Three‐dimensional cooperative guidance for simultaneous attack with specified impact time based on fixed‐time convergence

A cooperative guidance law with guaranteed convergence is proposed in this paper. First, the guidance law is derived based on the biased proportional navigation guidance (PNG) approach by applying the finite-time stability theory. Then, an auxiliary function is designed and inserted into the biased term to address the singularity issue. The biased term makes that the relative time-to-go errors decrease to zero before interception. After the convergence of errors, the guidance command converts to the PNG law to achieve the salvo attack. Furthermore, the closed-loop stability and the explicit settling time of the consensus error are discussed in the framework of Lyapunov analysis. The proposed design guarantees that the times-to-go of missile group can reach consensus before interception under different initial conditions. Thus, the proposed design is adaptive with no need to reselect the parameters for different scenarios. Finally, numerical simulations are provided to verify the designed cooperative guidance law.KeywordsGuidance lawFinite-time convergenceCommunication topologyMultiple missiles

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.

In this work, design of three-dimensional (3D) proportional navigation guidance law based on input-output linearization (IOL) for tactical missiles is proposed. For the three-dimensional nonlinear missile-target engagement dynamics, the line-of-sight (LOS) rates in pitch and yaw planes are taken as outputs and the IOL theory is used to derive the guidance laws without ignoring the cross-coupling terms. Simulations are carried out by considering maneuvering target, and the results are presented to showcase the efficacy of the proposed design. Further, comparison of the performance of the proposed guidance law with augmented proportional navigation guidance(APNG) laws is carried out and the related results are presented. Lastly, implementation issues of the proposed guidance law are discussed.

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

A novel biased proportional navigation guidance law for close approach phase

The extra-atmospheric aircraft model is established, and then the control system is designed. The control system consist of attitude control system and orbit control system, the attitude control system used PID controller and the orbit control system used augmented proportional navigation method. The traditional Proportional Navigation (PN) guidance law has higher accuracy. But for highly maneuvering targets, the accuracy of traditional PN guidance law is still not enough. An Augmented Proportional Navigation (APN) guidance law is designed, an acceleration compensation of the target is introduced on the basis of PN guidance law to overcome the effect of the acceleration on the guidance accuracy. And the engine control method is designed based on the fixed engine thrust. Simulation results indicated that, for homing against maneuverable targets, the APN guidance law is better than the PN guidance law in the following aspects: guidance accuracy is higher, miss distance is lower, interception time is shorter. And the new guidance law provides significant performance improvements over the commonly used classical proportional navigation law.

In this paper, a suboptimal guidance law with the terminal constraints on impact angle, acceleration, and time-derivative of acceleration (jerk) is presented. The proposed homing guidance problem is an over-determined problem, i.e., the number of constraints is much larger than the order of system. Since it is difficult to solve the problem by using the conventional optimal control theory, we newly introduce the control input which consists of an additional feed-forward command and the optimal feedback command. The additional feed-forward command is defined as a polynomial function of time-to-go with two degree-of-freedoms. Here, the coefficients of the function in the feed-forward command are determined to satisfy the constraints on terminal acceleration and jerk. The optimal feedback command in consideration of a feed-forward command is determined by Schwartz inequality. The guidance command obtained from the proposed scheme shows a similar form of the biased proportional navigation (BPN) guidance obtained by the optimal control theory. However, the proposed guidance law is less sensitive to the time-to-go estimation error than the BPN law, and it can be easily implemented in the real system. Furthermore, since the coefficients of time-to-go in the feed-forward command remain as design parameters, the proposed guidance law provides more flexibility in application aspect such as trajectory shaping. The characteristics of the proposed guidance law is studied and its performance is also evaluated through numerical simulation.

In this paper, the three-dimensional terminal guidance problem of a missile intercepting a maneuvering target is studied. Augmented proportional navigation (PN) guidance laws based on Lyapunov stability theory are presented. Augmented terms are target accelerations such that proposed guidance laws have the ability to track the target maneuver. But, target accelerations cannot be accurately obtained in practice. To solve this problem, the nonlinear disturbance observer (NDOB) technology is introduced to estimate target accelerations. Estimated target accelerations will be employed as compensation terms in the proposed augmented PN guidance laws. Composite guidance laws combining augmented PN guidance laws with NDOB are proposed. Finally, simulation comparison results are provided to demonstrate the effectiveness of the presented guidance laws.

This paper proposes a variation of the pure proportional navigation guidance law, called augmented pure proportional navigation, to account for target maneuvers, in a realistic nonlinear engagement geometry, and presents its capturability analysis. These results are in contrast to most work in the literature on augmented proportional navigation laws that consider a linearized geometry imposed upon the true proportional navigation guidance law. Because pure proportional navigation guidance law is closer to a realistic implementation of proportional navigation than true proportional navigation law, and any engagement process is predominantly nonlinear, the results obtained in this paper are more realistic than any available in the literature. Sufficient conditions on speed ratio, navigation gain, and augmentation parameter for capturability, and boundedness of lateral acceleration, against targets executing piecewise continuous maneuvers with time, are obtained. Further, based on a priori knowledge of the maximum maneuver capability of the target, a significant simplification of the guidance law is proposed in this paper. The proposed guidance law is also shown to require a shorter time of interception than standard pure proportional navigation and augmented proportional navigation. To remove chattering in the interceptor maneuver at the end phase of the engagement, a hybrid guidance law using augmented pure proportional navigation and pure proportional navigation is also proposed. Finally, the guaranteed capture zones of standard and augmented pure proportional navigation guidance laws against maneuvering targets are analyzed and compared in the normalized relative velocity space. It is shown that the guaranteed capture zone expands significantly when augmented pure proportional navigation is used instead of pure proportional navigation. Simulation results are given to support the theoretical findings.

Distributed cooperative guidance law for multiple missiles with input delay and topology switching

This chapter proposes a new trajectory shaping guidance law for impact time control and impact angle control with seeker’s field-of-view (FOV) limit. The proposed guidance law is derived by using the concept of biased PNG (BPNG). The guidance law developed leverages a nonlinear function to ensure the boundedness of velocity lead angle to cater for seeker’s FOV constraint. The finite-time convergence of the impact time error and impact angle error is theoretically analyzed. By investigating the optimality of the biased command, the physical meaning of the proposed trajectory shaping guidance law is revealed to support practical applications. Numerical simulations clearly demonstrate the effectiveness of the proposed formulation.

By combining the Lyapunov stability theorem with the proportional navigation guidance (PNG) law, a novel guidance law which can control the impact time is proposed. This paper treats the impact time control problem as the impact time error regulation problem. The impact time error is defined by the difference between the desired time and the estimated time-to-go.The Lyapunov candidate function is introduced concerning the impact time error, and the control parameter is proposed to satisfy the Lyapunov stability theorem. The impact time error will go to zero before the desired time, and the singularity issue of the acceleration command has been analyzed. Numerical simulations are carried out to prove the effectiveness of the proposed guidance law.

A collision avoidance algorithm for unmanned aerial vehicles (UAVs) based on the conventional proportional navigation (PN) guidance law is investigated. The proportional navigation guidance law being applied to a wide range of missile guidance problems is tailored to the collision avoidance of UAVs. This can be accomplished by guiding the relative velocity vector of the aircraft to a vector connecting the current aircraft position to the safety boundary of the target aircraft. Stability of the proposed algorithm is also studied using the circle criterion. The stability condition can be established by choosing the navigation coefficient within a certain bound. The guidance law is extended to 3-dimensional maneuver problems. Inherent simplicity and robustness of the PN guidance law provides satisfactory collision avoidance performance with different initial conditions.

Adaptive Impact Time Control Via Look-Angle Shaping Under Varying Velocity

In this paper realistic Six Degrees of Freedom simulation of a pursuer evader engagement during terminal guidance has been carried out using a class of nonlinear guidance law based on Feedback Linearization. This guidance law has been developed as a regulator problem based on nonlinear control theory where line of sight rate derivative along both yaw and pitch plane are made zero by taking line of sight angle and line of sight rate as output feedback. The line of sight angles and rates have been computed from noisy seeker measurements through a nonlinear state observer. The available seeker measurements are pursuer-evader relative range, relative rage rate, gimbal angles and line of sight rates along yaw and pitch plane in seeker inner gimbal frame. The present guidance law has been validated in presence of realistic non Gaussian and correlated seeker measurement noise, estimator, autopilot lag and highly time varying pursuer velocity during engagement. It is demonstrated through realistic Six Degrees of Freedom pursuer-evader engagement simulation in the presence of above constraints in a practical environment that the proposed guidance law is a viable option for intercepting maneuvering target with high heading error over the well known proportional navigation guidance law. This specific type of guidance law being not available in published literature, is claimed as quiet novel.