最优轨迹规划

基于控制向量参数化(CVP)方法, 研究了计算机数控(CNC)系统光滑时间最优轨迹规划方法. 通过在规划问题中引入加加速度约束, 实现轨迹的光滑给进. 引入时间归一化因子, 将加加速度约束的时间最优轨迹规划问题转化为固定时间的一般性最优控制问题. 以路径参数对时间的三阶导数(伪加加速度)和终端时刻为优化变量, 并采用分段常数近似伪加加速度, 将最优控制问题转化为一般的非线性规划(NLP)问题进行求解. 针对加加速度、加速度等过程不等式约束, 引入约束凝聚函数, 将过程约束转化为终端时刻约束, 从而显著减少约束计算. 构造目标和约束函数的Hamiltonian函数, 利用伴随方法获得求解NLP问题所需的梯度.     

基于双模型直接配置法的航天器轨迹优化

针对有限推力航天器轨迹优化问题,提出一种HLDL双模型直接配置法将航天器的飞行轨迹划分为最大推力弧段和零推力弧段.在两种弧段上分别采用了两种不同的建模方法并利用埃尔米特插值法将最优化问题转化为非线性规划问题(NLP).给出了节点和配置点数目的选取与所在弧段的平均曲率大小成正比的法则,解决用于有限推力航天器轨迹优化所涉及的关键问题.仿真结果表明提出的方法能有效的解决飞行器轨迹优化问题并具备很强的鲁棒性.     

最优控制问题的Legendre 伪谱法求解及其应用

伪谱法通过全局插值多项式参数化状态和控制变量,将最优控制问题(OCP)转化为非线性规划问题(NLP)进行求解,是一类具有更高求解效率的直接法。总结Legendre伪谱法转化Bolza型最优控制问题的基本框架,推导OCP伴随变量与NLP问题KKT乘子的映射关系,建立基于拟牛顿法的LGL配点数值计算方法,并针对非光滑系统,进一步研究分段伪谱逼近策略。基于上述理论开发通用OCP求解器,并对3个典型最优控制问题进行求解,结果表明了所提出方法和求解器的有效性。     

可重复使用航天器时间协同飞行轨迹优化

针对可重复使用航天器(RLV)时间协同飞行轨迹优化问题,提出了一种基于Radau伪谱法的轨迹优化方法。方法以再入飞行时间可知性、可控性为目标,使用Radau伪谱法对RLV的飞行时间进行预测,进而协调出多RLV的再入协同飞行时间,以此再入飞行时间为终端约束使用Radau伪谱法生成满足协同飞行要求的再入轨迹。仿真结果表明,上述轨迹优化方法可以得到满足时间协同约束、状态约束和控制约束的飞行轨迹,具有较高的稳定性和较快的求解速度。所提方法满足多架RLV时间协同再入飞行的需求,具有很强的实用价值。     

无人飞行器纵向剖面轨迹优化

对飞行管理系统的纵向剖面轨迹优化功能进行了研究.以固定距离最省油为优化指标,用能量法动态地建立了3阶段轨迹优化模型.区别于固定推力只对速度寻优的传统的模型求解方法,把发动机推力和速度同时作为寻优变量,并结合无人飞行器飞行的物理过程,将3阶段轨迹优化模型进一步变换成非线性规划问题,利用再开始FR(Fletcher-Revees)共轭梯度法进行求解.最后以某型无人飞行器为例进行仿真验证,结果表明将发动机推力设为变量比推力固定求得的纵向剖面最优轨迹更省油,对节省燃油降低经济成本有一定的实用参考价值.     

直接radau配置的多阶非线性模型预测聚合反应控制

针对半间歇聚合反应强非线性,模型参数的不确定性以及过程存在路径约束和终端约束等特点,将多阶非线性模型预测控制方法应用于半间歇聚合反应控制器的设计。该方法使用离散的场景树表示不确定量对系统的影响,使得未来的控制输入取决于先前的不确定量实现,从而构成闭环的鲁棒性控制方法。为了提高求解效率,使用基于有限元正交配置的联立法对问题求解,通过选取合适的radau配置点对控制变量和状态变量同时离散化,将动态优化问题转化为NLP问题,并使用内点法求解器IPOPT求解。在BASF SE公司提供的半间歇聚合反应模型上验证了提出方法的有效性。     

亚轨道飞行器任务中止再入轨迹优化设计

针对亚轨道飞行器上升段由于动力故障任务中止时再入返回的问题,考虑飞行模型简化和故障后的燃料处理方案,通过遗传算法优化设计最优返回轨迹,优化时选取经向飞行航程最远作为性能指标,并采用遗传算法,解决用于再入轨迹优化所涉及的关键问题,并进行仿真。仿真结果表明,方法不但满足飞行器返回过程中加热率、过载、动压约束以及终端状态约束,能够通过飞行航程最远消耗飞行器能量从而安全着陆,而且可以较快地搜索到全局最优解,能够用于亚轨道飞行器故障再入轨迹的优化设计。     

航模飞机实时定位及飞行轨迹记录方法研究

在航模飞机和其他小型飞行器研发和性能试验过程中,飞行轨迹及运动参数等始终是人们十分关注的问题;提出了一种简便方案,使用呈三角形分布的3台超声波测距仪与计算机相连,按照设定的采样时间间隔,同时从不同方位对飞行目标的空间位置进行测距,计算机通过推算将3个距离转换为空间坐标并按对应的时间顺序记录入数据库,连接这些坐标点就可得到飞行轨迹;利用得到的飞行轨迹可以方便地求解一系列飞行性能参数;该方法对分析飞行性能和优化航模飞机结构具有重要作用。     

区间非线性路径约束的动态优化问题求解

本文研究路径约束中含有区间参数形式的动态优化问题,提出了一种新的非线性路径约束的确定化描述形式,和采用惩罚函数法的求解算法。对于转化后的极大极小优化命题,论文提出采用Lagrangian多项式加权和的方法得到有限维的确定性优化求解形式。该算法可有效地描述和求解不确定参数动态优化问题。     

Reentry Trajectory Optimization for Hypersonic Vehicles Using Fuzzy Satisfactory Goal Programming Method

Constrained reentry trajectory optimization for hypersonic vehicles is a challenging job. In particular, this problem becomes more difficult when several objectives with preemptive priorities are expected for different purposes. In this paper, a fuzzy satisfactory goal programming method is proposed to solve the multi-objective reentry trajectory optimization problem. Firstly, direct collocation approach is used to discretize the reentry trajectory optimal-control problem with nonlinear constraints into nonlinear multiobjective programming problem with preemptive priorities, where attack angles and bank angles at nodes and collocation nodes are selected as control variables. Secondly, the preemptive priorities are transformed into the relaxed order of satisfactory degrees according to the principle that the objective with higher priority has higher satisfactory degree. Then the fuzzy satisfactory goal programming model is proposed. The balance between optimization and priorities is realized by regulating parameter λ, such that the satisfactory reentry trajectory can be acquired. The simulation demonstrates that the proposed method is effective for the multi-objective reentry trajectory optimization of hypersonic vehicles.     

Control variable parameterisation with penalty approach for hypersonic vehicle reentry optimisation

An efficient trajectory optimisation approach combining the classical control variable parameterisation (CVP) with a novel smooth technology and two penalty strategies is developed to solve the trajectory optimal control problems. Since it is difficult to deal with path constraints in CVP method, the novel smooth technology is firstly employed to transform the complex constraints into one smooth constraint. Then, two penalty strategies are proposed to tackle the converted path and terminal constraints to decrease the computational complexity and improve the constraints satisfaction. Finally, a nonlinear programming problem, which approximates the original trajectory optimisation problem, is obtained. Error analysis shows that the proposed method has good convergence property. A general hypersonic cruise vehicle trajectory optimisation example is employed to test the performance of the proposed method. Numerical results show that the path and terminal conditions are well satisfied and better trajectory profiles are obtained, showing the effectiveness of the proposed method.     

A novel trajectory planning strategy for aircraft emergency landing using Gauss pseudospectral method

To improve the survivability during an emergency situation, an algorithm for aircraft forced landing trajectory planning is proposed. The method integrates damaged aircraft modelling and trajectory planning into an optimal control framework, in order to deal with the complex aircraft flight dynamics, a solving strategy based on Gauss pseudospetral method （GPM） is presented. A 3-DOF nonlinear mass-point model taking into account the wind is developed to approximate the aircraft flight dynamics after loss of thrust. The solution minimizes the forced landing duration, with respect to the constraints that translate the changed dynamics, flight envelope limitation and operational safety requirements. The GPM is used to convert the trajectory planning problem to a nonlinear programming problem （NLP）, which is solved by sequential quadratic programming algorithm. Simulation results show that the proposed algorithm can generate the minimum-time forced landing trajectory in event of engine-out with high efficiency and precision.     

基于DE算法的再入飞行器横向机动能力研究

再入飞行器横向机动能力分析可以描述为一个具有多约束的最优控制问题,不便于求解。本文将控制量攻角和倾侧角同时离散化,把约束最优控制问题转化为约束参数优化问题;推导攻角的取值范围,缩小搜索空间,降低问题的复杂性;用改进的约束DE算法求解该优化问题。以X-33为例对算法进行仿真验证,仿真结果表明所提算法能够很好的处理约束,且优化结果的鲁棒性较好。     

基于重组优化的轮式移动机器人路径处理方法

针对轮式移动机器人采集GNSS（全球卫星导航系统）路径过程中容易出现无效路段的问题,提出了基于自适应分段重组的无效路径剔除方法和多目标优化的路径平滑方法。该方法首先按照航向将采集的GNSS路径划分为DRD(drive-reverse-drive)形式的路段组合,通过设定剔除规则来剔除其中的无效路段,并对剔除无效路段后的离散路段按照邻域路段长度进行第2次分段,以实现有效路段快速重组。其次以重组后的路径点集为决策变量,建立多目标优化函数、端点渐近约束和矩形区域约束,转化为二次规划型进行最优化求解,在保证路径平滑的同时减小与原有路径的位置差。实验结果表明,该方法能够有效处理不同道路形态下采集的无效GNSS路径,优化结果与重组路径平均位置偏差小于0.2 m,平均处理时间为8.8 ms,处理后的路径可用于无人车轨迹跟随。     

Smooth time-optimal tool trajectory generation for CNC manufacturing systems

An optimization approach is proposed in this paper for generating smooth and time-optimal path constrained tool trajectory for Cartesian computer numerical control (CNC) manufacturing systems. The desired smooth time-optimal trajectory generation (STOTG) problem is formulated as a general optimal control problem. And axis jerk (derivative of acceleration with respect to time) constraints are introduced into this problem to remove discontinuities of the acceleration profiles. The desired smoothness of the trajectory can be accomplished by adjusting the values of jerk constraints. A control vector parameterization (CVP) method is applied to convert the optimal control problem into a nonlinear programming (NLP) problem which can be solved conveniently and effectively. The third derivative of the path parameter with respect to time (pseudo-jerk) and jerk act as optimization variables. The pseudo-jerk is approximated as piecewise constant, thus for at least second-order continuous parametric path, the resulted optimized trajectory with respect to time is also at least second-order continuous. Sequential quadratic programming (SQP) method is used to solve the NLP problem, through which numerical solution is obtained. Non-smooth (i.e. without considering jerk constraints) time-optimal trajectory generation (non-STOTG) problem is also considered in this paper for the purpose of comparison. Solutions of time-optimal trajectory generation (TOTG) problems for two test paths are performed to verify the effectiveness of the proposed approach.     

基于交互车辆轨迹预测的自动驾驶车辆轨迹规划

针对城市道路等复杂行车场景,提出了一种基于交互车辆轨迹预测的自动驾驶车辆轨迹规划方法,将高维度的轨迹规划解耦为低维度的路径规划和速度规划;首先,采用五次多项式曲线和碰撞剩余时间规划车辆行驶路径;其次,在社会生成对抗网络Social-GAN的基础上结合车辆空间影响和注意力机制对交互车辆进行轨迹预测;然后,结合主车规划路径、交互车辆预测轨迹及碰撞判定模型得到主车S-T图,采用动态规划和数值优化方法求解S-T图,从而得到满足车辆动力学约束的安全、舒适最优速度曲线;最后,搭建PreScan-CarSim-Matlab&Simulink-Python联合仿真模型进行实验验证。仿真结果表明,提出的轨迹规划方法能够在对交互车辆有效避撞的前提下,保证车辆行驶的舒适性和高效性。     

Optimal 3D trajectory generation in delivering missions under urban constraints for a flying robot

Interest in applying flying robots especially quadcopters for civil applications, in particular for delivering purposes, has dramatically grown in the recent years. In fact, since quadcopters are capable of vertical takeoff and landing, they can be widely employed for nearly any aerial task where a human presence is hazardous or response time is critical. In this regard, quadcopters come to be very beneficial in delivering packages; accordingly, generating an optimal flight trajectory plays a preponderant role for meeting this vision. This paper is concerned with generation of a time-optimal 3D path for a quadcopter under municipal restrictions in delivering tasks. To this end, the flying robot’s dynamics is first modeled through Newton–Euler method. Subsequently, the problem is formulated as a time-optimal control problem such that the urban constraints, which are safe-margins of high-rise buildings located throughout the course, are first modeled and then imposed to the trajectory optimization problem as inequality constraints. After discretizing the trajectory by means of Hermit–Simpson method, the optimal control problem is transformed into a nonlinear programming problem and finally is solved by the direct collocation technique. Extensive simulations demonstrate the efficacy of the proposed method and correspondingly verify the effectiveness of the suggested method in generation of optimum 3D routes while all constraints and mission requirements are satisfied.