Midcourse Guidance Law Research Articles

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.

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.

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.

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.

Cooperative Midcourse Guidance Law with Communication Delay

The initial conditions of the cooperative terminal guidance law, which are the terminal conditions of the cooperative midcourse guidance, have a greater impact on its cooperation and guidance precision, so it is worthy of investigating the cooperative midcourse guidance. In addition, the problem of communication delay between the network nodes is inevitable and has a greater impact on the cooperative guidance law. To solve the above problems, a novel distributed cooperative midcourse guidance (DCMG) law with communication delay is proposed by combining the cooperative term with a distributed consensus protocol including communication delay under the directed communication topology. Firstly, a DCMG law with communication delay is designed by combining the trajectory shaping guidance with the distributed protocol including communication delay under the directed communication topology; secondly, the consensus of the proposed DCMG law with communication delay under the directed graph is proved; finally, the effectiveness and superiority of the proposed DCMG law are verified by numerical simulations.

Design of Missile Mid-Course Guidance for Constrained Impact Angle

This research develops a mid-course guidance law, which enables a constrained impact angle at the engagement, in response to the needs of modern missile design. To achieve this goal and share the workload with the terminal guidance, the mid-course guidance has to regulate the missile to a specific target location and a specific flight angle for a specific “time-to-go.” Therefore, conventional mid-course guidance laws are inadequate in this case. The proposed guidance law achieves this goal by recursively updating the target dynamics for the mid-course guidance, and applying optimal controls with frequently updated control parameters. Simulation results demonstrate the importance and effectiveness of the proposed method. In a simulation case, the interception missile is 100 kilometers away from the target missile, the flight speed of the two missiles are 1200 m/s and 800 m/s, respectively, and the requested impact angle is 150°. The proposed method achieves the positioning error and flight-path-angle error of 791 meters and 0.56°, at the end of mid-course guidance. When working with the previously developed terminal guidance, the miss distance and impact-angle error are 0.002m and 0.001° at the end of the engagement.

Midcourse Guidance for Exoatmospheric Interception Using Response Surface Based Trajectory Shaping

An exoatmospheric midcourse guidance law is proposed to intercept a ballistic missile during the free-flight phase. The proposed guidance law generates a thrust direction command for an antiballistic missile to hit the target at the predicted intercept point. For the predicted intercept point, the zero-effort-miss and zero-effort-velocity are determined based on the solutions of the two-body orbital boundary/initial value problems. The intercept point is predicted by using the trajectory shaping parameter that combines the zero effort trajectory and minimum time trajectory. A response surface model for the minimum interception time is constructed as a database, which is the polynomial function of the initial condition. The response surface model provides a predicted minimum time interception position for the midcourse guidance. Case studies are performed to demonstrate the performance of the proposed guidance law considering various uncertainties.

Three-Dimensional Cooperative Mid-Course Guidance Law Against the Maneuvering Target

Because of the limitation of the long-range detection capability of airborne sensors, it is very difficult for a single interceptor to achieve accurate mid-course guidance, especially for the long and medium range interceptors, and the maneuvering or invisible targets. As one of the solutions, the strategy of multi-interceptor cooperative intercepting can overcome the shortages of single-interceptor. Unfortunately, the existing mid-course guidance laws can't meet the requirements of cooperative intercepting strategy. To solve the problem, a novel cooperative mid-course guidance law is proposed in this paper by combining the traditional trajectory shaping guidance law and the cooperative parameter. Firstly, the cooperative mid-course guidance law is designed, and consensus of cooperative parameter characteristics is proved then. Secondly, the general expression of cooperative parameter and its convergence speed is analyzed. Finally, numeral simulations demonstrate the effectiveness and advantages of the proposed cooperative mid-course guidance law.

A New Midcourse Guidance Design for Near Space Target Interceptor

This study proposes a new midcourse guidance method, combining the trajectory optimization approach and the optimal sliding mode method, to decrease the larger relative velocity between the near space target and the interceptor. Firstly, the midcourse trajectory optimization model is established. Then, the trajectory optimization guidance law based on a sampling scheme is proposed to decrease the larger relative velocity and satisfy multiple constraints at the end time of the midcourse guidance phase. Thirdly, the optimal sliding mode guidance law is introduced to deal with the target maneuverability. Finally, numerical simulations were performed to verify the performance of the midcourse guidance law.

An Optimal Algorithm for Midcourse Guidance Law Under Wind Disturbance

The guidance laws are commonly designed to yield as small a miss distance as possible, harmonious with the missile’s acceleration capability. In recent decades, the concept of optimized guidance law is well understood in applications where information concerning the target range and line-of-sight angle is available. Researchers' efforts have been continually made to apply modern control theory to conventional and adaptive autopilot designs, even though the classical theory is still applicable to autopilots. It can be noted that it is desirable to perform a detailed computer-aided feasibility study within the context of a realistic missile-target engagement model. Development and evaluation of guidance and control laws for simplified missile-target engagement scenarios are extended and adapted to the air-to-air missile situation and implemented in a complete three-dimensional engagement model. Thus, this study proposed a computational method for constructing an optimal midcourse guidance law, which is based on the optimal control theory and initial boundary conditions. This proposed guidance law is derived from an optimal control theory with the boundary conditions such as allowed relative distance between missile and target at the final time, low line-of-sight rate. A numerical simulation verifies the performance of this guidance law with the impact of harmonic wind. The simulation results demonstrate that the quality of effectiveness as well as the applicability of this proposed algorithm.

Stage Optimization of Anti-Air Missiles Considering Guidance Laws

Abstract In this paper, stage optimization is addressed with midcourse guidance laws. In case of the optimal control, it is the optimal solution for a single scenario. Therefore, in order to apply the optimal control input to various scenarios, it should be stored, interpolated and used in an open loop form. In this paper, the real-time guidance laws used in anti-air missiles are considered. The parameters included in the guidance commands and stage weights are defined as optimization objective parameters. The result of weight optimization using guidance laws and optimal control input were compared, the difference in stage weights results occurs from 4 kg to 16 kg.

Dynamic pressure based mid-course guidance scheme for hypersonic boost-glide vehicle

In this study, a guidance scheme for an aerodynamically controlled hypersonic boost-glide class of flight vehicle is proposed. In this work, optimum glide dynamic pressure corresponding to maximum L/ D throughout the flight is calculated and a mid-course guidance law formulation to track the dynamic pressure while suppressing phugoid oscillations is proposed for real-time flight trajectory shaping. Efficacy of the proposed guidance scheme has been demonstrated through simulation studies. Robustness analysis on the proposed guidance algorithm is carried out using Monte Carlo technique. Lastly, a pattern search algorithm-based offline generated maximum L/ D optimal trajectory existing in literature, which meets minimum dynamic pressure, maximum airframe skin temperature, as well as other in-flight and terminal constraints is used as reference trajectory to evaluate the performance of the proposed guidance scheme.

Cooperative near-space interceptor mid-course guidance law with terminal handover constraints

A cooperative problem in mid-course guidance phase is addressed in this paper. For providing suitable initial conditions of successful terminal salvo attack, a novel finite-time cooperative mid-course guidance law with terminal handover constraints is proposed. Firstly, a three-dimensional guidance model of mid-course is decoupled in a planar line-of-sight frame as a two-point boundary value problem. The terminal handover constraints which can guarantee an ideal zero effort terminal engagement are proposed and analyzed. Secondly, the design of the cooperative mid-course guidance law is separated into two stages. The acceleration commands along the line-of-sight direction are developed based on the finite-time average-consensus protocol and super-twisting algorithm in the first stage. In the second stage, the model predictive static programming method is adopted to solve the two-point boundary value problem in line-of-sight frame with a known final time from first stage. Furthermore, sliding mode control theory is used in combination with model predictive static programming method to satisfy terminal handover constraints with bounded perturbation. Finally, numerical simulations of two four-interceptor cooperative scenario are carried out to verify the validity of the proposed cooperative guidance law. The simulation results reflect that all the four interceptors can reach their own predictive interception points with specific approach angles simultaneously.

Three-dimensional salvo attack guidance considering communication delay

This paper investigates the problem of salvo attack guidance law design for multiple missiles against a stationary target considering communication delay. The proposed guidance law requires no information on time-to-go and consists of two guidance stages. More specifically, a simple decentralized midcourse guidance law is proposed to provide desired initial conditions for the latter phase. As for the second guidance phase, all missiles are switched to classical pure proportional navigation guidance law. Considering the fact that the communication delay is inevitable in real applications, the corresponding allowed maximum upper bound of the communication delay among all interceptors is also derived analytically. Nonlinear numerical simulations clearly confirm the effectiveness of the proposed formulation.

Variable-Time-Domain Online Neighboring Optimal Trajectory Modification for Hypersonic Interceptors

The predicted impact point (PIP) of hypersonic interception changes continually; therefore the midcourse guidance law must have the ability of online trajectory optimization. In this paper, an online trajectory generation algorithm is designed based on neighboring optimal control (NOC) theory and improved indirect Radau pseudospectral method (IRPM). A trajectory optimization model is designed according to the features of operations in near space. Two-point boundary value problems (TPBVPs) are obtained based on NOC theory. The second-order linear form of transversality conditions is deduced backward to express the modifications of terminal states, costates, and flight time in terms of current state errors and terminal constraints modifications. By treating the current states and the optimal costates modifications as initial constraints and perturbations, the feedback control variables are obtained based on improved IRPM and nominal trajectory information. The simulation results show that when the changes of terminal constraints are not relatively large, this method can generate a modified trajectory effectively with high precision of terminal modifications. The design concept can provide a reference for the design of the online trajectory generation system of hypersonic vehicles.

A Singular Perturbation Based Midcourse Guidance Law for Realistic Air-to-Air Engagement

In this study, a singular perturbation based technique is used for synthesis and analysis of a near optimal midcourse guidance law for realistic air-to-air engagement. After designing the proposed midcourse guidance law using three dimensional point mass formulation it has been validated through detailed realistic six degrees of freedom simulation. During terminal phase only proportional navigation guidance have been used. The calculation of optimal altitude in present guidance law has been carried out using Newton’s method, which needs generally one iteration for convergence and suitable for real-time implementation. Extended Kalman filter based estimator has been used for obtaining evader kinetic information from both radar and seeker noisy measurements available during midcourse and terminal guidance. The data link look angle constraint due to hardware limitation which affects the performance of midcourse guidance has also been incorporated in guidance law design. Robustness of complete simulation has been carried out through Monte Carlo studies. Extension of launch boundary due to singular perturbation over proportional navigation guidance at a given altitude for a typical engagement has also been reported.<br />

Suboptimal mid-course guidance algorithm for accelerating missiles

This paper deals with the closed-loop form of mid-course guidance law design for accelerating missile system, whose acceleration is approximately constant. A midcourse guidance algorithm of feedback form is proposed to satisfy the engagement geometry conditions at the burn-out time for terminal homing performance enhancement. The effect of velocity change due to missile acceleration is explicitly considered in the derivation of the guidance law. The terminal constraint update algorithm is proposed under the assumption that the target trajectory is predicted precisely. Simulation results are provided to show the performance and characteristics of the proposed algorithm.

Midcourse Guidance Law Based on High Target Acquisition Probability Considering Angular Constraint and Line-of-Sight Angle Rate Control

Random disturbance factors would lead to the variation of target acquisition point during the long distance flight. To acquire a high target acquisition probability and improve the impact precision, missiles should be guided to an appropriate target acquisition position with certain attitude angles and line-of-sight (LOS) angle rate. This paper has presented a new midcourse guidance law considering the influences of random disturbances, detection distance restraint, and target acquisition probability with Monte Carlo simulation. Detailed analyses of the impact points on the ground and the random distribution of the target acquisition position in the 3D space are given to get the appropriate attitude angles and the end position for the midcourse guidance. Then, a new formulation biased proportional navigation (BPN) guidance law with angular constraint and LOS angle rate control has been derived to ensure the tracking ability when attacking the maneuvering target. Numerical simulations demonstrates that, compared with the proportional navigation guidance (PNG) law and the near-optimal spatial midcourse guidance (NSMG) law, BPN guidance law demonstrates satisfactory performances and can meet both the midcourse terminal angular constraint and the LOS angle rate requirement.