Impact Angle Control Guidance Research Articles

Field-of-view limited guidance with impact angle constraint and feasibility analysis

A look angle shaping guidance law with impact angle and seeker's field-of-view (FOV) constraints considering the time-varying speed is proposed. A look angle profile with respect to the relative range is first constructed as a cubic polynomial. The desired impact angle and the maximum look angle are expressed as functions of a parameter in the look angle profile. The impact angle constraint under limited FOV is achieved by solving this parameter with boundary conditions. Moreover, the feasible region of the desired impact angle is derived to ensure seeker's lock-on condition. By combining the first order look angle dynamics and the reference look angle profile, the impact angle control guidance (IACG) law with FOV constraint is obtained. The proposed guidance law is derived without relying on the linearized engagement kinematics, switching logic, constant speed assumption, and the LOS rate information during the guidance process. Moreover, the proposed guidance technique is helpful for user/designers to select feasible impact angle constraints in advance without tuning parameters. Finally, numerical simulations under a realistic model are performed to validate the effectiveness of the proposed guidance law.

Closed-Form Impact-Angle-Control Guidance of Nose-Dive Missiles for Maximum Terminal Speed

This paper addresses an impact angle control guidance problem for nose-dive missiles to achieve the maximum terminal speed against a fixed target in the same vertical plane. By modeling the aerodynamic drag as a drag polar, we set up the nonlinear system equations needed to pursue an analytic closed-form solution. This paper shows that maximizing the terminal speed is equivalent to minimizing a weighted quadratic cost of the curvature of trajectory, and can be used as an equivalent problem to the original problem. Applying Pontryagin’s maximum principle to the equivalent problem, we obtained a closed-form optimal guidance law, described in terms of air density parameters as well as heading error angle, flight path angle, range-to-go, and time-varying speed.

Autonomous cooperative guidance based on distributed consensus and self-management

As for the time-space cooperative guidance under complex offense–defense game conditions, this article proposes a distributed time-space cooperative guidance strategy based on consensus theory and missile group (MG) self-management. The strategy consists of a three-layer cooperative guidance system: the lower layer is the impact time and angle control guidance (ITACG) based on optimal control with minimum energy consumption. The middle layer is the time-space cooperative control strategy via distributed consistency with the time-to-go as the coordination variable. The upper layer is the MG self-management strategy considering the complex attack–defense conditions. The simulation results show that the cooperative strategy can achieve simultaneous attack at different directions and improve the penetration probability and the ability to respond to the attack–defense situation effectively.

Trajectory shaping guidance law design using constraint-combining multiplier

A new design method for trajectory shaping guidance laws with the impact angle constraint is proposed in this study. The basic idea is that the multiplier introduced to combine the equations for the terminal constraints is used to shape a flight trajectory as desired. To this end, the general form of impact angle control guidance (IACG) is first derived as a function of an arbitrary constraint-combining multiplier using the optimal control. We reveal that the constraint-combining multiplier satisfying the kinematics can be expressed as a function of state variables. From this result, the constraint-combining multiplier to achieve a desired trajectory can be obtained. Accordingly, when the desired trajectory is designed to satisfy the terminal constraints, the proposed method directly can provide a closed form of IACG laws that can achieve the desired trajectory. The potential significance of the proposed result is that various trajectory shaping IACG laws that can cope with various guidance goals can be readily determined compared to existing approaches. In this study, several examples are shown to validate the proposed method. The results also indicate that previous IACG laws belong to the subset of the proposed result. Finally, the characteristics of the proposed guidance laws are analyzed through numerical simulations.

Field-of-View Constrained Guidance Law for a Maneuvering Target With Impact Angle Control

Most existing impact angle control guidance (IACG) laws that consider the reduced seeker field-of-view (FOV) focus only on a stationary or a nonmaneuvering moving target. In actual warfare, however, a number of targets are capable of maneuvering with lateral acceleration, which prohibits the existing FOV-constrained IACG laws from guaranteeing the reliable performance. In this article, we develop a guidance law that ensures the accurate IACG with obeying the FOV constraint against a maneuvering target. The proposed guidance law is based on the engagement kinematics against a maneuvering target and structured as a sliding mode controller to cope with unknown disturbance such as the normal acceleration of the target. The introduced sliding surface structure includes a sigmoid function of which output is limited in magnitude in order to restrict the missile look angle within the preset limits. In consequence, the proposed law has the capability to fulfill IACG without violating the FOV constraint against a maneuvering moving target. Numerical simulations that support the effectiveness of the proposed guidance law are also included in this article.

Field-of-view-constrained impact angle control guidance with error convergence before interception considering speed changes

An impact angle control guidance law is proposed for stationary target interception considering missile's field-of-view limit and speed changes. The proposed impact angle control guidance law is structured as a biased proportional navigation with a time-varying bias. The proposed guidance law does not involve any switching logic for maintaining lock-on; hence, the guidance command is continuous during the entire engagement. Unlike the most existing studies, the proposed method guarantees that the impact angle error converges to zero before interception without the constant-speed assumption. To realize these desirable properties, the positive invariance of the bounded look angle interval and the change of independent variable are utilized. Numerical simulations are conducted to demonstrate the performance of the proposed guidance law.

Three-dimensional impact angle control guidance with field-of-view constraint

Traditional analytical impact angle control guidance laws with field-of-view (FOV) constraint were studied in two-dimensional cases. This paper deals with this problem in a three-dimensional engagement scenario by proposing a new nonlinear non-switching guidance strategy for attacking a stationary ground target. The nonlinear relation of the two partial lead angles of the missile is decoupled, and the guidance strategies for a vertical impact case and a non-vertical impact case are studied, respectively. The design problem is converted to be the nonlinear tracking control issues of yaw and pitch subsystems with partial state constraint. Novel model transformations are introduced to the two subsystems based on the properties of sine function and hyperbolic tangent function, then the guidance laws are derived by utilizing nonlinear mapping-based backstepping technique. It is proved with Lyapunov approach that the missile line-of-sight angles can be regulated to the desired ones for impact angle control, and that the overall lead angle is always restricted within the prescribed region for FOV limit as well as it converges to zero eventually for homing constraint. Simulation results show that the missile can impact the target from various desired directions successfully without violating FOV limitation.

Direct impact angle control guidance for passive homing missiles

A guidance problem for impact angle control applicable to a missile equipped with a passive seeker is investigated. The proposed guidance law based on the sliding mode control consists of the proportional navigation guidance term with a varying navigation constant and the additional biased term which is a function of the novel sliding surface. The guidance law directly uses the impact angle error but does not require any range information to be estimated by the additional filter loop of the passive seeker. The asymmetric limit of the passive seeker’s field-of-view is also taken into account, which is not violated by introducing a continuous switching function. The finite time convergence properties are analyzed, and nonlinear simulations are performed to investigate the effectiveness of the proposed guidance law.

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.

Impact Angle Control Guidance Law With Seeker’s Field-of-View Constraint Based on Logarithm Barrier Lyapunov Function

In recent years, the strapdown system has become the significant trend of the development of precision guided weapons. In order to effectively hit the lightly armored targets, researchers have done a series of studies on the impact angle control. However, most of them ignored the field-of-view constraint of the strapdown seeker. The existing impact angle control guidance laws with the field-of-view constraint have obvious drawbacks to some extent. For example, most of them are only applicable against nonmaneuvering targets and some of them suffer sudden hopping of guidance command due to the use of switching logic. Taking the strapdown seeker missile as the research object, this paper studies the field-of-view constrained impact angle control guidance problem against stationary targets, constant speed targets and maneuvering targets. According to the sliding mode control theory, two kinds of sliding surfaces are designed to make the missile achieve high precision attack under a desired impact angle within the field-of-view constraint. A quadratic barrier Lyapunov function and a logarithm barrier Lyapunov function are used to guarantee that the sliding surfaces designed for the impact angle constraint and the field-of-view constraint can converge to zero in finite time respectively. Then, a nonlinear extended state observer is proposed to estimate the unmeasurable disturbance of the system and alleviate the undesirable chattering by compensating it with the estimation of the disturbance. Finally, the feasibility of the proposed law is verified by numerical simulations.

Impact Angle Control Guidance Law Considering the Seeker’s Field-of-View Constraint Applied to Variable Speed Missiles

Recently, multiple constraints have been considered in the design of guidance laws. Most of the existing impact angle control guidance laws considering the seeker's field-of-view constraint are only applicable to constant speed missiles and have other limits to some extent. This paper is concerned with the field-of-view constrained impact angle control guidance law applied to variable speed missiles based on the sliding mode control theory. In the design of the sliding mode controller, we use a quadratic Lyapunov function to achieve the impact angle control. Moreover, we introduce an integral barrier Lyapunov function with an adaptive control item to address the field-of-view constraint and prevent the undesirable chattering caused by the disturbance of the nonlinear system. Then, the asymptotic stability of this close-looped system is verified. Eventually, numerical simulations are provided to demonstrate the performance of the proposed guidance law.

Time-Varying Asymmetric Barrier Lyapunov Function-Based Impact Angle Control Guidance Law With Field-of-View Constraint

A prerequisite for implementing precision strike is to keep the target locked within the seeker's field-of-view (FOV). To address this constraint, a novel impact angle control guidance law based on the dynamic surface control and time-varying asymmetric Barrier Lyapunov Function is proposed. The FOV constraint, in this article, is equally transformed to a time-varying asymmetric limitation on the missile-target relative velocity perpendicular to the line-of-sight (LOS). Under the proposed guidance law, the velocity component is prevented from overstepping its limitation and eventually approaches zero, thus satisfying the homing requirement and the FOV constraint in an integrated manner. Compared to previous studies, the proposed guidance law does not require the target information and is applicable against moving targets. Also, the proposed guidance law does not use any switching logic, and consequently the synthesized guidance command is free from abrupt-jumping phenomenon. Numerical simulations and performance comparison fully demonstrates the effectiveness and superiority of the proposed guidance law.

Off-Target Look Angle Control Guidance Law for Moving Targets

An off-target look angle control guidance law for nonmaneuvering moving targets is proposed. Unlike impact angle control guidance laws whose angle requirement is defined on the target, the proposed guidance law controls a look angle on a virtual circle centered on the moving target in the horizontal plane. A closed-form solution is derived using optimal control theory for a nonlinear problem formulation. The resulting guidance law can be expressed as a version of biased proportional navigation. It is shown how the new off-target look angle control can be applied in midcourse guidance problems to handover to terminal homing. The scenarios described include generating a collision course condition at a designated distance from a moving target, circling over a moving target, and attaining a desired look angle on the circle for a fixed target.

Three-Dimensional Impact Time and Angle Control Guidance Based on MPSP

A new nonlinear guidance law for air-to-ground missile cooperation attacks is proposed in this paper. This guidance law enables missiles with different initial conditions to attack targets simultaneously, and it can also precisely satisfy the terminal impact angle conditions in both flight-path angle and heading angle. The guidance law is devised using the model predictive static programming (MPSP) method, and the control saturation constraint is incorporated in the MPSP algorithm. The first-order-lag acceleration of the missile is taken as the state variable to realize the convergence of the terminal acceleration to zero. Moreover, a collision avoidance strategy for three-dimensional missile cooperative flight is proposed. The simulation results show that the guidance law can make the missiles hit the target accurately at the same time with the ideal impact angles and can realize the control saturation constraints of the missiles. This can increase the attack effects and is significant for collaborative attacks.

Nonlinear mapping based impact angle control guidance with seeker's field-of-view constraint

A novel nonlinear mapping based guidance strategy is proposed for attacking stationary and non-maneuvering moving targets with desired impact angle and seeker's field-of-view (FOV) constraints. In this paper, the impact angle is related with the line-of-sight (LOS) angle, and the seeker's FOV constraint is transformed to be the limit of the relative speed perpendicular to the LOS between missile and target. Firstly, the second-order nonlinear state equations of the guidance system are established, and backstepping control technique is used for the guidance commands design. The LOS angle is regulated in the first step by a bounded virtual guidance law designed based on hyperbolic tangent function. By introducing a one-to-one nonlinear mapping in the second step, the relative speed perpendicular to the LOS is controlled to track the virtual guidance law without exceeding the prescribed limit by a real guidance law. Then the stability of the closed loop system and the nonsingularity of the guidance commands are proved. Finally, the performances of the proposed guidance law are illustrated with numerical simulations.

Impact time and angle control guidance independent of time-to-go prediction

A novel cruise guidance method that can meet the terminal latitude and longitude, time and angle constraints independent of time-to-go prediction is studied in this paper. The impact time and angle control guidance (ITACG) goal is achieved through two steps. The first step is the construction of the complete motion model, the constant altitude and velocity guidance laws, and the optimal proportional guidance law which can satisfy the terminal position constraint based on the in-plane relative motion equation. The impact time control is the second step, which can be achieved by the integrated utilization of optimal guidance and maneuvering flight. Additional maneuvering trajectories used to control the impact time are designed in both cases with and without angle constraint, and the maneuvering parameters are directly solved online without time-to-go prediction. Simulation results verify the effectiveness of the guidance method, as well as the adaptability to different initial conditions and terminal constraints.

Adaptive Polynomial Guidance With Impact Angle Constraint Under Varying Velocity

Considering the velocity of the missile cannot remain constant in most applications due to the effect of aerodynamic drag and thrust, a feasible adaptive impact angle control guidance law under varying velocity is proposed. The design of the guidance command is transformed into the design of the flight path angle, which is proposed as a general polynomial function of time-to-go with unknown coefficient. In addition, the unknown coefficient can be acquired from the boundary condition of the position. To cope with unpredictable disturbances, the adaptive scheme to initialize and recalculate the control parameter at each time step is also adopted. First, the guidance law is proposed with constant velocity. Then the law is extended to a more practical situation by considering varying velocity, and the estimation of time-to-go under varying velocity is proposed. Different simulations are carried out to verify the performance of the proposed guidance law.

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.

New Design Methodology for Impact Angle Control Guidance for Various Missile and Target Motions

This brief introduces a new design methodology for impact angle control guidance (IACG) laws. The proposed methodology can extend any proven homing guidance laws to their impact angle control versions if the expressions of the estimated terminal flight path angles under those guidance laws are given. The time derivatives of the estimated terminal flight path angles are obtained as functions of the guidance commands. The IACG versions of the homing guidance laws are derived from those functions and the desired error dynamics of the estimated terminal flight path angle. The guidance law of each IACG version has two terms: the first term maintains the characteristics and capturability of the original guidance law and the second term drives the estimated terminal flight path angle to converge to the specified flight path angle. When a well-understood homing guidance law for a certain combination of target and missile models is given, an IACG law for that combination is easily derived without reformulating the guidance problem again. The usefulness of the proposed method is demonstrated by several examples, deriving new IACG laws for various target and missile models.

Impact Time Control Based on Time-to-Go Prediction for Sea-Skimming Antiship Missiles

This paper proposes a novel approach for guidance law design to satisfy the impact-time constraints for a certain class of homing missiles. The proposed guidance law provides proper lateral acceleration commands that make the impact time error converge to zero by the time of impact. This scheme can be applied to any existing guidance law for which a formula of predicted time to go is available. Convergence of time-to-go errors is supported by Lyapunov stability. The optimal guidance law and the impact angle control guidance law are extended by the proposed method for impact-time-control guidance and impact-time-and-angle-control guidance, respectively. The performance of the extended guidance laws is demonstrated by numerical simulation.