Midcourse Trajectory Research Articles

탐색기 시야각 제한을 고려한 장거리 공대공 유도탄의 중기 궤적최적화

This paper describes a midcourse trajectory optimization for long-range missiles with a seeker field-of-view limit. Trajectory optimization is performed using convex programming, which is effective for real-time applications. Field-of-view limit, minimum dynamic pressure, and angle-of-attack limit are considered as path constraints. The terminal velocity is used as a performance index to ensure maneuverability in the terminal homing phase. The discontinuity of dynamics at the end of boost time is solved by separating the flight phase into a boost phase and a glide phase. The nonlinear dynamics are converted to input affine form using new input variables and partially linearized. The admissible input set is relaxed into a convex set through lossless convexification. Slack variables are introduced in the quadratic trust region and linearized path constraint, where they are augmented into the performance index for robust convergence. The transformed dynamics are discretized through a pseudo-spectral method and optimal trajectory is obtained using sequential convex programming. The effectiveness and robustness of the proposed method are verified through numerical simulation.

Dynamic Scattering Analysis of Midcourse Ballistic Targets with Separation Movements

In the midcourse trajectory of ballistic targets, warhead releasing and decoy throwing are two of the several types of target separation events. In the early stages, multiple targets are close to each other, and coupling scattering usually leads to variations in the radar cross section and polarization. If these variation features are investigated clearly, the tracking and recognition ability of an early warning radar will improve for ballistic targets. In this study, dynamic scattering of ballistic targets with three types of separation movements is analyzed; and several separation features that promote the action recognition development of midcourse ballistic targets are proposed.

컨벡스 프로그래밍을 이용한 추진-활공 유도탄의 중기궤적 최적화

탐색기를 탑재한 유도탄의 중기궤적은 탐색기 시야(FOV : Field-Of-View) 내에서 표적을 탐지하며, 전환 시점에서의 기동성을 최대화하도록 설계하는 것이 요구된다. 유도탄의 비행궤적 최적화 문제는 여러 구속조건이 적용된 비선형 문제로 일반적인 해석해를 도출하기 어렵기 때문에 그 동안 다양한 계산적인 방법들이 제시되어 왔다. 본 논문에서는 추진-활공 유도탄의 중기궤적 최적화 문제를 컨벡스 최적화 기법인 2차 원뿔 프로그래밍을 이용하여 산출하였다. 먼저, 운동방정식의 상태변수를 최소화하기 위해서 제어변수 구속조건이 추가된 제어변수 추가 형태의 운동방정식을 구성하였다. 또한, 자유 종말시간 문제와 추진시간 문제를 대처하기 위하여 정규화된 시간 변수를 독립 변수로 설정하였다. 그리고, 운동방정식과 제어변수 구속조건을 컨벡스 형태로 변환하기 위하여 각각 부분 선형화와 무손실 컨벡스 변환을 적용하였다. 마지막으로, 본 논문에서 제시된 방안의 타당성을 확인하기 위하여 비선형 최적화 프로그래밍 결과와 비교하였다.

A New Midcourse Guidance Design for Near Space Target Interceptor

This study proposes a new midcourse guidance method, combining the trajectory optimization approach and the optimal sliding mode method, to decrease the larger relative velocity between the near space target and the interceptor. Firstly, the midcourse trajectory optimization model is established. Then, the trajectory optimization guidance law based on a sampling scheme is proposed to decrease the larger relative velocity and satisfy multiple constraints at the end time of the midcourse guidance phase. Thirdly, the optimal sliding mode guidance law is introduced to deal with the target maneuverability. Finally, numerical simulations were performed to verify the performance of the midcourse guidance law.

A Convex Programming Approach to Mid-course Trajectory Optimization for Air-to-Ground Missiles

This paper addresses trajectory optimization in the mid-course phase of an air-to-ground missile, when the main objectives are (a) to ensure that the target is locked on in the center of the missile’s field-of-view at a specified flight path angle and (b) to attain maximum possible speed to allow for sufficient maneuverability in the terminal phase. The method presents as a second-order cone program (SOCP) formulation for this trajectory optimization, taking advantage of partial linearization and lossless convexification techniques that effectively handle underlying non-convex characteristics of the problem. A well-established SOCP solver can then be readily used to obtain the optimal solution to this convex program. The proposed approach is validated by (a) proving the losslessness of the convexification, and (b) numerically comparing the results with an existing pseudo-spectral method.

Optimal midcourse trajectory planning considering the capture region

An optimal midcourse trajectory planning approach that considers the capture region (CR) of the terminal guidance is proposed in this article based on the Gauss pseudospectral method (GPM). Firstly, the planar CR of the proportional navigation in terminal guidance is analyzed and innovatively introduced in the midcourse trajectory planning problems, with the collision triangle (CT) serving as the ideal terminal states parameters of the midcourse phase, and the CR area serving as the robustness against target maneuvers. Secondly, the midcourse trajectory planning problem that considers the path, terminal and control constraints is formulated and the well-developed GPM is used to generate the nominal trajectory that meets the CR demands. The interceptor will reshape the trajectory only when the former CR fails to cover the target, which has loosened the critical demand for frequent trajectory modification. Finally, the simulations of four different scenarios are carried out and the results prove the effectiveness and optimality of the proposed method.

A novel capture region of retro proportional navigation guidance law for intercepting high-speed nonmaneuvering targets

In this paper, the capturability of retro proportional navigation against high-speed nonmaneuvering targets is analyzed. By using a modified polar coordinate, the equations describing the relative dynamics of the guidance problem become simple. The novel capture region of retro proportional navigation, which is the necessary and sufficient conditions for the interception, is derived by utilizing an auxiliary function. A new constraint condition is added to the derivation of the capture region, which can guarantee capture high-speed targets successfully. Meanwhile, the optimal aiming and the optimal position of interceptor are derived which are used to acquire the excellent initial conditions to capture the high-speed targets. The results show that the capture region of retro proportional navigation is larger compared with pure proportional navigation. Additionally, initial constraint conditions of interceptor in the case of planar engagement are described based on the capture region of retro proportional navigation, which can provide a reference for midcourse trajectory planning. Finally, simulation is performed to verify the feasibility of the initial conditions of the interceptor.

Online optimal midcourse trajectory modification algorithm for hypersonic vehicle interceptions

This paper presents an online optimal midcourse trajectory modification algorithm for the hypersonic interceptions based on the neighboring optimal control theory, which takes the current states deviations and the revised terminal constraints as inputs and generates the optimal control modifications. Firstly, the midcourse guidance for hypersonic interception is introduced as an optimal control problem, which is solved with the well-developed Gauss Pseudospectral Method (GPM) to generate a nominal trajectory that satisfies the first order optimality conditions. Secondly, the Neighboring Optimal Trajectory Existence Theory (NOTET) is given and the first order optimality equations are further differentiated to second order to acquire the control modifications. The perturbations of the terminal co-states are expressed with the current states perturbations and the revised terminal constraints by solving the second order equations and inversely integrating the perturbation dynamic equations. The optimality of the proposed algorithm is proved. Finally, five different interception scenarios are simulated and comparisons are made with particle swarm optimization (PSO) method and GPM. Simulation results reveal that the proposed method has the merits of high precision equivalent with GPM and better computing efficiency than PSO and GPM, which testifies the effectiveness and online application feasibility.

Midcourse trajectory correction for solar sail starships

Hyperthin solar sails deployed as close to the Sun as possible are the only currently feasible approach to extrasolar solar exploration and interstellar travel. This paper quantifies and investigates the effects of timing errors in the unfurlment (or inflation) of solar sails at the perihelion of parabolic solar orbits upon the spacecraft's trajectory direction. Methods of correcting such aim errors include on-board solar-, radioisotope-, or nuclear-electric thrusters, electromagnetic thrustless turning, application of electric or magnetic sails, and a new application of toroidal magnetic ion scoops.

弹道导弹中段突防弹道设计与验证

弹道导弹中段突防弹道设计与验证

Error Analysis and Trajectory Correction Maneuvers of Lunar Transfer Orbit

For a returnable lunar probe, this paper studies the characteristics of both the Earth-Moon transfer orbit and the return orbit. On the basis of the error propagation matrix, the linear equation to estimate the first midcourse trajectory correction maneuver (TCM) is figured out. Numerical simulations are performed, and the features of error propagation in lunar transfer orbit are given. The advantages, disadvantages, and applications of two TCM strategies are discussed, and the computation of the second TCM of the return orbit is also simulated under the conditions at the reentry time.

Design of Midcourse Trajectory for Tactical Ballistic Missile Intercept on the Basis of Zero Effort Miss

Since the maneuverability of the tactical ballistic missile, the midcourse trajectory of interception missile needs design online. Firstly, this paper reasonably simplifies the models and explores the analytical expressions of their relative motion state to obtain a kind of rapid and high-precision computing method of zero effort miss. Secondly, it applies constant thrust for the interception missile, burns out shut-down solid engine, reflects on the index requirement of overloaded interception missile, and designs midcourse trajectory of the interception missile with Pontryagin maximal principle, in accordance with the analytical expressions of zero effort miss. Finally, with the simulating calculation, the prediction methods of zero effort miss and trajectory design method provided by this paper are applied to a situation simulation which is close to the fact as much as possible so as to verify the applicability in the interception of tactical ballistic missile.

Study on the Trajectory Simulation of the Ballistic Missile

Based on the geocentric coordinate system, the object coordinate system as well as the theory of elliptic trajectory, it makes research and analysis of the ballistic-parameter-based trajectory generation method of the ballistic missile and, meanwhile, verifies the effectiveness and rationality of this method. It, under the assumed condition of elliptic trajectory, also researches the solution process of the ballistic parameters in the midcourse of the ballistic missile and, meanwhile, makes the simulation verification on the midcourse trajectory of the ballistic missile according to the radar sights variation relation in the object coordinate system during the motion process.

스트랩다운 탐색기를 탑재한 유도탄의 관측각 제어 유도

Conventional proportional navigation guidance law is not adequate for missiles with a strapdown seeker, because the strapdown seeker cannot measure line-of-sight rate directly. This paper suggests a guidance loop design method, in which the look angle, measured by the strapdown seeker directly, is controlled to deliver a missile to a target. Basically, the look angle control loop is regarded as an attitude control loop. By using the proposed method, it is possible to shape the midcourse trajectory by choosing the reference look angle properly. The look angle control loop can robustly maintain target lock-on against disturbances because the target is always captured in the field of view of the seeker. The performance of the proposed method is verified via 6-DOF simulations of a true short range tactical missile model.

Trajectory Optimization for a Missile Using a Multitier Approach

A two-tier approach to the midcourse trajectory design for a surface-to-air missile to maximize the probability of hit is presented. The e rst tier represents the midcourse trajectory of the missile, and the second tier represents the terminal homing phase. The e rst-tier trajectory is optimized with an auxiliary constraint on the value of the approach angle to the intercept at handover to the terminal phase. The handover approach angle is used as the governing parameter in generating a e eld of optimum e rst-tier midcourse trajectories. The second-tier model estimates the probability of hit including a full suite of stochastic error sources on the seeker and missile. The optimal approach angleand midcoursetrajectory aredemonstrated to bedependent on the terminal homing noise contributors and the target maneuver.

Terminal homing performance of semiactive missiles against multitarget raids

The effects of low altitude multitarget raids against surface ships with command midcourse/semiactive rf terminal homing defensive missiles are investigated in terms of terminal homing miss distance. The scenario presently considered is that several defensive missiles are fired with each assigned a target to engage. A missile must engage its designated target for a successful intercept, and the miss distance is measured relative to the designated target. Raid geometry and the approach angle of the interceptor relative to the raid scintillation axis were found to be important parameters in determining miss distance. The stream raid and the closely spaced stacked raid had resolution ranges so short as to be practically unresolvable. Reasonable variations in the heading and seeker pointing errors had little effect on terminal miss distance for these unresolvable scenarios. For larger stacked raid separations, which are just resolved at handover, the handover errors can cause a loss of resolution and poor homing performance. Thus, a highly accurate handover is of use only for a band of separation spacings for the stacked raid and has little benefit against the stream raid. A method to counter the stream raid is to control the missile handover aspect angle through midcourse trajectory shaping so as to approach antiparallel to the raid velocity. For stacked raids, minimizing the handover range while using the midcourse guidance to bias the handover heading error allows more tightly spaced raids to be successfully engaged.