Impact Angle Constraint Research Articles

Adaptive terminal guidance law with impact-angle constraint

ABSTRACTThis paper proposes an adaptive guidance law for attacking a ground target based on motion camouflage strategy. The coefficients of normal and bi-normal feedback guidance law are given according to the relative motion relationship under Frenet frame. Utilizing the coefficients, the motion camouflage proportional guidance law is derived. In order to improve the initial overload characteristic of the missile, an adaptive feedback coefficient is introduced. Then, the adaptive guidance law is applied to a longitudinal plane interception problem with impact-angle constraint. Finally, the validity of this guidance law for air-to-ground missiles is proved by simulations.

Generalized optimal impact-angle-control guidance with terminal acceleration response constraint

To study the optimal impact-angle-control guidance problem with multiple terminal constraints, a generalized optimal impact-angle-control guidance law with terminal acceleration response constraint (GOIACGL-TARC) is proposed. In the deriving, a time-to-go − nth power weighted object function is adopted to derived the GOIACGL-TARC and a general expression of GOIACGL-TARC is presented. Based on the general expression of GOIACGL-TARC, three guidance laws, GOIACGL-TARC1/TACC0/TACC1 are proposed and the inheritance relationship between GOIACGL-TACC0/TACC1/TARC1 and the conventional optimal guidance law with impact angle constraint is demonstrated. Performance analysis of the proposed guidance laws shows that in the case of GOIACGL-TACC0, the terminal acceleration is not zero at n = 0 and only as n > 0, the terminal acceleration converges to zero; in the case of GOIACGL-TACC1 and GOIACGL-TARC1, GOIACGL-TARC1 can guarantee the acceleration response to reach the exactly zero value but GOIACGL-TACC1 cannot, which can only guarantee the acceleration command to reach the exactly zero value. It is pointed out that compared with the biased proportional navigation guidance law, GOIACGL-TARC1 has an outstanding guidance performance in acceleration response, miss distance, and terminal impact angle error.

Sliding mode guidance for impact time and angle constraints

This paper proposes a guidance strategy, which caters to both impact angle and impact time terminal constraints. This guidance scheme is based on switching between impact time and impact angle guidance laws. Unlike the existing impact time guidance laws, the proposed guidance strategy takes into account the curvature of the trajectory due to requirement of impact angle. The guidance law is derived using sliding mode control theory with the switching surface based on impact time error. The interceptor first corrects its course to nullify the impact time error and then aims to achieve interception with desired impact angle. In order to reduce transitions between the two guidance laws, a novel hysteresis loop is introduced in the switching conditions. The guidance law is initially designed for stationary targets, and later it is extended to constant velocity targets using the notion of predicted interception point. In order to validate the efficacy of the proposed guidance strategy, simulation results are presented with constant as well as realistic time-varying speed interceptor models for different engagement scenarios against stationary and constant velocity targets. The performance of the guidance law is evaluated under noisy measurements and the presence of system lag and its performance is compared with other existing guidance laws.

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.

Three‐Dimensional Impact Angle Constrained Guidance Laws with Fixed‐Time Convergence

AbstractIn this paper, three dimensional coupled engagement dynamics are firstly transformed into a state‐space form without decoupling three dimensional engagement dynamics into two mutually orthogonal planes to avoid degrading the performance of the guidance law. Specially, fixed‐time guidance laws are proposed to guarantee that the line‐of‐sight (LOS) angular rates can be steered to zero before the final time of the guidance process at the same time. The exact convergence time can be set beforehand with respect to the LOS rates, and it is independent of initial conditions with respect to the guidance system. Moreover, impact angle constraint is taken into account, and these guidance laws are robust against maneuvering targets by sliding mode techniques. Simulation results validate the effectiveness of the proposed algorithms.

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).

Three-dimensional Robust Guidance Law with Impact Angle Constraint and Compensation of Channels Coupling

To deal with the coupling between channels in the guidance system for a bank-to-turn missile and the uncertainty of the measurement signal, a novel three-dimensional guidance law with impact angle constraint and compensation of channels coupling is proposed based on the robust control theory. Firstly, lineof- sight rate is described through vector description, and the representation of channels coupling is presented. Secondly, a guidance law which fulfills L2 performance index is designed by taking the measurement uncertainties as exogenous disturbance under the nonlinear robust control theory. A novel form of guidance law is obtained after joining the coupling term. Simulation results show that the proposed robust guidance law can guarantee the integrity of guidance information, also satisfy the requirements of guidance precision and impact angle constraint, and more robust than the traditional guidance law.

Three-dimensional cooperative guidance law for multiple missiles with finite-time convergence

For the three-dimensional terminal guidance problem of multiple missiles cooperatively intercepting a maneuvering target, a novel finite-time cooperative guidance law with impact angle constraints is proposed. It is continuous and requires no information on target maneuvers. Firstly, the multiple missiles cooperative guidance model with impact angle constraints is constructed. We subsequently divide the process of cooperative guidance law design into two stages. In the first stage, based on the adaptive super-twisting algorithm and integral sliding mode, a new finite-time consensus protocol, i.e., the acceleration command on the line-of-sight direction, is designed to guarantee that all missiles reach the maneuvering target simultaneously. In the second stage, a new adaptive nonsingular fast terminal sliding mode control law, i.e., the acceleration command on the normal direction of the line-of-sight, is developed to ensure the finite-time convergence of the line-of-sight angular rate and line-of-sight angle between individual missile and the target. Furthermore, the detailed finite-time stability analysis is given based on the Lyapunov theory. Finally, numerical simulations demonstrate the effectiveness of the proposed cooperative guidance law.

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.

Time-varying sliding mode guidance scheme for maneuvering target interception with impact angle constraint

In this paper, a guidance scheme for impact angle control against maneuvering targets with unknown target acceleration is proposed. In this scheme, the unknown target acceleration is estimated via a linear extended state observer; a novel time-varying global slide mode control technique is presented to eliminate the reaching phase and enforce a desired impact angle exactly at the time of interception with finite-time convergence, good robustness, high precision and smooth guidance command. Moreover, feasible guidance logics are developed to achieve all-aspect interception with the tolerance of large initial heading errors. Numerical simulations in various scenarios are performed to verify the performance of the proposed guidance scheme.

Adaptive backstepping impact angle control with autopilot dynamics and acceleration saturation consideration

SummaryThis paper presents a robust impact angle constraint guidance law for maneuvering target interception in the presence of autopilot dynamics and input saturation. The presented guidance law is designed on the basis of a combination of adaptive backstepping control technique and higher‐order sliding mode differentiator. Different from existing impact angle constraint guidance law using sliding mode control, the line‐of‐sight angular rate and impact angle tracking error are regulated by two different virtual control laws. Because the future course of action of the target, an independent entity, cannot be predicted beforehand, adaptive laws are introduced in guidance law derivation for disturbance rejection. Unlike dynamic surface control approach, higher‐order sliding mode differentiator is adopted here as an alternative way to obtain the derivatives of the virtual control laws, thus leading to the exact tracking performance of backstepping control. Detailed stability analysis shows that both the line‐of‐sight angular rate and impact angle error can be stabilized in a small region around zero asymptotically. Simulation results explicitly show that accurate interception is achieved with a wide range of impact angles. Copyright © 2017 John Wiley & Sons, Ltd.

Two-Phase Optimal Guidance Law considering Impact Angle Constraint with Bearings-Only Measurements

The implementation of advanced guidance laws with bearings-only measurements requires estimation of the range information. To improve estimation accuracy and satisfy the impact angle constraint, this paper proposes a two-phase optimal guidance law consisting of an observing phase and an attacking phase. In the observing phase, the determinant of Fisher information matrix is maximized to achieve the optimal observability and a suboptimal solution expressed by leading angle is derived analytically. Then, a terminal sliding-mode guidance law is designed to track the desired leading angle. In the followed attacking phase, an optimal guidance law is integrated with a switching term to satisfy both the impact angle constraint and the field-of-view constraint. Finally, comparison studies of the proposed guidance law and a traditional optimal guidance law are conducted on stationary targets and maneuvering targets cases. Simulation results demonstrate that the proposed guidance law is able to improve the range observability and achieve better terminal performances including impact angle accuracy and miss distance.

Time-to-go Polynomial Guidance with Impact Angle Constraint for Missiles of Time-Varying Velocity

Time-to-go Polynomial Guidance with Impact Angle Constraint for Missiles of Time-Varying Velocity

Design of sliding mode guidance law with dynamic delay and impact angle constraint

A sliding mode guidance law with dynamic delay and impact angle constraints is designed for the relative motion between the missile and the target in the intercepting plane. First of all, the missile’s first order dynamic delay is involved into the system model to design the guidance law based on sliding mode variable dynamic method. Secondly, the target’s maneuvering is taken as the system disturbance, and a non-homogeneous disturbance observer is applied to estimate such maneuvering in finite time rapidly, which, through dynamic compensation, realizes the missiles precision attack to targets of different maneuvering at a desired line-of-sight (LOS) angle. Finally, numerical simulations are performed to demonstrate the effectiveness of the designed guidance law.

An integrated guidance and control approach in three-dimensional space for hypersonic missile constrained by impact angles

A new robust three-dimensional integrated guidance and control (3D-IGC) approach is investigated for sliding-to-turn (STT) hypersonic missile, which encounters high uncertainties and strict impact angle constraints. First, a nonlinear state-space model with more generality is established facing to the design of 3D-IGC law. With regard to the as-built nonlinear system, a robust dynamic inversion control (RDIC) approach is proposed to overcome the robustness deficiency of traditional DIC, and then it is applied to construct the basic 3D-IGC law combining with backstepping method. In order to avoid the problems of “explosion of terms” and high-frequency chattering, an improved 3D-IGC law is further proposed by introducing dynamic surface control and continuous approximation approaches. From the computer simulation on a hypersonic missile, the proposed 3D-IGC law not only guarantees the stable flight, but also presents the precise control on terminal locations and impact angles. Moreover, it possesses smooth control output and strong robustness.

Strictly convergent nonsingular terminal sliding mode guidance law with impact angle constraints

In this paper, we develop a strictly convergent nonsingular terminal sliding mode guidance law for missiles with impact angle constraints. A novel nonsingular terminal sliding mode (NNTSM) control scheme is first proposed to improve the effectiveness of conventional terminal sliding mode in the whole phase plane, where the time taken to reach both the sliding surface and equilibrium point is guaranteed to be finite time. The proposed NNTSM control scheme is then applied to the guidance law of missiles with impact angle constraints, where extended state observer is designed to estimate the target acceleration. Simulation results are presented to validate the proposed guidance law.

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.

Trajectory reshaping based guidance with impact time and angle constraints

This study presents a novel impact time and angle constrained guidance law for homing missiles. The guidance law is first developed with the prior-assumption of a stationary target, which is followed by the practical extension to a maneuvering target scenario. To derive the closed-form guidance law, the trajectory reshaping technique is utilized and it results in defining a specific polynomial function with two unknown coefficients. These coefficients are determined to satisfy the impact time and angle constraints as well as the zero miss distance. Furthermore, the proposed guidance law has three additional guidance gains as design parameters which make it possible to adjust the guided trajectory according to the operational conditions and missile’s capability. Numerical simulations are presented to validate the effectiveness of the proposed guidance 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.