Impact Angle Control Research Articles

Adaptive fixed-time observer-based impact angle control guidance law for intercepting maneuvering target

Adaptive fixed-time observer-based impact angle control guidance law for intercepting maneuvering target

Trajectory shaping guidance for impact angle control of planetary hopping robots.

This paper presents a novel optimal trajectory-shaping control concept for a planetary hopping robot. The hopping robot suffers from uncontrolled in-flight and undesired after-landing motions, leading to a position drift at landing. The proposed concept thrives on the Generalized Vector Explicit (GENEX) guidance, which can generate and shape the optimal trajectory and satisfy the end-point constraints like the impact angle of the velocity vector. The proposed concept is used for a thruster-based hopping robot, which achieves a range of impact angles, reduces the position drift at landing due to the undesired in-flight and after-landing motions, and handles the error in initial hopping angles. The proposed approach's conceptual realization is illustrated by lateral acceleration generated using thruster orientation control. Extensive simulations are carried out on horizontal and sloped surfaces with different initial and impact angle conditions to demonstrate the effect of impact angle on the position drift error and the viability of the proposed approach.

Generalized Time-to-Go Inversion Guidance with Impact Time and Angle Constraints

A major challenge in homing guidance is that accurately predicting the time to go for missiles is generally difficult, which limits the practical application of a certain class of guidance laws with impact-time constraints or cooperative capabilities. To address this issue, a generalized method referred to as the time-to-go inversion guidance is presented, where the time to go is first specified as an explicit function and then the corresponding guidance law is inversely derived. By employing this new method, a variety of guidance laws and their globally accurate time-to-go solutions can be developed, regardless of whether the impact-angle constraint is considered or not. Different from all existing studies, the proposed method addresses the problem of time-to-go estimation without relying on any linearizing approximations or numerical iterations. To enhance the practicality of the proposed method, it is augmented with bias commands to result in either the impact time control guidance law or the impact time and angle control guidance law. Numerical simulation results demonstrate the higher accuracy, larger feasible solution region, and lower computational demand of the proposed guidance laws even for the missiles with nonconstant speeds.

Reentry vehicle fixed-time terminal guidance and attitude control with impact angle constraints

The motivation of this paper is to handle the terminal guidance and attitude control problem for the unpowered reentry vehicle in the diving phase, which is crucial for interception to the target. The most important objectives of this study are to intercept the maneuvering target with the miss distance and impact angle error as small as possible. First, the second-order derivatives of the aerodynamic angles are derived with the fin deflections as control input, which is objective to avoid the tracking of reentry vehicle body angle rate command in the traditional methods. Second, a novel fixed-time time-varying parameter nonsingular terminal sliding mode guidance law is proposed to improve the convergence speed of line-of-sight angle rate, which can avoid control input singularity without switching to the polynomial form when the error approaches the origin. Thirdly, a new global time-varying sliding mode is developed to design the attitude controller, with the predefined fixed convergence time and analytical solution. The system states are proved to be fixed-time convergence based on the Lyapunov stability theory. Six-degree-of-freedom flight simulations are conducted to validate the superiority of the proposed algorithm in terms of miss distance, impact angle error, intercepting time and control input energy.

Data-Driven-Method-Based Guidance Law for Impact Time and Angle Constraints

To increase the hit efficiency and lethality of a flight vehicle, it is necessary to consider the vehicle’s guidance law concerning both impact time and angle constraints. In this study, a novel and straightforward impact time and angle control guidance law that is independent of time-to-go and small angle approximations is proposed with two stages using a data-driven method and proportional navigation guidance. First, a proportional navigation guidance-based impact angle control guidance law is designed for the second stage. Second, from various initial conditions on the impact angle control guidance simulation with various initial conditions, the input and output datasets are obtained to build a mapping network. Using the neural network technique, a mapping network model that can output the ideal flight path angle in flight is constructed for impact time control in the first stage. The proposed impact time and angle control guidance law reduces to the proportional navigation guidance law when the flight path angle error converges to zero. The simulation results show that the proposed guidance law delivers excellent performance under various conditions (including cooperative attack) and features better acceleration performance and less control energy than does the comparative impact time and angle control guidance law. The results of this research are expected to supplement those exploring various paradigms to solve the impact time and angle control guidance problem, as concluded in the current literature.

Cooperative attack strategy during the terminal guidance phase for loitering munitions based on impact angle and impact time constraints

In order to solve the cooperative attack problem during the terminal guidance phase for loitering munition swarm, a cooperative attack strategy for loitering munitions with impact angle constraints is proposed. By using the small deviation method, an offset proportional guidance law with impact angle constraints is derived in order to solve the problem of directional strike in the longitudinal plane. Combining with the present guidance scheme, a method for estimating the remaining time of proportional control and angle control is derived. In the lateral plane, a time control bias term with time-varying coefficients and no singularity in the division of zero is designed to solve the time control problem. In addition, taking the remaining time as the coordination variable, a two-layer cooperative architecture is used to solve the problem of coordinated directional strike of multiple loitering munitions. The simulation results show that the cooperative guidance strategy has a good performance of impact angle control and cooperative attack for low-speed loitering munitions.

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

In modern warship, coordinated combat strategies require missiles hit targets simultaneously, sometimes even require angle constraints, which is difficult to replicate in three-dimensional (3-D) models. This paper proposes a novel 3-D sliding mode guidance law with multiple constraints. First, the 3-D no-thrust guidance model is derived in the coordinate system with [Formula: see text]-axis upward. Second, a novel guidance strategy is proposed. In pitch direction, a fast nonsingular sliding mode surface algorithm is proposed to satisfy the desired line-of-sight elevation angle. In yaw direction, based on the guidance conditions, a special sliding mode surface is proposed, which can achieve desired line-of-sight azimuth angle and desired impact time when reaching the sliding surface. Finally, simulations and comparisons verify the good performance.

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.

Nonlinear Three-Dimensional Guidance for Impact Time and Angle Control With Field-of-View Constraint

Nonlinear Three-Dimensional Guidance for Impact Time and Angle Control With Field-of-View Constraint

Four-Stage Guidance Law for Impact Time and Angle Control based on the Bezier Curve

Four-Stage Guidance Law for Impact Time and Angle Control based on the Bezier Curve

Improved Fixed-Time Convergence Guidance Scheme Design and Its Application to Missile

This study presents a fixed-time convergence guidance scheme for impact time and angle control. First, two improved fixed-time stable systems are presented, which have smaller initial control command and better terminal convergence.16 An improved fixed-time extended state observer is proposed to provide accurate estimation of system states and disturbance, which effectively solves peaking value problem. Furthermore, an improved fixed-time sliding mode controller is derived, which avoids the singular problem and achieves faster convergence rate with smaller initial control command. Second, a new guidance scheme with impact angle and impact time constraints is proposed for intercepting a stationary target. By introducing a virtual target, the guidance process is divided into two stages. The proposed fixed-time controller is employed in the first stage. The method with a virtual leader ensures that the missile intercept the virtual target with desired line-of-sight angles at a specific time. By using the proportional navigation guidance law, the missile keeps travelling with desired flight-path angles to hit the real target in the second stage,17 so as to achieve the impact time and angle control. Finally, the feasibility and effectiveness of the proposed guidance scheme in different engagement scenarios are verified by numerical simulations with comparisons.

Multi-Constrained Geometric Guidance Law with a Data-Driven Method

A data-driven geometric guidance method is proposed for the multi-constrained guidance problem of variable-velocity unmanned aerial vehicles (UAVs). Firstly, a two-phase flight trajectory based on a log-aesthetic space curve (LASC) is designed. The impact angle is satisfied by a specified straight-line segment. The impact time is controlled by adjusting the phase switching point. Secondly, a deep neural network is trained offline to establish the mapping relationship between the initial conditions and desired trajectory parameters. Based on this mapping network, the desired flight trajectory can be generated rapidly and precisely. Finally, the pure pursuit and line-of-sight (PLOS) algorithm is employed to generate guidance commands. The numerical simulation results validate the effectiveness and superiority of the proposed method in terms of impact time and angle control under time-varying velocity.

Distributed observer‐based fixed‐time cooperative guidance law against maneuvering target

SummaryThis paper presents a fixed‐time cooperative guidance law for leader‐following missiles, comprising one leader missile with the target seeker and several seeker‐less follower missiles. The aim is to achieve a simultaneous attack on a maneuvering target at desired impact angles. First, a guidance law with impact angle control for the leader missile against a maneuvering target is proposed based on nonsingular fast terminal sliding mode (NFTSM) control algorithm. Then, the design of cooperative guidance law for the follower missiles is composed of two parts: along the follower‐to‐leader line of sight (LOS) direction, the guidance command derived from bi‐homogeneous property is designed to ensure that the follower‐leader ranges keep proportional consensus with the range‐to‐go of the leader missile, thus avoiding the estimation of time‐to‐go (); in the normal follower‐to‐leader LOS direction, considering the relative impact angle constraints which is determined by the leader LOS angle, the guidance command is proposed based on predefined‐time sliding mode control method. What's more, a distributed fixed‐time observer is designed for the follower missiles to compensate for unobtainable leader missile information. The fixed‐time stability of the proposed methods is demonstrated using the Lyapunov theory and bi‐homogeneous property. Finally, simulation results confirm the effectiveness and superiority of the proposed fixed‐time cooperative guidance law with leader‐following strategy.

Observer-based robust impact angle control three-dimensional guidance laws with autopilot lag

Considering an air-based missile intercepting maneuvering target with desired impact angles, robust guidance laws with autopilot lag in three-dimensional coupling space are presented in this paper. First, combining the fixed-time stability theory and adaptive sliding mode control technique, a novel dual-layer adaptive fixed-time sliding mode disturbance observer is proposed to estimate the unknown target maneuver. The proposed disturbance observer releases the requirement of information on either the target maneuver or its derivative. To achieve interception with the desired impact angles, a novel guidance law based on the nonsingular terminal sliding mode (NTSM) with an exponent coefficient is provided. The proposed control framework prevents singular problems and ensures the fixed-time stability of the guidance system. In addition, autopilot dynamics are taken into consideration, and the dynamics surface control (DSC) method is used to address the nonlinear static feedback system. Meanwhile, the improved fixed-time differentiator is used to acquire the derivative of virtual control laws. This prevents the inherent “differential explosion” of the backstepping technique. The uniform boundedness of the closed-loop system is demonstrated via the Lyapunov method. Finally, numerous numerical simulations are carried out, and the simulation results verify the effectiveness of the proposed guidance laws.

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.

Minimizing Look Angle Rate Guidance Law Considering Impact Angle and Field-of-View Limit

This study proposes a look angle rate minimizing optimal guidance law with impact angle control and look angle limit. The optimal control theory is adopted to solve the look angle rate minimization problem which has the state inequality on the look angle limit and constraint for impact angle control at the final time. The performance of the proposed guidance law is shown demonstrated by simulations for engagement scenarios of several look angle limits and impact angle constraints. The comparative study shows that the proposed guidance law outperforms on the energy and look angle managing ability.