Terminal Impact Angle Constraint Research Articles

Analytical Prescribed Performance Guidance with Field-of-View and Impact-Angle Constraints

Aiming at the impact-angle-control guidance with field-of-view constraint in the three-dimensional space, a novel analytical prescribed performance guidance law is proposed. First, a new prescribed performance function is designed in the relative range domain, and the common drawbacks of most existing prescribed performance functions, such as large overshoot, time dependency, and infinite-time convergence, are avoided. Second, the three-dimensional biased pure proportional navigation guidance frame is selected. The biased term is derived based on the prescribed performance control theory and the optimal error dynamic method, for realizing the terminal impact-angle constraint. After that, the analytical solution of missile lead angle is derived under some linearization approximations, and two methods are respectively developed for obtaining the range of the guidance gain and updating its value to guarantee the satisfaction of the field-of-view constraint during the guidance process. Moreover, for the proposed guidance law and methods, the tracking error could be ensured to remain in the predefined performance boundaries. Finally, numerical simulations are conducted to verify the effectiveness of the new theoretical findings.

Nonlinear three dimensional all-aspect guidance with terminal impact angle constraints

In this paper, a nonlinear three dimensional all-aspect guidance law, to intercept maneuvering target at pre-specified orientation, is presented. Without decoupling the engagement kinematics into two perpendicular planes, the proposed guidance law is derived in three dimensions directly. More importantly, the proposed strategy is an ‘all-aspect’ guidance law, which allows missile to intercept the target at the desired impact angle, even in the presence of very large initial pointing errors. First, in order to design a guidance law with all-aspect interception capability, the collision conditions analysis process is carefully developed and an additional necessary constraint condition is derived. Then, based on chattering reduction sliding mode control, a nonlinear three dimensional terminal impact angle constrained guidance law is derived considering maneuvering targets. After capturability analysis, an additional sliding mode surface and a switching logic are further designed, so that the all-aspect capability is guaranteed. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed guidance strategy.

Synthesis of Suboptimal Guidance Law for Anti-Tank Guided Missile with Terminal Impact Angle Constraint Based on the SDRE Technique

In this paper, the homing-phase guidance law is proposed against a stationary target in the planar engagement scenario. In this problem, two technical criteria that the guidance law must achieve are: first, zero terminal miss distance, and second, satisfying the desired impact angle constraint at the final time. This guidance law is synthesized as a nonlinear optimal control problem with an infinite-time horizon and is solved using the state-dependent Riccati equation (SDRE) method. To obtain a guidance law with a finite-time horizon, a state weighting matrix based on the time-to-go is utilized in the SDRE control scheme. The synthesized guidance law is applied to a new generation anti-tank guided missile class, with specific thrust and drag parameters. Nonlinear simulations are conducted to demonstrate the fundamental properties, applicability, and effectiveness of the proposed guidance law.

Impact angle constraint guidance law using fully-actuated system approach

Aiming at the terminal impact-angle constraint in the interception of large maneuvering targets, this paper proposes a three-dimensional (3D) interception guidance law combined with the high-order fully-actuated system approach and the cascaded linear extended state observer (LESO). First, a complete second-order nonlinear model with full actuated characteristics is developed for the missile-target relative dynamics without small-angle assumption. Subsequently, the nonlinear system is transformed into a quasi-feedback system, and then, a high-order fully-actuated model is developed. A cascaded LESO able to estimate the system state and target maneuver information is introduced, and the controller is designed to convert the closed-loop system into a linear time-invariant closed-loop system with the desired characteristic structure, which makes the closed-loop system have the desired closed-loop poles. Finally, the controller parameter matrix is solved using the desired closed-loop poles, and the convergence is validated by the Lyapunov stability theory. Consequently, the linearization of the 3D nonlinear system is realized, and the channel coupling is eliminated. The effectiveness of the proposed method is verified by simulation and analysis.

Multiple Constraints-Based Adaptive Three-Dimensional Back-Stepping Sliding Mode Guidance Law against a Maneuvering Target

This paper addresses the issue of a complex three-dimension (3-D) terminal guidance process that is used against maneuvering targets while considering both the terminal impact angle (TIA) and field-of-view (FOV) angle constraints. According to the highly coupled and nonlinear 3-D terminal guidance model, an adaptive back-stepping sliding-mode guidance law algorithm is proposed in order to guarantee the stability and robustness of the guidance system. Considering the explicit expression of the line-of-sight (LOS) angle in the kinematics and dynamics of the terminal guidance process, the TIA constraint is transformed into an LOS constraint based on their well-known relationship. In view of the challenges in obtaining the motion information of maneuvering targets, an adaptive law design is introduced in order to estimate and compensate for external disturbances caused by the maneuvering of the target and modeling uncertainty. In addition, because the FOV angle represented by the overall leading angle is not a state variable in the sliding-mode guidance system, it is decoupled into two partial leading angles based on a specific transformation relation, so the 3-D terminal guidance control problem is converted into separate tracking system control issues in the pitch and yaw planes. Then, the Lyapunov stability theory is utilized to substantiate the stability of the guidance system, where the Lyapunov functions in both of the subsystems consist of the LOS and partial FOV state error terms. Finally, a series of simulations of various motion states of maneuvering targets under different terminal cases were carried out. It was proved that the terminal guidance design based on the strategies presented above was able to obtain the desired LOS constraints with satisfying the FOV limitation, and the simulation results verified the effectiveness, universality, and significance for practical applications of the proposed guidance design method.

Novel Particle Swarm Optimization Guidance for Hypersonic Target Interception with Impact Angle Constraint

Considering that the terminal impact angle constraint can improve the interception performance of hypersonic target, a novel particle swarm optimization guidance (NPSOG) algorithm is proposed to satisfy the impact angle constraint. Two-dimensional dynamics engagement mode for hypersonic target interception is formulated. The performance index is positively correlated with the line-of-sight (LOS), LOS rate, and the relative distance between missile and target. The weight coefficients among the three are adaptively adjusted by the fuzzy logic controller. The particle swarm optimization (PSO) algorithm is utilized to generate the guidance commands. Numerical examples are given to verify the performance of the proposed guidance law in various engagement scenarios, and the performance of the algorithm is validated comparing with several heuristic guidance methods and nonheuristic guidance methods.

Three-dimensional impact angle constrained distributed cooperative guidance law for anti-ship missiles

This paper investigates the problem of distributed co-operative guidance law design for multiple anti-ship missiles in the three-dimensional (3-D) space hitting simultaneously the same target with considering the desired terminal impact angle constraint. To address this issue, the problem formulation including 3-D nonlinear mathematical model description, and communication topology are built firstly. Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight (LOS) which satisfies the impact time constraint. However, the normal accelerations are designed to guarantee the convergence of the LOS angular rate. Furthermore, consider the terminal impact angle constraints, a nonsingular terminal sliding mode (NTSM) control is introduced, and a finite time convergent control law of normal acceleration is proposed. The convergence of the proposed guidance law is proved by using the second Lyapunov stability method, and numerical simulations are also conducted to verify its effectiveness. The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.

Midcourse Guidance Strategy for Multistage Interceptors with Coasting Phase

This paper proposes a new approach on the impact angle control guidance problem for the multistage interceptor with nonmaneuvering phases, called coasting phase, and high acceleration buildup during the boosting phase. First, the required coasting time is determined to reach the target within the given time span considering operation time of the kill vehicle. Then, the required flight path angle profiles and corresponding guidance commands during the boosting phase are derived, in order to achieve the desirable impact angle and to minimize guidance errors at the end of the flight. To do so, the position and velocity changes of each phase are analytically calculated, and then the relationship between the time derivative of the flight path angle during the boosting phase and guidance errors accumulated throughout the flight is established. Some practical error compensation algorithms for the proposed guidance strategy are also presented. The significance of this paper lies in that it is the new analytic approach on how to determine flight path profiles of a multistage interceptor to achieve a terminal impact angle constraint considering both booting and coasting. The proposed guidance strategy is evaluated and proven to be effective through a case study with nonlinear simulations.

Integrated guidance and control of interceptors with impact angle constraint against a high-speed maneuvering target

An integrated guidance and control method is investigated for interceptors with impact angle constraint against a high-speed maneuvering target. Firstly, a new control-oriented model with impact angle constraint of the integrated guidance and control system is built in the pitch plane by combining the engagement kinematics and missile dynamics model between the interceptor and target. Secondly, the flight path angle of the target is estimated by extended Kalman filter in order to transform the terminal impact angle constraint into the terminal line-of-sight angle constraint. Thirdly, a nonlinear adaptive sliding mode control law of the integrated guidance and control system is designed in order to directly obtain the rudder deflection command, which eliminates time delay caused by the traditional backstepping control method. Then the Lyapunov stability theory is used to prove the stability of the whole closed-loop integrated guidance and control system. Finally, the simulation results confirm that the integrated guidance and control method proposed in this paper can effectively improve the interception performance of the interceptor to a high-speed maneuvering target.

Look Angle Constrained Impact Angle Control Guidance Law for Homing Missiles With Bearings-Only Measurements

This paper presents an impact angle control guidance law that confines the missile look angle during homing in order to not exceed a seeker's field-of-view limit. A sliding surface variable whose regulation guarantees the interception of a stationary target at the desired impact angle is designed, and the guidance law is derived to make the surface variable go to the sliding mode. Using a magnitude-limited sigmoid function in the surface variable, the proposed law prohibits the look angle from exceeding the specified limit during the entire homing. This capability to confine the missile look angle is valuable when a seeker's field-of-view is restricted, since imposing the terminal impact angle constraint demands the missile to fly a curved trajectory. Furthermore, the proposed law can be implemented under bearings-only measurements because the command does not involve any information of the relative range and line-of-sight rate. Numerical simulations are conducted to demonstrate the validity of the proposed law. The result shows that the proposed guidance law accomplishes the impact angle constraint without violating the prescribed look angle limit although it only uses the information of bearing angles.

Guidance law to control impact angle and time based on optimality of error dynamics

In this work, a new guidance law with a meaningful performance index is designed to satisfy terminal impact angle and impact time constraints based on optimal error dynamics, which can be used for salvo attacks or cooperative missions of multi-missile. The analytical solution of the proposed guidance law is a combination of trajectory shaping guidance law and an additional impact time error feedback term that is proportional to the difference between the desired and the true impact times. Trajectory shaping guidance law aims to achieve the desired terminal impact angle and zero miss distance, whereas the extra term aims to meet the desired impact time. The minimum and maximum feasible impact times that consider the seeker's field-of-view limit, terminal impact angle constraint, and missile's maneuvering acceleration limit are calculated to provide the feasible boundary range of the desired impact time. Numerical simulations of several engagement situations demonstrate the effectiveness of the proposed guidance law in the accuracy of terminal impact angle and impact time.

A Two-Phased Guidance Law for Impact Angle Control with Seeker’s Field-of-View Limit

A two-phased guidance problem with terminal impact angle constraints and seeker’s field-of-view limit is addressed in this paper for a missile against a nonmaneuvering incoming target. From the conventional PN guidance without any constraints, it is found that satisfying the impact angle constraint causes a more curved missile trajectory requiring a large look angle. To avoid the look angle exceeding the seeker’s physical limit, a two-phased look angle control guidance scheme with the terminal constraint is introduced. The PN-typed guidance law is designed for each guidance phase with a specific switching condition of line-of-sight. The proposed guidance law is comprised of two types of acceleration commands: the one in the initial phase which aims at controlling the missile’s look angle to reach the limit and the other for final phase which is produced by switching the navigation gain. The monotonicity of the line-of-sight angle and look angle is analyzed and proved to support the proposed method. To evaluate the specific navigation gains for both initial and final phases, the scaling coefficient between them is discussed by solving a quadratic equation with respect to the initial navigation gain. To avoid a great abrupt acceleration change at the switching instant, a minimum coefficient is chosen. Extensive simulations are performed to validate the efficiency of the proposed approach.

Observer-Based Guidance Law With Impact Angle Constraint

Accounting for the autopilot as second-order dynamics, an observer-based guidance law with terminal impact angle constraint is designed using the dynamic surface control method. Some first-order low-pass filters are introduced into the designing process to avoid the occurrence of high-order derivatives of the line of sight (LOS) angle in the expression of the guidance law such that the guidance law can be implemented in practical applications. The proposed guidance law is effective in compensating for the second-order autopilot lag. In simulation of intercepting targets with sinusoidal acceleration, the guidance law is compared with the biased proportional navigation guidance (BPNG) law in the presence of missile autopilot lag. Simulation results show that the proposed observer-based guidance law with terminal impact angle constraint is able to guide a missile with large autopilot lag to impact a target with a desired angle and achieve a small miss distance, even if the target escapes in a great and fast maneuver.

A nonlinear impact-angle guidance law

PurposeThe purpose of this paper is to propose a new nonlinear guidance law to satisfy terminal impact-angle constraints against a stationary target in every possible planar surface-to-surface engagement scenario. The proposed guidance scheme is developed based on the geometry of a circular arc trajectory. The proposed guidance scheme is developed based on the geometry of circular arc trajectory. This trajectory is calculated based on the terminal impact angle and target range. The efficacy of the proposed guidance scheme is demonstrated through numerical simulations. The proposed scheme is compared with existing guidance schemes and relevant analysis is provided.Design/methodology/approachThe paper develops a new nonlinear guidance law to satisfy terminal impact-angle constraints against a stationary target in every possible planar surface-to-surface engagement scenario. The proposed guidance scheme is developed based on the geometry of a circular arc trajectory. This guidance scheme is further extended to moving targets.FindingsThe proposed guidance intercepts a stationary target with a smooth lateral acceleration command, which is desirable for realistic implementation. The efficacy of the approach is demonstrated through numerical simulation. A comparative study with the existing algorithm is presented and it is shown that the proposed algorithm is better on many counts.Originality/valueThere are many approach exists in the literature for impact-angle guidance laws. The paper proposes a computationally efficient guidance law using geometric and kinematic properties. As the approach produces smooth command, it has a practical relevance. A comparative study shows superiority on some counts (miss distance, flight time, smoothness).

Effect of seeker disturbance rejection rate on performance of optimal guidance laws with terminal impact angle constraint

In order to study the effect of seeker disturbance rejection rate on performance of optimal guidance law, based on guidance law with terminal impact angle(GLTIA) and extended guidance law with terminal impact angle(EGLIA), the regularization of strapdown seeker disturbance rejection rate on the stability of guidance system was studied. Using adjoint method the miss distance of GLTIA and EGLIA were analyzed. The results show that the stable domain of guidance system is larger when strapdown seeker parasitic loop is negative feedback than positive feedback, the stability will reduce when the value of disturbance rejection rate gets bigger. Though EGLIA has more excellent guidance performance than GLTIA, but the influence of a parasitic loop of seeker disturbance rejection rate will be more serious, the sufferable value of seeker disturbance rejection rate for EGLIA is about 2.5%, and the GLTIA is about 3.5%. In the practical application, if the guidance law would work with advanced performance, the value of seeker disturbance rejection rate should be much stricter to reduce the effect of parasitic loop.

Optimal pulsed guidance law with terminal impact angle constraint

An optimal pulsed guidance law with a time-varying weighted quadratic cost function that enables imposing a predetermined intercept angle is presented. Due to the characteristic of impulse force, admissible variance of control is redefined. The optimal pulsed guidance law is deduced via extended maximum principle. The optimal pulsed guidance law is eventually transformed to solve the two-point boundary value problem. To decide a shooting point, an efficient algorithm is proposed by combining particle swarm optimization and Kriging surrogate model method. The optimal pulsed guidance law is implemented in several representative engagements. From simulation results, it can be seen that the proposed guidance law can achieve small miss distance with terminal impact angle constraint under different conditions. Moreover, the performance of the proposed guidance law is satisfactory with the comparison of sliding-mode pulsed guidance law.

Finite time convergence cooperative guidance law based on graph theory

A new cooperative guidance law with impact time and impact angle constraints is presented for multiple flight vehicles to against the stationary target. The proposed guidance law has two projection components: the one that along the line-of-sight (LOS) ensures that all flight vehicles reach the target simultaneously with impact time constraints, another one that normal the LOS guarantees the convergence of the LOS angular rate with terminal impact angle constraints. Using the second Lyapunov stability method, we prove that the time-to-go of all flight vehicles reach at agreement in finite time if the connecting time of the communication topology is larger than the required convergent time. Nonlinear simulations demonstrate the effectiveness of the proposed law.

Fuzzy sliding mode control guidance law with terminal impact angle and acceleration constraints

In this paper, a novel fuzzy sliding mode control (FSMC) guidance law with terminal constraints of miss distance, impact angle and acceleration is presented for a constant speed missile against the stationary or slowly moving target. The proposed guidance law combines the sliding mode control algorithm with a fuzzy logic control scheme for the lag-free system and the first-order lag system. Through using Lyapunov stability theory, we prove the sliding surface converges to zero in finite time. Furthermore, considering the uncertain information and system disturbances, the guidance gains are on-line optimized by fuzzy logic technique. Numerical simulations are performed to demonstrate the performance of the FSMC guidance law and the results illustrate the validity and effectiveness of the proposed guidance law.

Bank-to-Turn Guidance Law with Terminal Impact-Angle Constraint

AbstractTo avoid the mathematical singularity of polar converting in bank-to-turn (BTT) guidance and to provide the specified terminal impact angle, a BTT guidance law with impact-angle constraint (BTT-GL/IA) is presented. Considering the influence of the impact-angle control and target maneuver to the miss-distance, a new form zero-effort miss-distance with impact angle (ZEM/IA) is introduced. Referring to the Lyapunov-like approach used to drive the guidance law in the prior literature, a Lyapunov function is constructed in terms of ZEM/IA. Based on the Lyapunov stability theorem, a negative definite function is designed, and the BTT-GL/IA is derived. Next, BTT-GL/IA is implemented in another form with the variables as the line-of-sight angle and its rate, which are easily measured by the seeker. When using BTT-GL/IA, the guidance law tends to maintain smooth and continuously-varied body acceleration and roll-angle commands while satisfying the impact position and angle constraints. The problem of a mat...

Diving guidance via feedback linearization and sliding mode control

A novel guidance algorithm using feedback linearization and sliding mode control is proposed to realize high precision guidance and maneuvering flight for hypersonic vehicle in dive phase. First, the longitudinal ellipse trajectory which can satisfy both the terminal impact point and angle constraints is designed, and the lateral maneuver trajectory is also generated to improve the penetration capability. Second, it introduces feedback linearization to decouple the original motion equations into linear guidance subsystems in longitudinal and lateral channel. With the linear equations, the tracker is designed with the help of sliding mode control, and the practical tracking guidance law can also be obtained by substituting the tracker into the original system. In addition, the stability of the guidance system is proven using the Lyapunov theorem. This tracking guidance is independent of the relative motion information and relative equation, while only the current motion states are needed. Besides, the results of CAV-H vehicle guidance test show that maneuvering flight and high precision guidance can be realized with the novel proposed algorithm, and the robustness is also validated through different guidance missions and Monte Carlo simulation.