Terminal Impact Angle Research Articles

Multi-UAV DMPC Cooperative Guidance with Constraints of Terminal Angle and Obstacle Avoidance

This paper studies the salvo attack problem for multiple unmanned aerial vehicles (UAVs) against a maneuvering target, and a guidance scheme based on distributed model predictive control (DMPC) is presented to achieve cooperative interception with constraints of terminal impact angle and no-fly zone (or obstacle) avoidance. Firstly, for guaranteeing the synchronization of UAVs in calculating their acceleration commands, the assumed predictive trajectories are introduced, whose deviation from the actual state trajectories is limited by the designed compatibility constraints. Secondly, based on the velocity-obstacle model, the obstacle avoidance constraints are presented, and for guaranteeing the convergence of impact time and impact angles, the auxiliary controller and terminal ingredients are developed, which complete the design of DMPC cooperative guidance scheme. Subsequently, the rigorous proof for the convergence of the proposed guidance scheme is provided. Based on the above design, a complete implementation process of the guidance scheme is presented, in which each UAV uses the particle swarm optimization algorithm to solve the preprocessed local optimization problem, and only the shared information among neighbors is utilized for calculation. Finally, the numerical simulations are conducted under diverse cases, which demonstrate the effectiveness of the proposed guidance scheme when solving cooperative interception problems with terminal angle and obstacle avoidance constraints.

Nonlinear three dimensional all-aspect guidance with terminal impact angle constraints

In this paper, a nonlinear three dimensional all-aspect guidance law, to intercept maneuvering target at pre-specified orientation, is presented. Without decoupling the engagement kinematics into two perpendicular planes, the proposed guidance law is derived in three dimensions directly. More importantly, the proposed strategy is an ‘all-aspect’ guidance law, which allows missile to intercept the target at the desired impact angle, even in the presence of very large initial pointing errors. First, in order to design a guidance law with all-aspect interception capability, the collision conditions analysis process is carefully developed and an additional necessary constraint condition is derived. Then, based on chattering reduction sliding mode control, a nonlinear three dimensional terminal impact angle constrained guidance law is derived considering maneuvering targets. After capturability analysis, an additional sliding mode surface and a switching logic are further designed, so that the all-aspect capability is guaranteed. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed guidance strategy.

Synthesis of Suboptimal Guidance Law for Anti-Tank Guided Missile with Terminal Impact Angle Constraint Based on the SDRE Technique

In this paper, the homing-phase guidance law is proposed against a stationary target in the planar engagement scenario. In this problem, two technical criteria that the guidance law must achieve are: first, zero terminal miss distance, and second, satisfying the desired impact angle constraint at the final time. This guidance law is synthesized as a nonlinear optimal control problem with an infinite-time horizon and is solved using the state-dependent Riccati equation (SDRE) method. To obtain a guidance law with a finite-time horizon, a state weighting matrix based on the time-to-go is utilized in the SDRE control scheme. The synthesized guidance law is applied to a new generation anti-tank guided missile class, with specific thrust and drag parameters. Nonlinear simulations are conducted to demonstrate the fundamental properties, applicability, and effectiveness of the proposed guidance law.

Multiple Constraints-Based Adaptive Three-Dimensional Back-Stepping Sliding Mode Guidance Law against a Maneuvering Target

This paper addresses the issue of a complex three-dimension (3-D) terminal guidance process that is used against maneuvering targets while considering both the terminal impact angle (TIA) and field-of-view (FOV) angle constraints. According to the highly coupled and nonlinear 3-D terminal guidance model, an adaptive back-stepping sliding-mode guidance law algorithm is proposed in order to guarantee the stability and robustness of the guidance system. Considering the explicit expression of the line-of-sight (LOS) angle in the kinematics and dynamics of the terminal guidance process, the TIA constraint is transformed into an LOS constraint based on their well-known relationship. In view of the challenges in obtaining the motion information of maneuvering targets, an adaptive law design is introduced in order to estimate and compensate for external disturbances caused by the maneuvering of the target and modeling uncertainty. In addition, because the FOV angle represented by the overall leading angle is not a state variable in the sliding-mode guidance system, it is decoupled into two partial leading angles based on a specific transformation relation, so the 3-D terminal guidance control problem is converted into separate tracking system control issues in the pitch and yaw planes. Then, the Lyapunov stability theory is utilized to substantiate the stability of the guidance system, where the Lyapunov functions in both of the subsystems consist of the LOS and partial FOV state error terms. Finally, a series of simulations of various motion states of maneuvering targets under different terminal cases were carried out. It was proved that the terminal guidance design based on the strategies presented above was able to obtain the desired LOS constraints with satisfying the FOV limitation, and the simulation results verified the effectiveness, universality, and significance for practical applications of the proposed guidance design method.

Optimal Look-Angle Guidance with Field-of-View and Impact Angle Constraints for Strapdown Munition

A strapdown seeker with limited field-of-view (FOV) can simplify and decrease cost of the guidance system for a munition. However, the inherent defect of the strapdown seeker is that it could not provide the necessary line-of-sight (LOS) angular information for typical guidance application. This paper proposed an optimal look-angle guidance law (OLAGL) which directly utilized seeker angle information and satisfies the constraints of FOV and terminal impact angle. The coefficient determination, effects of switching threshold, and gains for the guidance law are analyzed and detailed. The simulation results compared with typical trajectory shaping guidance for a ground target show that the presented guidance law can satisfy the impact angle constraint under the limitation of FOV and provide a well engineering reference.

Novel Particle Swarm Optimization Guidance for Hypersonic Target Interception with Impact Angle Constraint

Considering that the terminal impact angle constraint can improve the interception performance of hypersonic target, a novel particle swarm optimization guidance (NPSOG) algorithm is proposed to satisfy the impact angle constraint. Two-dimensional dynamics engagement mode for hypersonic target interception is formulated. The performance index is positively correlated with the line-of-sight (LOS), LOS rate, and the relative distance between missile and target. The weight coefficients among the three are adaptively adjusted by the fuzzy logic controller. The particle swarm optimization (PSO) algorithm is utilized to generate the guidance commands. Numerical examples are given to verify the performance of the proposed guidance law in various engagement scenarios, and the performance of the algorithm is validated comparing with several heuristic guidance methods and nonheuristic guidance methods.

Nonlinear Guidance Laws for Maneuvering Target Interception With Virtual Look Angle Constraint

For the problem of intercepting a maneuvering target with a desired terminal impact angle, we propose a guidance law in this article based on a nonlinear relative virtual guidance model in which the origin is attached to the target. In this way, the original maneuvering target is transformed to a stationary one. We introduce the idea of polynomial guidance in the range domain into the relative virtual guidance model, then the acceleration command is obtained considering the terminal line-of-sight angle constraint and the terminal virtual look angle constraint. After linearization, the proposed law turns to a similar structure with the trajectory shaping guidance law, which is the optimal guidance law in the linear system. Finally, the performance of the proposed guidance law is demonstrated through numerous nonlinear simulations <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</b>

Terminal Impact Angle Control Guidance Law Considering Target Observability

The problem of the terminal impact angle control guidance law, considering the target observability for passive guidance with bearing-only measurement, is investigated in this paper. Modified line-of-sight (LOS) angle error dynamics and their closed-loop analytical solution are developed to enhance the target observability, and then their characteristics are studied, which makes the LOS angular rate oscillate in the early stage. The terminal impact angle control guidance law with the global sliding mode is designed to eliminate the approaching stage of sliding mode control, which makes the system robust throughout the entire process of control. Finally, numerical simulations are presented to demonstrate the performance of the proposed guidance law under various conditions, which achieves the desired results.

Three-dimensional impact angle constrained distributed cooperative guidance law for anti-ship missiles

This paper investigates the problem of distributed co-operative guidance law design for multiple anti-ship missiles in the three-dimensional (3-D) space hitting simultaneously the same target with considering the desired terminal impact angle constraint. To address this issue, the problem formulation including 3-D nonlinear mathematical model description, and communication topology are built firstly. Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight (LOS) which satisfies the impact time constraint. However, the normal accelerations are designed to guarantee the convergence of the LOS angular rate. Furthermore, consider the terminal impact angle constraints, a nonsingular terminal sliding mode (NTSM) control is introduced, and a finite time convergent control law of normal acceleration is proposed. The convergence of the proposed guidance law is proved by using the second Lyapunov stability method, and numerical simulations are also conducted to verify its effectiveness. The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.

Midcourse Guidance Strategy for Multistage Interceptors with Coasting Phase

This paper proposes a new approach on the impact angle control guidance problem for the multistage interceptor with nonmaneuvering phases, called coasting phase, and high acceleration buildup during the boosting phase. First, the required coasting time is determined to reach the target within the given time span considering operation time of the kill vehicle. Then, the required flight path angle profiles and corresponding guidance commands during the boosting phase are derived, in order to achieve the desirable impact angle and to minimize guidance errors at the end of the flight. To do so, the position and velocity changes of each phase are analytically calculated, and then the relationship between the time derivative of the flight path angle during the boosting phase and guidance errors accumulated throughout the flight is established. Some practical error compensation algorithms for the proposed guidance strategy are also presented. The significance of this paper lies in that it is the new analytic approach on how to determine flight path profiles of a multistage interceptor to achieve a terminal impact angle constraint considering both booting and coasting. The proposed guidance strategy is evaluated and proven to be effective through a case study with nonlinear simulations.

Integrated guidance and control of interceptors with impact angle constraint against a high-speed maneuvering target

An integrated guidance and control method is investigated for interceptors with impact angle constraint against a high-speed maneuvering target. Firstly, a new control-oriented model with impact angle constraint of the integrated guidance and control system is built in the pitch plane by combining the engagement kinematics and missile dynamics model between the interceptor and target. Secondly, the flight path angle of the target is estimated by extended Kalman filter in order to transform the terminal impact angle constraint into the terminal line-of-sight angle constraint. Thirdly, a nonlinear adaptive sliding mode control law of the integrated guidance and control system is designed in order to directly obtain the rudder deflection command, which eliminates time delay caused by the traditional backstepping control method. Then the Lyapunov stability theory is used to prove the stability of the whole closed-loop integrated guidance and control system. Finally, the simulation results confirm that the integrated guidance and control method proposed in this paper can effectively improve the interception performance of the interceptor to a high-speed maneuvering target.

Three-Dimensional Impact Time and Angle Control Guidance Based on MPSP

A new nonlinear guidance law for air-to-ground missile cooperation attacks is proposed in this paper. This guidance law enables missiles with different initial conditions to attack targets simultaneously, and it can also precisely satisfy the terminal impact angle conditions in both flight-path angle and heading angle. The guidance law is devised using the model predictive static programming (MPSP) method, and the control saturation constraint is incorporated in the MPSP algorithm. The first-order-lag acceleration of the missile is taken as the state variable to realize the convergence of the terminal acceleration to zero. Moreover, a collision avoidance strategy for three-dimensional missile cooperative flight is proposed. The simulation results show that the guidance law can make the missiles hit the target accurately at the same time with the ideal impact angles and can realize the control saturation constraints of the missiles. This can increase the attack effects and is significant for collaborative attacks.

Learning to Guide: Guidance Law Based on Deep Meta-Learning and Model Predictive Path Integral Control

In this paper, we present a novel guidance scheme based on model-based deep reinforcement learning (RL) technique. With model-based deep RL method, a deep neural network is trained as a predictive model of guidance dynamics which is incorporated into a model predictive path integral (MPPI) control framework. However the traditional MPPI framework assumes the actual environment similar to the training dataset for the deep neural network which is impractical in practice with different maneuvering of target, other perturbations and actuator failures. To address this problem, our method utilize meta-learning technique to make the deep neural dynamics model adapt to such changes online. With this approach we can alleviate the performance deterioration of standard MPPI control caused by the difference between actual environment and training data. Then, a novel guidance law for a varying velocity interceptor intercepting maneuvering target with desired terminal impact angle under actuator failure is constructed based on aforementioned techniques. Simulation and experiment results under different cases show the effectiveness and robustness of the proposed guidance law in achieving successful interceptions of maneuvering target.

Look Angle Constrained Impact Angle Control Guidance Law for Homing Missiles With Bearings-Only Measurements

This paper presents an impact angle control guidance law that confines the missile look angle during homing in order to not exceed a seeker's field-of-view limit. A sliding surface variable whose regulation guarantees the interception of a stationary target at the desired impact angle is designed, and the guidance law is derived to make the surface variable go to the sliding mode. Using a magnitude-limited sigmoid function in the surface variable, the proposed law prohibits the look angle from exceeding the specified limit during the entire homing. This capability to confine the missile look angle is valuable when a seeker's field-of-view is restricted, since imposing the terminal impact angle constraint demands the missile to fly a curved trajectory. Furthermore, the proposed law can be implemented under bearings-only measurements because the command does not involve any information of the relative range and line-of-sight rate. Numerical simulations are conducted to demonstrate the validity of the proposed law. The result shows that the proposed guidance law accomplishes the impact angle constraint without violating the prescribed look angle limit although it only uses the information of bearing angles.

Guidance law to control impact angle and time based on optimality of error dynamics

In this work, a new guidance law with a meaningful performance index is designed to satisfy terminal impact angle and impact time constraints based on optimal error dynamics, which can be used for salvo attacks or cooperative missions of multi-missile. The analytical solution of the proposed guidance law is a combination of trajectory shaping guidance law and an additional impact time error feedback term that is proportional to the difference between the desired and the true impact times. Trajectory shaping guidance law aims to achieve the desired terminal impact angle and zero miss distance, whereas the extra term aims to meet the desired impact time. The minimum and maximum feasible impact times that consider the seeker's field-of-view limit, terminal impact angle constraint, and missile's maneuvering acceleration limit are calculated to provide the feasible boundary range of the desired impact time. Numerical simulations of several engagement situations demonstrate the effectiveness of the proposed guidance law in the accuracy of terminal impact angle and impact time.

Three-Dimensional Nonlinear Impact Angle Guidance for Maneuvering Targets

Guidance system, which is an integral part of missile flight control system, plays a key role in achieving a desired performance subjected to various criteria. This paper focuses on the design of terminal impact angle constrained guidance laws, against maneuvering targets, for three-dimensional engagements. Impact angles are defined by the elevation and azimuth angles of line-of-sight with respect to the inertial frame of reference. The derivation of guidance strategies are performed with the nonlinear coupled engagement kinematics using dynamic inversion and sliding mode control techniques. The proposed guidance laws are applicable even for large heading angle errors. The comparative study of performance of both guidance laws is done using numerical simulations for various engagement scenarios.

A Two-Phased Guidance Law for Impact Angle Control with Seeker’s Field-of-View Limit

A two-phased guidance problem with terminal impact angle constraints and seeker’s field-of-view limit is addressed in this paper for a missile against a nonmaneuvering incoming target. From the conventional PN guidance without any constraints, it is found that satisfying the impact angle constraint causes a more curved missile trajectory requiring a large look angle. To avoid the look angle exceeding the seeker’s physical limit, a two-phased look angle control guidance scheme with the terminal constraint is introduced. The PN-typed guidance law is designed for each guidance phase with a specific switching condition of line-of-sight. The proposed guidance law is comprised of two types of acceleration commands: the one in the initial phase which aims at controlling the missile’s look angle to reach the limit and the other for final phase which is produced by switching the navigation gain. The monotonicity of the line-of-sight angle and look angle is analyzed and proved to support the proposed method. To evaluate the specific navigation gains for both initial and final phases, the scaling coefficient between them is discussed by solving a quadratic equation with respect to the initial navigation gain. To avoid a great abrupt acceleration change at the switching instant, a minimum coefficient is chosen. Extensive simulations are performed to validate the efficiency of the proposed approach.

Generalized optimal impact-angle-control guidance with terminal acceleration response constraint

To study the optimal impact-angle-control guidance problem with multiple terminal constraints, a generalized optimal impact-angle-control guidance law with terminal acceleration response constraint (GOIACGL-TARC) is proposed. In the deriving, a time-to-go − nth power weighted object function is adopted to derived the GOIACGL-TARC and a general expression of GOIACGL-TARC is presented. Based on the general expression of GOIACGL-TARC, three guidance laws, GOIACGL-TARC1/TACC0/TACC1 are proposed and the inheritance relationship between GOIACGL-TACC0/TACC1/TARC1 and the conventional optimal guidance law with impact angle constraint is demonstrated. Performance analysis of the proposed guidance laws shows that in the case of GOIACGL-TACC0, the terminal acceleration is not zero at n = 0 and only as n &gt; 0, the terminal acceleration converges to zero; in the case of GOIACGL-TACC1 and GOIACGL-TARC1, GOIACGL-TARC1 can guarantee the acceleration response to reach the exactly zero value but GOIACGL-TACC1 cannot, which can only guarantee the acceleration command to reach the exactly zero value. It is pointed out that compared with the biased proportional navigation guidance law, GOIACGL-TARC1 has an outstanding guidance performance in acceleration response, miss distance, and terminal impact angle error.

Observer-Based Guidance Law With Impact Angle Constraint

Accounting for the autopilot as second-order dynamics, an observer-based guidance law with terminal impact angle constraint is designed using the dynamic surface control method. Some first-order low-pass filters are introduced into the designing process to avoid the occurrence of high-order derivatives of the line of sight (LOS) angle in the expression of the guidance law such that the guidance law can be implemented in practical applications. The proposed guidance law is effective in compensating for the second-order autopilot lag. In simulation of intercepting targets with sinusoidal acceleration, the guidance law is compared with the biased proportional navigation guidance (BPNG) law in the presence of missile autopilot lag. Simulation results show that the proposed observer-based guidance law with terminal impact angle constraint is able to guide a missile with large autopilot lag to impact a target with a desired angle and achieve a small miss distance, even if the target escapes in a great and fast maneuver.

A nonlinear impact-angle guidance law

PurposeThe purpose of this paper is to propose a new nonlinear guidance law to satisfy terminal impact-angle constraints against a stationary target in every possible planar surface-to-surface engagement scenario. The proposed guidance scheme is developed based on the geometry of a circular arc trajectory. The proposed guidance scheme is developed based on the geometry of circular arc trajectory. This trajectory is calculated based on the terminal impact angle and target range. The efficacy of the proposed guidance scheme is demonstrated through numerical simulations. The proposed scheme is compared with existing guidance schemes and relevant analysis is provided.Design/methodology/approachThe paper develops a new nonlinear guidance law to satisfy terminal impact-angle constraints against a stationary target in every possible planar surface-to-surface engagement scenario. The proposed guidance scheme is developed based on the geometry of a circular arc trajectory. This guidance scheme is further extended to moving targets.FindingsThe proposed guidance intercepts a stationary target with a smooth lateral acceleration command, which is desirable for realistic implementation. The efficacy of the approach is demonstrated through numerical simulation. A comparative study with the existing algorithm is presented and it is shown that the proposed algorithm is better on many counts.Originality/valueThere are many approach exists in the literature for impact-angle guidance laws. The paper proposes a computationally efficient guidance law using geometric and kinematic properties. As the approach produces smooth command, it has a practical relevance. A comparative study shows superiority on some counts (miss distance, flight time, smoothness).