基于改进分段Gauss伪谱法的带推力高超声速 飞行器再入轨迹规划

再入轨迹规划是高超声速飞行器领域的热点问题,已吸引了众多国内外专家的关注. Gauss伪谱法以及分段Gauss伪谱法是解决含有多约束轨迹规划问题的一类有效工具.然而,发动机多次点火熄火导致推力不连续以及点火时刻控制输入的连续性要求是带推力高超声速飞行器再入轨迹优化面临的新挑战.本文将问题简化为多脉冲再入轨迹规划问题,基于改进分段Gauss伪谱法生成满足多条件约束的最优再入轨迹.通过设置分段Gauss伪谱法连续性条件,确保飞行器状态与控制输入在分段点处连续衔接.通过无动力自由再入与带推力再入算例对改进分段Gauss伪谱法进行说明,仿真结果也表明,改进分段Gauss伪谱法可有效求解带推力高超声速飞行器再入轨迹规划.     

考虑关节柔性的模块机器人动力学参数辨识

提出了一种基于3维运动测量系统Optotrak3020的柔性关节模块机器人动力学模型参数辨识方法.首先将机器人的动力学模型参数化为不包括刚度力矩的线性形式,避免了参数矩阵的标定问题.激励轨迹基于有限的傅里叶级数函数,采用自适应遗传算法得出了优化的傅里叶级数系数.机器人每一关节单独跟随优化激励轨迹进行运动,同时电机位置、...     

考虑导弹速度时变的角度约束最优中制导律

以导弹逆轨拦截高速运动目标为背景,本文运用间接高斯伪谱法设计带攻击角度约束的最优中制导律.通过零化弹目相对法向速度,将攻击角度约束转化为视线角约束.考虑导弹速度时变的情况,建立带角度约束的制导方程.根据极小值原理推导最优中制导律的解析表达式,运用高斯伪谱法对最优中制导律进行离散化,把微分方程转化为代数方程,避免了求解Riccati方程.该方法不需要预先知道导弹未来的速度信息,计算量小,具有较好的实时性.仿真结果表明该中制导律可以满足逆轨拦截对弹目交会角的约束,且中制导末端的过载较小.     

基于hp自适应伪谱法的空间机器人路径规划

针对空间机器人运动过程中基座姿态产生较大扰动的问题,基于hp自适应高斯伪谱法提出了一种以基座所受反作用力矩最小为目标函数的空间机器人路径规划方法.首先,综合考虑空间机器人运动过程中存在的关节角度约束、关节角速度约束、控制力矩约束及初始状态和终端状态约束等约束条件,将空间机器人路径规划问题看成满足一系列约束条件和边界条件并实现特定性能指标最优的最优控制问题.其次,结合hp自适应高斯伪谱法（hp-AGPM）与非线性规划技术,求解带有边界约束和路径约束的优化控制问题,得到满足约束且性能指标最优的空间机器人运动轨迹.最后,以平面2自由度空间机械臂为例对所设计方法进行仿真验证,并与其他伪谱法进行对比分析.仿真结果表明：本文算法能在10.6 s的时间内规划出满足各约束条件且容许偏差低于10^-6的最优运动轨迹,并且在计算速度和配点数量上都优于其他伪谱法.     

翻滚目标逼近的虚拟域逆动力学轨迹规划

针对追踪星自主逼近和跟踪翻滚目标特定部位的最优规划问题,提出了一种基于虚拟域逆动力学的多约束最优逼近轨迹规划方法.首先,在翻滚目标本体系下建立追踪星相对于翻滚目标特定部位的相对轨道动力学方程,并建立追踪星本体系相对于翻滚目标期望固连坐标系的相对姿态动力学方程;其次,考虑目标星外形、敏感器视场和执行机构控制能力等约束条件,建立时间/能量最优规划模型;然后,采用序列二次规划(sequential quadratic programming,SQP)方法求解时间/能量最优规划问题;最后,数值仿真验证了该方法在满足多约束条件下,可实现对翻滚目标自主逼近与跟踪的最优轨迹规划,同时与高斯伪谱法进行了对比,验证了本方法在计算效率方面的优势.     

最小二乘法在高斯拘束函数求解中的应用

高斯最小拘束原理是一种典型的微分变分原理,以加速度为变量,通过寻求拘束函数极值的变分方法直接得出系统的运动规律.目前,国内常用的求解高斯拘束函数的方法为拉格朗日乘子法,通过引入拉格朗日乘子将高斯拘束函数的条件极值问题转化为带有拉格朗日乘子的无条件极值问题,这种求解方法会增加未知变量的个数.为减少变量个数,进一步提高运算效率,文章首先对高斯拘束函数进行简单变形,引入加速度形式的约束方程将高斯拘束函数化为最小二乘形式,直接运用最小二乘法导出使高斯拘束函数取极小值时系统真实加速度的表达式.最后通过对曲柄滑块机构正动力学问题的分析和计算,验证了该方法的有效性.     

求解最优控制问题的Chebyshev-Gauss伪谱法

提出了一种求解最优控制问题的Chebyshev-Gauss伪谱法, 配点选择为Chebyshev-Gauss点. 通过比较非线性规划问题的Kaursh-Kuhn-Tucker条件和伪谱离散化的最优性条件, 导出了协态和Lagrange乘子的估计公式. 在状态逼近中, 采用了重心Lagrange插值公式, 并提出了一种简单有效的计算状态伪谱微分矩阵的方法. 该法的独特优势是具有良好的数值稳定性和计算效率. 仿真结果表明, 该法能够高精度地求解带有约束的复杂最优控制问题.     

基于Gauss伪谱法的飞机最优目标瞄准控制

为实现战对抗时对逃逸目标的最优瞄准,提出了一种基于高斯伪谱法(GPM)的控制方法。建立了考虑敏捷性、多约束的飞机动态方程,推导了两阶段目标瞄准条件表达式,并设计优化指标,在此基础上将飞机最优瞄准概括为带约束终端时间未知的多阶最优控制问题。利用高斯伪谱法将此连续的边值最优控制问题离散并转化为等价的非线性规划(NLP)问题,通过遗传算法(GA)解算其初值,并应用序列二次规划(SQP)算法求解。仿真结果表明：所设计的控制方法能有效实现对目标的瞄准,满足武器发射条件。     

火箭返回着陆问题高精度快速轨迹优化算法

针对垂直起降可重复使用运载火箭子级返回着陆问题,提出一种高精度快速轨迹优化算法.算法将凸化技术与伪谱离散方法有机结合,将非凸、非线性优化问题转化为凸优化问题,进而充分利用凸优化求解快速性、收敛确定性以及伪谱法离散精度高的理论基础.在优化精度方面,建立了高保真优化模型,分析了发动机开机/终端时刻值设计对轨迹最优性的影响;采用flip-Radau谱法对连续最优控制问题进行离散,并利用伪谱法的独特离散时域映射,将开机和终端时刻设计为特殊控制变量,提高了优化结果的精度和最优性.在快速性方面,为利用凸优化方法求解非凸问题,基于一种新的信赖域更新策略,提出了改进序列凸化算法,减少了算法迭代次数,提高了算法收敛性能.数值实验验证了算法的有效性.高精度的优化结果和较高的计算速度,使得算法具有发展为在线最优制导方法的潜力.     

基于最小二乘法的SIMO傅里叶神经网络研究

利用傅里叶级数的原理，构造单输入、多输出(SIMO)傅里叶神经网络，将非线性映射转化成为线性映射，将求解神经网络权值的方法由非线性优化方法转化成为线性优化方法，并采用最小二乘法计算网络的权值，从而大大提高了神经网络的收敛速度并避免了局部极小问题.而且，在训练输出样本受白噪声影响时，最小二乘法具有良好的降低噪声影响的功能．     

基于自适应MPC算法的轨迹跟踪控制研究

为了保证智能车辆在低附着且变速条件下跟踪控制的精确性和稳定性,提出一种基于自适应模型预测控制（MPC）的轨迹跟踪控制算法。针对低附着条件下轨迹跟踪存在行驶稳定性较差的问题,对车辆动力学模型添加侧偏角软约束,分别设计有无添加侧偏角约束的MPC控制器。仿真结果表明,添加侧偏角约束后MPC控制器性能更优,车辆行驶稳定性得到有效提高。在此基础上,又提出了一种自适应的轨迹跟踪控制策略,能够根据车辆速度的变化,实时产生预测时域[(Hp)],分别设计自适应的MPC控制器与4组定值[Hp]的MPC控制器。仿真结果表明,基于自适应模型预测控制的轨迹跟踪控制算法在提高低附着且变速条件下智能车辆轨迹跟踪控制的精度和稳定性方面具有一定的有效性和先进性。     

面向非完全姿态约束问题的旋转矩阵群中的垂线理论

在很多机器人领域,有很多给定任务要求并不需要3维空间的完整姿态约束,而是只限定了目标姿态某一轴的方向．这类问题称为非完全姿态约束问题．针对该问题,定义了旋转矩阵群中测地线的垂足和垂线,并给出了其解析表达式．基于垂线理论,提出了沿垂线规划的点到点轨迹生成算法．最后通过仿真实验求解操作臂的轨迹规划问题,仿真以6自由度的PUMA 560为平台,并依次固定第6关节、第4关节得到5自由度和4自由度的操作臂．提出的算法不仅适用于具有功能冗余的6自由度操作臂,也可应用于不具有冗余特性的5自由度和4自由度操作臂．实验结果验证了提出的理论和算法在解决非完全姿态约束问题上的通用性．同时,该算法还能避免参数表示方法中的奇异性问题．     

A novel physical based meta-heuristic optimization method known as Lightning Attachment Procedure Optimization

In this article, A novel nature-inspired optimization algorithm known as Lightning Attachment Procedure Optimization (LAPO) is proposed. The proposed approach mimics the lightning attachment procedure including the downward leader movement, the upward leader propagation, the unpredictable trajectory of lightning downward leader, and the branch fading feature of lightning. Final optimum result would be the lightning striking point. The proposed method is free from any parameter tuning and it is rarely stuck in the local optimum points. To evaluate the proposed algorithm, 29 mathematical benchmark functions are employed and the results are compared to those of 9 high quality well-known optimization methods The results of the proposed method are compared from different points of views, including quality of the results, convergence behavior, robustness, and CPU time consumption. Superiority and high quality performance of the proposed method are demonstrated through comparing the results. Moreover, the proposed method is also tested by five classical engineering design problems including tension/compression spring, welded beam, pressure vessel designs, Gear train design, and Cantilever beam design and a high constraint optimization problem known as Optimal Power Flow (OPF) which is a high constraint electrical engineering problem. The excellence performance of the proposed method in solving the problems with large number of constraints and also discrete optimization problems are also concluded from the results of the six engineering problem.     

基于虚约束的Acrobot动态伺服控制统一设计方法

提出一种基于虚约束的统一设计方法,以解决Acrobot系统中动态伺服控制问题,使系统沿着经过目标点的周期轨迹运动.将虚约束设计、虚约束作用下系统零动态微分方程分析以及轨道周期性判定相结合,获得了符合目标的周期轨道方程;基于Lyapunov方法设计了光滑反馈控制器,克服了基于线性二次型调节器（LQR）的控制器对零动态微分方程解析解的依赖性问题.实际算例的仿真结果表明了统一设计方法的有效性.     

快速连续反应-避障作业环境下的七自由度灵巧臂轨迹规划

人类经长期学习训练后能对高速物体 (如棒球、乒乓球等)具有快速连续反应作业的运动技能, 从深层次上揭示是由于人体在其训练过程中不断学习优选了相应手臂的动作轨迹, 并储存了丰富的经验和知识. 受人体手臂动作此行为机制启发, 本文提出一种 7-DOF灵巧臂快速连续反应-避障作业的轨迹规划方法. 该方法将灵巧臂对高速物体目标作业的轨迹规划问题转化为动作轨迹参数化优选问题, 考虑作业过程中灵巧臂的机构物理约束和障碍约束条件, 以灵巧臂目标可作业度指标构建适应度函数, 采用粒子群优化 (Particle swarm optimization, PSO)方法优选作业轨迹中的冗余参数; 在此基础上 利用灵巧臂动作轨迹参数化优选方法构建相应作业环境下的知识数据库, 实现灵巧臂对高速物体目标的快速连续反应作业. 以仿人机器人乒乓球对弈作业为例, 将该方法应用于 7-DOF灵巧臂乒乓球作业的轨迹规划中. 数值实验及实际对弈试验结果表明, 该方法不仅能使灵巧臂所规划的轨迹 满足灵巧臂机构物理约束与障碍约束条件, 同时能实现灵巧臂对乒乓球体的快速连续反应作业, 验证了该方法的有效性.     

Nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors

This paper exploits a nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors subject to thrust constraint and inertial parameter uncertainty to accomplish trajectory tracking missions. Because of under‐actuated nature of the quadrotor, a hierarchical control strategy is available; and position and attitude loop controllers are synthesized according to adaptive sliding mode control projects, where adaptive updates with projection algorithm are developed to ensure bounded estimations for uncertain inertial parameters. Further, during the position loop controller development, an auxiliary dynamic system is introduced, and selection criteria for controller parameters are established to maintain the thrust constraint and to ensure the non‐singular requirement of command attitude extraction. It has demonstrated that, the asymptotically stable trajectory tracking can be realized by the asymptotically stable cascaded closed‐loop system and auxiliary dynamic system. Simulations validate and highlight the proposed control approach. Copyright © 2016 John Wiley & Sons, Ltd.     

基于活动约束系统的变量化设计

在变量化设计过程中设计对象可以看作是一个几何约束系统,这个系统由几何元素以及作用于几何元素之间的各种约束关系构成。一个复杂的设计对象所对应的几何约束系统往往包含大量几何元素和约束关系,如果不加区别地把所有的几何元素和约束关系纳入变量化求解的范围,则很难满足交互设计的需要。而另一方面几何约束系统又往往是稀疏系统：（1）作用于任一几何元素的约束很少;（2）与任一约束相关的几何元素很少。基于这一事实给出了一种预处理策略从原始几何约束系统中搜索得到一个规模较小的活动约束系统,变量化求解在活动约束系统上进行。该方法已在自行研制的参数化造型系统GEMS5．0中实现。     

Flat trajectory design and tracking with saturation guarantees: a nano-drone application

Abstract

This paper deals with the problem of trajectory planning and tracking of a quadcopter system based on the property of differential flatness. First, B-spline characterisations of the flat output allow for optimal trajectory generation subject to waypoint constraints, thrust and angle constraints while minimising the trajectory length. Second, the proposed tracking control strategy combines feedback linearisation and nested saturation control via flatness. The control strategy provides bounded inputs (thrust, roll and pitch angles) while ensuring the overall stability of the tracking error dynamics. The control parameters are chosen based on the information of the a priori given reference trajectory. Moreover, conditions for the existence of these parameters are presented. The effectiveness of the trajectory planning and the tracking control design is analysed and validated through simulation and experimental results over a real nano-quadcopter platform, the Crazyflie 2.0.     

Distributed Time-Varying Formation Tracking Analysis and Design for Second-Order Multi-Agent Systems

Distributed time-varying formation tracking analysis and design problems for second-order multi-agent systems with one leader are studied respectively, where the states of followers form a predefined time-varying formation while tracking the state of the leader. Different from the previous results on formation tracking control, the formation for the followers can be described by specified time-varying vectors and the trajectory of the leader can also be time-varying. A distributed formation tracking protocol is constructed using only neighboring relative information. Necessary and sufficient conditions for second-order multi-agent systems with one leader to achieve time-varying formation tracking are proposed by utilizing the properties of the Laplacian matrix, where the formation tracking feasibility constraint is also given. An approach to design the formation tracking protocol is proposed by solving an algebraic Riccati equation. The presented results can be applied to deal with the target enclosing problems and consensus tracking problems for second-order multi-agent systems with one target/leader. An application in the target enclosing of multiple vehicles is provided to demonstrate the effectiveness of the theoretical results.     

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.