Desired Impact Time Research Articles

Adaptive Sliding Mode Guidance With Impact Time and Angle Constraints

Based on adaptive sliding mode control method, this paper considers the interception problem to deal with both impact time and angle constraints. The stability and convergence characteristic of proposed guidance law are analyzed. The requirements of the terminal constraints and minimum miss distance can be satisfied. An adaptive law is put forward to adjust the guidance gain. The simulation results indicate that the missile with proposed guidance law can intercept the target successfully with not only desired impact time but also expected impact angle. The interception task can be fulfilled in a satisfactory manner.

Nonsingular PNG-Based Impact Time Control Guidance with Lower Dependence on Time-to-Go Estimate

In a bid to take advantage of natural characteristics of the proportional navigation guidance (PNG) in practical engineering, the PNG-based impact time control guidance (ITCG) continues to be a popular alternative for achieving the desired impact time of a missile. For most such ITCG, the performance is dependent on the accuracy of the time-to-go estimation. Along the lines of the development of PNG-based ITCG in earlier studies, a nonsingular ITCG is proposed on the basis of nonlinear formulations. It is demonstrated that, by theoretical analysis and numerical simulation, this proposed ITCG is shown to be advantageous in certain circumstances. By deriving a novel additional acceleration command, the proposed law is of lower dependence on time-to-go estimate and is capable of eliminating some singularities, leading to wider adjustable range of the desired impact time and better adaptability to more conditions. This research is expected to be supplementary to those presented in the current research literature.

Circular Impact-Time Guidance

A guidance concept to impose a desired impact time is presented and investigated. The guidance concept is based on the geometrical principle that constrains the interceptor to follow a circular trajectory to the target. The concept is extended for moving targets, varying interceptor speed, and a constrained field of view of the interceptor. Implementation is demonstrated for a salvo-attack scenario where, by scheduling the launches of the interceptors, not only the desired impact time but also the desired impact angles are enforced. Application of the guidance concept for standoff tracking of stationary and moving targets is also demonstrated. Performance in various scenarios is investigated via nonlinear simulations.

Terminal sliding mode control based impact time and angle constrained guidance

In this paper, an impact time and angle constrained guidance (ITACG) is proposed based on the nonsingular terminal sliding mode control (NTSMC) theory. First, the guidance law is derived for stationary targets. The proposed ITACG consists of two parts. One part is designed for a missile to intercept a target from the desired impact angle and the other part aims to achieve the desired impact time. Two different terminal sliding mode surfaces are designed so that the missile can satisfy the impact time and angle constraints simultaneously. Corresponding to the designed sliding mode surfaces, two different Lyapunov candidate functions are proposed and analyzed, and stability conditions are obtained. Then, we extend the proposed guidance for constant acceleration targets. The time-to-go estimation method is modified based on the conception of predicted-intercept-point (PIP) with the constant acceleration targets and stability conditions are also revised. Compared with traditional sliding mode control (SMC) based ITACG, the proposed guidance law is a direct online method. It does not need to design the line-of-sight angle curve off-line, nor does it need to switch between impact time constrained guidance and impact angle constrained guidance. In the end, numerical simulation results show that the proposed impact time and angle constrained guidance law has a good performance even though the missile has a constant acceleration. Salvo attack of multi-missiles against one target is shown in the simulation part by applying the proposed guidance law.

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.

Guidance Law Design for Impact Time Attack Against Moving Targets

This paper considers the impact time attack problem against nonmaneuvering targets. A novel impact time guidance law is designed in two-dimensional (2-D) space, which can not only drive the estimated impact time error to zero in finite time, but also make the estimated impact time converge to the actual one. Therefore, the proposed guidance law can accurately achieve the desired impact time with zero miss distance. Then, the results are extended to 3-D impact time guidance design and applied to 3-D simultaneous attack. The effectiveness of the proposed guidance laws is verified through numerical simulations.

Guidance law to control impact angle and time based on optimality of error dynamics

In this work, a new guidance law with a meaningful performance index is designed to satisfy terminal impact angle and impact time constraints based on optimal error dynamics, which can be used for salvo attacks or cooperative missions of multi-missile. The analytical solution of the proposed guidance law is a combination of trajectory shaping guidance law and an additional impact time error feedback term that is proportional to the difference between the desired and the true impact times. Trajectory shaping guidance law aims to achieve the desired terminal impact angle and zero miss distance, whereas the extra term aims to meet the desired impact time. The minimum and maximum feasible impact times that consider the seeker's field-of-view limit, terminal impact angle constraint, and missile's maneuvering acceleration limit are calculated to provide the feasible boundary range of the desired impact time. Numerical simulations of several engagement situations demonstrate the effectiveness of the proposed guidance law in the accuracy of terminal impact angle and impact time.

Cooperative guidance law considering the randomness of the unreliable communication network

The cooperative attack problem of multiple missiles considering the randomness of the unreliable communication network is investigated. Firstly, the stochastic communication network is described by a Bernoulli random model. And the cooperative guidance law with unreliable communication network is proposed, which is composed of the upper consensus algorithm of desired impact time and the local proportional navigation with time-varying navigation gain. Each node of the upper cooperative system uses different update gain to adjust the desired impact time to improve the cooperative performance. Secondly, the mean square stability of the upper cooperative system is analyzed and proved. The explicit necessary and sufficient conditions of the mean square stability are presented for the two-missile cooperative attack system. And the analytic expression of the mean of the cooperative impact time is derived since it influences the attack precision directly and significantly. Thirdly, the effectiveness of the proposed cooperative guidance law with unreliable communication network is verified by simulation. And the influence of the update gain, the communication step, and the mean of link probability on the cooperative attack precision is analyzed.

Sliding-Mode Impact Time Guidance Law Design for Various Target Motions

In this paper, two kinds of sliding-mode guidance laws with impact time constraint are proposed for intercepting various target motions, including nonmaneuvering and maneuvering targets. To achieve the desired impact time, the line-of-sight (LOS) dynamics is controlled to track a novel time-varying LOS profile created by the LOS rate-shaping approach. Unlike the existing LOS rate-shaping approaches that transform the equations of motion with the downrange variable as the independent variable, no such manipulation is necessary in this technique by virtue of a polynomial LOS profile in time. To nullify the LOS tracking error, the terminal sliding-mode technique is used to obtain a finite time convergent guidance law against nonmaneuvering targets, and it is combined with the inertial-delay control to derive an ultimately bounded guidance law against maneuvering targets. Furthermore, fast online determination of the single tuning parameter involved in the LOS profile is provided via a systematic parameter selection methodology. This technique is user/designer-friendly in that it does not involve the error-prone estimates of time-to-go and predictive interception point. Numerical simulations under time-varying velocities and various target maneuvers are conducted to validate the effectiveness and robustness of the proposed guidance law.

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 Angle and Time Control Guidance Under Field-of-View Constraints and Maneuver Limits

This paper proposes a guidance law which considers the constraints of seeker field-of-view (FOV) as well as the requirements on impact angle and time. The proposed guidance law is designed for a constant speed missile against a stationary target. The guidance law consists of two terms of acceleration commands. The first one is to achieve zero-miss distance and the desired impact angle, while the second is to meet the desired impact time. To consider the limits of FOV and lateral maneuver capability, a varying-gain approach is applied on the second term. Reduction of realizable impact times due to these limits is then analyzed by finding the longest course among the feasible ones. The performance of the proposed guidance law is demonstrated by numerical simulation for various engagement conditions.

New Impact Time and Angle Guidance Strategy via Virtual Target Approach

In this paper, a new guidance strategy is proposed for intercepting stationary and constant-velocity moving targets with desired impact time and angle via a virtual target approach, subject to nonlinear engagement kinematics and lateral-acceleration limits. The guidance procedure is divided into two stages by introducing a virtual target. Specifically, for the first stage, the nonsingular terminal sliding-mode guidance law is employed to intercept the virtual target with a specified impact angle in finite time. Furthermore, to achieve the desired impact angle on the real target, the proportional navigation guidance law is used in the second stage to keep the missile traveling with invariant flight-path angle. The impact time and angle on the real target are simultaneously controlled by selecting a proper guidance parameter whose optimal value is obtained via an optimization routine with a small number of iterations. This technique is user/designer-friendly in that it does not involve the time-to-go estimation procedure. In addition, less control energy is required in the overall guidance process. Numerical simulations with comparisons are conducted to validate the effectiveness and feasibility of the proposed guidance strategy in different engagement scenarios.

Guidance law to control impact time constraining the seeker’s field of view?

PurposeThe purpose of this paper is to present a novel guidance law that is able to control the impact time while the seeker’s field of view (FOV) is constrained.Design/methodology/approachThe new guidance law is derived from the framework of Lyapunov stability theory to ensure interception at the desired impact time. A time-varying guidance gain scheme is proposed based on the analysis of the convergence time of impact time error, where finite-time stability theory is used. The circular trajectory assumption is adopted for the derivation of accurate analytical estimation of time-to-go. The seeker’s FOV constraint, along with missile acceleration constraint, is considered during guidance law design, and a switching strategy to satisfy it is designed.FindingsThe proposed guidance law can drive missile to intercept stationary target at the desired impact time, as well as satisfies seeker’s FOV and missile acceleration constraints during engagement. Simulation results show that the proposed guidance law could provide robustness against different engagement scenarios and autopilot lag.Practical implicationsThe presented guidance law lays a foundation for using cooperative strategies, such as simultaneous attack.Originality/valueThis paper presents further study on the impact time control problem considering the seeker’s FOV constraint, which conforms better to reality.

Quad-segment polynomial trajectory guidance for impact-time control of precision-munition strike

Accurate calculation of time to go until impact is an essential component in coordinating multiple precision-guided munitions for a simultaneous strike. Conventional means for calculating time to go contain potential errors, due in part to the trajectory curvatures, and may fall short on the accuracy required to achieve a desired impact time, especially if velocity changes rapidly due to atmospheric drag and gravity. A closed-loop guidance law will be presented in which an optimized, piecewise continuous, and smooth family of polynomial trajectories is parameterized in terms of downrange distance and has a closed-form solution of arc length for improved calculation of time to go.

Impact time guidance for large heading errors using sliding mode control

In this paper, sliding mode control-based impact time guidance laws are proposed. Even for large heading angle errors and negative initial closing speeds, the desired impact time is achieved by enforcing a sliding mode on a switching surface designed by using the concepts of collision course and estimated time-to-go. Unlike existing guidance laws, the proposed guidance strategy achieves impact time successfully even when the estimated interception time is greater than the desired impact time. Simulation results are also presented.

GUIDANCE LAW FOR IMPACT TIME AND ANGLE CONTROL WITH CONTROL COMMAND RESHAPING

In this article, a more generalized form of the impact time and angle control guidance law is proposed based on the linear quadratic optimal control methodology. For the purpose on controlling an additional constraint such as the impact time, we introduce an additional state variable that is defined to be the jerk (acceleration rate). Additionally, in order to provide an additional degree of freedom in choosing the guidance gains, the performance index that minimizes the control energy weighted by an arbitrary order of time-to-go is considered in this work. First, the generalized form of the impact angle control guidance law with an additional term which is used for the impact time control is derived. And then, we also determine the additional term in order to achieve the desired impact time. Through numbers of numerical simulations, we investigate the superiority of the proposed guidance law compared to previous guidance laws. In addition, a salvo attack scenario with multiple missile systems is also demonstrated.

Cooperative Rendezvous Guidance using Sliding Mode Control for Interception of Stationary Targets

In this paper, a cooperative rendezvous guidance, or salvo attack guidance strategy, using impact time constrained guidance law, is proposed for stationary targets. The impact time constrained guidance law is derived using nonlinear engagement dynamics and the concept of sliding mode control. The proposed guidance scheme is based on combining the idea of coordination algorithm and impact time control guidance law. The coordination among all the interceptors are established by using a centralized coordination algorithm. Here, the desired impact time is determined in real-time in such a way as to minimize the total switching surface deviations. In order to calculate the desired impact time, only time-to-go information of all the interceptors are required. Numerical simulation results are presented to validate the proposed guidance schemes.

Homing Guidance Law for Cooperative Attack of Multiple Missiles

Homing Guidance Law for Cooperative Attack of Multiple Missiles