Classical Proportional Navigation Research Articles

Improvements in Classical Proportional Navigation Guidance Using Fuzzy Logic

The performance of classical Proportional Navigation guidance is limited against highly maneuvering targets and in presence of measurements noise resulting into large miss distances and lower hit probability. Also, the advanced Augmented PN guidance technique requires target state estimation. In this paper, fuzzy logic has been used to implement PN guidance and Membership Functions of fuzzy logic has been tuned using genetic algorithm. The proposed Fuzzy Based PN (FBPN) guidance gives superior performance than PN and APN in terms of lower miss distance, higher hit ratio and better ability to handle measurement noise at all target attack aspects. Deterministic simulations have proved the superior performance and robustness of proposed scheme for various conditions such as step target maneuver upto 9g, weaving maneuver and presence of measurement noise. Further, Monte Carlo simulations have proved that proposed scheme enhances interception performance in realistic scenarios by improving the hit ratio upto 48% and rms miss distance upto 41%. Limitations of APN scheme in terms of target state estimation is also mitigated in the proposed guidance scheme. Finally, global asymptotic stability of fuzzy homing guidance loop is proved using circle criterion.

Cooperative augmented proportional navigation and guidance for proximity to uncooperative space targets

Navigation and proximity to non-cooperative targets have garnered the interest of both academia and industry. This paper proposes a new space operation concept that would enable two CubeSats equipped with only optical sensor to achieve autonomous and robust proximity with uncooperative satellites. This is a novel strategy for distributed spacecraft missions and applications.Because optical sensors are lightweight and therefore reduce reliance on external measurement sources, the case for their use is compelling. Designing robust guidance and control algorithm is the greatest challenge for optical sensors because relative distance information is unavailable, whereas range information is required for safe proximity. The purpose of this paper is to propose a novel concept in which two CubeSats cooperate and share angle measurement data to approach uncooperative targets despite their maneuverability.This paper introduces a new guidance scheme for proximity operations, namely cooperative augmented proportional navigation (CAPN). Modern control law is applied along line-of-sight (LOS) while classical proportional navigation is applied in the normal direction of LOS. By measuring only elevation and azimuth angles between each chaser and the target, the algorithm can account for a maneuvering target. The cooperative scheme offers estimation-based distance measurement, which enhances the observability of angle-only navigation.Target’s maneuverability and different control parameter settings have been considered in simulation scenarios. The degree of observability (DOO) is then introduced as the quantitative observability analysis metric to validate the effectiveness of the guidance scheme and precision of the estimation. The results of simulations have demonstrated that the CAPN proposed in this paper is capable of completing challenging proximity missions.

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).

Intercepting Higher-Speed Targets Using Generalized Relative Biased Proportional Navigation

To intercept a higher-speed target in the terminal guidance phase, this paper proposes a generalized relative biased proportional navigation (BPN) law. In order to enlarge the capture domain of the classical proportional navigation (PN) law and make full use of the maneuverability of a missile, the paper designs time-varying navigation coefficients; thus the modified PN guidance law integrates the advantages of the PN guidance law with those of the retro-PN guidance law. In order to intercept high-speed targets with impact angle constraints, the relative BPN law is introduced, and the impact angle is achieved by controlling the relative flight-path angle. In order to improve the performance of the guidance law for intercepting higher-speed maneuvering targets, some compensation measures are designed for guidance commands. Extensive simulations are conducted to verify the design features of the proportional navigation law.

Nonlinear Augmented Proportional Navigation for Midrange Rendezvous Guidance and Performance Assessment

Guidance systems are important to autonomous rendezvous with uncooperative targets such as an active debris removal (ADR) mission. A novel guidance frame is established in rotating line-of-sight (LOS) coordinates, which resolves the coupling effect between pitch and yaw planes in a general 3D scenario. The guidance law is named augmented proportional navigation (APN) by applying nonlinear control along LOS and classical proportional navigation normal to LOS. As saving time is a critical factor in space rescue and on-orbit service, the finite time convergence APN (FTCAPN) is further proposed which proves to possess convergence and high robustness. This paper builds on previous efforts in polynomial chaos expansion (PCE) to develop an efficient analysis technique for guidance algorithms. A large scope of uncertainty sources are considered to make state evaluation trustworthy and provide precise prediction of trajectory bias. The simulation results show that the accuracy of the proposed method is compatible with Monte Carlo simulation which requires extensive computational effort.

Linear Quadratic Optimal Control-Based Missile Guidance Law With Obstacle Avoidance

Two missile guidance algorithms are proposed for the intercept and for the rendezvous of a maneuvering target, while avoiding a static obstacle by a specified avoidance distance. The guidance algorithms are derived as solutions of a linear quadratic optimal control problem and they are expressed as formulas reminiscent of the classical (augmented) proportional navigation type guidance laws. These formulas include correction terms that are responsible for obstacle avoidance and are parameterized by the minimum avoidance distance. Simulation results are used to demonstrate the performance of the two algorithms.

Adaptive three-dimensional guidance of flying vehicle at fixed point with specified approach direction

The problem of steering a flying vehicle to a fixed point with a specified orientation of the terminal velocity is studied. The method is based on a modification of the well-known proportional navigation method in which the navigation parameter relating the angular rotation velocities of the line of sight and the velocity vector is chosen based on the current characteristics of the trajectory. The adaptivity of the method is ensured by the periodic correction of this parameter. For three-dimensional (3D) trajectories, a combination of two motions—(a) guidance in the plane formed by the given direction of the terminal velocity and the current state of the vehicle (in this plane, the specified terminal velocity direction is ensured using the modified proportional navigation) and (b) control in the orthogonal plane based on the classical proportional navigation with a fixed navigation parameter to minimize the rotation of the guidance plane. The proposed method does not require onboard trajectory prediction but forms the control using the current navigation data. Examples of various types of 3D trajectories of a gliding vehicle with a high lift-to-drag ratio are discussed.

Epipole-Based Guidance for an Autonomous Glider

Two strategies based on epipolar geometry are proposed to guide an aerial vehicle to a desired position defined by a reference image. The starting point to design the strategies is the engagement geometry of two images: the online image provided by the onboard camera and the reference image. A full closed-loop system is derived combining the concept of classical proportional navigation, with the input–output nonlinear control technique, and the tracking of epipolar references. The main contribution of this paper is the definition of a guidance algorithm based on the partial linearization of the full closed-loop system by means of pure image-based information: the epipolar geometry across two views. The proposed formulation avoids the requirement of estimating the range between the current and target positions. Conditions for stability are established for both strategies. Simulation experiments show the interception of the target position by the aerial vehicle and, additionally, a simple attitude control.

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.

Study of Proportional Guidance Trajectory based on Guiding Principle

In missile guidance systems, classical proportional navigation law has been used most widely. But with the increasing of the maneuverability of the targets, the classical proportional navigation guidance law has been unable to meet the requirements of people on the ballistic parameters. So this paper will further study the algorithm error of guidance law. Based on the previous theoretical results and the working principle of aircraft in the homing guidance system, this paper studies a guidance trajectory guidance principle which based on the ratio, and has carried on the analysis and the simulation theory. And simulation accuracy analysis has been carried on with practical examples. The results show that the method is put forward to effectively reduce the guided ballistic calculation method of error.

Study of Increment Proportional Guidance Law for High Maneuvering Target

For the inadequacies of the classical proportional navigation law, the mathematical model of increment proportional navigation law is established in this paper. According to the mathematical model comes to attacking targets uniform linear motion trajectory simulation. The trajectory simulation of classical proportional navigation law and incremental proportional navigation law about attacking high maneuvering target are compared. Simulation results show that incremental proportional navigation law can reduce the meet time, and stabilize the missile desired normal overload beating phenomenon in the end of the curve, also it can hit the high maneuvering target in the design requirements, and its performance is superior to classical proportional navigation law.

Three-dimensional cooperative guidance laws against stationary and maneuvering targets

This paper presents the cooperative strategies for salvo attack of multiple missiles based on the classical proportional navigation (PN) algorithm. The three-dimensional (3-D) guidance laws are developed in a quite simple formulation that consists of a PN component for target capture and a coordination component for simultaneous arrival. The centralized algorithms come into effect when the global information of time-to-go estimation is obtained, whereas the decentralized algorithms have better performance when each missile can only collect information from neighbors. Numerical simulations demonstrate that the proposed coordination algorithms are feasible to perform the cooperative engagement of multiple missiles against both stationary and maneuvering targets. The effectiveness of the 3-D guidance laws is also discussed.

Partial stability of some guidance dynamic systems with delayed line-of-sight angular rate

In this paper, for a class of the guidance dynamic system proposed by Moon, Kim, and Kim (Journal of Guidance, Control and Dynamics, vol. 24, no. 4, pp. 659–664, 2001) and Shafiei and Binazadeh (ISA Transactions, vol. 51, pp. 298–303, 2012), a new nonlinear missile guidance law with delayed line-of-sight (LOS) angular rate is introduced, and then partial stability is studied by using the method of Lyapunov functionals and stability theory of functional differential equations. The time delay in the LOS angular rate comes from the missile guidance dynamic system in which a low-cost sensor is used to obtain LOS rate information by image processing techniques. Furthermore, for a class of classical proportional navigation control system with delayed line-of-sight rate studied by Dhananjay, Lum, and Xu (IEEE Transactions on Control Systems Technology, vol. 21, pp. 247–253, 2013), a new stability region is obtained by using the method of Lyapunov-Razumikhin.

Optimal Guidance-to-Collision Law for an Accelerating Exoatmospheric Interceptor Missile

A guidance-to-collision law is presented. The guidance law is derived, using the optimal control methodology, for an accelerating exoatmospheric interceptor. It is dependent on a unique zero-effort heading angle error and on a variable denoted as the zero-effort angle of attack. The guidance law enables an accelerating interceptor to fly toward the interception point along a straight line, after the initial heading error is nulled. In addition, the guidance-to-collision law enables interception of the target with a terminal body angle. Moreover, the trajectory imposed by this guidance law enables an accelerating interceptor to estimate the target’s acceleration by using bearings-only measurements. This is possible due to the imposed line-of-sight rotation, making the range between the two vehicles observable. Using a nonlinear two-dimensional simulation, the performance of the guidance law is analyzed, showing superior performance compared to that of classical proportional navigation.

Spacecraft Guidance Algorithms for Asteroid Intercept and Rendezvous Missions

This paper presents a comprehensive review of spacecraft guidance algorithms for asteroid intercept and rendezvous missions. Classical proportional navigation (PN) guidance is reviewed first, followed by pulsed PN guidance, augmented PN guidance, predictive feedback guidance, Lambert guidance, and other guidance laws based on orbit perturbation theory. Optimal feedback guidance laws satisfying various terminal constraints are also discussed. Finally, the zero-effort-velocity (ZEV) error, analogous to the well-known zero-effort-miss (ZEM) distance, is introduced, leading to a generalized ZEM/ZEV guidance law. These various feedback guidance laws can be easily applied to real asteroid intercept and rendezvous missions. However, differing mission requirements and spacecraft capabilities will require continued research on terminal-phase guidance laws.

Retro-Proportional-Navigation: A New Guidance Law for Interception of High Speed Targets

In this paper, a new proportional-navigation guidance law, called retro-proportional-navigation, is proposed. The guidance law is designed to intercept targets that are of higher speeds than the interceptor. This is a typical scenario in a ballistic target interception. The capture region analysis for both proportional-navigation and retro-proportional-navigation guidance laws are presented. The study shows that, at the cost of a higher intercept time, the retro-proportional-navigation guidance law demands lower terminal lateral acceleration than proportional navigation and can intercept high-velocity targets from many initial conditions that the classical proportional navigation cannot. Also, the capture region with the retro-proportional-navigation guidance law is shown to be larger compared with the classical proportional-navigation guidance law.

Iterative solution to differential geometric guidance problem

PurposeTo study the application of three‐dimensional differential geometric (DG) guidance commands to a realistic missile defense engagement, and the application of the Newton's iterative algorithm to DG guidance problems.Design/methodology/approachThe classical differential geometry theory is introduced firstly to transform all the variables in DG guidance commands from an arc length system to the time domain. Then, an algorithm for the angle‐of‐attack and the sideslip angle is developed by assuming the guidance curvature command and guidance torsion command equal to its corresponding value of current trajectory. Furthermore, Newton's iteration is utilized to develop iterative solution of the stated algorithm and the two‐dimensional DG guidance system so as to facilitate easy computation of the angle‐of‐attack and the sideslip angle, which are formulated to satisfy the DG guidance law.FindingsDG guidance law is viable and effective in the realistic missile defense engagement, and it is shown to be a generalization of gain‐varying proportional navigation (PN) guidance law and performs better than the classical PN guidance law in the case of intercepting a maneuvering target. Moreover, Newton's iterative algorithm has sufficient accuracy for DG guidance problem.Originality/valueProvides further study on DG guidance problem associated with its iterative solution.

Neoclassical Guidance for Homing Missiles

A new approach to guidance of homing missiles is considered. Like classical proportional navigation (PN), the new guidance law utilizes line-of-sight (LOS) rate measurement only. However, its performance is superior to PN, in the sense that zero-miss-distance (ZMD) is obtained against highly maneuvering targets. This merit is achieved withneithertheestimationoftargetmaneuvernortimetogo.Inthederivationofthenewguidancelaw,alinearized formulation of the PN interception kinemtics is used. Based on themethod ofadjoints, it is proved analytically that whentheoveralltransferfunctionofthemissileisbiproper,thatis, thedegreeofthenumeratorequalsthedegreeof thedenominator,ZMDisobtained.TheZMDpropertyholdsinthefollowingcases:deterministictargetmaneuvers, random target maneuvers, deterministic target maneuvers with random starting times, fading noise, and passiveand active-receiver noise. The realization of the new guidance law requires lead compensation. When LOS rate measurement is corrupted by noise, lead ‐lag compensation can be used instead. These design considerations are illustrated in simulations, which verify that negligiblemissdistanceagainst highly maneuvering targetsis obtained even when the LOS rate measurement is noisy.

A New Look at Classical vs Modern Homing Missile Guidance

Modern guidance systems are generally accepted to yield better performance than classical proportional navigation systems. However, it is not always recognized that this better performance carries with it certain costs in improved components or additional instruments. This paper compares a modern guidance system (MGS) to a classical proportional navigational (PN) homing missile guidance system in terms of performance, robustness, and ease of implementation. Quantitative first-order miss distances are compared to show that MGS has the smallest miss if component tolerances can be met, but as component tolerances or measurement errors degrade, MGS degrades faster than PN until, at relatively large component or measurement errors, PN has less miss distance than MGS.