现实真比例导引拦截任意机动目标捕获区域

主动机动突防技术的发展给大气层外动能拦截带来了严重困难。假设目标机动加速度方向垂直于弹目视线、形式任意且有界，分析了用于大气层外拦截制导的现实真比例导引律（RTPN）对该任意机动目标的捕获区域。首先在考虑拦截器存在机动过载饱和限制的情况下，推导了比例导引系数的选择范围，可使RTPN的制导指令加速度在拦截过程中不超过拦截器饱和过载；其次基于不等式分析方法，在不考虑拦截器过载限制时，推导了RTPN对任意机动目标的捕获区域；然后结合拦截器机动过载限制，推导了RTPN对任意机动目标的更加实用的捕获区域；最后通过数值仿真算例，验证了所提出的理论。     

飞行器比例导引综述

基于导弹制导和机器人控制等领域，对追踪／截获动目标——导引问题的研究，综观几十年来大量国内外研究成果，系统分析与比较了各种比例导引律的含义、特点与性能。指出纯比例导引及其改进是非常有效的导引方式，可以有效地用于机动目标追踪／截获导引，能为相关领域机动目标导引问题的研究，包括战斗机追踪导引设计提供参考。     

某型战机追踪导引研究

基于对广泛应用与研究的各种比例导引律的比较与分析，提出应用纯比例导引实现战机追踪导引的方法，并通过追踪以不同机动方式逃逸的飞行目标的仿真，说明了它的正确性与可行性。     

空间机械臂绳索式末端执行器柔顺抓捕策略研究

针对机械臂抓捕非合作目标过程碰撞冲击大易造成基体偏转或目标逃逸的问题,提出并实现了快速接近-慢速接触-速度跟踪(FA-SC-VT)的末端捕获策略,并基于建立的系统全数字仿真模型对捕获策略进行了仿真验证,结果表明FA-SC-VT捕获策略与匀速捕获策略相比,可大幅减小机械臂捕获目标过程末端产生的冲击力,并可有效解决目标捕获过程中的逃逸问题。     

过载约束下的大机动目标协同拦截

研究了非线性拦截几何下具有过载约束的多枚弱机动能力的导弹拦截强机动能力的目标的协同拦截问题。首先，在建立导弹的可达域、导弹的可行域以及目标的逃逸域这3个概念的基础上提出了非线性拦截几何下的基于逃逸域覆盖的协同拦截策略，并提出了基于标准弹道的设计方法。然后，给出了协同拦截制导律的形式，研究了导弹的末制导初始阵位、制导律参数以及导弹对目标机动的覆盖区域这三者间的关系，并设计了数值求解算法来实现对多弹的覆盖区域的分配、协同制导律的设计以及多弹初始拦截阵位的配置。最后，对理论结果进行仿真。结果显示，多枚机动性较小的导弹，通过初始拦截阵位的合理配置和协同拦截制导律的合理设计，可以实现对机动性能较强的目标的协同拦截。     

一种弹体前置追踪过渡导引律(英文)

为了使弹体追踪法适用于空地导弹的过渡导引,提出了弹体前置追踪法,即在弹体追踪法的姿态角指令中增加前置角,从而使弹轴指向弹目视线上方。最大射程弹道仿真结果表明,使用弹体追踪法作为过渡导引律时初始时刻舵偏角达到10°饱和值,导引律交接段舵偏角突变较大,命中点落角小于60°;而使用弹体前置追踪法时全弹道舵偏角均小于5°,导引律过渡平稳,落角大于60°。针对不同目标分布情况,推算了前置角的计算公式,多条弹道仿真结果表明,使用弹体前置追踪过渡导引律并依据该计算公式选取前置角,各弹道均能达到需用舵偏角小于5°,落角大于60°的指标要求。     

捷联寻的制导系统弹体追踪导引方法研究

对捷联寻的系统的简易制导方法—弹体追踪法进行全面剖析 ,解析分析了弹体追踪法对导弹速度、目标速度的约束 ,以及弹体阻尼、滞后、舵偏到攻角之间的传递系数对弹体追踪导引性能的影响。通过数学推导及应用控制理论分析与仿真 ,弹体追踪法较比例导引和速度追踪法在导引特性和打击机动目标时性能较差 ,但其成本较低 ,是一种降低制导武器成本的简易制导方法。但采用弹体追踪法时 ,导弹和目标的速度不能太大 ,当制导武器系统在形成导引误差信号存在固有滞后时 ,弹体稳定回路需要有一定阻尼 ,且舵偏到攻角之间的传递系数不能太大 ,即飞行过程中攻角要较小。     

最优导引律研究

与常规导引律不同，直接以追踪器航迹角为优化控制变量，基于最优控制理论，借助追踪末端的几何关系，设计了基于非线性追踪模型的时间最优导引律；之后，针对工程实现，又对它进行了改进研究，以克服理论设计的两点不足：一是数值计算存在误差，会削弱导引性能；二是最优条件过于理想化，目标轨迹无法预先知道，难于工程实现。仿真研究表明：本文提出的2种改进方法，基于分段优化计算和基于分段预测控制的最优导引方法，能够有效地克服理论设计的不足，使得所设计的导引律成为真正意义上的最优导引律。     

基于弹道逃逸和小推力捕获的地月转移轨道设计

针对地月空间货运任务和环月轨道空间设施建设任务,提出一种弹道逃逸和小推力捕获相结合的新型地月轨道转移模式,并建立了一整套该类型轨道设计方法。首先,在三体模型假设下分别建立地心弹道逃逸轨道和月心小推力捕获轨道的二维极坐标动力学模型。对于弹道逃逸轨道,将地心旋转系对准角和地月转移加速速度增量作为控制变量,提出初值估计解析公式,并应用序列二次规划算法进行快速求解。对于小推力捕获轨道,以月心距为参考量设置与弹道逃逸轨道的拼接点约束,提出能量匹配方法预估飞行时间,采用最优螺旋轨道的初始伴随状态解析式预估近月点伴随变量初值。基于混合法和轨道逆推思想,采用人工免疫算法进行小推力捕获轨道求解。仿真结果表明,基于弹道逃逸和小推力捕获的地月轨道转移方式大幅降低了近月制动燃料消耗,能快速穿越地球辐射带,且飞行时间适中;同时,提出的轨道设计方法能快速搜索到基于弹道逃逸和小推力捕获的地月转移轨道,验证了该方法的有效性。     

主动雷达型空空导弹截获概率分析

误差是影响主动雷达型中远距空空导弹武器系统截获得性能的重要因素，通过引入截获目标时间的经验分布函数，提出了基于蒙特卡洛仿真计算导弹截获概率，以及定量评估误差对截获概率影响的方法。仿真结果表明，该方法能够有效分析误差因素对导弹截获得概率的影响，为武器系统误差配置提供计算参考。     

Satellite proximate interception vector guidance based on differential games

This paper studies the proximate satellite interception guidance strategies where both the interceptor and target can perform orbital maneuvers with magnitude limited thrusts. This problem is regarded as a pursuit-evasion game since satellites in both sides will try their best to capture or escape. In this game, the distance of these two players is small enough so that the highly nonlinear earth-centered gravitational dynamics can be reduced to the linear Clohessy-Wiltshire (CW) equations. The system is then simplified by introducing the zero effort miss variables. Saddle solution is formulated for the pursuit-evasion game and time-to-go is estimated similarly as that for the exo-atmospheric interception. Then a vector guidance is derived to ensure that the interception can be achieved in the optimal time. The proposed guidance law is validated by numerical simulations.     

Ideal proportional navigation for exoatmospheric interception

Ideal proportional navigation (IPN) is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two- dimensional ideal proportional navigation was conducted in previous public literature, whereas the practical interception happens in the three-dimensional space. A novel set of relative dynamic equations is adopted in this paper, which is with the advantage of decoupling relative motion in the instantaneous rotation plane of the line of sight from the rotation of this plane. The dimension-reduced IPN is constructed in this instantaneous plane, which functions as a three-dimensional guidance law. The trajectory features of dimension-reduced IPN are explored, and the capture regions of dimension-reduced IPN with limited acceleration against nonmaneuvering and maneuvering targets are analyzed by using phase plane method. It is proved that the capture capability of IPN is much stronger than true proportional navigation (TPN), no matter the target maneuvers or not. Finally, simulation results indicate that IPN is more effective than TPN in exoatmospheric interception scenarios.     

Linear Quadratic Differential Game Strategies with Two-pursuit Versus Single-evader

In order to intercept the future targets that are characterized by high maneuverability, multiple interceptors may be launched and aimed at single target. The scenario of two missiles P and Q intercepting a single target is modeled as a two-pursuit single-evader non-zero-sum linear quadratic differential game. The intercept space is decomposed into three subspaces which are mutually disjoint and their union covers the entire intercept space. The effect of adding the second interceptor arises in the intercept space of both P and Q (PQ-intercept space). A guidance law is derived from the Nash equilibrium strategy set (NESS) of the game. Simulation studies are focused on the PQ-intercept space. It is indicated that 1) increasing the target’s maneuverability will enlarge PQ-intercept space; 2) the handover conditions will be released if the initial zero-effort-miss (ZEM) of both interceptors has opposite sign; 3) overvaluation of the target’s maneuverability by choosing a small weight coefficient will generate robust performance with respect to the target maneuvering command switch time and decrease the fuel requirement; and 4) cooperation between interceptors increases the interception probability.     

Direct Intercept Guidance using Differential Geometry Concepts

This paper examines the application of differential geometry to the engagement of both nonmanoeuvring and manoeuvring targets. The kinematics of the engagement for both manoeuvring and nonmanoeuvring target are developed and expressed in differential geometric terms. Two-dimensional geometry is then used to determine the intercept conditions for a straight line target and a constant manoeuvre target. The intercept conditions for both targets are developed for the case when the interceptor missile guides onto a straight line interception. These two cases are shown to have a common set of core conditions such that it enables a unified guidance law to be developed. The guidance law is shown to be globally stable using Lyapunov theory, so that guidance capture is assured for any initial condition. The analysis and guidance law design does not rely on local linearisation and can be shown to produce guidance trajectories that mirror proportional navigation for the straight line interception of a nonmanoeuvring target for which proportional navigation was originally developed. The paper finishes with simulation in two dimensions, illustrating the convergence and solution properties of the approach.     

True proportional navigation with maneuvering target

We analytically obtain the capture regions for the true proportional navigation (TPN) missile guidance law against an intelligently maneuvering target. Two versions of TPN are considered. The first is the original TPN which assumes the commanded lateral acceleration to be directly proportional to the line-of-sight (LOS) rate only, the proportionality factor being an arbitrary constant or dependent only on the initial closing velocity. The other, known as RTPN (realistic TPN), assumes the commanded lateral acceleration to be directly proportional to the LOS rate and also the current closing velocity. The target is assumed to maneuver in such a way as to increase the LOS rate and thus directly oppose the proportional navigation (PN) philosophy of annulling the LOS rate. A necessary and sufficient condition for capture is derived for the original TPN, and using it, the exact capture region is obtained. A sufficient condition for capture is derived for RTPN and is used to obtain its capture region partially. Some necessary conditions for capture are also derived for RTPN and are used to obtain an upper bound on its complete capture region. Using these conditions some important results on the existence of capture regions and a comparative study of capturability of TPN laws are also presented     

An optimal one-way cooperative strategy for two defenders against an attacking missile

This paper investigates a cooperative strategy for protecting an aerial target.The problem is solved as a game among four players(a target,two defenders,and a missile).In this scenario,the target launches two defenders(defender-1 and defender-2)simultaneously,to establish a oneway cooperation system(OCS)against an attacking missile.A new optimal evasion strategy for the target is also derived.During the engagement,the target takes into account the reaction of the attacking missile,and guides defender-1 to the interception point by receiving information from defender-1.Depending on the control effort of the target,defender-2 can choose appropriate launch conditions and use very limited maneuvering capability to intercept the missile.For adversaries with first-order dynamics,simulation results show that the OCS allows two defenders to intercept the missile.During the engagement,even if one defender or communication channel is broken,the OCS still allows an interception to be made,thus increasing the target’s survivability.     

Obstacle avoidance for multi-missile network via distributed coordination algorithm

A distributed coordination algorithm is proposed to enhance the engagement of the multi-missile network in consideration of obstacle avoidance. To achieve a cooperative interception,the guidance law is developed in a simple form that consists of three individual components for target capture, time coordination and obstacle avoidance. The distributed coordination algorithm enables a group of interceptor missiles to reach the target simultaneously, even if some member in the multi-missile network can only collect the information from nearest neighbors. The simulation results show that the guidance strategy provides a feasible tool to implement obstacle avoidance for the multi-missile network with satisfactory accuracy of target capture. The effects of the gain parameters are also discussed to evaluate the proposed approach.     

Differential-game-based guidance law using target orientation observations

Modern 4th generation air-to-air missiles are quite capable of dealing with today's battlefield needs. Advanced aerodynamics, highly efficient warheads and smart target acquisition systems combine to yield higher missile lethality than ever. However, in order to intercept highly maneuverable targets, such as future unmanned combat air vehicles (UCAV), or to achieve higher tracking precision for missiles equipped with smaller warheads, further improvement in the missile guidance system is still needed. A new concept is presented here for deriving improved differential-game-based guidance laws that make use of information about the target orientation, which is acquired via an imaging seeker. The underlying idea is that of using measurements of the target attitude as a leading indicator of target acceleration. Knowledge of target attitude reduces the reachable set of target acceleration, facilitating the computation of an improved estimate of the zero-effort miss (ZEM) distance. In consequence, missile guidance accuracy is significantly improved. The new concept is applied in a horizontal interception scenario, where it is assumed that the target maneuver direction, constituting a partial attitude information, can be extracted via processing target images, acquired by an imaging sensor. The derivation results in a new guidance law that explicitly exploits the direction of the target acceleration. The performance of the new guidance law is studied via a computer simulation, which demonstrates its superiority over existing state-of-the-art differential-game-based guidance laws. It is demonstrated that a significant decrease in the miss distance can be expected via the use of partial target orientation information.     

Capturability of 3D RTPN guidance law against true-arbitrarily maneuvering target with maneuverability limitation

The capturability of the Three-Dimensional(3D) Realistic True Proportional Navigation(RTPN) guidance law is thoroughly analyzed. The true-arbitrarily maneuvering target is considered, which maneuvers along an arbitrary direction in 3D space with an arbitrary but upperbounded acceleration. The whole nonlinear relative kinematics between the interceptor and target is taken into account. First, the upper-bound of commanded acceleration of 3D RTPN is deduced,using a novel Lyapunov-like approach. Sec...