Trajectory reshaping based guidance with impact time and angle constraints

This study presents a novel impact time and angle constrained guidance law for homing missiles. The guidance law is first developed with the prior-assumption of a stationary target, which is followed by the practical extension to a maneuvering target scenario. To derive the closed-form guidance law, the trajectory reshaping technique is utilized and it results in defining a specific poly-nomial function with two unknown coefficients. These coefficients are determined to satisfy the impact time and angle constraints as well as the zero miss distance. Furthermore, the proposed guidance law has three additional guidance gains as design parameters which make it possible to adjust the guided trajectory according to the operational conditions and missile’s capability. Numerical simulations are presented to validate the effectiveness of the proposed guidance law. ? 2016 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).     

Sliding mode control based guidance law with impact angle constraint

The terminal guidance problem for an unpowered lifting reentry vehicle against a sta- tionary target is considered. In addition to attacking the target with high accuracy, the vehicle is also expected to achieve a desired impact angle. In this paper, a sliding mode control （SMC）-based guidance law is developed to satisfy the terminal angle constraint. Firstly, a specific sliding mode function is designed, and the terminal requirements can be achieved by enforcing both the sliding mode function and its derivative to zero at the end of the flight. Then, a backstepping approach is used to ensure the finite-time reaching phase of the sliding mode and the analytic expression of the control effort can be obtained. The trajectories generated by this method only depend on the initial and terminal conditions of the terminal phase and the instantaneous states of the vehicle. In order to test the performance of the proposed guidance law in practical application, numerical simulations are carried out by taking all the aerodynamic parameters into consideration. The effec- tiveness of the proposed guidance law is verified by the simulation results in various scenarios.     

Guidance law with impact time and impact angle constraints

A novel closed-form guidance law with impact time and impact angle constraints is pro- posed for salvo attack of anti-ship missiles, which employs missile’s normal acceleration (not jerk) as the control command directly. Firstly, the impact time control problem is formulated as tracking the designated time-to-go (the difference between the designated impact time and the current flight time) for the actual time-to-go of missile, and the impact angle control problem is formulated as tracking the designated heading angle for the actual heading angle of missile. Secondly, a biased proportional navigation guidance (BPNG) law with designated heading angle constraint is constructed, and the actual time-to-go estimation for this BPNG is derived analytically by solving the system differential equations. Thirdly, by adding a feedback control to this constructed BPNG to eliminate the time-to-go errorthe difference between the standard time-to-go and the actual time-to-go, a guidance law with adjustable coefficients to control the impact time and impact angle simultaneously is developed. Finally, simulation results demonstrate the performance and feasibility of the proposed approach.     

Two-phase guidance law for impact time control under physical constraints

An impact-time-control guidance law is required for the simultaneous attack of suicide attack unmanned aerial vehicles. Based on the nonlinear model, a two-phase guidance strategy is proposed. The impact time is derived in a simple analytical form of initial states and switching states, and it can be controlled by switching at an appropriate range. Firstly, a two-phase guidance law is designed to make the magnitude of the heading error decrease monotonically from its initial value to zero. And t...     

Modified rolling guidance law for single moving mass controlled reentry vehicle against maneuvering target with impact angle constraints

This paper deals with the problem of guidance law design for the single moving mass controlled reentry vehicle when impact angle constraints and maneuvering target are taken into consideration. More specifically, a modified rolling guidance law is proposed with the interactive virtual target and the landing point prediction strategy. First, considering the fact that the roll channel can be controlled directly, the relative motion between the single moving mass controlled reentry vehicle and the ...     

基于终端角度约束的二阶滑模制导律设计

针对空地导弹具有终端角度约束条件的制导律设计问题,提出了一种在有限时间内稳定的新型二阶滑模制导律。首先,在弹目相对运动学模型基础上,将终端弹道倾角约束转化为终端视线(LOS)角度约束,作为制导系统的终端控制目标。其次,通过选取一种新型二阶滑模面,结合螺旋控制算法的思想,设计了一种二阶滑模变结构制导律,来抑制系统中的不确定性因素,从而满足零化视线角速率和制导系统的终端角度约束条件的要求。采用一种新的Lyapunov函数,基于Lyapunov稳定性理论,严格证明了制导系统在有限时间内的稳定性。最后,对空地导弹制导系统进行数字仿真,通过和一阶传统滑模制导律以及基于超螺旋算法的二阶滑模制导律进行对比分析,验证了所设计的制导律在保证制导精度的同时,更能在有限时间内提高终端约束角度的精度,并且避免了超螺旋算法中参数选取较多的问题。     

Composite impact vector control based on Apollo descent guidance

A new three-dimensional missile guidance law to control the impact vector against a stationary target is proposed. The composite guidance law has two well-known components: Apollo descent guidance and trajectory shaping guidance. These respectively linear and planar guidance laws are combined to achieve a specified impact direction. The main idea is to define an impact plane and to steer the missile onto this plane using Apollo descent guidance while concurrently performing trajectory shaping wi...     

An adaptive fast fixed-time guidance law with an impact angle constraint for intercepting maneuvering targets

Sliding mode guidance laws based on a conventional terminal sliding mode guarantees only finite-time convergence, which verifies that the settling time is required to be estimated by selecting appropriate initial launched conditions. However, rapid convergence to a desired impact angle within a uniform bounded finite time is important in most practical guidance applications. A uniformly finite-time/fixed-time convergent guidance law means that the convergence (settling) time is predefined independently on initial conditions, that is, a closed-loop convergence time can be estimated a priori by guidance parameters. In this paper, a novel adaptive fast fixed-time sliding mode guidance law to intercept maneuver targets at a desired impact angle from any initial heading angle, with no problems of singularity and chattering, is designed. The proposed guidance law achieves system stabilization within bounded settling time independent on initial conditions and achieves more rapid convergence than those of fixed-time stable control methods by accelerating the convergence rate when the system is close to the origin. The achieved acceleration-magnitude constraints are rigorously enforced, and the chattering-free property is guaranteed by adaptive switching gains. Extensive numerical simulations are presented to validate the efficiency and superiority of the proposed guidance law for different initial engagement geometries and impact angles.     

Cascade-type guidance law design for multiple-UAV formation keeping

A procedure to compute guidance commands for controlling the relative geometry of multiple unmanned aerial vehicles (UAVs) in formation flight is proposed. The concepts of branch, global leader, and local leader/follower are used to represent the whole formation geometry. A positive-definite function defined in terms of the formation error is then introduced and the Lyapunov stability theorem is used to obtain the cascade type guidance law. This scheme leads to the synchronized flight of all UAVs while maintaining formation geometry. The results of a high fidelity nonlinear simulation of a reconnaissance and surveillance mission example are presented to show the effectiveness of the proposed guidance law.     

导弹速度时变的攻击时间与攻击角度控制导引律

针对导弹速度非定常情况下的协同制导问题,提出了两种分别满足攻击时间约束、攻击时间与攻击角度约束的导引律.首先通过求解导弹在比例导引(PN)及带攻击角度约束的偏置比例导引(BPNIAC)下的系统微分方程,得到导弹飞行的实际剩余航程,并根据指定的攻击时间与导弹的实际速度曲线构造标称剩余航程,将攻击时间控制问题转化为导弹实际剩余航程对标称剩余航程的跟踪问题.然后,在PN及BPNIAC的基础上附加反馈控制项使导弹实际的剩余航程跟踪标称值,从而实现导弹速度时变情况下攻击时间的控制要求.仿真结果验证了该方法的有效性,实际应用中可根据预测速度曲线及在线更新策略对标称剩余航程进行估算.     

基于时间最优的攻击角度控制研究

为了提高导弹的杀伤力,对攻击角度提出了一定的要求,而导弹以最小的飞行时间来完成带攻击角度约束的制导律,可减少被导弹防御系统发现概率而提高生存概率。采用Bang-Bang控制原理给出控制量受限情况下攻击角度约束的时间最优的控制律,并给出两种求解控制区间的几何方法:解析几何法和微分几何法。仿真结果验证了控制律的性能。     

攻击角约束的拦截弹制导控制一体化设计

针对拦截弹的攻击角约束制导问题,提出了一种基于反演滑模和扩张状态观测器(ESO)的制导控制一体化(IGC)设计方法。首先,基于弹目相对运动方程和拦截弹的非线性动力学方程,建立了拦截弹IGC模型,设计了ESO估计目标加速度和自动驾驶仪回路的干扰;在此基础上,基于干扰估计值和反演滑模方法,设计了IGC算法获取虚拟控制力矩,同时基于李雅普诺夫理论分析了闭环系统的稳定性;然后,利用动态控制分配技术将所获取的期望控制力矩分配到实际执行机构;最后,通过仿真结果验证了所设计的IGC+ESO算法的有效性。     

基于终端角度约束的滑模制导律设计

针对打击地面目标的制导问题,提出了一种新的具有终端角度约束的鲁棒滑模制导律。在建立地面目标和导弹的相对运动学关系的基础上,基于零化弹目视线角速率的思想,采用变结构控制理论的方法,通过选择理想的终端角度确定一个光滑的非线性滑动模态,代替传统末制导律设计的滑动模态,利用Lyapunov稳定理论设计得到了具有鲁棒性的滑模末制导律,实现了在有限时间精确打击目标,满足终端角度的要求。数字仿真表明,这种制导律对目标的运动具有很好的鲁棒性和适应性,并能获得良好的制导精度和指定的终端角度要求。     

基于最优误差动力学的时间角度控制制导律

针对带有攻击时间和终端攻击角度约束的导弹制导问题,设计了一种基于最优误差动力学的时间角度控制制导律,并给出了明确的性能指标。推导广义最优角度控制制导律作用下的剩余飞行时间估算表达式,在广义最优角度控制制导律的基础上增加攻击时间误差反馈项,将攻击时间误差看做跟踪误差,设计的制导律使跟踪误差以最优模式在有限时间内收敛到零,最终实现攻击时间和终端攻击角度的共同控制。对不同参数下的情况进行仿真,验证了所提制导律的有效性。     

基于预测控制的角度约束制导律设计

针对低高度、大倾角末端姿态约束问题,提出了一种弹道跟踪制导律.离线优化得到满足终端约束的基准弹道.为了避免出现奇异,将对位置的跟踪转换为对视线角及视线角速度的跟踪.根据当前状态,利用连续时间非线性预测控制,以弹道跟踪误差和控制能量的组合为性能指标,在线滚动优化得到制导指令,分析了制导律的参数选取,最后对该制导律进行了全...     

Three-dimensional time-varying sliding mode guidance law against maneuvering targets with terminal angle constraint

This paper deals with the problem of intercepting maneuvering targets with terminal angle constraints for missiles subjected to three-dimensional non-decoupling engagement geometry.To achieve the finite-time interception and satisfactory overload characteristics, a time varying sliding mode control methodology is developed based on a time base generator function. The main feature of the proposed guidance law guarantees the Line-of-Sight(LOS) angles to converge to small neighborhoods of the desir...     

基于轨迹成型的攻击角度与时间控制

假定所成型的导弹飞行轨迹由圆弧段和直线段构成,直线段经过目标点且满足导弹末端攻击角度的要求,圆弧段起始于导弹初始位置且与直线段相切于待定的点,该点由指定的导弹攻击时间通过迭代算法得到。给出了可行的攻击时间范围。在轨迹成型的基础上,提出一种新的虚拟目标轨迹跟踪控制方法：在圆弧段提出一种前馈加反馈的复合控制方案,在直线段提出一种带角度控制的比例导引方案。该方法是一种几何方法,易于工程实施。仿真结果表明,该方法可以有效地同时对攻击角度与攻击时间进行控制。     

三轴轮控航天器姿态大角度机动控制器设计

研究了飞轮作为执行机构的航天器姿态大角度机动问题。建立了飞轮控制的姿态动力学模型;基于Lya-punov稳定性定理,设计了闭环控制器并给出了参数自适应律的解析表达式;分析了有界噪声作用下该模型的控制效果。仿真结果表明,所设计的控制器具有较强的鲁棒性和抗干扰能力。     

Impact time control guidance against maneuvering targets based on a nonlinear virtual relative model

Aiming at the problem of high-precision interception of air-maneuvering targets with impact time constraints, this paper proposes a novel guidance law based on a nonlinear virtual relative model in which the origin is attached to the target. In this way, the original maneuvering target is transformed into a stationary one. A polynomial function of the guidance command in the range domain with two unknown coefficients is introduced into the virtual model, one of the coefficients is determined to ...     

Distributed formation control of multiple aerial vehicles based on guidance route

Formation control of fixed-wing aerial vehicles is an important yet rarely addressed problem because of their complex dynamics and various motion constraints, such as nonholonomic and velocity constraints. The guidance-route-based strategy has been demonstrated to be applicable to fixed-wing aircraft. However, it requires a global coordinator and there exists control lag, due to its own natures. For this reason, this paper presents a fully distributed guidance-route-based formation approach to address the aforementioned issues. First, a hop-count scheme is introduced to achieve distributed implementation, in which each aircraft chooses a neighbor with the minimum hop-count as a reference to generate its guidance route using only local information. Next, the model predictive control algorithm is employed to eliminate the control lag and achieve precise formation shape control. In addition, the stall protection and collision avoidance are also considered. Finally, three numerical simulations demonstrate that our proposed approach can implement precise formation shape control of fixed-wing aircraft in a fully distributed manner.