Impact Time Control Guidance Law Design

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 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.

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.

In this paper, distributed three‐dimensional (3D) cooperative guidance laws are designed for leader–follower multiple missiles to achieve simultaneous attack at a specified time. The guidance laws are derived from the biased proportional navigation guidance (PNG) law. Two fixed‐time distributed algorithms with time‐varying coefficients are proposed to track the state of the leader under undirected and directed topologies, respectively. The upper bounds of convergence times for the tracking algorithms are obtained. The biased guidance terms of followers are designed to track the leader with the proposed algorithms and the biased guidance term of the leader is designed to achieve specified impact time. Then, an auxiliary function is included into the biased guidance terms to meet the field‐of‐view (FOV) constraints. The leading angles' properties and convergence times under the proposed guidance laws are further analyzed. Numerical simulations are given to verify the effectiveness of the proposed cooperative guidance laws.

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

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

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.

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.

P ROPORTIONAL navigation (PN) is a popular guidance law because of its robustness, simplicity, and ease of implementation. PN guidance law is capable of intercepting both nonmaneuvering and maneuvering targets [1]. PN is also an optimal control effort guidance law in the linearized setting [2]. Modern tactical guidance laws are designed not only to intercept a target but to satisfy other constraints [3] like impact time, impact angle, and other optimality constraints. These guidance laws can often be represented as being comprising of a PN component and other components designed to satisfy other constraints. As these guidance laws require an estimate of the time-to-go, it is important to develop methods to obtain an accurate estimate of the time-to-go for the PNguidance law. An interesting application requiring the estimation of time-to-go is in salvo attack problems [4], in which several missiles, launched at different times, need to achieve interception of the target simultaneously. Using PN guidance law to achieve this task requires an accurate estimation of time-to-go. Impact time, impact angle, and other optimal guidance laws also need information of the time-to-go to compute the guidance command. One of the simplest ways to estimate time-to-go is by computing range over closing velocity (or the negative of the range rate). The range over range rate estimate is accurate only when the closing velocity is constant and the initial heading error is small. Improved methods for time-to-go estimation by solving a linear quadratic control problem is discussed in York and Pastrick [5]. In Tahk et al. [6], a recursive time-to-go method is discussed in which the timeto-go estimates are updated recursively. The time-to-go estimate is updated in every guidance cycle time and a compensationmethod for the time-to-go error is obtained. The time-to-go estimate improves as the engagement proceeds because the guidance law used reduces the heading error. In Sang et al. [7] the commanded guidance history is considered to obtain the time-to-go estimate. The time-to-go estimate in Jeon et al. [4] is obtained as a function of the initial range and heading error. Our time-to-go estimation method also depends on the initial conditions and hence, our results are compared with Jeon et al. [4]. In this Note, an accurate method to obtain a time-to-go estimate of PN guidance law for a stationary target is proposed. The time-to-go for a stationary target is obtained accurately by a simple interpolation. It is shown that from the time-to-go estimate of a particular initial condition, the time-to-go estimate of any other initial condition can be obtained by a simple but elegant time scaling property of the PN guidance law. The time-to-go estimate as a function of the heading error for the particular initial condition is used as the base solution for estimating the time-to-go for other initial conditions. This method also gives estimates for initial conditions with large initial heading errors; even for cases when the missile is launched with a high heading error. Themethod can be used to obtain time-to-go estimates for any initial condition and navigation gain. The time-to-go estimation is extended to constant velocity targets by a simple iterative process. The time-to-go obtained after the initial iteration is exact and need not be computed in every guidance cycle time.

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.

The performance of proportional navigation guidance (PNG) laws in the presence of line-of-sight (LOS) angular rate delay is discussed in this paper. In the missile systems considered, LOS angular rate is provided by optical image processing means, which in practice leads to a computation delay. Because of the measurement lag, our control objective is to ensure that the missile-to-target range can enter a certain region within finite time. The analysis assumes the LOS angular-rate error caused by the delay is bounded by a known constant when the missile-to-target range is outside the prescribed region. Then, by an appropriate choice of the navigation constant, the control target can be guaranteed theoretically. Next, considering the error bound generally is unknown, to facilitate practical implementation, two different algorithms are further proposed to estimate the LOS angular rate error due to the delay. Moreover, based on such estimates, we discuss how to find the minimum prescribed region.

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.

An improved three dimensional adaptive robust guidance law is proposed for the passive homing guidance in which only line-of-sight angular rate can be measured when target maneuvered. The nonlinear control system of missile is designed according to relative motion model of missile and target, which regards coupling and target acceleration as interference. Then a sliding surface and control law is designed based on approximate parallel approaching principle and variable structure control theory. The self-learning ability of RBF neural network is used to approximate the uncertain nonlinear time-varying functions in the control law online. Finally, the network weights adaptive law is proposed according to Lyapunov theory. This method can assure the excellent adaptive ability and robustness of the system. Simulation results indicate that the guidance law is better than traditional proportional navigation and variable structure guidance law in performance.

Implementation of Linear Homing Guidance Law on a Two-Part Homing Missile

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