Impact Angle Control Guidance Law Research Articles

A novel impact angle control guidance law design via predefined time convergence theory

A predefined time guidance law with impact angle control is proposed for intercepting the stationary target. With such a guidance law, the convergence time of the impact angle error for the missile is independent of the initial conditions, and it can be selected at the will of the designer. First, a heading error shaping method based on the Lyapunov asymptotic stability theory will be introduced, which ensures the missile hits the target. Then, a bias term will be designed and introduced into this method, which can make sure the impact angle error converges to zero in the predefined time. The Lyapunov stability analysis is discussed in detail for the resulting predefined-time convergent guidance system. Finally, simulation examples are carried out to illustrate the effectiveness of the proposed guidance law.

3-D Impact Time and Angle Control Guidance Law Based on Sliding Mode without Speed Control

3-D Impact Time and Angle Control Guidance Law Based on Sliding Mode without Speed Control

Three-Dimensional Spatial–Temporal Cooperative Guidance Without Active Speed Control

This paper investigates the three-dimensional (3D) spatial–temporal cooperative guidance problem for multiple missiles with time-varying speeds, which is addressed by a progressive design strategy. First, the zero miss distance and desired impact directions are realized by a 3D vector impact angle control guidance (IACG) law whose time-to-go is predicted accurately and efficiently by a numerical algorithm. Then, by introducing an implicit trajectory-to-go function, the time-to-go control mechanism is clearly revealed under missile speed variation. Accordingly, a coordinated biased term is added to the 3D vector IACG law to ensure a simultaneous attack. Finally, considering the seeker’s field-of-view (FOV) limit, the resultant cooperative guidance law is further augmented by another biased term to prevent the lead angle from exceeding its upper bound. Unlike similar existing results, the proposed one can satisfy multiple complex spatial–temporal constraints without active speed control, thereby manifesting great practical significance. Several numerical simulations are provided to show the effectiveness and advantages of the proposed cooperative guidance law.

Impact Angle Control Guidance Considering Seeker’s Field-of-View Limit Based on Reinforcement Learning

This study proposes a computational impact angle control guidance law against a stationary target considering the seeker’s field-of-view (FOV) limit based on a deep reinforcement learning (RL) method. The proposed guidance law generates the acceleration command as a sum of the baseline command and bias command where the bias command is learned through a sequence of learning stages. Each stage trains an RL agent that addresses the impact angle and the FOV limit constraint individually. This approach is favorable in that the succeeding training process tends to preserve the functionality of the guidance law attained in the previous stage. In addition, the proposed method can be easily extended to a missile model with additional elements such as rotational dynamics without the necessity of modifying the algorithm. The proximal policy optimization algorithm is used for training the RL agents. Numerical simulation is carried out under various conditions to analyze the performance and the effects of a design parameter on the performance. The learning strategy proposed in this study provides a way to apply a data-driven method to developing a guidance law under multiple design objectives and more realistic missile models.

Three-dimensional predefined-time impact angle control guidance law with field-of-view limit

In this paper, an impact angle control guidance (IACG) law with predefined convergence time and seeker’s field-of-view (FOV) limit is proposed in three-dimensional (3D) scenario. First, a predefined-time error dynamic is developed whose significance is revealed by comparison with conventional methods. Second, based on coupled engagement dynamics, a 3D predefined-time IACG law is derived by applying the proposed error dynamic. To tackle the FOV limit, two auxiliary functions are introduced into the IACG law. The robustness against disturbances and uncertainties is further improved by utilizing the terminal sliding mode technique. With the proposed guidance law, the impact-angle error can converge to zero exactly at a tunable predefined time. Finally, the effectiveness and performance of the proposed IACG law are shown by several simulations with comparative study.

Impact angle, speed and acceleration control guidance via polynomial trajectory shaping

An Impact Angle, Speed and Acceleration Control Guidance (IASAG) law against the stationary target is proposed, which is critical for the effectiveness of the air-to-surface guided weapons. It is hard to address multiple terminal constraints problem for unpowered missile, especially including terminal speed constraint, which is uncontrollable state. Based on Line-of-Sight (LOS) angle, a fourth-order polynomial function is designed to make the number of coefficients of the function equal to number of boundary conditions. Through analytic calculation and transformation, the relation between the specified boundary conditions and the coefficients are established. The coefficient equations are reduced to a univariate nonlinear equation whose solution is determined by terminal speed constraint. Based on the characteristic of the nonlinear equation, we propose a Particle Swarm Optimization(PSO) method to find the coefficient that satisfies terminal speed constraint. According to Lyapunov stability theory, an asymptotically stable trajectory tracking controller is designed to track the reference leading angle with respect to range-to-go to guarantee the impact angle, speed and acceleration constraints. The effectiveness of the proposed guidance law is verified through numerical simulations.

Computational Optimal Impact Angle Control Guidance Laws Weighted by Arbitrary Functions

This paper presents a computational impact angle control guidance law based on the energy cost weighted by arbitrary functions in order to shape the acceleration command as desired. The optimal guidance problem is established in the impact angle frame and is solved by the Gauss orthogonal collocation method. The proposed guidance law is formulated from the generalized optimal control framework, thus a new guidance law that allows achieving a specific guidance goal can be easily obtained in the way of devising a proper weighting function (smooth, piecewise, nonsmooth, or even discontinuous). This property provides more degrees of freedom in the guidance law design to accomplish a specified guidance objective. A hardware experiment is conducted to evaluate the real-time computational capacity of the proposed computational guidance law. Illustrative examples with several types of weighting functions, including smooth, piecewise, nonsmooth, and discontinuous functions, are provided to demonstrate the advantages and capacity of the proposed guidance law.

Three-Dimensional Impact Angle and Time Control Guidance Law Based on Two-Stage Strategy

In this article, a 3-D nonlinear guidance law is developed for attacking a stationary target with desired impact angle and time. The guidance law is divided into two stages—impact angle control guidance (IACG) and proportional navigation guidance (PNG). In the IACG stage, a sliding-mode guidance law is established to guarantee the satisfaction of the impact angle constraint, and in the second stage, the 3-D PNG law is applied to ensure zero miss distance. The switch between the IACG and the PNG stages is determined by a guidance parameter related to the impact time constraint. By the virtue of Newton iteration method, an appropriate guidance parameter is obtained by solving an implicit nonlinear equality after a small number of iterations. Several numerical simulations are conducted to verify the feasibility and effectiveness of the proposed guidance law under different scenarios.

Field-of-View Constrained Three-Dimensional Impact Angle Control Guidance for Speed-Varying Missiles

This article develops a three-dimensional (3-D) impact angle control guidance law with the field-of-view (FOV) constraint. The impact error is defined as the difference between the predicted impact angle by proportional navigation guidance and the desired impact angle. The derived guidance command enables the impact angle error trajectory to follow a desired impact angle error dynamic. It can guarantee that the impact error converges to zero before the time of interception. Meanwhile, zero terminal guidance command is achieved, and the FOV constraint is always met during the guidance process. Furthermore, the trajectory of a guided missile is not affected by the variation of missile speed even under the FOV constraint, which reveals that the impact angle control performance is independent of time-varying missile speed. Numerical simulations are conducted to demonstrate the effectiveness of the proposed guidance law.

Gravity-compensated guidance for impact-angle interception of a moving target

This paper proposes an impact-angle control guidance (IACG) law for anti-ship and anti-tank missiles in which the command converges to zero at the point of interception, even in a gravity field. The desired line-of-sight (LoS) angle that satisfies the terminal impact-angle and acceleration constraints is first defined. The guidance command is then derived as a solution that realizes the convergence of the actual LoS angle to the desired LoS angle during the terminal stage of homing in on a target. Gravity is considered when designing the guidance law such that the desired terminal constraints are accurately satisfied, even under realistic pitch-axis engagement. We also investigated whether the proposed law is optimal for minimizing the total expense of maneuvering while performing IACG in a gravity field. The results of the numerical simulations included in this study demonstrate that the proposed guidance law achieves accurate impact-angle interception with the command converging to zero at the end of homing.

Terminal Impact Angle Control Guidance Law Considering Target Observability

The problem of the terminal impact angle control guidance law, considering the target observability for passive guidance with bearing-only measurement, is investigated in this paper. Modified line-of-sight (LOS) angle error dynamics and their closed-loop analytical solution are developed to enhance the target observability, and then their characteristics are studied, which makes the LOS angular rate oscillate in the early stage. The terminal impact angle control guidance law with the global sliding mode is designed to eliminate the approaching stage of sliding mode control, which makes the system robust throughout the entire process of control. Finally, numerical simulations are presented to demonstrate the performance of the proposed guidance law under various conditions, which achieves the desired results.

A New Guidance Law for Impact Angle Constraints with Time-Varying Navigation Gain

AbstractIn this study, a new impact angle control guidance law is proposed against a stationary target in the three-dimensional (3D) plane. A time-varying navigation gain is derived to achieve the specific terminal angle in a longitudinal plane without phased or adding a bias term. A proportional guidance law is also adopted in the lateral plane to achieve an accurate strike. The monotonicity of the look angle and the convergence of the acceleration are analysed and proven to support the proposed method. For the proposed guidance law, estimating time-to-go or giving a switch strategy is unnecessary; the navigation is continuous, which would not result in sudden changes in control input, and is convenient to implement. Extensive simulations, including autopilot lag or real missile model, are performed to validate the efficiency of the proposed method.

Impact Angle Control Guidance to Intercept Moving Targets by Virtual Target Technique

To solve the problem regarding the impact angle of the missile, this paper proposes a novel guidance law, which can control the missile to hit the target at the desired angle. The key of the guidance law is selecting a moving point on the collision line as the virtual target, and the tactical requirements can be fulfilled by the missile directly pursuing the virtual target. The Lyapunov stable theory is used to prove the convergence of the proposed guidance law. The guidance command is generated by a PID controller to make the missile towards the virtual target. The proposed guidance law makes the lateral acceleration of the missile converge to zero, which leads the angle of attack to zero, and it theoretically guarantees the flight path angle equals the attitude angle. Numerical simulations demonstrate this impact angle control guidance law is very accurate and robust. Regardless of whether the initial heading error is large or small, the missile which employs the proposed guidance law can always hit the target from the preset direction and the guidance process is smooth.

Impact-Angle-Constrained Cooperative Guidance for Salvo Attack

This paper proposes distributed cooperative guidance laws for multiple missiles with constant speeds to achieve impact-angle-constrained salvo attack against a stationary target in both two-dimensional (2D) and three-dimensional (3D) scenarios. First, the 2D cooperative guidance law is derived based on an optimal impact angle control guidance (IACG) law, which is augmented by a cooperative guidance term to ensure consensus of times-to-go in a fixed time before interception. To avoid singularity, an auxiliary function with three candidates is introduced into the cooperative guidance term. Then, coplanar cooperative guidance (CCG) and planar pursuit guidance (PPG) commands are, respectively, derived to construct the 3D cooperative guidance law. The CCG command is based on the coplanar assumption and the 2D cooperative guidance law, whereas the PPG command drives the velocity, line of sight (LOS), and desired impact vectors onto one engagement plane by geometric operations of vectors. Unlike existing 3D cooperative guidance laws, the proposed one does not require missile speed adjustment for salvo attack. The fixed-time stability and effectiveness of the proposed guidance laws are theoretically analyzed. The criteria for selecting all guidance parameters are provided to facilitate the guidance design. Finally, numerical simulations are conducted to support the analytical findings.

Impact angle guidance law to prevent the detection degradation of a seeker

An impact angle control guidance (IACG) law applicable to a homing missile equipped with a strapdown imaging seeker is investigated against a stationary target. Given an impact angle constraint, usually a detour is generated and the change of the look angle is inevitable. A rapid change of the look angle can cause a fast relative target motion in the seeker’s image plane, which can lead to a motion blur effect. The main contribution of the paper is that an IACG law is designed to minimize the look angle rate to prevent the loss of the target signal. Based on the variational approach, the optimal look angle rate that satisfies the impact angle constraint is derived, and the guidance law is designed to follow the optimal look angle rate. Using various weighting functions, a guidance law that has low sensitivity to the initial condition is also developed. Numerical simulation supports the performance of the guidance law. The result illustrates that the proposed guidance law reduces the rate of look angle in comparison with other IACG laws.

Generalized Guidance Formulation for Impact Angle Interception with Physical Constraints

This paper proposes an optimal impact angle control guidance law for homing missiles with a narrow field-of-view of the seekers. As groundwork for designing a guidance law, we first present a general guidance structure that can achieve any terminal constraint of the line-of-sight rate based on the optimal control theory. We configure the desired profile of the line-of-sight rate using a saturation function whose exact form is determined to satisfy the required boundary conditions. By combining the line-of-sight rate profile with the optimal guidance structure, we develop a guidance law that achieves an impact angle interception with the field-of-view constraint. Herein, as the entire guidance structure is derived based on exact kinematics without any approximation, the proposed law ensures the accurate impact angle interception for various engagement scenarios. This precise consideration of the engagement kinematics also accurately ensures the energy optimality of preventing the excessive use of control inputs when homing. To evaluate the performance of the proposed method, numerical simulations with various engagement scenarios are conducted, and the results demonstrate that the proposed law allows missiles to accurately intercept their targets with the desired impact angles and without violating the prescribed field-of-view constraint.

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.

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.