Ideal Proportional Navigation Research Articles

Optimal Vehicle-Target Assignment: A Swarm of Pursuers to Intercept Maneuvering Evaders Based on Ideal Proportional Navigation

The problem of vehicle-target assignment (VTA) to capture a team of evading targets using a swarm of pursuing vehicles is investigated in this article. The VTA problem is formulated as an integer linear programming (ILP), such that the time to intercept all the targets is minimized subject to a number of constraints. To obtain closed-form formulas for the time-to-go matrix in the framework of ILP optimization, a one-on-one pursuit-evasion problem based on the ideal proportional navigation (IPN) guidance law is investigated. By considering two different scenarios of non-maneuvering and maneuvering evaders, analytical closed-form solutions for the pursuit-evasion time-to-go as explicit functions of the position and velocity vectors of the pursuers and evaders are developed, and efficient evasion strategies based on IPN guidance scheme are presented. The efficacy of the theoretical results in estimating the elements of time-to-go matrix is demonstrated by solving the VTA problem in simulations.

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.

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.

Analysis of General Ideal Proportional Navigation Guidance Laws

AbstractIn this work, the capture region of the general ideal proportional navigation guidance law is analyzed with the following constraints: (i) the target's input acceleration is subject to independent or magnitude saturation, and (ii) the missile's input acceleration is subject to magnitude saturation. In addition to the case of unbounded maneuverability of missile with or without knowing the target acceleration, the necessary and sufficient condition for a bounded maneuvering missile that captures a nonmaneuvering target is also derived. Furthermore, the conditions that result in zero impact velocity are discovered and discussed in some of the cases. The capture regions that cannot be obtained analytically are determined numerically by a powerful classifier, the least square support vector machines. To have the capture region ready for least square support vector machines, all the state variables are transformed into modified polar variables and non‐dimensionalized to reduce the number of independent variables. In order to make the implementation possible in real time, an approximation of the Gaussian radial basis function is adopted to obtain the corresponding nonlinear feature mapping function. Through numerous numerical experiments, the proposed technique is found to be adequate for storing the capture region in an onboard fire control computer.

Ideal proportional navigation for exoatmospheric interception

Ideal proportional navigation (IPN) is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two-dimensional ideal proportional navigation was conducted in previous public literature, whereas the practical interception happens in the three-dimensional space. A novel set of relative dynamic equations is adopted in this paper, which is with the advantage of decoupling relative motion in the instantaneous rotation plane of the line of sight from the rotation of this plane. The dimension-reduced IPN is constructed in this instantaneous plane, which functions as a three-dimensional guidance law. The trajectory features of dimension-reduced IPN are explored, and the capture regions of dimension-reduced IPN with limited acceleration against nonmaneuvering and maneuvering targets are analyzed by using phase plane method. It is proved that the capture capability of IPN is much stronger than true proportional navigation (TPN), no matter the target maneuvers or not. Finally, simulation results indicate that IPN is more effective than TPN in exoatmospheric interception scenarios.

Proportional Navigation Against MultipleTargets

The basic block diagrams of proportional navigation are revisited. The effect of initial conditions on the miss distance is studied. Using the important case of multiple targets, two proportional navigation block diagrams are compared. The first, the ideal proportional navigation, applies the true line-of-sight rate, which is calculated by an analytic derivative of the line-of-sight angle. The block diagram resulting from this guidance loop is minimal. The second applies an approximate derivative of the line-of-sight angle. Because of zero-pole cancellation at the origin, the block diagram resulting from this guidance loop is unobservable with respect to target displacement. The consequence is that for the target-displacement initial condition the two diagrams do not result in the same miss distance. Moreover, several solutions that can resolve the above difficulty are suggested. One of the solutions is to reset the derivative filter with the correct initial conditions. Another solution is to skip the first few samples of the derivative filter right after target separation. Nomenclature m = miss distance N 0 = navigation constant nT = target acceleration normal to line of sight tgo = time-to-go Vc = closing velocity VM = missile velocity y = relative position � = line-of-sight angle _ � = line-of-sight rate � = missile time constant

Capture Region of a GIPN Guidance Law for Missile and Target with Bounded Maneuverability

In this paper, a novel method is used to analyze the capture area of three-dimensional general ideal proportional navigation (GIPN) guidance laws. Using a line-of-sight (LOS) fixed natural coordinate and three modified polar variables (MPVs), the expression of relative dynamics between target and missile becomes simple, and no trigonometric functions are involved, which makes possible the analysis of the capture region when both target and missile are subject to bounded maneuverability. It can be shown that the determination of the desired capture area requires only the first two of the MPVs no matter if the maneuverability of missile and target are bounded or not. For the case of unbounded missile acceleration and known target acceleration, the capture region can be found analytically, while for the other cases, the capture region can be obtained graphically in a two-dimensional phase plane. The boundaries of these capture regions are characterized by the stable and unstable manifolds of related equilibrium points, which can only be determined numerically in general at this moment. The results of this work indicate that knowing the target acceleration and utilizing larger navigation coefficients increase the area of the capture region, which agrees with known results in literature.

Unified approach to missile guidance laws: a 3D extension

Since the proportional navigation guidance law was first introduced, many of the researchers had proposed different methodologies to investigate the corresponding performances of all the existing guidance laws. Even though a unified approach was proposed a few years ago, other authors found that under the proposed framework, all the existing guidance laws, namely ideal proportional navigation (IPN), true proportional navigation (TPN), and pure proportional navigation (PPN), were indeed special cases of the mentioned general guidance law. However, the results were restricted to two-dimensional space. In this paper, the author not only extends the results to three-dimensional space, but also to general IPN (GIPN), general TPN (GTPN), and PPN. Unlike conventional researchers, a modified polar coordinate (MPC) is adopted. It is shown that with the property of this MPC, for the line of sight (LOS) based guidance laws (GIPN and GTPN) the number of differential equations required to fully describe the relative dynamics can be reduced from six to three, however, for the missile's velocity-based guidance law, i.e., PPN, five differential equations are required. All the terms of differential equations involve only products and additions of variables. For all the mentioned guidance laws in this paper, only two transformed variables are required to describe the capture region, while the third variable is required to provide the condition of finite turn rate.

Navigation-Guidance-Based Robotic Interception of Moving Objects in Industrial Settings

An important task for autonomous industrial robotic systems is the interception of moving objects. In order to achieve this objective, an on-line robot-motion planning technique that utilizes real-time sensory feedback about the object's motion is needed. In this paper, an Ideal Proportional Navigation Guidance (IPNG) based technique is utilized for on-line robot-motion planning. One must note, however, that navigation-guidance techniques were originally developed for bringing the interceptor into a collision course with (hostile) airborne targets. Therefore, in our case, a conventional tracking technique must be utilized as a subsequent phase to an initial IPNG-based robot-motion planning phase in order to ensure smooth interception. The implementation of the hybrid scheme in industrial settings, where one may not have access to the robot's dynamic model nor to the joints' controllers, is discussed. Real-time experimental results using an industrial robot and a computer-vision system are presented, confirming the (interception-time) superiority of our proposed scheme over conventional tracking techniques.

Robotic interception of moving objects using an augmented ideal proportional navigation guidance technique

Presents an approach to online, robot-motion planning for moving-object interception. The proposed approach utilizes a navigation-guidance-based technique, that is robust and computationally efficient for the interception of fast-maneuvering objects. Navigation-based techniques were originally developed for the control of missiles tracking free-flying targets. Unlike a missile, however, the end-effector of a robotic arm is connected to the ground, via a number of links and joints, subject to kinematic and dynamic constraints. Also, unlike a missile, the velocity of the robot and the moving object must be matched for a smooth grasp, thus, a hybrid interception scheme, which combines a navigation-based interception technique with a conventional trajectory tracking method is proposed herein for intercepting fast-maneuvering objects. The implementation of the proposed technique is illustrated via numerous simulation examples.

Robotic interception of moving objects using ideal proportional navigation guidance technique

This paper presents a novel approach to on-line, robot-motion planning for moving-object interception. The proposed approach utilizes a navigation-based technique, which is robust and computationally efficient for the interception of fast-maneuvering objects. Navigation-based techniques were originally developed for the control of missiles tracking free-flying targets. Unlike a missile, however, the end-effector of a robotic arm is connected to the ground, via a number of links and joints, subject to kinematic and dynamic constraints. Also, unlike a missile, the velocity of the robot and the moving object must be matched for a smooth grasp, thus, a hybrid interception scheme, which combines a navigation-based interception technique with a conventional trajectory tracking method is proposed herein for intercepting fast-maneuvering objects. The implementation of the proposed technique is discussed via numerous simulation examples.

A unified approach to proportional navigation

In this paper, the two major classes of proportional navigation (PN), namely, true proportional navigation (TPN) and pure proportional navigation (PPN) are analyzed and solved by a unified approach. The analytical tools used in the line-of-sight (LOS) referenced systems such as TPN, realistic true proportional navigation (RTPN), generalized true proportional navigation (GTPN) and ideal proportional navigation (IPN), are extended here to handle the interceptor velocity referenced systems such as PPN and its variants. It is found that the above two branches of guidance systems belong to a more general PN scheme which defines the acceleration of the interceptor as being proportional to the LOS rate with direction normal to an arbitrarily assigned vector L/spl I.oarr/. For example, L/spl I.oarr/ of TPN is LOS, and L/spl I.oarr/ of PPN is the interceptor's velocity. Every PN scheme associates with a specific form of L/spl I.oarr/. The optimal PN (OPN) problem which concerns the determination of the optimal direction L/spl I.oarr/ is also addressed. Under the proposed general PN scheme, its six special cases, i.e., TPN, RTPN, GTPN, IPN, PPN, and OPN are solved in a unified way from which many new relations among them can be revealed, and their performances can be compared on a common basis.

Method for improving autopilot lag compensation in intercept guidance

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Optimal pointing control of robotic manipulators with state inequality constraints

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Ideal proportional navigation

Proportional navigation has been proved to be a useful guidance technique in several surface-to-air and air-to-air homing systems for interception of airborne targets. Besides the familiar pure, true, and generalized proportional navigation guidance laws, a new guidance scheme, called ideal proportional navigation, with commanded acceleration applied in the direction normal to the relative velocity between interceptor and target, is presented. In this study the closed-form solutions of ideal proportional navigation are completely derived for maneuvering and nonmaneuvering targets, and some important characteristics related to the system performance are introduced. Under this scheme the capture criterion is related to the effective proportional navigation constant only, no matter where the initial condition and target maneuver are. With some more energy consumption, this new guidance scheme has a larger capture area and is much more effective than the other schemes.