Midcourse Guidance Research Articles

An optimal midcourse guidance method for dual pulse air-to-air missiles using linear Gauss pseudospectral model predictive control method

This paper proposes an optimal midcourse guidance method for dual pulse air-to-air missiles, which is based on the framework of the linear Gauss pseudospectral model predictive control method. Firstly, a multistage optimal control problem with unspecified terminal time is formulated. Secondly, the control and terminal time update formulas are derived analytically. In contrast to previous work, the derivation process fully considers the Hamiltonian function corresponding to the unspecified terminal time, which is coupled with control, state, and costate. On the assumption of small perturbation, a special algebraic equation is provided to represent the equivalent optimal condition for the terminal time. Also, using Gauss pseudospectral collocation, error propagation dynamical equations involving the first-order correction term of the terminal time are transformed into a set of algebraic equations. Furthermore, analytical modification formulas can be derived by associating those equations and optimal conditions to eliminate terminal error and approach nonlinear optimal control. Even with their mathematical complexity, these formulas produce more accurate control and terminal time corrections and remove reliance on task-related parameters. Finally, several numerical simulations, comparisons with typical methods, and Monte Carlo simulations have been done to verify its optimality, high convergence rate, great stability and robustness.

DDPG-Based Convex Programming Algorithm for the Midcourse Guidance Trajectory of Interceptor

To address the problem of low accuracy and efficiency in trajectory planning algorithms for interceptors facing multiple constraints during the midcourse guidance phase, an improved trajectory convex programming method based on the lateral distance domain is proposed. This algorithm can achieve fast trajectory planning, reduce the approximation error of the planned trajectory, and improve the accuracy of trajectory guidance. First, the concept of lateral distance domain is proposed, and the motion model of the midcourse guidance segment in the interceptor is converted from the time domain to the lateral distance domain. Second, the motion model and multiple constraints are convexly and discretely transformed, and the discrete trajectory convex model is established in the lateral distance domain. Third, the deep reinforcement learning algorithm is used to learn and train the initial solution of trajectory convex programming, and a high-quality initial solution trajectory is obtained. Finally, a dynamic adjustment method based on the distribution of approximate solution errors is designed to achieve efficient dynamic adjustment of grid points in iterative solving. The simulation experiments show that the improved trajectory convex programming algorithm proposed in this paper not only improves the accuracy and efficiency of the algorithm but also has good optimization performance.

Trajectory prediction-based guidance law

This paper proposes a guidance law based on trajectory prediction, aiming to address the difficulty of traditional guidance laws in meeting high-speed and highly maneuverable vehicles. The unscented Kalman filtering (UKF) technique is employed to estimate the target’s motion and predict the virtual impact point using the Singer model and measuring model. The midcourse guidance law is applied to the virtual target, taking into account the constraint of the intersection angle, while the terminal guidance utilizes modified proportional guidance. To mitigate the overload chattering in the transition sections of both midcourse and terminal guidance, the distance is used to modify the transition section of the terminal guidance. Simulation results demonstrate that the proposed guidance law effectively reduces both the encounter angle and the required maneuvering. Furthermore, to minimize midcourse guidance errors, the prediction results of the virtual target are continually updated during the trace process. This method can also be applied to trail other highly maneuverable targets.

Integrated Target Assignment and Trajectory Optimization for Many-to-Many Midcourse Guidance

Integrated Target Assignment and Trajectory Optimization for Many-to-Many Midcourse Guidance

Composite Zero-Effort-Miss Guidance with Predictor–Corrector Steps for Ballistic Interception

In this paper, a midcourse guidance law for exoatmospheric interception using a solid-propellant rocket is presented. Existing guidance laws based on the zero-effort-miss concept lack consideration for remaining thrust, potentially resulting in the excessive magnitude and rate of the thrust direction command. To address this issue, the zero-effort-miss concept is combined with an iterative predictor–corrector-based guidance law that is adapted for solid-propellant rockets. To apply the iterative predictor–corrector-based guidance law to the interception problem with a solid-propellant rocket, a composite zero-effort-miss concept is introduced, and the correction step is formulated as an online convex optimization problem. The composite zero-effort-miss consists of two zero-effort-misses. One miss is obtained from current state and the other miss is obtained from predicted state at burnout. Those render the proposed guidance law robust to thrust uncertainty allow for a noniterative approach and eliminate the singularity problem. Also, the proposed guidance law reduces maneuvering during the early part of the midcourse phase, leading to less velocity loss, and resolves intercept performance degradation due to the rate limit of thrust vectoring. Numerical simulations comparing the proposed method with the modified zero-effort-miss guidance demonstrate its effectiveness and robustness.

Semi-Analytical Midcourse Guidance for Coordinated Interception of Multiple Exo-Atmospheric Targets

The simultaneous interception of multiple exo-atmospheric threat targets can leave no buffer time for the targets and greatly reduces targets’ penetration probability. This paper proposes centralized and decentralized two midcourse guidance methods to solve the coordinated interception of multiple exo-atmospheric targets. First, the free-time cooperative interception problem minimizing the total impulses is established, where the nonlinear dynamics of the interceptors and targets, the initial impulse constraints, and the terminal interception constraints are considered. Second, the necessary conditions for the optimal cooperative interception problem are derived and then approximated using higher-order Taylor expansions, which result in a series of analytical nonlinear equations. Then, the semi-analytical centralized guidance mode is designed to achieve simultaneous interception of targets by directly solving the analytical nonlinear equations. To improve computational efficiency, the decentralized cooperative guidance mode is further proposed by using the developed iterative freezing trajectory method, where each interceptor uses information from other interceptors in the previous iteration for prediction and distributed computation. Numerical examples verify the effectiveness and robustness of the proposed two guidance methods. Results show that the computational efficiency of the decentralized guidance mode is more efficient compared with the centralized midcourse guidance mode.

A novel adaptive parameter strategy differential evolution algorithm and its application in midcourse guidance maneuver decision-making

In this paper, a novel Adaptive Parameter Strategy Differential Evolution (APSDE) algorithm is proposed to overcome the parameters dependence and avoid local optima. The Parameter Update Mechanism (PUM), which has three different strategies, is used to reduce the dependence on parameters of DE. The Adaptive Proportion Adjustment Mechanism (APAM) is used to balance the proportion of PUM strategies in different development terms of exploitation and exploration, and the Random Restart Mechanism (RRM) is used to improve population diversity when exploitation is in stagnation. The proposed algorithm is verified in the CEC2018 test functions and the results show that APSDE has good abilities of exploitation, exploration, convergence, and stability. Secondly, Midcourse Guidance Maneuver Decision-making (MGMD) in Beyond Visual Range (BVR) air combat is studied and transformed into a single objective variational optimization problem, a MGMD system based on APSDE is established. Finally, the simulation of MGMD is carried out. The APSDE ranks first in the typical MGMD scenario experiment. In the adaptive Midcourse guidance confrontation, the winning rate of APSDE is 54%, and the statistical results show that the APSDE has an excellent MGMD ability.

Correction Strategy of Online Midcourse Guidance for High-Speed Gliding Target Interceptor

During the interception of a high-speed gliding vehicle (HGV), the predicted intercept point (PIP) is updated many times, so the interceptor must continuously adjust its trajectory. In this paper, we propose an online guidance correction algorithm for the interceptor, which can effectively meet the position constraints and energy management of the guidance process. Firstly, we simplify the interceptor’s maneuvering problem to a two-body orbital transfer problem. The Lambert orbit transfer method is used to enable the interceptor to maneuver towards the target’s PIP. Secondly, by comparing the target’s high probability existence area (THPEA) with the interceptor-interceptable area (IIA), the engine start threshold is set in stages to avoid frequent redundancy maneuvers caused by frequent engine starting during missile correction. This approach achieves energy management. Simulation results show that our midcourse guidance strategy is effective.

Online Trajectory Planning Method for Midcourse Guidance Phase Based on Deep Reinforcement Learning

Concerned with the problem of interceptor midcourse guidance trajectory online planning satisfying multiple constraints, an online midcourse guidance trajectory planning method based on deep reinforcement learning (DRL) is proposed. The Markov decision process (MDP) corresponding to the background of a trajectory planning problem is designed, and the key reward function is composed of the final reward and the negative step feedback reward, which lays the foundation for the interceptor training trajectory planning method in the interactive data of a simulation environment; at the same time, concerned with the problems of unstable learning and training efficiency, a trajectory planning training strategy combined with course learning (CL) and deep deterministic policy gradient (DDPG) is proposed to realize the progressive progression of trajectory planning learning and training from satisfying simple objectives to complex objectives, and improve the convergence of the algorithm. The simulation results show that our method can not only generate the optimal trajectory with good results, but its trajectory generation speed is also more than 10 times faster than the hp pseudo spectral convex method (PSC), and can also resist the error influence mainly caused by random wind interference, which has certain application value and good research prospects.

Ensemble Transfer Learning Midcourse Guidance Algorithm for Velocity Maximization

This paper proposes an ensemble transfer learning guidance algorithm for angular-constrained midcourse guidance to maximize the terminal velocity. The algorithm developed improves the generalization capability of the trained deep neural network to adapt to a new environment. First several deep neural guidance networks are trained for some specific working environments via supervised learning. A small-scale ensemble transfer learning network is then leveraged to fuse the knowledge of different pretrained deep neural network. This requires much less labeled data to transfer existing knowledge to a new working environment and hence greatly improves the learning efficiency, compared to the supervised learning philosophy. Extensive numerical simulations are performed to demonstrate the effectiveness of the proposed algorithm.

Trajectory prediction in pipeline form for intercepting hypersonic gliding vehicles based on LSTM

The interception problem of Hypersonic Gliding Vehicles (HGVs) has been an important aspect of missile defense systems. In order to provide interceptors with accurate information of target trajectory, a model based on an improved Long Short-Time Memory (LSTM) network for trajectory prediction pipeline is proposed for the interception of a skip gliding hypersonic target. Firstly, for trajectory prediction required by intercepting guidance laws, the altitude, velocity and velocity direction of the target are formulated in the form of analytic functions, consisting of linear decay terms and amplitude decay sinusoidal terms. Then, the dynamic characteristics of the model parameters are analyzed, and the target trajectory prediction pipeline is proposed with the prediction error considered. Finally, an improved LSTM network is designed to estimate parameters in a dynamically-updated manner, and estimation results are used for the calculation of the final trajectory prediction pipeline. The proposed prediction algorithm provides information on the velocity vector for midcourse guidance with the effect of prediction errors on interception taken into account. Simulation is conducted and the results show the high accuracy of the algorithm in HGVs’ trajectory prediction which is conducive to increasing the interception success rate.

Design of finite time cooperative mid-course guidance law for unmanned target drone aircrafts

For cooperative mid-course guidance problem of multiple unmanned target drone aircrafts(UTDA), a novel cooperative guidance law with impact angle constraints is proposed in this study. Firstly, the relative motion equation of UTDAs and target, and the multiple-UTDA cooperative guidance model with impact angle constraints are constructed. Then, the process of cooperative guidance law design is divided into two stages. In the first stage, the acceleration command on the LOS direction is designed based on the fixed-time consensus theory, the speed dimension is introduced which can guarantee the consensus of all UTDAs' impact times in fixed time. In the second stage, an impact-angle-control guidance law is proposed based on the approaches of variable coefficients sliding mode control and finite-time convergence theory to reach the virtual targets, the acceleration command on the direction of perpendicular to the LOS is developed, which can ensure that all the LOS angles converge to the desired terminal LOS angle in finite-time and some mobility when approaching the virtual targets is achieved, and the Lyapunov stability is adopted. Finally, numerical simulations express that the cooperative mid-course guidance law designed in this study can make each UTDA reach the virtual target at the same time with small miss distance and meet the LOS constraint, and demonstrate the effectiveness of the proposed mid-course guidance law.

Active-set pseudospectral model predictive static programming for midcourse guidance

This paper focuses on the midcourse guidance law for the interceptor to engage the hypersonic gliding vehicles (HGVs). Firstly, an active-set pseudospectral model predictive static programming (APS-MPSP) algorithm is presented, which entails two major improvements: the application of pseudospectral discretion and handling of control constraint using active-set iteration strategy. Except inheriting the high efficiency of the MPSP, this new algorithm can address the control constraint directly. Secondly, the optimal predictive guidance design is established, which embeds the target prediction into the guidance framework by formulating a simultaneous nonlinear optimal problem. Employing the APS-MPSP algorithm to solve this optimal problem efficiently, the predictive guidance command that ensures interceptor reach an appropriate predicted interception point (PIP) can be obtained directly. This strategy has the merits of no need to precompute the PIP or time-to-go and high prediction accuracy. The reliability and efficiency of the proposed methods are verified by numerical examples and comparisons with already methods.

Midcourse Guidance Using Neural Networks

This work explores the concept of using neural network for the purpose of mid-course guidance in air vehicles. The idea is to use the neural network in real-time to retrieve a guidance command, based on the current state and target requirements. This forms a closed loop guidance approach, instead of following a pre-designed and fixed trajectory, which doesn't change according to deviations from the nominal states due to real-life conditions. This work explores the architecture and training of such a network, its performance, and compares this network to the Neighboring Extremals method.

A Midcourse Guidance Method Combined with Trajectory Prediction for Antinear-Space-Gliding Vehicles

Near-space-gliding vehicles have variable maneuver modes and dramatic changes in their ballistic parameters, which lead to a need to accurately predict an intercept point based on predictions of their trajectories. First, a trajectory prediction method builds a set of time-varying maneuver models based on flight missions combined with an adaptive grid to infer maneuver modes. An interactive multiple-model method of variable structure is proposed to identify the characteristics of the maneuver mode by introducing a fading factor and the modified Markov probability transfer matrix and then predict the trajectory through numerical integration. In the midcourse guidance method, the prediction of the target trajectory is introduced, and the zero-control interception manifold with intersection angle constraints is designed as the midcourse guidance terminal constraint. For the calculation of the starting time of the boost phase, the optimization solution satisfying the remaining flight time constraint is realized based on the Newton-Raphson iterative method. The analytical expression of a guidance command based on zero-error-miss/zero-error-velocity is established on the basis of the optimal control theory to provide an optimal flight path guiding an NSGV fly toward a point of interception. The simulation results show that the trajectory-prediction method has high prediction accuracy and strong convergency for typical maneuver modes, and the proposed midcourse guidance algorithm meets the requirements of the zero-effort intercept manifold with the intersection angle constraints, which is of important theoretical significance and acts as a reference value for intercepting high-velocity maneuver targets.

Fast Trajectory Generation Method for Midcourse Guidance Based on Convex Optimization

To generate the midcourse guidance trajectory for intercepting the high-speed and high maneuvering target, which is a strongly nonlinear and strongly constrained problem, a two-stage convex optimization method is proposed to solve the optimal trajectory quickly. In the first stage, an initial trajectory generation method is proposed, by which the trajectory’s terminal state is close to the terminal position. And the generated trajectory is used as the initial solution of the convex optimization method. In the second stage, the original nonconvex optimization problem is transformed into a convex optimization problem by linearization and relaxation methods and then solved discretely. In the numerical simulation, the effectiveness of the proposed method is verified, and the robustness of the method is verified in different initial and terminal states. Then, several ablation experiments are operated to verify the advantage of the rapid initial trajectory generation method in the first stage. Finally, compared with the gauss pseudospectral method (GPM), the proposed method is proved to be efficient and has the potential of online trajectory generation.

Midcourse Iterative Guidance Method for the Impact Time and Angle Control of Two-Pulse Interceptors

To address the need for flexible energy management and impact angle control in the midcourse guidance of modern long-range antiballistic interceptors, an impact time and angle guidance law is designed for the exoatmospheric midcourse flight of antiballistic interceptors, which covers two pulse sections and two coast sections. The problem is described as an optimal control model with discontinuities in the system equations at interior points, and an iterative guidance method is used to efficiently solve the two-point boundary value problem. Simulation results demonstrate the effectiveness of the proposed guidance law; the obtained miss distance accuracy has an order of magnitude of 1 m, and the impact angle accuracy has a 1° order of magnitude while the angle can be achieved.

Optimal midcourse guidance law for the exo-atmospheric interceptor with solid-propellant booster

This paper focuses on the midcourse guidance law for the exo-atmospheric interceptor with solid-propellant booster to intercept a target in the Keplerian orbit, in which the thrust direction command is provided under the typical framework of predictor-corrector algorithm. Firstly, an analytical solution is derived to predict the burnout velocity and position vectors, in which the thrust vector is assumed to be along the velocity vector. Secondly, the predicted values are used to formulate a set of nonlinear algebraic equations to determine the desired burnout velocity direction to impact the target. Actually, those equations are transcendental because Lambert's problem with unspecified time-of-flight is involved. Then, Newton-Raphson method is used to solve the problem. In the calculation process, the Jacobian matrix corresponding to the equations is derived in an analytical manner, which significantly improves the computational efficiency. Thirdly, an optimal correction guidance law is constructed to steer the interceptor to achieve the desired burnout velocity direction. Finally, convergence evaluation, optimality verification, and Monte Carlo simulations are carried out to test the performance of the proposed guidance law. The results show that it not only performs well in providing the optimal guidance command, but also has high computational efficiency and guidance accuracy. Moreover, it has great robustness even in large dispersions and uncertainties.

CMAC Trained Optimum Mid course Guidance for Tactical Flight Vehicle

This paper discusses design and validation of neural network based mid-course guidance law of a surface to air flight vehicle. In present study, initially different optimal trajectories have been generated off-line of different pursuer-evader engagements by ensuring minimum flight time, maximum terminal velocity and favorable handing over conditions for seeker based terminal guidance. These optimal trajectories have been evolved by nonlinear programming based direct method of optimisation. The kinematic information of both pursuer and evader, generated based on these trajectories have been used to train cerebellar model articulate controller (CMAC) neural network. Later for a given engagement scenario an on-line near optimal mid-course guidance law has been evolved based on output of trained network. Training has been carried out by CMAC type supervisory neural network. The tested engagement condition is within input/output training space of neural network. Seeker based homing guidance has been used for terminal phase. Complete methodology has been validated along pitch plane of pursuer-evader engagement. During mid-course phase, the guidance demand has been tracked by attitude hold autopilot and during terminal phase, the guidance demanded lateral acceleration has been tracked by acceleration autopilot. System robustness has been studied in presence of plant parameter variations and sensor noise under Monte Carlo Platform.

Noniterative feedback midcourse guidance for exo-atmospheric interception of ballistic targets using virtual impact point steering

This paper proposes a noniterative feedback midcourse guidance algorithm for intercepting a ballistic target. The virtual impact point (VIP) concept, which is the intersection point between the defense missile trajectory and the sphere defined by the hit altitude, is introduced. Then the motion of the virtual impact point caused by the external acceleration applied to the missile is derived. The proposed guidance algorithm generates the acceleration command that moves the VIP to the PIP along the shortest path without any iterative procedure and has high potential as an onboard midcourse guidance algorithm. The validity of the proposed guidance algorithm has been demonstrated through the case study.