Non-maneuvering Targets Research Articles

Impact time guidance law for arbitrary lead angle using sliding mode control

PurposeThis paper aims to investigate a novel impact time control guidance (ITCG) law based on the sliding mode control (SMC) for a nonmaneuvering target using the predicted interception point (PIP).Design/methodology/approachTo intercept the target with the minimal miss distance and desired impact time, an estimation of time-to-go is introduced. This estimation results in a precise impact time for multimissiles salvo attack the target at the same time. Even for a large lead angle, the desired impact time is achieved by using the sliding mode and Lyapunov stability theory. The singularity issue of the proposed impact time guidance laws is also analyzed to achieve an arbitrary lead angle with the desired impact time.FindingsNumerical scenarios with desired impact time are presented to illustrate the performance of the proposed ITCG law. Comparison with the state-of-art impact time guidance laws proves that the guidance law in this paper can enable the missile to intercept the target with minimal miss distance and final impact time error. This method enables multiple missiles to attack the target simultaneously with different distances and arbitrary lead angles.Originality/valueAn ITCG law based on sliding mode and Lyapunov stability theory is proposed, and the switching surface is designed based on a novel estimation time-to-go for the missile to intercept the target with minimal miss distance. To intercept the target with initial arbitrary lead angles and desired impact time, the authors analysis the singular issue in SMC to ensure that the missile can intercept the target with arbitrary lead angle. The proposed approach for a nonmaneuvering target using the PIP has simple forms, and therefore, they have the superiority of being implemented easily.

Multiple passive-sensor distributed target tracking approach with Machine Learning Feedback

In this paper, a novel recursive state estimation approach in three-dimensional space for a non-maneuvering target is developed. The proposed technique employs angle and amplitude information in a distributed fusion setup, tackling the issue of target state estimation in cluttered environments, as well as target detection with a machine learning feedback mechanism with sequence measurements from multiple passive sensors. A new Integrated Probabilistic Data Association technique with Machine Learning Feedback (IPDA-MLF) is proposed. Most of the clutter measurements are eliminated by fusing angles and amplitude information in the Local Sensor tracker with an Integrated Probabilistic Data Association algorithm (LS-IPDA) framework. To deal with low observability issues, as well as to fuse information from multiple sensors, a Machine Learning (ML) algorithm is deployed, which utilizes a convolutional neural networks-based algorithm. The proposed IPDA-MLF algorithm resolves possible track-to-track associations and provides feedback to the local tracker for increased track retention. The refined information from local trackers is again converted to heat maps and the ML-based solution is used to fuse the local tracks at a central level. Simulation results show that the performance of the proposed algorithm is improved by the incorporation of the machine learning feedback, reducing false tracks, increasing true track retention, and eliminating mismatched fusion at the central tracker.

Multivariable secure guidance for interceptors against cyber-attacks in guidance commands

Secure guidance for missiles against cyber-attacks is an interesting topic of both theoretical and practical importance, but so far few results are available. In this paper, two multivariable secure guidance laws are proposed for precise strikes interceptors with cyber-attacks in guidance commands. Different engagement scenarios are studied in three-dimensional space. Against highly maneuvering targets, the proposed secure guidance law can guarantee some states related to the line-of-sight (LOS) angular rates to converge to zero within finite time, where the cyber-attacks are indirectly estimated and compensated with the aid of an attack observer. Moreover, against non-maneuvering targets with impact angle constraints, the proposed secure guidance law is designed based on the backstepping technique, where the cyber-attacks are directly estimated and compensated. Particularly, prescribed performance functions are introduced in the second guidance law to flexibly determine the convergence rates of the LOS angles. Numerical simulations are performed to illustrate the effectiveness of the proposed schemes.

Polynomial Shaping-based Field-of-View Constrained Impact Time Guidance against Non-maneuvering Targets

This paper proposes polynomial shaping-based guidance strategies that assure interception of non-maneuvering targets at a pre-defined time without violating the seeker's field-of-view constraint. One of the proposed guidance strategies is obtained after expressing relative distance between the interceptor and the target as a nonlinear polynomial function of time-to-go. In contrast, the other guidance scheme shapes the line-of-sight angle as a polynomial function of the relative range between the two vehicles. The coefficients of both of these polynomials are obtained using the necessary boundary conditions that are consistent with required terminal and in-flight constraints. Using these coefficients, the desired set of look angles of the interceptor to achieve the mission objectives are first computed and then a nonlinear dynamic inversion-based controller is designed to track these reference values for achieving the guidance objectives. The performances of the proposed guidance strategies are validated and compared with each other using numerical simulations.

Cooperative Circular Guidance of Multiple Missiles: A Practical Prescribed-Time Consensus Approach

This paper develops a new class of distributed cooperative guidance laws under both undirected and directed communication topologies based on the circular guidance and the practical prescribed-time consensus. The circular guidance law is augmented with a bias term to achieve impact time synchronization within a prescribed time. The analytical time-to-go expression under the circular guidance law is utilized to ensure the impact time cooperation accuracy. Not only convergence rate but also acceleration magnitude reduction is guaranteed due to the merits of the practical prescribed-time consensus. Moreover, based on the predicted interception point, the proposed guidance laws are extended to a nonmaneuvering target. Finally, numerical simulations in both two-dimensional and three-dimensional scenarios verify the effectiveness, robustness, and superiority of the proposed guidance laws.

Research on Head Pursuit Interception Strategy for Hypersonic Target

In the wake of countries competing to develop high-efficiency offensive weapons, high-precision systems have also developed. Due to the high speed and high maneuverability of hypersonic targets, it is always difficult to meet the accuracy and rapidity requirements by using the traditional interception mode. In order to improve the accuracy of the hypersonic target interception, a head pursuit guidance strategy is developed for hypersonic target interception in this study. Firstly, a dynamic model is established by analyzing the relative motion between the interceptor and the target, which needs to place the low-speed interceptor before the high-speed target. Subsequently, a head pursuit interception guidance strategy is presented, which controls the interceptor flight trajectory by controlling its normal acceleration to achieve a successful interception target. Finally, for the maneuvering and non-maneuvering targets, the dynamic characteristics of interceptor are analyzed, respectively, and full trajectory dynamic simulations under different conditions for the hypersonic target interception are worked out to illustrate the feasibility and robustness of the proposed guidance strategy.

Covariance Analysis of the Optimal Orbital Interception With Navigation Errors

This paper derives the analytical linear covariances for the optimal single-impulse orbital interception problems with navigation errors. The initial position and velocity errors are considered for both the interceptor and the non-maneuvering target. Firstly, for free impulse time and free interception time, the necessary conditions for the minimum-fuel and the minimum-time interceptions are derived, and the optimal solutions are obtained by two-dimensional numerical search methods. Then, the linear covariance method is used to derive the error covariances for the minimum-fuel solution and the minimum-time solution, respectively. Finally, based on the first-order and second-order partial derivatives, the error covariances of the optimal impulse time, the optimal interception time, the required impulse vector and the interception position vector are analytically obtained. Numerical results indicate that the proposed analytical linear covariance method is accurate for both the minimum-fuel and the minimum-time interception problems.

Analysis of Line-of-Sight Angle Characteristics for Intercepting a Non-Maneuvering Target With Impact Angle Constraints

With the widespread informationization in modern warfare, higher requirements are required for monitoring the high-value target’s movement state and the corresponding attack conditions. Since the impact-angle constraint guidance law can improve the striking effect of a missile, the study of the hitting conditions and corresponding angle range of the attack angle constraint guidance law has become particularly important. This paper proposes a relationship between the missile’s line-of-sight and flight-path angle under terminal conditions and defines the line-of-sight selection region. Then, we analyze the selection method of the line-of-sight restriction at the end of the missile’s terminal phases. Additionally, Cauchy’s inequality is used to derive the mathematical expressions for line-of-sight selection region under extreme and ideal conditions when employing the developed guidance law to intercept non-maneuvering targets. Finally, a thorough analysis and numerous simulations demonstrate that the line-of-sight angle always falls within the extreme selection region during the entire flight and before hitting the target at the expected impact angle. Compared with a head-on interception, the line-of-sight selection region of the tail-chase case is broader, and the selection region range increases with the upward trend of the acceleration limit.

Spherical Earth Based Measurement Modeling for Practical OTHR Target Tracking

We revisit the problem of modeling of the over-the-horizon radar (OTHR) target tracking. The accuracy of target kinematic and measurement models are critical factors affecting tracking performance. In most of the existing literature, a flat Earth OTHR measurement model is used. This has two obvious drawbacks: (1) a state vector with components of ground range, range-rate, bearing, and bearing-rate cannot be used directly in common kinematic models such as the nearly constant velocity (NCV), nearly constant acceleration (NCA), nearly constant turn (NCT), and a combination of these. (2) The curvature of Earth is ignored, which affects the measurement accuracy of the OTHR. We develop a spherical Earth based measurement model. First, the target kinematic state is modeled in a two-dimensional tracker coordinate frame (T frame), which is suitable for the common kinematic models. Second, the measurement modeling is completed using the spherical Earth model, which fully considers the curvature of Earth among the receiver, transmitter, and target. Furthermore, the inverse mapping for track initiation is derived. Finally, the effectiveness of the developed model is demonstrated by a non-maneuvering target moving with the NCV motion and a maneuvering target moving with a sequence of NCV, NCT, and NCV motions. The interacting multiple model (IMM) algorithm is used for state estimation of the maneuvering target. The unscented Kalman filter (UKF), cubature Kalman filter (CKF), and quadrature Kalman filter (QKF) are compared for state estimation.

Three-dimensional vector guidance law with impact time and angle constraints

The three-dimensional (3D) impact time and angle guidance problem is of great practical significance but remains open because of the coupling nonlinearity and multiple constraints. To solve this problem, a 3D vector guidance law is proposed in this paper to intercept a non-maneuvering target at the desired impact conditions. First, a 3D vector impact angle constrained guidance law with explicit time-to-go estimation is developed by extending the planar one into the 3D space. Then, the intercepting component of the above guidance law is augmented by a time-to-go feedback term, which leads to the proposed 3D vector impact time and angle guidance law. Stability analysis and parameter selection criteria are presented to show the advantageous features of the proposed design. In particular, the proposed guidance law does not require the switch logic, numerical algorithms, or decoupling strategy, which outperforms similar existing results in terms of continuous command and convenient implementation. Finally, several numerical simulations are performed to validate the theoretical findings.

Time-optimal moving target interception with impact angle constraint

The time-optimal guidance law with impact angle constraint to intercept a nonstationary nonmaneuvering target in three-dimensional (3D) space by Unmanned Aerial Vehicles (UAVs) is discussed in this paper. To achieve less computational complexity, the guidance law proposed here is based on the proportional navigation (PN) law existing in the literature. Three stages are used with different values of the Navigation gains of PN law to intercept the target moving in any given direction. To calculate the final position of each phase, a geometric based optimal path calculation technique has been adopted. Another important factor of this guidance law is that the lateral acceleration bound has also been taken into account in designing the guidance law. The simulation results show that the presented scheme performs better than the existing work in literature based on the Sliding Mode Control (SMC).

A Deployment Approach Toward Time-Energy Efficient Robust Performance for Interceptors

Abstract This paper proposes an automatic time-energy efficient robust control (ATERC) deployment approach for selecting either a near-optimal closed-loop control law or a robust control law based on the requirement of the system. The near-optimal closed-loop control law is designed by applying the population-based sine-cosine algorithm (SCA) to the considered interceptor problem. While the robust control law is formulated by using an artificial time delayed control (TDC) approach. In presence of external disturbances, the ATERC methodology deploys the TDC-based robust guidance law to the interceptor, while in the absence of such uncertainties the SCA-based near-optimal guidance law is applied in order to improve the time-energy minimization. This guidance approach also incorporates input saturation which expands its applicability. Using Lyapunov stability analysis, this work establishes an uniformly ultimately bounded (UUB) stability for the discussed system on application of the proposed control approach. Extensive simulation studies involving nonmaneuvering targets and targets performing bank-to-bank maneuver, affirms the efficiency of the proposed approach.

Integrated impact time guidance and control against non-maneuvering targets

This paper proposes integrated guidance and control for skid-to-turn cruciform canard-controlled interceptors for controlling impact time along with interception of non-maneuvering targets. This approach circumvents the possible difficulties associated with designing guidance and control subsystems independently. An interceptor control surface deflection for achieving appropriate lateral acceleration to achieve the guidance objectives are derived using sliding-mode control considering nonlinear engagement dynamics, thereby remaining effective even for engagement with large initial heading errors. The switching surface is chosen to be a function of time-to-go and its rate with different time-to-go estimates against stationary and moving targets. The time-to-go estimate for stationary target accounts for the heading angle errors, while that for constant velocity target provides an exact value. Unlike many of the existing strategies, the proposed approaches enable the interceptor to achieve an impact time, even less than its initial estimates. The efficacy of the proposed guidance strategies is validated through numerical simulations for various initial engagement geometries. Furthermore, the performance of the proposed integrated guidance and control approach is also compared with the separate design of guidance and control subsystems, and shown to be superior.

True-proportional-navigation inspired finite-time homing guidance for time constrained interception

This paper addresses the problem of controlling impact time against various types of target – stationary, constant velocity, or maneuvering. Analytical expression of time-to-go, that is exact for non-maneuvering target but approximate for maneuvering ones, is first presented based on true-proportional-navigation guidance concepts. Guidance strategies are then derived, using Lyapunov theory, to meet impact time constraints, without linearizing the engagement dynamics. Hence, the proposed strategies remain effective even for large initial heading errors. Further, a cooperative guidance strategy to achieve simultaneous target interception by multiple interceptors is also proposed. Guidance commands that ensure consensus among the time-to-go values of the interceptors are utilized for this purpose. Using judicious choices of gains, the common time of target interception may be either pre-fixed, or the same may be decided cooperatively during the engagement. Stability analysis of the possible equilibria in heading angle dynamics, for different choices of parameters, is also performed. For both one-to-one and cooperative homing, simulation results are presented for various engagement scenarios to demonstrate the effectiveness of the proposed strategies.

Design of Guidance Law with Predefined Upper Bound of Settling Time

The paper considers the design of guidance law with predefined upper bound of settling time for planar motion. The proposed scheme is based on a switched control action which results into a desired convergence of the line-of-sight (LOS) rate to zero or a small neighborhood of zero. With this technique, the convergence time of the LOS rate can be chosen as per will of the designer. This scheme considers both the cases where the target acceleration is known and when it is known with certain upper bound. Thus, the designed guidance law is applicable for both maneuvering and non-maneuvering targets. The sufficient condition for Lyapunov stability analysis is established for both the cases. The method is illustrated by considering a numerical example which shows the effectiveness of the proposed technique.

Guaranteed Safe Spacecraft Docking With Control Barrier Functions

This paper presents a strategy for control of a spacecraft docking with a non-maneuvering target in the presence of safety constraints and bounded disturbances. The presence of disturbances prevents convergence to a unique docking state, so in our formulation, docking is defined as occurring within a set constructed using prescribed tolerances. Safety is ensured via application of Robust Control Barrier Functions to render a designated safe set forward invariant for any allowable disturbance. However, this safety strategy necessarily presumes a worst-case disturbance, and thus restricts trajectories to a subset of the safe set when a worst-case disturbance is not present. The presented controller accounts for this restriction, and guarantees that the spacecraft both remains safe and achieves docking in finite time for any allowable disturbance. The controller is then validated in simulation for a spacecraft landing on an asteroid, and two spacecraft docking in low Earth orbit.

Cooperative integrated guidance and control design for simultaneous interception

This work proposes two different cooperative integrated guidance and control schemes for a group of interceptors, each steered by combined effects of canard and tail aerodynamic surfaces, aiming a simultaneous interception of a non-maneuvering target. The first approach is based on a leader-follower framework, in which the time of interception can be prescribed before homing, while the second approach is of a leaderless framework, in which the time of interception is decided during engagement. The proposed integrated guidance and control design for multi-body engagement is carried out under nonlinear settings, with time-to-go formulations that relax the restrictive assumption of interceptors' small heading angles. This facilitates wide applicability of the proposed design in scenarios necessitating large terminal time requirements. In addition to the nonlinearity in kinematics of engagement and interceptors' dynamics, effect of actuators are also considered, making the design suitable for practical implementation. Since canard and tail aerodynamic surfaces have different capabilities, a weighted effort allocation scheme is devised to apportion the total effort in both control surfaces in a suitable manner. Finally, various engagement scenarios have been considered in simulations to substantiate the efficacy of the proposed schemes.

Three-Dimensional Optimal Guidance with Lyapunov Redesign for UAV Interception

Three-dimensional guidance laws are designed to intercept non-maneuvering targets and maneuvering targets in this paper. An optimal control approach with constant or time-variant feedback gain is proposed for interception. The cost function is designed with considerations on energy-efficiency and time-efficiency in the transient process. Lyapunov redesign method is applied to treat the target acceleration, where the precise information of target accelerations is not necessarily required. Efficacy of the proposed guidance laws is proved theoretically and verified by simulation results.

FOV constrained guidance law for nonstationary nonmaneuvering target interception with any impact angle

This paper presents the nonstationary nonmaneuvering target interception with all possible desired impact angles in a two-dimensional (2D) aerial engagement scenario, where the target can move in any direction. The paper also considers the field-of-view (FOV) constraint for designing the guidance law so that the target is always visible while following the missile trajectory in the entire engagement time, which makes it feasible for real world applications. The guidance law is based on the pure proportional navigation (PPN) to achieve any impact angle of the entire angular spectrum. The proposed guidance law is then simulated for intercepting a nonstationary nonmaneuvering target using a kinematic model of a missile to demonstrate the efficacy of the presented scheme. A comparison with the related work existing in the literature has also been added to establish the superiority of the present work.

Research on an Obstacle Avoidance Method for UAV

With the continuous development of UAV technology, UAV has been widely used in various industries. In the flight process of UAV, UAV often changes the given path because of obstacles (including static nonliving body and moving living body). According to the properties of obstacles and the characteristics of UAV, standard Kalman filter is used for nonmaneuvering targets, and sigma point Kalman filter is used for maneuvering targets. In the aspect of obstacle avoidance, the minimum search method is used to get the initial population of local programming. Then, the improved genetic algorithm is run. Combined with the predicted obstacle features, the local planning path can be obtained. Finally, the local planning path and global planning path are combined to generate the planning path with new obstacles. At the end of the paper, the obstacle avoidance strategies of static and moving obstacles are simulated. The simulation results show that this method has fast convergence speed and good feasibility and can flexibly deal with the obstacle avoidance and local path planning of various new obstacles.