Augmented Proportional Navigation Guidance Law Research Articles

Variable Coefficient Terminal-Phase Guidance Design for Deep Space High-Speed Impact

Asteroid impact poses a major threat to human survival. High-speed direct impact is a feasible and effective means to change the orbit of an asteroid. This paper takes Bennu, a potentially hazardous asteroid , as object to design the terminal guidance law of deep space high-speed impact. In view of the characteristics of high relative speed and high impact accuracy, the acceleration command is derived based on the Augmented Proportional Navigation Guidance law (APNG), considering the acceleration of the target. Moreover, the proportional coefficient is designed as a function of the relative distance to meet both the requirements of reducing fuel consumption and improving impact accuracy. An ignition strategy is designed to convert the continuous command into impulse command, without the need to give maneuvering time in advance. The simulation results show the effectiveness of the proposed algorithm. The miss distance constraint is satisfied, and the ignition times and fuel consumption are less than those of the constant proportional coefficient algorithm.

Cooperative guidance law for active aircraft defense with intercept angle constraint

In this paper, the three-body engagement scenario is considered where a target aircraft fires a defender missile to intercept the attacker missile. A cooperative guidance law with the intercept angle constraint for both of the defender missile and target has been presented. With the assumption that the attacker missile uses augmented proportional navigation guidance law, the nonlinear relative motion model of target-attacker-defender engagement is built. Considering the requirement of miss distance and satisfying the intercept angle constraint, the function index is established. The cooperative guidance law is derived based on optimal control theory. Moreover, given initial launch condition, the feasible intercept angle region of defender is analyzed, considering the limited maneuverability of defender and target and the intercept time constraint which means the attacker must be intercepted by the defender prior to hitting the target. Similarly, the feasible launch region of defender is obtained with the given designated intercept angle, variable overload of defender and target, and intercept time constraint. The simulation results further demonstrate that within the feasible region of designated intercept angle and launching condition, the defender can intercept the attacker with designated intercept angle successfully despite of the limited maneuverability. Compared with conventional uncooperative situation, the target-defender cooperation could significantly reduce the maneuverability requirements for the defender.

A robust three-dimensional cooperative guidance law against maneuvering target

This paper proposes a robust three-dimensional cooperative guidance law (RTCGL) against a maneuvering target. When some missiles are intercepted during the engagement, this RTCGL integrated with a local filtering algorithm can ensure that the rest missiles hit the maneuvering target simultaneously. The pitch acceleration command is designed based on an augmented proportional navigation guidance law and can make the missile’s trajectory fall into its yaw plane. Then the three-dimensional cooperative problem is converted into a planar one. The yaw acceleration command consists of a guidance component for homing and a coordination component for simultaneous arrival. Numerical simulation results are presented to verify the effectiveness of the cooperative guidance law.

A Novel Recurrent Convolutional Neural Network-Based Estimation Method for Switching Guidance Law

This paper presents a recurrent convolutional neural network-based estimation method of guidance parameters of the pursuer under augmented proportional navigation (APN) guidance law with a time-varying switching navigation ratio. For the highly maneuvering pursuit-evasion process, realistic factors in the guidance law estimation are considered, such as the pursuer's estimation error and delay of the evader's acceleration in the APN guidance law. In view of the enormous measurement data, time dependency, transient change and unknown factors' disturbance in switching guidance law estimation, a novel neural network structure is built. 1-D CNN layer is used to extract features from enormous data obtained by the multiple previous measurements. The features extracted are processed by the recurrent cell to exploit the time dependency and eliminate the error caused by unknown factors. The result of ablation test shows the proposed RCNN's improved performance over single CNN or RNN. Compared to the multiple model guidance law estimation method, the proposed method can simplify the design of guidance law estimation system and reduce calculation load. The estimation result for switching guidance law shows the proposed method has higher accuracy and faster convergence rate than traditional interactive multiple model methods.

Novel augmented proportional navigation guidance law for mid-range autonomous rendezvous

In this paper, a novel augmented proportional navigation (APN) guidance law is proposed for the mid-range autonomous rendezvous. The line-of-sight (LOS) rotation coordinate system is used, which can decouple the three-dimensional relative motion between the chaser and target into the relative motion in the engagement plane and the rotation of this plane. The APN guidance law is consisted of two parts. The first one is a novel nonsingular terminal sliding mode control (NTSMC) along LOS to drive the relative distance and approaching speed to the desired values in finite time. The second one is the modified true proportional navigation (TPN) guidance law perpendicular to LOS to control the LOS rate in a certain range. It has been proven that, even when there are disturbances and uncertainties along and perpendicular to LOS, the proposed APN can guarantee the finite time convergence of the relative distance and approaching speed and limit the LOS rate within a certain acceptable range. Hence, the mid-range autonomous rendezvous can be perfectly realized. The new theoretical findings are demonstrated by numerical simulation results.

A generalized design method for three-dimensional guidance laws

The true proportional navigation guidance law, the augmented proportional navigation guidance law, or the adaptive sliding-mode guidance law, is designed based on the planar target-to-missile relative motion dynamics. By a proper construction of a nonlinear Lyapunov function for the line-of-sight angular rates in the three-dimensional guidance dynamics, it is shown that the three guidance laws mentioned above are able to ensure the asymptotic convergence of the angular rates as they are directly applied to the three-dimensional guidance environment. Furthermore, considering the missile autopilot dynamics as a first-order lag, we design three-dimensional nonlinear guidance laws by using the backstepping technique for three cases: (1) the target does not maneuver; (2) the information of target acceleration can be acquired; and (3) the target acceleration is not available but its bound is known a priori. In the first step of the backstepping design of the control law, there is no need to cancel the nonlinear coupling terms in the three-dimensional guidance dynamics in such way that the final expressions of the proposed guidance laws are significantly simplified. Thus, the proposed nonlinear Lyapunov function for the line-of-sight angular rates is a generalized function for designing three-dimensional guidance laws. Simulation results of a missile interception mission show that the proposed guidance laws are highly effective.

Stochastic fast smooth second-order sliding modes terminal guidance law design

Aiming at handling the track imprecision caused by inertial lag, model uncertainties and atmospheric environment disturbances, as well as stochastic noises, a terminal guidance law based on stochastic fast smooth second-order sliding modes control theory is proposed. This paper considers targets performing evasive maneuvers and develops a high-order sliding mode observer. A concept of finite-time mean-square practical convergence, considering the non-equilibrium additive noise of the guidance system, is presented. And according to this concept, the finite-time convergent guidance law is deduced. The feasibility of the new guidance law is exemplified through computer simulations and the guidance performance is compared with augmented proportional navigation guidance law, sliding mode guidance law and nonsingular terminal sliding mode guidance law.

Research on Extra-Atmospheric Aircraft Modeling and Control Based on Maneuvering Target

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.

All-Aspect Three-Dimensional Guidance Law Based on Feedback Linearization

A nonlinear three-dimensional all-aspect guidance problem of an acceleration-constrained missile is dealt with. The feedback linearization method is applied to derive a three-dimensional guidance law, which enables the missile to intercept a maneuvering target under all-aspect initial boresight and heading conditions. The new guidance law is characterized by convergence to a collision course. It is shown that the proposed guidance law enables interception where the proportional navigation and the augmented proportional navigation guidance laws fail. Simulations demonstrate that the proposed law has the capability to perform several interception trials.

Research on the Improved Proportional Navigation Guidance Law Using CADET

This paper mainly talks about the Covariance Analysis Describing Equation Technique (CADET), which is used for the improved proportional guidance law. Firstly, the principle of this method is introduced. Secondly, the related conclusion and validation of Gaussian assumption is analyzed. Thirdly, an improved augmented proportional navigation guidance law (APNG) is analyzed by this method. Finally, the higher guidance accuracy of this improved APNG is demonstrated by stimulated experiments.

Robust Estimation for Optimal Guidance Laws

The aim of the paper is to present an alternative filtering method for the Augmented Proportional Navigation Guidance (APNG). Two main aspects distinguish the proposed filtering technique with respect to the ones used in the existing APNG laws. The first is the fact that by contrast with the classical Kalman filtering, some state-dependent noises in the measurements are taken into account. The second aspect is the use of a mixed filter for models with state-dependent noise which combines the benefits of the and Kalman type filtering. The aim is to cover the situations when the unknown target meneuvers are generated both by stochastic or by deterministic exogenous inputs. A case study together with comparative analysis of the numerical results illustrate and validate the proposed approach.

A novel robust proportional navigation guidance law design for missile considering autopilot dynamic

In this paper, a novel robust proportional navigation guidance (RPNG) law is derived for missiles by integrating sliding mode control theory and proportional navigation guidance law in order to achieve robustness against target accelerations. A first-order autopilot dynamic is taken into account in the state space equations of the nonlinear missile-target engagement dynamic. The robustness of the designed guidance law against external disturbances is proved by the second method of Lyapunov. Some coefficients that appear in the proposed RPNG law are obtained using the genetic algorithm. Performance of the new designed guidance law is compared with the well known augmented proportional navigation guidance (APNG) law. Considering different types of target accelerations and several scenarios, numerical simulations are presented. Simulation results show that the proposed guidance law has much better robustness in comparison with the APNG law. Moreover, it is simple and easy to implement from the point of view of practical applications.

A Novel Nonlinear Robust Guidance Law Design Based On SDRE Technique

A nonlinear robust guidance law is designed for missiles against a maneuvering target by incorporating sliding-mode and optimal control theories based on the state dependent Riccati equation (SDRE) to achieve robustness against target accelerations. The guidance law is derived based on three-dimensional nonlinear engagement kinematics and its robustness against disturbances is proved by the second method of Lyapunov. A new switching surface is considered in the sliding-mode control design. The proposed guidance law requires the maximum value of the target maneuver, and therefore opposed to the conventional augmented proportional navigation guidance (APNG) law, complete information about the target maneuver is not necessary, and hence it is simple to implement in practical applications. Considering different types of target maneuvers, several scenario simulations are performed. Simulation results confirm that the proposed guidance law has much better robustness, faster convergence, and smaller final time and control effort in comparison to the sliding-mode guidance (SMG) and APNG laws.

Applying a novel extended Kalman filter to missile–target interception with APN guidance law: A benchmark case study

This paper considers the estimation of the target acceleration with unknown dynamics along with other states of a benchmark example of a nonlinear 2D missile–target engagement system in presence of model uncertainties and measurement noises. The objective is to implement the augmented proportional navigation (APN) guidance law for the missile–target interception to minimize the distance between the missile and the target. The estimated target acceleration can be treated as an unknown input to the nonlinear 2D missile–target engagement system. A novel analytical recursive approach referred to as extended Kalman filter with unknown inputs without direct feedthrough (EKF-UI-WDF) is derived with the weighted least squares estimation for an extended state vector including states and unknown inputs which can be any type of signals without prior information. By applying the proposed EKF-UI-WDF approach to a 2D missile–target interception control system, simulation results demonstrate that this approach is capable of (i) estimating the states and unknown input (target acceleration) well, and (ii) achieving more reasonable interception performance comparing with the traditional extended Kalman filter (EKF) approach.

Acceleration-Compensated Zero-Effort-Miss Guidance Law

This paper shows that true proportional navigation guidance can be derived directly from a zero-effort-miss guidance law, and explains why the augmented proportional navigation guidance law does not take full advantage of the knowledge of target acceleration. A simple acceleration-compensated zero-effortmiss guidance law has been derived, which does take advantage of the knowledge of target acceleration. This paper also demonstrates that this new guidance law will outperform proportional navigation guidance and augmented proportional navigation guidance, even when the target acceleration is not perfectly known.

Smooth second-order sliding modes: Missile guidance application

A new smooth second-order sliding mode control is proposed and proved using homogeneity-based technique for a system driven by sufficiently smooth uncertain disturbances. The main target application of this technique—the missile-interceptor guidance system against targets performing evasive maneuvers is considered. The smooth second-order sliding mode control-based guidance law is designed and compared with augmented proportional navigation guidance law via computer simulations of a guided missile intercepting a maneuvering ballistic target.

Performance evaluation of two fuzzy-logic-based homing guidance schemes

Homing guidance schemes based on fuzzy logic have been developed for a planar engagement model, with randomly jinking target maneuver and line-of-sight (LOS) rate measurement corrupted with glint noise. Two versions of fuzzy guidance schemes have been proposed, the first one using information required for proportional navigation (PN) and the second one using the information required for augmented PN (APN). The performance of the two fuzzy guidance schemes, in terms of commanded acceleration profiles and the values of the terminal miss distance, have been compared with PN and APN, respectively. It is observed that the fuzzy guidance schemes are able to match closely the performance of PN and APN guidance laws, and in cases where the measurements are noisy and the estimates are inaccurate, the fuzzy guidance schemes are shown to perform better than PN and APN.