Missile Guidance Law Research Articles

Near-Optimal Evasion from Acceleration Bounded Modern Pursuers

Target evasion from modern missiles is a very challenging task because modern interception missiles usually have substantial agility and maneuver advantages over the target. This paper proposes novel near-optimal evasion strategies from any linear missile guidance law that exploit the pursuer’s two main weaknesses: the inherent time delay of the evader’s acceleration estimate and the pursuer’s acceleration bound. In the derivation, the pursuer and the evader are assumed to have arbitrary-order linear dynamics with bounded acceleration commands. The pursuer is assumed to have a delayed evader acceleration estimation, and the evader is assumed to know the pursuer’s guidance law. The problem is posed as a bounded optimal control problem with the miss distance as the performance index, and the necessary analytical optimality conditions are derived. The problem is then solved iteratively using backward and forward propagation of the costate and state dynamics until the solution converges. Furthermore, an additional gradient-descent-based algorithm is derived to improve the performance and robustness of the solution. The evasion strategies are extensively evaluated in deterministic and stochastic Monte Carlo simulations. It is shown that the proposed evasion strategies have substantially better evasion performance than state-of-the-art evasion strategies that only exploit the pursuer’s estimation delay.

Missile Guidance Law Design Based on Free-Time Convergent Error Dynamics

Missile Guidance Law Design Based on Free-Time Convergent Error Dynamics

Three-dimensional adaptive dynamic surface guidance law for missile with terminal angle and field-of-view constraints

In this paper, an adaptive dynamic surface (DSC) guidance law for missile is designed to intercept the maneuvering target with field-of-view (FOV) and terminal angle constraints in three-dimensional(3D) space, and the missile autopilot dynamics is considered. Firstly, the time-varying transformation function related to line of sight (LOS) is used to replace the FOV constraints, transforming the process-constrained control problem into the output-constrained control problem. Meanwhile, the 3D coupled relative kinematics model considering missile autopilot dynamics and maneuvering target acceleration is established. Secondly, a novel time-varying asymmetric barrier Lyapunov function (TABLF) with dead-zone characteristics is introduced to the adaptive dynamic surface guidance law design process to improve the robustness of parameter debugging. Thirdly, with the help of a nonlinear adaptive filter, the ‘explosion of complexity’ problem can be avoided effectively, which is caused by analytic computation of virtual signal derivatives. Furthermore, aiming at the problem of autopilot dynamic errors, target acceleration disturbances, and unmeasurable parameters in the model, a novel adaptive law is used to evaluate online. Then, the stability of the closed-loop system is rigorously proven using Lyapunov criteria. Ultimately, Numerical simulations with various constraints and comparison studies have been considered to show the feasibility and effectiveness of the proposed missile guidance law.

Neuro-evolution-based generic missile guidance law for many-scenarios

Designing efficient aerial interceptors is an important task. Using Pareto-optimality, this paper presents a novel approach for generating guidance laws that are generic for many aerial pursuit-evasion scenarios. In particular, the pure-proportional navigation law is combined with a neural network to create adaptive guidance laws, which adapt according to the current state of the system. First, a many-objective optimization problem is formulated in which each objective aims at the best performance in one of the scenarios. Next, using simulations with a many-objective evolutionary algorithm, a population of guidance laws is evolved towards the Pareto-optimal ones. The obtained guidance laws from multiple runs are statistically analyzed and compared with a set of Pareto-optimal pure-proportional navigation laws. The results suggest that the proposed approach provides a significant improvement as compared with the pure-proportional navigation law over the entire set of scenarios.

Distributed observer‐based fixed‐time cooperative guidance law against maneuvering target

SummaryThis paper presents a fixed‐time cooperative guidance law for leader‐following missiles, comprising one leader missile with the target seeker and several seeker‐less follower missiles. The aim is to achieve a simultaneous attack on a maneuvering target at desired impact angles. First, a guidance law with impact angle control for the leader missile against a maneuvering target is proposed based on nonsingular fast terminal sliding mode (NFTSM) control algorithm. Then, the design of cooperative guidance law for the follower missiles is composed of two parts: along the follower‐to‐leader line of sight (LOS) direction, the guidance command derived from bi‐homogeneous property is designed to ensure that the follower‐leader ranges keep proportional consensus with the range‐to‐go of the leader missile, thus avoiding the estimation of time‐to‐go (); in the normal follower‐to‐leader LOS direction, considering the relative impact angle constraints which is determined by the leader LOS angle, the guidance command is proposed based on predefined‐time sliding mode control method. What's more, a distributed fixed‐time observer is designed for the follower missiles to compensate for unobtainable leader missile information. The fixed‐time stability of the proposed methods is demonstrated using the Lyapunov theory and bi‐homogeneous property. Finally, simulation results confirm the effectiveness and superiority of the proposed fixed‐time cooperative guidance law with leader‐following strategy.

Finite-time Cooperative Guidance Law for Multiple Missiles with Impact Angle Constraints and Switching Communication Topologies

Finite-time Cooperative Guidance Law for Multiple Missiles with Impact Angle Constraints and Switching Communication Topologies

Platooning in UAM airspace structures: applying trajectory shaping guidance law and exploiting cooperative localization

A novel control technique for the platooning of aerial vehicles is here introduced, and its stability is analyzed. The controller applies a missile guidance law that was initially adapted for path-following and subsequently extended to platooning. The positions of all agents within a platoon employing this controller are estimated by exploiting cooperative localization, and these estimated positions are fed back into the controller. Using simulation, the agents within a platoon are demonstrated to follow their desired path and avoid collision, even in environments with intermittent Global Positioning System signals and limited sensing ranges.

Reinforcement learning-based missile terminal guidance of maneuvering targets with decoys

In this paper, a missile terminal guidance law based on a new Deep Deterministic Policy Gradient (DDPG) algorithm is proposed to intercept a maneuvering target equipped with an infrared decoy. First, to deal with the issue that the missile cannot accurately distinguish the target from the decoy, the energy center method is employed to obtain the equivalent energy center (called virtual target) of the target and decoy, and the model for the missile and the virtual decoy is established. Then, an improved DDPG algorithm is proposed based on a trusted-search strategy, which significantly increases the train efficiency of the previous DDPG algorithm. Furthermore, combining the established model, the network obtained by the improved DDPG algorithm and the reward function, an intelligent missile terminal guidance scheme is proposed. Specifically, a heuristic reward function is designed for training and learning in combat scenarios. Finally, the effectiveness and robustness of the proposed guidance law are verified by Monte Carlo tests, and the simulation results obtained by the proposed scheme and other methods are compared to further demonstrate its superior performance.

Design of Guidance Law for Smart Missile Based on Direct Mode Configuration with Implicit Dynamic-Inverse

The design of guidance law for smart missile based on implicit dynamic-inverse direct mode configuration is described in this paper. The dynamic-inverse theory and direct mode algorithm are applied to the design of guidance law. The pitching acceleration and yaw acceleration are designed for the pitch channel by using the augmented proportional guidance and for the yaw channel by using the dynamic-inverse theory respectively. The attacking time parameter and the attack time error equation are introduced as the constraint criteria for the design of the dynamic-inverse. According to the singular perturbation theory, the fast and slow subsystems are designed by dynamic-inverse control, and then the required control quantities are obtained by solving the relative motion equations of the missile and the target. The simulation results showed that the guidance law can fully meet the guidance trajectory performance requirements of the smart missile.

Appointed-Time Cooperative Guidance Law With Line-of-Sight Angle Constraint and Time-to-go Control

This study proposes a three-dimensional appointed-time cooperative guidance law for multiple missiles. The maneuvering target can be hit simultaneously by multiple missiles with different expected line-of-sight (LOS) angles. It is worth noting that the actual convergence time of the LOS error or time-to-go can be treated as a tuning parameter along the LOS direction and the normal direction of LOS. Firstly, the simultaneous attack problem of multiple missiles can be regarded as a consensus problem. In the LOS direction, a distributed cooperative guidance law is presented to guarantee the time-to-go of all missiles to be consensus at the appointed time. Subsequently, a guidance law is also presented in the normal direction of LOS to achieve the expected LOS angles at the appointed time. Finally, to improve the robustness of the cooperative guidance system, an appointed-time extended state observer (ATESO) is developed for compensating the guidance commands. The stability of the proposed cooperative guidance law is fully proved by the rigorous theoretical derivation. Numerical simulation results verify the efficacy of this scheme.

Cooperative trajectory shaping guidance law for multiple anti-ship missiles

Abstract To enhance the performance of anti-ship missiles cooperative attack, this paper proposes a finite-time trajectory shaping-based cooperative guidance law (TSCGL). Firstly, the cooperative guidance model is established on segmented linearisation of the missile’s heading angle. Then, a trajectory shaping guidance law for a single missile is derived by a weighted optimal energy cost function and Schwarz inequality. On this basis, a finite-time TSCGL is proposed combined with trajectory shaping technology and finite-time theory. The desirable finite-time convergence performance can ensure a simultaneous attack. Through an improved method of time-to-go estimation, it is independent of small-angle assumption and relaxes the launching conditions of the missiles. Additionally, the proposed finite-time TSCGL can achieve better damage performance through energy management. Finally, simulation results demonstrate the effectiveness and superiority of the proposed finite-time TSCGL.

Adaptive second order sliding mode guidance law for missile-target interception with fuzzy logic system

This paper presents the design of a 3D missile guidance law based on a second order sliding mode control technique employing an adaptive tuning law and a fuzzy gain scheduling. At the outset, the super-twisting sliding mode guidance law is obtained to overcome the chattering phenomenon. Then, without the knowledge about the bounds of disturbances, an adaptive law is used to determine the control gains. The results are enhanced using a fuzzy module that provides the controller parameters according to a set of linguistic rules. Finally, a comparative set of simulation results are given. To verify the performance and effectiveness of the proposed guidance law, we compare the performances of the traditional sliding mode (SM) guidance law, the traditional super-twisting sliding mode (STWSM) guidance law, the adaptive super-twisting sliding mode (ASTWSM) guidance law and the adaptive fuzzy super-twisting, sliding mode (AFSTWSM) guidance law. The simulation scenarios consider fundamental target movements. The results demonstrate that the proposed adaptive guidance laws display better performance in terms of miss distance, intercept time, and final closing velocity compared the alternatives considered in this study.

Learning-based design optimization of second-order tracking differentiator with application to missile guidance law

Tracking differentiator is widely used to estimate the differential signal of noisy systems with unknown structures. However, there still lacks an efficient approach to tracking differentiator design and optimization, partly due to the nonlinearity by nature, and the high dimension of design parameters. Thus, this paper proposes a learning-based design optimization method. First, neural networks are trained to approximate the multivariate influence on tracking differentiator performance. The resultant learning-based surrogate model is then used to optimize the parameters of tracking differentiator by differential evolution algorithm. The proposed method is applied to Sigmoid-type tracking differentiator and further compared to the unscented Kalman filter with various input signals. The estimation error of the optimized tracking differentiator is reduced by 65.70% compared to that of the benchmark method. The second-order tracking differentiator is integrated into an angular acceleration-based guidance law. Simulation results of tracking moving targets show that the miss distance and control resource are separately lowered by at least 35.70% and 74.12% as opposed to the crude guidance law.

An event-triggered distributed cooperative guidance law for simultaneous attack with autopilot lag consideration

This article proposes an event-triggered distributed cooperative guidance law for multiple missiles to simultaneously attack a stationary target with consideration of autopilot lag and unknown disturbances. In order to achieve a consensus on each missile’s impact time and save communication costs, the guidance law is designed on the basis of an auxiliary variable consisting of the time-to-go expression and its time derivative. Driven by the properly designed event-triggered mechanism, the information interaction among missiles performs in a need-based scheme and there is no need to continuously monitor the consensus errors between neighbor missiles. By this means, the communication burden is significantly reduced while satisfactory guidance performance is still guaranteed. The proposed guidance law can be extended to a communication failure case where one of the missiles suddenly cannot receive information from its neighbors. An integral sliding mode controller is integrated with the nominal guidance law to eliminate the adverse effects caused by unknown disturbances. Numerical simulations are carried out to illustrate the effectiveness of the proposed guidance design.

Time and FOV constraint guidance applicable to maneuvering target via sliding mode control

This paper focuses on designing a novel homing missile guidance law applicable to intercepting maneuvering target while considering time and field-of-view (FOV) constraints. To realize accurate zero miss-distance and time control, a sliding mode manifold consisting of the range-to-go, expected impact time and two newly-defined weighting functions is constructed based on a nonlinear model, which can guarantee the interception at a prescribed impact time once the sliding mode has reached. Then, an overall guidance command is derived by taking both finite time convergence of sliding mode manifold and non-singularity into consideration. A new guidance strategy with boundary conditions is proposed to satisfy FOV requirement. Furthermore, the feasibility for intercepting maneuvering target is demonstrated via a Lyapunov-like approach. Numerical simulations validate the performance of the proposed guidance law, and a comparative study indicates that the proposed method is superior to relative guidance laws in terms of maneuvering target interception.

Design of Missile Guidance Law Using Takagi-Sugeno-Kang (TSK) Elliptic Type-2 Fuzzy Brain Imitated Neural Networks

The exploiting of missile guidance law is one of the most important issue of defense systems. However, it is a complex nonlinear guidance control problem. In recent years, several intelligent algorithms have been employed for the missile guidance law design. This paper aims to provide a more effective intelligent neural network, and then apply it to missile guidance control. An elliptic type-2 function (ET2F) combined with a Takagi-Sugeno-Kang (TSK) fuzzy system (FS) based on a wavelet function and a brain imitated neural network (BINN) is proposed to produce a new Takagi-Sugeno-Kang elliptic type-2 fuzzy brain imitated neural network (TSKET2FBINN). The proposed TSKET2FBINN is then incorporated into the missile guidance law. The proposed missile guidance control system includes the TSKET2FBINN controller and a robust compensation controller. A Lyapunov function is used to generate parameter adjustment adaptive laws so as to guarantee system stability with fast tracking performance of missile guidance control system. By presenting three missile control scenarios, the effectiveness of the proposed method is then demonstrated. The miss-distance (MD) of the proposed method is calculated and compared to other recent guidance methods to demonstrate its superior performance.

Angular acceleration compensation guidance law for passive homing missiles

Abstract Proportional navigation guidance law (PNG) is widely used for passive homing missiles. But PNG often suffers from inaccurate tracking of target or even failure when the target is maneuvering quickly or releasing artificial decoys. In order to solve this problem, the angular acceleration compensation guidance law (AACG) is constructed by using line of sight (LOS) angular velocity and LOS angular acceleration. The stability analysis with Lyapunov stability theory shows that AACG system is asymptotically stable on a large scale under certain stability constraint conditions. AACG command is designed to be perpendicular to the LOS and optimized by gravity compensation. AACG is neither dependent on target acceleration nor the distance between the missile and the target. The numerical simulation results indicate that AACG has good guidance performance on air-to-air missiles when the target maneuvers violently or releases artificial decoys in the endgame term.

All-aspect attack guidance law for agile missiles based on deep reinforcement learning

This paper presents an all-aspect attack guidance law for agile missiles based on deep reinforcement learning (DRL), which can effectively cope with the aerodynamic uncertainty and strong nonlinearity in the high angle-of-attack (AOA) flight phase. First, to make the training environment more authentic, the full flight envelope of the missile is modeled and highly accurate aerodynamic data is obtained through Computational Fluid Dynamics (CFD) technique. Subsequently, the DRL algorithm is applied to generate an AOA guidance law for the agile turn phase. A hierarchical scheme that consists of a meta-controller for real-time decision making according to combat scenario and a sub-controller for generating guidance command is designed, which enables the guidance law to cover the whole process of the engagement and ensures the convergence of the training in the agile turn phase. Considering the current limitations of missile maneuverability, two agile turn guidance laws are developed to accommodate both limited and unlimited AOA scenarios. Moreover, the proposed guidance law has excellent generalization capability and ensures the implementation of static training and dynamic execution, which means that the missile can adapt to the realistic combat scenarios that have not been encountered during the training. Simulation results indicate that the DRL-based guidance law is nearly optimal and robust to disturbances. In addition, the proposed guidance law enables the missile to track time-varying desired turn angles to lock the maneuvering target in the rear hemisphere during the agile turn phase, providing advantageous initial conditions for the terminal guidance. Furthermore, the computational efficiency is high enough to satisfy the requirement on onboard application.

Three-dimensional cooperative guidance law for multiple missile based on sliding mode control

Based on the missile-target three-dimensional relative motion model, a multi-missile coordinated three-dimensional guidance law with attack time constraints is designed for attacking stationary targets. The sliding mode variable structure control is adopted in the pitch channel, and the dynamic inverse control is adopted in the yaw channel. By maneuvering in the yaw channel, adjusting the missile's attack time and comparing with the results of using augmented proportional guidance, the simulation results show that the algorithm designed in this article can achieve coordinated attack and high hitting accuracy, which verifies the correctness and superiority of the algorithm.

Avoiding Obstacles via Missile Real-Time Inference by Reinforcement Learning

In the contemporary battlefield where complexity has increased, the enhancement of the role and ability of missiles has become crucial. Thus, missile guidance systems are required to be further developed in a more intelligent and autonomous way to deal with complicated environments. In this paper, we propose novel missile guidance laws using reinforcement learning, which can autonomously avoid obstacles and terrains in complicated environments with limited prior information and even without the need of off-line trajectory or waypoint generation. The proposed guidance laws are focused on two mission scenarios: the first is with planar obstacles, which is used to cope with maritime operations, and the second is with complex terrain, which is used to cope with land operations. We present the detailed design processes for both scenarios, including a neural network architecture, reward function selection, and training method. Simulation results are provided to show the feasibility and effectiveness of the proposed guidance laws and some important aspects are discussed in terms of their advantages and limitations.