Impact Time Control Guidance Law Research Articles

Impact time guidance law for arbitrary lead angle using sliding mode control

PurposeThis paper aims to investigate a novel impact time control guidance (ITCG) law based on the sliding mode control (SMC) for a nonmaneuvering target using the predicted interception point (PIP).Design/methodology/approachTo intercept the target with the minimal miss distance and desired impact time, an estimation of time-to-go is introduced. This estimation results in a precise impact time for multimissiles salvo attack the target at the same time. Even for a large lead angle, the desired impact time is achieved by using the sliding mode and Lyapunov stability theory. The singularity issue of the proposed impact time guidance laws is also analyzed to achieve an arbitrary lead angle with the desired impact time.FindingsNumerical scenarios with desired impact time are presented to illustrate the performance of the proposed ITCG law. Comparison with the state-of-art impact time guidance laws proves that the guidance law in this paper can enable the missile to intercept the target with minimal miss distance and final impact time error. This method enables multiple missiles to attack the target simultaneously with different distances and arbitrary lead angles.Originality/valueAn ITCG law based on sliding mode and Lyapunov stability theory is proposed, and the switching surface is designed based on a novel estimation time-to-go for the missile to intercept the target with minimal miss distance. To intercept the target with initial arbitrary lead angles and desired impact time, the authors analysis the singular issue in SMC to ensure that the missile can intercept the target with arbitrary lead angle. The proposed approach for a nonmaneuvering target using the PIP has simple forms, and therefore, they have the superiority of being implemented easily.

Impact time control guidance law with time-varying velocity based on deep reinforcement learning

This paper investigates the problem of impact-time-control guidance law with the time-varying velocity caused by gravity and aerodynamic drag. Using the deep reinforcement learning (DRL) algorithm, we propose a novel impact time control guidance (ITCG) law in which a DRL agent is trained from scratch without using any prior knowledge. Different from the traditional ITCG law, the proposed method doesn't rely on the time-to-go estimation, which is difficult to derive and inaccurate with the time-varying velocity. Further, a prioritized experience replay method and a novel action exploration method are introduced in the DRL algorithm to improve learning efficiency. Additionally, the agent action is shaped to provide smooth guidance command, which avoids the problem that the guidance command generated by the intelligent algorithm may not be continuous. Numerical simulations are conducted to support the validity of the proposed algorithm.

Look angle tracking based three‐dimensional impact time control guidance law with field‐of‐view constraint

AbstractThis article proposes a three‐dimensional impact time control guidance (ITCG) law without using time‐to‐go estimation, where the constrained field‐of‐view (FOV) is also considered. The guidance law design process is divided into two steps. First, the direction of the guidance command is selected to steer the look angle efficiently. Then, the desired look angle is constructed for controlling the impact time, and the guidance command magnitude is designed to track the desired look angle precisely in a prescribed time. By analyzing the look angle dynamics, the control gain is properly selected to guarantee satisfaction of the FOV constraint during the engagement. In addition, the feasible region of the desired impact time is derived. The effectiveness of the designed guidance law is validated by a series of numerical simulations.

Three-dimensional impact-time-constrained proportional navigation guidance using range-varying gain

This paper presents a novel feedback guidance law to address the impact time control problem of homing missiles in three-dimensional (3D) space. First, a range-varying gain is incorporated into the conventional proportional navigation guidance (PNG) law, which leads to globally precise time-to-go solution and achievable impact time region. Next, an impact time control guidance (ITCG) law is developed by augmenting the proposed varying-gain PNG law with a feedback biased term. Unlike most existing studies, the proposed ITCG law does not involve any linearized approximations or numerical iterative schemes. Furthermore, it can achieve the desired impact time and high-precision interception for a wide launch envelop with arbitrary initial leading angles. Finally, extensive numerical simulations, including comparison studies and Monte Carlo assessments, are carried out to validate the theoretical findings.

Lyapunov-Based Impact Time Control Guidance Law with Performance Prediction

This paper proposes an impact time control guidance law based on exact nonlinear kinematics equations. To address the impact time control problem of providing enhanced intercept accuracy, we formulated an error variable whose regulation ensures the fulfillment of the required tasks without time-to-go estimation. Based on the Lyapunov stability theory, a desired line-of-sight rate profile that satisfies the convergence of the error variable was constructed, from which the guidance command was designed using the optimal tracking formulation. The simple structure of the proposed guidance law enables the prediction of interceptor behavior during homing, thereby allowing the interceptor to maneuver along feasible trajectories. In addition, although the structure of the proposed guidance law is simple and similar to that of proportional navigation, it is theoretically guaranteed to execute the required mission precisely at the end of homing. Numerical simulations demonstrated that the proposed guidance law achieved effective target interception under various terminal constraint settings.

Varying-Gain Proportional Navigation Guidance for Precise Impact Time Control

This paper proposes a varying-gain proportional navigation guidance (PNG) law that can serve as the baseline for precise control of impact time. First, a varying-gain PNG law is developed by an inverse design strategy from the explicit time-to-go estimation of the conventional PNG law, which leads to high control efficiency and accurate time-to-go prediction. Next, to show its potential significance, the varying-gain PNG law is augmented with a biased feedback command to obtain an impact time control guidance (ITCG) law. As a step forward in more practical applications considering missile speed variation induced by thrust, drag, and gravity, another ITCG law is derived from an efficient time-to-go prediction method by taking the exact trajectory-to-go as the independent variable. Further, the varying-gain PNG law and the planar ITCG laws are extended to the three-dimensional guidance scenario by steering the missile to fly on an engagement plane. Compared with similar existing results, the proposed ITCG laws based on the varying-gain PNG law do not involve any linearized approximations in the derivation, and thus possess higher impact precision, wider feasible region, and less energy consumption. Finally, several numerical simulations are performed to support the analytical findings.

Deep reinforcement learning-based impact time control guidance law with constraints on the field-of-view

This paper proposes a novel three-dimensional (3D) intelligent impact time control guidance (ITCG) law with the field-of-view (FOV) strictly constrained based on nonlinear relative motion relationship. This novel guidance law can be utilized to coordinate multiple missiles to attack a target simultaneously. Firstly, the precise time-to-go estimation approach of the 3D coupling proportional navigation guidance (PNG) law is derived, which can improve accuracy of impact time. Secondly, a modified time biased term c⁎ including the guidance gain k1 which can accelerate the convergence rate is incorporated into 3D-PNG by feeding back the FOV error. Therefore, the optimal trajectory can be got to achieve precise impact time, in the meantime, the FOV constraint can be satisfied strictly. Then, the guidance gain k1 is obtained by deep deterministic policy gradient (DDPG) in the reinforcement learning (RL) framework, which makes the proposed guidance law meet smaller time error and has less energy loss. Furthermore, the proposed intelligent law can obtain optimal guidance gains quickly and avoid the tedious manual setting. Ultimately, simulation results demonstrate that missiles can impact the target precisely at desired impact times without violating FOV limit and the optimal guidance gain k1 is obtained adaptively and quickly in various initial conditions.

A hybrid proportional navigation based two-stage impact time control guidance law

To improve applicability and adaptability of the impact time control guidance (ITCG) in practical engineering, a two-stage ITCG law with simple but effective structure is proposed based on the hybrid proportional navigation, namely, the pure-proportional-navigation and the retro-proportional-navigation. For the case with the impact time error less than zero, the first stage of the guided trajectory is driven by the retro-proportional-navigation and the second one is driven by the pure-proportional-navigation. When the impact time error is greater than zero, both of the stages are generated by the pure-proportional-navigation but using different navigation gains. It is demonstrated by two-and three-dimensional numerical simulations that the proposed guidance law at least has comparable results to existing proportional-navigation-based ITCG laws and is shown to be advant-ageous in certain circumstances in that the proposed guidance law alleviates its dependence on the time-to-go estimation, consumes less control energy, and adapts itself to more boundary conditions and constraints. The results of this research are expected to be supplementary to the current research literature.

Impact Time Control Guidance Law for Large Initial Lead Angles Based on Sliding Mode Control

In view of the interception scenario where a missile intercepts a stationary target in the longitudinal plane, an impact time control guidance (ITCG) law is proposed by utilizing the sliding mode control (SMC). An amendatory approach of t go (time-to-go) is adopted where there is no need to take the small-angle assumption into consideration. Under the basis of SMC, the error of impact time is selected as a sliding mode variable, which can converge to be zero in finite time by using the fast power reaching law (FPRL). The guidance law performance has been conducted in one-to-one engagement with different desired impact time. Simulation results demonstrate that the proposed guidance scheme can operate effectively even with a large initial lead angle of the missile, which broadens the initial launch conditions of the missile as well as improving the application capability of the guidance law.

Three Dimensional Impact Time Control Guidance Law with Field of View Constraint

Three Dimensional Impact Time Control Guidance Law with Field of View Constraint

Sliding Mode Guidance Law for Impact Time Control Without Explicit Time-to-Go Estimation

This paper presents an impact time control guidance law that does not perform explicit time-to-go estimation. In order to satisfy the interception and the desired impact time constraint simultaneously, a sliding surface variable formulated as a sum of the relative range and the desired time-to-go is defined, weighted by two nonzero weighting functions. Then, the achievement of the sliding mode satisfies the following equivalence: The relative range is zero if and only if the elapsed time equals to the desired impact time. It means that both the interception and impact time control can be satisfied at the same time in the sliding mode. The impact time control guidance law is derived to enforce the defined surface variable to the sliding mode. Because the law is designed based on the capture condition without separate time-to-go estimation process, the achievement of the sliding mode always guarantees the interception of the target at the desired impact time. In addition, the proposed law can be applied to an engagement considering nonstationary targets in a straightforward manner because the corresponding time-to-go estimation is not needed. Simulation results demonstrate that the proposed guidance law has better performance in comparison with the existing guidance law, in respect of satisfying the desired impact time constraint against a nonstationary target.

Backstepping-Based Impact Time Control Guidance Law for Missiles With Reduced Seeker Field-of-View

This paper proposes a guidance law that achieves the desired terminal impact time without violating a seeker's field-of-view (FOV) limits. In order to derive the guidance law, kinematic conditions for impact time control are defined, and the backstepping control technique is applied for the satisfaction of the conditions. As a virtual control input for the backstepping structure, the missile lead angle, which represents the angle between the line-of-sight (LOS) and missile velocity vector, is used and its magnitude is limited by a prescribed limit. Then, the seeker's look angle can also be confined within a specific range because the seeker look angle is mainly determined by the difference between the LOS and the velocity vector. This capability to confine the seeker's look angle with achieving the desired impact time is the main contribution of the paper. To evaluate the performance of the proposed law, numerical simulation is conducted. The result demonstrates that the proposed guidance law enables the missile to simultaneously achieve the interception and desired impact time without violating the prespecified FOV limits.

A composite impact-time-control guidance law and simultaneous arrival

A new composite impact time control guidance law is proposed for simultaneous attack against a ground target. The guidance strategy is composed of two phases. Specifically, the first phase is to guide the missile to proper switching relative range for the second phase. After which, the second phase will lead the missile to the target with a desired impact time by using the proposed Lyapunov based guidance scheme. The impact time is given in a simple analytical form of initial states and switching relative range, the value of which is determined to control the impact time. The proper range of the switching state is analyzed considering the line of sight angle constraint. And the permissible range for impact time can be calculated corresponding to the proper switching state. Two classes of simultaneous attack are considered to demonstrate the effectiveness of the impact time control. One is the sequential launch, and the other is a salvo launch of multiple missiles from different positions. Numerical simulations are carried out to verify the performance of the proposed methodology.

Impact time control guidance law for large heading errors

Impact time control guidance law for large heading errors

Impact-Time-Control Guidance Law With Constraints on Seeker Look Angle

An impact-time-control guidance (ITCG) law is required for simultaneous attack of multiple missiles. In application of ITCG, the limit of seeker look angle should be regarded as an important factor in homing engagement scenarios. To avoid the loss of target tracking during engagement, the seeker's look angle should be confined to the seeker's field-of-view limit. This paper suggests a new ITCG law for a realistic situation with constraints on seeker look angle driven by the exact nonlinear equations of motion in plane. The proposed guidance law ensures the seeker's look angle to reduce monotonically from the initial value to zero at the intercept point. The resulting solution is presented in the form of proportional navigation guidance law with a time-varying navigation gain. The closed-form navigation gain can be obtained from information on the current missile-to-target range and heading angle.

Impact-Time-Control Guidance Law for Missile with Time-Varying Velocity

The problem of impact-time-control guidance (ITCG) for the homing missile with time-varying velocity is addressed. First, a novel ITCG law is proposed based on the integral sliding mode control (ISMC) method. Then, a salvo attack algorithm is designed based on the proposed guidance law. The performances of the conventional ITCG laws strongly depend on the accuracy of the estimated time-to-go (TTG). However, the accurate estimated TTG can be obtained only if the missile velocity is constant. The conventional ITCG laws were designed under the assumption that the missile velocity is constant. The most attractive feature of this work is that the newly proposed ITCG law relaxes the constant velocity assumption, which only needs the variation range of the missile velocity. Finally, the numerical simulation demonstrates the effectiveness of the proposed method.

IMPACT-TIME-CONTROL GUIDANCE LAWS FOR COOPERATIVE ATTACK OF MULTIPLE MISSILES

Two major simultaneous attack strategies have been introduced, as one of cooper- ative attack of multiple missiles. One strategy is an undesignated time attack, in which the mis- siles communicate among themselves to synchronize the arrival times by reducing the mutual differences of times-to-go of multiple missiles during the homing. The other is a designated time attack, in which a common impact time is commanded to all members in advance, and thereafter each missile tries to home on the target on time independently. For this individual homing, Impact-Time-Control Guidance (ITCG) law is required. After introducing coopera- tive proportional navigation (CPN) for the first strategy, this article presents a new closed-form ITCG guidance solution for the second strategy. It is based on the linear formulation, employ- ing base trajectories driven by PNG with various navigation constants. Nonlinear simulation of several engagement situations demonstrates the performance and feasibility of the proposed ITCG law.

Impact time control guidance with field-of-view constraint accounting for uncertain system lag

The problem of impact time control guidance with seeker’s field-of-view constraint in the presence of uncertain system lag is addressed. A novel two-step control approach based impact time control guidance law with seeker’s field-of-view constraint is proposed. Specifically, in the first step, a state constrained robust adaptive control law, using the dynamic surface control method combining with the control integral barrier Lyapunov function technique, is synthesized to achieve the required robust tracking performance with respect to the desired trajectory of lead angle in the presence of uncertain system lag and other uncertainties. In the second step, the desired trajectory of lead angle is generated online to guarantee target interception at the designated impact time under the assumption of ideal autopilot dynamics while not violating the seeker’ field-of-view constraint. The proposed guidance law ensures the seeker’s field-of-view constraint does not be violated in the presence of uncertain system lag and other uncertainties. Numerical simulations are provided to illustrate the effectiveness of the proposed guidance law.

Impact time control guidance law with large impact angle constraint

The problem of impact time control with large impact angle constraint is addressed. The dynamics of impact time error under the biased proportional navigation based impact angle control guidance law is first derived for the case of large impact angle constraint. Based on the impact time error dynamics, an additional control term is designed to drive the impact time error to converge in finite time. The resultant impact time and impact angle control guidance law comprises the biased proportional navigation based impact angle control guidance law and an additional term. The first term is used to achieve zero miss distance with the designated impact angle, and the second term is used to control the impact time. Compared with the existing impact time and impact angle control guidance law, which is shown to be only applicable for the case of small impact angle constraint, its application is not limited by the magnitude of the designated impact angle. Finite time convergence of the closed-loop guidance system under the proposed impact time and impact angle control guidance law is proved. Numerical simulations are performed to verify the effectiveness of the proposed impact time and impact angle control guidance law, especially for case of large impact angle constraint.

Impact time control guidance law with field of view constraint

The problem of Impact Time Control Guidance (ITCG) with field-of-view (FOV) constraint is investigated. The proposed ITCG law is a combination of the well-known Proportional Navigation Guidance (PNG) law and an additional biased term of impact time error, which is defined as the difference between the impact time by PNG and the prescribed one. A rule of the cosine of weighted leading angle in the biased term is used to guarantee that the FOV constraint is not violated during the engagement. Stability of the closed-loop guidance system is proved strictly. Numerical simulation results are presented to demonstrate the effectiveness of the proposed guidance law.