Augmented Proportional Navigation Guidance Research Articles

Robust nonlinear guidance strategies for survival of cooperating unmanned aerial vehicles against pursuing attackers

In this paper, cooperative guidance strategies for the survival of cooperating team of two unmanned aerial vehicles (UAVs) against two attackers are proposed. The guidance schemes are designed under the assumptions that each UAV is being pursued by one attacker without cooperation with other attacker. The guidance schemes are designed to combat attackers guided either by proportional navigation (PN) or augmented PN guidance methodologies. The attackers are lured onto a collision course with each other such that intra-attacker interception is achieved before the target UAVs are captured. Sliding mode control techniques are employed to satisfy the sufficiency conditions for the survival within a finite time. Due to the nonlinear framework used for guidance design, the proposed strategies remain effective even for the engagements with large heading angle errors. Numerical simulations are presented to demonstrate the effectiveness of the proposed guidance strategies under various engagement geometries.

Minimum Effort Pursuit Guidance with Multiple Delayed Engagement Decisions

This paper presents a guidance algorithm for a pursuer in a many-on-many intercept scenario that includes the possibility of dynamic weapon–target (re)assignment based on a simple target priority scheme. Given the probabilities of success of each preceding pursuer against each possible evading target, a guidance algorithm is designed that provides minimum average quadratic effort over all the possible outcomes of the engagements that may take place during the time of flight. The result is a guidance algorithm in the form of a linear combination of (augmented) proportional navigation guidance terms with time-varying weights. Effectively, this is a one-against-many guidance law. An efficient algorithm for the implementation of the guidance law is presented, and numerical simulations based on the nonlinear equations of motion are used to demonstrate its performance.

Survival of Unmanned Aerial Vehicles by Luring Pursuers in Angle Constrained Interception

In this paper, a sliding mode control-based cooperative guidance strategy for a team of two unmanned aerial vehicles (aircraft), which ensures their survival against pursuers, is proposed. The pursuing interceptors are assumed to employ augmented proportional navigation guidance. The cooperating aircraft maneuver in a way to lure their respective pursuers to an impact angle constrained collision. The problem of controlling impact angle is first transformed to that of tracking line-of-sight angle and its rate, and then the same is achieved by enforcing sliding mode on appropriate chosen switching surface. Furthermore, the allocation of aircraft’s lateral accelerations is performed in a way to minimize the instantaneous aerodynamic drag acting on both unmanned aerial vehicles. Numerical simulations are presented to validate the effectiveness of the proposed guidance strategy under different engagement geometries.

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.

A New Guidance Algorithm Against High-Speed Maneuvering Target

This paper aims to propose a new guidance algorithm for intercepting a high-speed maneuvering target, such as a tactical ballistic missile that flies in a quasi-ballistic trajectory. The motivation of this study lies in the fact that the classical proportional navigation guidance (PNG) undergoes the performance degradation under the above engagement scenario due to its intrinsic property. To deal with the issue, an accurate collision course that reflects the motion characteristics of the ballistic target and missile is first analyzed. The desired look angle that leads to achieving the accurate collision course is then determined with the help of a novel time-to-go calculation method. Finally, the proposed guidance law providing the desired look angle is obtained by leveraging the concept of the biased PNG. Since the proposed method is designed to achieve an accurate collision course, it does not lead to unnecessary maneuvering near the target under the engagement scenario. This property is desirable for reserving the operational margin of maneuverability for reacting to unexpected situations during the engagement. It could improve the capturability of the target. Finally, the performance of the proposed method is verified through numerical simulations in a way to compare with the existing methods such as PNG and the augmented PNG (APNG).

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.

Experimental Evaluation of Certain Pursuit and Evasion Schemes for Wheeled Mobile Robots

Pursuit-evasion games involving mobile robots provide an excellent platform to analyze the performance of pursuit and evasion strategies. Pursuit-evasion has received considerable attention from researchers in the past few decades due to its application to a broad spectrum of problems that arise in various domains such as defense research, robotics, computer games, drug delivery, cell biology, etc. Several methods have been introduced in the literature to compute the winning chances of a single pursuer or single evader in a two-player game. Over the past few decades, proportional navigation guidance (PNG) based methods have proved to be quite effective for the purpose of pursuit especially for missile navigation and target tracking. However, a performance comparison of these pursuer-centric strategies against recent evader-centric schemes has not been found in the literature, for wheeled mobile robot applications. With a view to understanding the performance of each of the evasion strategies against various pursuit strategies and vice versa, four different proportional navigation-based pursuit schemes have been evaluated against five evader-centric schemes and vice-versa for non-holonomic wheeled mobile robots. The pursuer′s strategies include three well-known schemes namely, augmented ideal proportional navigation guidance (AIPNG), modified AIPNG, angular acceleration guidance (AAG), and a recently introduced pursuer-centric scheme called anticipated trajectory-based proportional navigation guidance (ATPNG). Evader-centric schemes are classic evasion, random motion, optical-flow based evasion, Apollonius circle based evasion and another recently introduced evasion strategy called anticipated velocity based evasion. The performance of each of the pursuit methods was evaluated against five different evasion methods through hardware implementation. The performance was analyzed in terms of time of interception and the distance traveled by players. The working environment was obstacle-free and the maximum velocity of the pursuer was taken to be greater than that of the evader to conclude the game in finite time. It is concluded that ATPNG performs better than other PNG-based schemes, and the anticipated velocity based evasion scheme performs better than the other evasion schemes.

Minimum-Effort Intercept Angle Guidance with Multiple-Obstacle Avoidance

This paper presents an intercept angle guidance law against moving targets in an environment with several static obstacles. The guidance law is derived based on linearized kinematics model. By minimizing the guidance effort subjected to the conditions where the target is intercepted at the specified impact angle and the obstacles are avoided by specified minimum distances, the basic guidance algorithm is obtained. The special cases of one and two obstacles are separately considered. The proposed guidance law has a form similar to that of augmented proportional navigation guidance with some additional bias terms. These bias terms correspond to the correction for the impact angle error and the generation of the required maneuvers to avoid the obstacles. Finally, numerical simulations are used to illustrate the efficacy of the proposed guidance law.

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.

Fast adaptive guidance against highly maneuvering targets

An adaptive guidance law applicable to a short-range homing missile is investigated against a highly maneuvering target that has the same maximum maneuver acceleration as the missile. In practice, it is difficult to measure the target acceleration with precision and without time delay. The objective of this study is to design a guidance law that can intercept a target within the acceptable miss distance in the presence of unknown target acceleration and guidance command saturation. For this, the main idea of this paper is to apply the fast adaptive control approach to estimating the tangential component of the unknown target acceleration. Moreover, the auxiliary signal is introduced to prevent the presence of the guidance command saturation from destroying the desired adaptive performance. The proposed guidance law can be classified as an augmented proportional navigation guidance (PNG) law with the actual target acceleration component being replaced by its accurate estimate. Simulation results illustrate the satisfactory performance of the proposed guidance law in comparison with other guidance laws with the absence and presence of measurement noise.

Optimality of augmented ideal proportional navigation for maneuvering target interception

The augmented ideal proportional navigation guidance law is derived as the closed-loop nonlinear optimal feedback solution for maneuvering target interception. The derived guidance law minimizes a performance index that is similar to the range-weighted control energy of relative motion. The optimal solution is obtained without any linearization of the engagement kinematics or assumption of a near-collision course condition. A method to implement the optimal guidance solution for a constant-speed pursuer is also proposed.

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.

Capturability of Augmented Pure Proportional Navigation Guidance Against Time-Varying Target Maneuvers

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.

Generalized Model Predictive Static Programming and Angle-Constrained Guidance of Air-to-Ground Missiles

A new generalized model predictive static programming technique is presented for rapidly solving a class of finite-horizon nonlinear optimal control problems with hard terminal constraints. Two key features for its high computational efficiency include one-time backward integration of a small-dimensional weighting matrix dynamics, followed by a static optimization formulation that requires only a static Lagrange multiplier to update the control history. It turns out that under Euler integration and rectangular approximation of finite integrals it is equivalent to the existing model predictive static programming technique. In addition to the benchmark double integrator problem, usefulness of the proposed technique is demonstrated by solving a three-dimensional angle-constrained guidance problem for an air-to-ground missile, which demands that the missile must meet constraints on both azimuth and elevation angles at the impact point in addition to achieving near-zero miss distance, while minimizing the lateral acceleration demand throughout its flight path. Simulation studies include maneuvering ground targets along with a first-order autopilot lag. Comparison studies with classical augmented proportional navigation guidance and modern general explicit guidance lead to the conclusion that the proposed guidance is superior to both and has a larger capture region as well.

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.