编队飞行星座的地球扁率摄动和大气阻力摄动分析

在前一篇文章推导的运动学模型的基础上,推导了J2项摄动下编队构型在x,y,z三个方向上随时间变化的解析式,详细分析了J2项摄动对三个方向上相对距离的影响。并研究了大气阻力摄动对各轨道参数的影响,给出了几条有益的结论。     

卫星编队构型设计与轨道机动算法优化

卫星编队与轨道机动是完成在轨监视与捕获等空间任务的关键技术。针对追踪航天器在相对目标航天器的绕飞过程中特殊构型的编队飞行问题,提出了三种特殊的编队构型机动方案;针对近距离轨道逼近问题,分析了同平面轨道变轨策略和轨道转移能耗最优化问题,在此基础上给出了三脉冲升降轨机动方法,并可以根据需要将其扩展为N脉冲机动。以目标星运行轨道高度780 km为例进行仿真分析,结果表明平行四边形编队中追踪星在各交点处完成变轨所需的速度脉冲向量分别为0.1172m/s、0.1843 m/s,而花形编队和菱形编队中追踪星在各交点处完成变轨所需的速度脉冲向量均为0.1978m/s,从而验证了所提出方法的有效性。     

近圆参考轨道卫星编队洛仑兹力控制

基于运动电荷在磁场中切割磁力线受到洛仑兹力作用的物理规律,分析了两种带电模式对经典轨道根数长期变化的影响:(1)卫星恒定带电模式;(2)前半个轨道周期卫星带电、后半周期不带电的非恒定带电模式.恒定带电模式可以有效地改变轨道升交点赤经、近地点幅角以及平近点角,对轨道半长轴、偏心率和倾角几乎不产生长期影响;而非恒定带电模式则可以有效地改变轨道偏心率.基于洛仑兹力作用下轨道根数长期变化规律以及轨道根数差描述的带电副星相对于不带电主星的运动,提出了利用洛仑兹力以及两种带电模式实现地球低轨近圆参考轨道卫星编队的控制策略,包括编队绕飞椭圆大小重构与编队中心漂移控制,解析求解了副星所需的带电量,并利用数值仿真验证了洛仑兹力控制的可行性.需要指出的是,洛仑兹力轨道控制无需消耗推进工质.      

壳体翻滚失准角模型最小二乘辨识方法

为了提高空间稳定惯性导航系统的姿态角测量精度,建立了壳体翻滚失准角模型,给出了从壳体翻滚失准角幅值和初始相位到当地水平坐标系下的姿态转换矩阵的传递规律.利用静态下平台运动学方程中壳体翻滚失准角与框架角的定量关系,进行了壳体翻滚失准角模型最小二乘辨识方法仿真,结果表明模型系数估计精度是足够的.针对实验系统,经过模型补偿,姿态角计算误差峰峰值小于0.5′.     

基于地平仪两轴姿态测量的卫星自主相对导航

针对近圆轨道编队卫星,提出了一种仅需要地平仪两轴姿态测量的卫星自主相对导航滤波方法,利用星间相对测量与偏航姿态运动的弱相关性,解决了欠偏航量测下的相对位置估计以及三轴姿态确定问题。可观性分析证明了该方法的可行性及对编队构型参数的适应性。大量仿真表明,对于绕飞和伴飞构型,该方法均收敛,性能特性与理论分析一致。针对当前典型的地平仪与星间测量能力,相对位置滤波精度均优于2 m(3σ),绕飞构型偏航姿态精度优于1.0°(3σ),伴飞构型偏航姿态精度优于0.5°(3σ),是对中等精度编队卫星配置简化的有益探索。     

时变通信延迟下的无人机编队鲁棒自适应控制

在时变通信延迟下研究了无人机群编队的鲁棒自适应控制问题。对于无人机编队系统中存在外部扰动和模型不确定性的情况,通过选取包含位置跟踪误差和速度跟踪误差的辅助变量,提出了一种适用于时变通信延迟的鲁棒自适应编队控制策略。提出了自适应律对无人机质量、外界扰动的上界等未知参数进行估计,并且利用Lyapunov稳定性理论分析了闭环系统的渐近稳定性,给出了系统渐近稳定所需要满足的条件。数值仿真结果表明,所提出的控制方法既能抑制外界扰动和模型不确定性对控制器的影响,同时队形跟踪和队形保持的稳态误差分别小于0.1 m和0.05 m。     

多星编队构型重构全局优化策略1）--第七届全国空间轨道设计竞赛乙题解法

第七届全国空间轨道设计竞赛乙组题目以近地轨道卫星编队的燃料最优构型重构问题为背景,要求合理设计从星的相对飞行轨迹,构建尽可能多的目标构型,并考虑燃料消耗均衡分配问题.本文介绍了该题目的解法,包括问题分析、求解方案以及相关计算结果.由于燃料最优控制问题可用能量最优控制问题近似,文中采用能量最优连续推力优化模型近似计算燃料最优控制律.首先通过优化分析两两构型之间的燃料消耗,确定了构建4种目标构型的次序;然后综合考虑构型保持时间约束以及相位约束,采用混合PSO（particle swarm optimization）算法进行全局优化;最后将影响燃料消耗指标的从星相对飞行轨迹的连续推力段转化为bang-bang控制.     

多星编队构型重构全局优化策略——第七届全国空间轨道设计竞赛乙题解法

第七届全国空间轨道设计竞赛乙组题目以近地轨道卫星编队的燃料最优构型重构问题为背景,要求合理设计从星的相对飞行轨迹,构建尽可能多的目标构型,并考虑燃料消耗均衡分配问题.本文介绍了该题目的解法,包括问题分析、求解方案以及相关计算结果.由于燃料最优控制问题可用能量最优控制问题近似,文中采用能量最优连续推力优化模型近似计算燃料最优控制律.首先通过优化分析两两构型之间的燃料消耗,确定了构建4种目标构型的次序;然后综合考虑构型保持时间约束以及相位约束,采用混合PSO(particle swarm optimization)算法进行全局优化;最后将影响燃料消耗指标的从星相对飞行轨迹的连续推力段转化为bang-bang控制.     

导弹编队协同攻击分布式鲁棒自适应控制

在有向通信拓扑下研究了导弹编队的鲁棒自适应协同跟踪控制问题。针对导弹编队系统中队形跟踪、外部扰动和模型不确定性的情况,通过选取包含位置跟踪误差和速度跟踪误差的辅助变量,提出了一种基于有向通信拓扑的鲁棒自适应编队控制策略。提出了自适应律对未知参数进行估计,并且利用Lyapunov稳定性理论分析了闭环系统的渐近稳定性。进一步,对于通信时滞的情况,给出了系统渐近稳定所需要满足的条件。与滑模控制等传统鲁棒控制不同,所设计的鲁棒自适应控制器是连续的,更便于导弹编队系统的实现。数值仿真结果表明,队形跟踪误差小于0.03 m,队形保持误差小于0.07 m,所设计的控制器能实现高精度的编队跟踪控制。     

基于深度强化学习的多无人车系统编队控制

针对多智能体编队控制问题,研究了基于DDQN深度强化学习算法的多无人车系统的编队控制器,采用一致性控制与伴随位形相结合的方法对编队控制问题进行建模和简化.建立了基于相对距离和速度的状态空间,使得控制输入不依赖于全局信息,然后设计了基于九大典型运动方向的动作空间,并设计了基于相对距离和相对速度的奖励函数,基于以上参数进行了神经网络架构的设计和网络训练与运动仿真环境的搭建,并成功训练出有效的控制器.该控制器可以直接应用于带有非完整约束的欠驱动无人车的编队任务,且控制器的网络训练只需要运动数据而不需要精确模型,是一种无模型控制方法.最后,通过大量不同场景下的运动仿真验证了控制器的有效性,包括多队形、多位置、多轨迹仿真以及时变队形、时变通讯和通讯故障等特殊情况的检验,该控制器在所有场景中均能有效完成控制任务.最后优化了编队起始阶段的策略,定义了等候条件与启动条件,有效节约了控制的能耗,利用运动仿真和对比分析验证了优化作用.     

Review of station keeping strategies for elliptically orbiting constellations in along-track formation

Three techniques for station keeping an orbiting constellation of satellites in an elliptical orbit are developed: (1) based on an application of the linearized Tschauner–Hempel (TH) equations for the motion of a daughter satellite relative to a reference (mother) satellite together with the linear quadratic regulator (LQR) control strategy which can be used in a piecewise adaptive manner; (2) since the mathematical model is inherently nonlinear and time varying, a control law based on a non-linear Lyapunov function is applied to daughter satellites’ osculating orbital elements; (3) by carefully selecting relative orbital design parameters so that the relative secular drifts due to the non-spherical Earth’s perturbation in the longitude of the ascending node, the argument of perigee and mean anomaly could vanish or be constrained to a desired value.     

THE CONTROL OF MEGA-CONSTELLATION AT LOW EARTH ORBIT BASED ON TLE

近几年来,美国SpaceX, OneWeb等创新型企业纷纷计划打造低轨巨型卫星星座,引发卫星互联网的发展热潮。本文利用公开的两行轨道根数(two-line element, TLE)对国外星座控制策略进行分析,重点分析了铱星、一网、星链星座的控制规律。通过相对相位偏差分析,反演得到星座中不同卫星之间的平半长轴差,避免了小控制量条件下难以通过平半长轴判断卫星是否进行了轨控的问题。获得了国外星座控制频次和控制精度等重要信息,所得结论能够为我国未来互联网星座的建设提供参考。     

316L不锈钢随动强化模型改进研究

本文对316L不锈钢进行了单轴与多轴非比例路径下的应力控制棘轮试验,考察了应力幅值、平均应力和加载历程对棘轮特性的影响。同时进行了应变控制循环试验以研究材料的应力松弛特性。试验结果表明轴向棘轮效应在对称剪切荷载下效果明显,同时棘轮应变随应力幅值和平均应力的增加而增加。研究了Chen-Jiao随动强化模型与Jiang-Sehitoglu随动强化模型采用的单轴与多轴参数对背应力分量增量方向的影响,将Chen-Jiao模型中的多轴系数替换为界面饱和率,并在此基础上引入新的参数对塑性模量系数进行修正,计算结果表明修正后的模型能提升应力控制下多轴棘轮的预测精度,并能很好的预测应力松弛现象,表明了新模型的正确性与有效性。     

Grain- and macro-scale kinematics for granular micromechanics based small deformation micromorphic continuum model

Macro-scale deformation of granular solids comprising large number of grains (>10⁶) are most efficiently described within the framework of continuum mechanics. It is notable, however that the micro-scale deformations in these materials are concentrated at the grain-boundaries or grain-contacts. Thus, the deformation energies in these systems must be modeled by considering the deformations concentrated in the neighborhood of the grain-boundaries or grain-contacts. To address this issue, grain-interactions has been widely described in the Hertzian sense by considering the relative movement of points on either side of a grain boundary or contact treated as an imperfect interface. This communication introduces the relevant kinematic variables given in the terms of the grain displacements, spins and size that can be used to estimate the relative movement of a grain boundary or contact. The macro-scale kinematic variables useful for continuum modeling are then identified with the grain-scale kinematic variables. The deformation energy density of the granular solid can thus be expressed both in terms of the grain-scale as well as the macro-scale kinematic variables providing the necessary pathway for micro-macro identification which can lead to non-classical micromorphic continuum models that incorporate grain-scale representation.     

A multi-body optimization framework with a knee kinematic model including articular contacts and ligaments

Multi-body optimization is one of the methods proposed to reduce the errors due to soft-tissue artifact in gait analysis based on skin markers. This method uses a multi-body kinematic model driven by the marker trajectories. The kinematic models developed so far for the knee joint include a lower pair (such as a hinge or a spherical joint) or more anatomical and physiological representations including articular contacts and the main ligaments. This latter method allows a better representation of the joint constraints of a subject, potentially improving the kinematic and the subsequent static and dynamic analyses, but model definition and mathematical implementation can be more complicated. This study presents a mathematical framework to implement a kinematic model of the knee featuring articular contacts and ligaments in the multi-body optimization. Two penalty-based methods (minimized and prescribed ligament length variations) consider deformable ligaments and are compared to a further method (zero ligament length variation) featuring isometric ligaments. The multi-body optimization is performed on one gait cycle for five asymptomatic male subjects by means of a lower limb model including the foot, shank, thigh and pelvis. The mean knee kinematics, ligament lengthening and contact point positions are compared over the three methods. The results are also consistent with results from the literature obtained by bone pins or biplanar fluoroscopy. Finally, a sensitivity analysis is performed to evaluate how the joint kinematics is affected by the weights used in the penalty-based methods. The approach is purely kinematic, since the penalty-based framework does not require the solution of the joint static or dynamic analyses and makes it possible to consider ligament deformations without the definition of ligament stiffness that generally cannot be identified through in vivo measurements. Nevertheless, as far as a knee kinematic model is concerned, particularly in musculoskeletal modeling, this approach appears to be a good compromise between standard non-physiological kinematic models and complex deformable dynamic models.     

Modeling aspects of low plastic strain amplitude multiaxial cyclic plasticity in conventional and ultrafine grain nickel

Aspects of the cyclically saturated responses of initially annealed, conventional grain size (average grain diameter of approximately 50 μm) and electrodeposited, ultrafine grain (grains from 20 to 500 nm) nickel to reversed proportional and 90° out-of-phase axial-torsional, strain-controlled cycling at a nominally constant equivalent inelastic strain amplitude of approximately 100 μ strain are reported. An anisotropic, axial-torsional subspace version of Abdel-Karim and Ohno’s kinematic hardening model is presented. Within the framework of conventional small strain, rate-independent plasticity, this approach is used to model the responses. An anhysteretic, phenomenolically based, magnetomechanical model is coupled to the rate-independent plasticity model to include the cyclic magnetostriction response. The kinematic hardening parameter determination scheme, using the proportional path responses, is described. The model correlations achieved are presented and the ability of the resulting models to capture the 90° out-of-phase responses is examined. The model parameter sets, as determined from the proportional responses, require small changes to result in more accurate correlation of the 90° out-of-phase responses and the implications of this are discussed. The relative values of the model parameters between the two materials reflect the initial microstructures. Persistent mean stresses associated with mean total strains imposed are successfully modeled for the proportional strain path responses but not for the 90° out-of-phase responses.     

Predictive Capabilities of an Improved Cubic k–ε Model for Inert Steady Flows

Through an improved ε transport equation, a major quality enhancement of the cubic k–ε model, earlier developed in[13], is obtained. The ε-equation of [13],yielding good results for wall-bounded and rotating flows, is combined with the one derived by Shih et al. [20], which produces good results for free shear flows (e.g. the plane jet–round jet anomaly is resolved).Results are presented for the following flows: fully developed stationary and rotating channel and pipe, backward-facing step, sudden pipe expansion, smooth channel expansion and contraction, plane and round jet. Heat transfer predictions in turbulent impinging jets are also discussed. Accurate results are obtained for the mean flow quantities for all test cases, without case dependent model tuning. This revised version was published online in July 2006 with corrections to the Cover Date.     

Numerical study of the noninertial systems: application to train coupler systems

Car coupler forces have a significant effect on the longitudinal train dynamics and stability. Because the coupler inertia is relatively small in comparison with the car inertia; the high stiffness associated with the coupler components can lead to high frequencies that adversely impact the computational efficiency of train models. The objective of this investigation is to study the effect of the coupler inertia on the train dynamics and on the computational efficiency as measured by the simulation time. To this end, two different models are developed for the car couplers; one model, called the inertial coupler model, includes the effect of the coupler inertia, while in the other model, called the noninertial model, the effect of the coupler inertia is neglected. Both inertial and noninertial coupler models used in this investigation are assumed to have the same coupler kinematic degrees of freedom that capture geometric nonlinearities and allow for the relative translation of the draft gears and end of car cushioning (EOC) devices as well as the relative rotation of the coupler shank. In both models, the coupler kinematic equations are expressed in terms of the car body and coupler coordinates. Both the inertial and noninertial models used in this study lead to a system of differential and algebraic equations that are solved simultaneously in order to determine the coordinates of the cars and couplers. In the case of the inertial model, the coupler kinematics is described using the absolute Cartesian coordinates, and the algebraic equations describe the kinematic constraints imposed on the motion of the system. In this case of the inertial model, the constraint equations are satisfied at the position, velocity, and acceleration levels. In the case of the noninertial model, the equations of motion are developed using the relative joint coordinates, thereby eliminating systematically the algebraic equations that represent the kinematic constraints. A quasistatic force analysis is used to determine a set of coupler nonlinear force algebraic equations for a given car configuration. These nonlinear force algebraic equations are solved iteratively to determine the coupler noninertial coordinates which enter into the formulation of the equations of motion of the train cars. The results obtained in this study showed that the neglect of the coupler inertia eliminates high frequency oscillations that can negatively impact the computational efficiency. The effect of these high frequencies that are attributed to the coupler inertia on the simulation time is examined using frequency and eigenvalue analyses. While the neglect of the coupler inertia leads, as demonstrated in this investigation, to a much more efficient model, the results obtained using the inertial and noninertial coupler models show good agreement, demonstrating that the coupler inertia can be neglected without having an adverse effect on the accuracy of the solution.     

On shakedown analysis in hardening plasticity

The extension of classical shakedown theorems for hardening plasticity is interesting from both theoretical and practical aspects of the theory of plasticity. This problem has been much discussed in the literature. In particular, the model of generalized standard materials gives a convenient framework to derive appropriate results for common models of plasticity with strain-hardening. This paper gives a comprehensive presentation of the subject, in particular, on general results which can be obtained in this framework. The extension of the static shakedown theorem to hardening plasticity is presented at first. It leads by min-max duality to the definition of dual static and kinematic safety coefficients in hardening plasticity. Dual static and kinematic approaches are discussed for common models of isotropic hardening of limited or unlimited kinematic hardening. The kinematic approach also suggests for these models the introduction of a relaxed kinematic coefficient following a method due to Koiter. Some models for soils such as the Cam-clay model are discussed in the same spirit for applications in geomechanics. In particular, new appropriate results concerning the variational expressions of the dual kinematic coefficients are obtained.     

Polycrystalline kinematics: An extension of single crystal kinematics that incorporates initial microstructure

Single crystal F^eF^P kinematics are widely used as the basis for many crystal plasticity models. Within this kinematic framework, geometrically necessary dislocations (GNDs) initially do not exist and then they evolve as needed in the material. A shortcoming of this kinematic model is that there is no rigorous way to define the initial and evolving GND state in the same manner. By augmenting the single crystal F^eF^P kinematics with a geometric argument, a consistent methodology for determining the initial and evolving GND state has been derived. The augmented kinematics describe GND related microstructural features in the undeformed material like low angle sub-grain boundaries and high angle grain boundaries. Therefore these kinematics are particularly applicable to polycrystalline materials.