Three-dimensional Cooperative Guidance Research Articles

Three-Dimensional Cooperative Guidance Law Against Maneuvering Target with Time-Varying Communication Delays

Three-Dimensional Cooperative Guidance Law Against Maneuvering Target with Time-Varying Communication Delays

A generalized three-dimensional cooperative guidance law for various communication topologies with field-of-view constraint

In this paper, a generalized three-dimensional (3D) cooperative guidance law with seeker’s field-of-view (FOV) constraints is designed for multiple missiles to achieve salvo attack against a stationary target. The proposed generalized guidance law is composed of two parts: a proportional navigation guidance (PNG) component for target capture and a biased feedback component for simultaneous arrival. Two novel auxiliary functions are integrated into the biased feedback component to guarantee the satisfaction of FOV constraint. Furthermore, a time-varying lower bound that contains the impact time error is utilized to avoid the guidance command singularity. The proposed guidance law can be easily applied to various missile communication topologies, including centralized connected, distributed connected, and no-connected topologies. The convergence of impact time error, FOV constraint satisfaction, and command non-singularity of the proposed guidance law are theoretically analyzed and proved. Extensive numerical simulations with comparative studies are conducted to demonstrate the effectiveness and advantages of the proposed guidance law.

Three-dimensional cooperative guidance law for intercepting hypersonic targets

This paper proposes a three-dimensional adaptive sliding mode cooperative guidance law using multiple low-speed interceptors with time-varying speeds for effectively intercepting hypersonic targets. The guidance commands are divided into commands along and normal to the line-of-sight (LOS). First, based on the algebraic graph and consensus theories, the guidance command along the LOS is designed to ensure that multiple interceptors achieve finite-time convergence to simultaneously intercept a hypersonic target. Second, to address the external disturbance caused by the manoeuvring of the hypersonic target in the direction normal to the LOS, finite-time disturbance observers are designed to accurately estimate the acceleration information of the hypersonic target with rapid convergence. Next, the guidance command normal to the LOS is formulated based on the sliding mode control method, which can nullify the LOS angular rate, ensuring progressive convergence to zero at interception. Moreover, thrust and drag models are incorporated to ensure that the guidance model is reasonably realistic. Numerical simulations are performed for different manoeuvring modes of the hypersonic target, and comparative simulations are conducted using the proportional navigation and sliding mode cooperative guidance laws. The simulation results demonstrate the superiority and effectiveness of the proposed guidance law.

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.

Three-dimensional prescribed performance cooperative guidance law with spatial constraint for intercepting manoeuvring targets

This paper proposes three-dimensional cooperative guidance laws with prescribed performance. To avoid degradation in performance due to error in the estimation of the time-to-go, the relative distance between the missiles and the target is chosen as a coordination variable, and a fixed-time cooperative guidance law along the direction of the line-of-sight (LOS) is proposed. The guidance laws with prescribed performance for the elevation and direction of the azimuth of the LOS are then developed by combining the LOS angle tracking error with a performance constraint function to formulate a transformed error function. The problem of prescribed performance control is transformed into that of the boundedness of the transformed error function. A fixed-time convergence disturbance observer is designed to discuss the problem whereby information on aggregate uncertainty, including on the target, is unavailable. The results of simulations show that the proposed guidance laws are effective.

Three-dimensional cooperative guidance law to control impact time and angle with fixed-time convergence

This article proposes a new terminal cooperative guidance law to control both impact time and impact angle in three-dimensional engagement. The presented guidance law employs on and normal line-of-sight accelerations to control the impact time and angle together. Two parts are included in this guidance law, that is, the guidance laws with impact time constraint and impact angle constraint. The first is designed based on fixed-time consensus theory to fulfill the salvo attack of the target, and the second is developed based on fixed-time nonsingular fast terminal sliding mode control method to achieve the desired impact angles. The stability analysis of this guidance law based on Lyapunov theory is also presented in detail. Moreover, the maneuvering target can be intercepted successfully with the presented guidance law, and the fixed-time stability and less control energy are well ensured. Additionally, the effectiveness and applicability of the proposed guidance scheme are explicitly verified through simulation tests.

Terminal Impact Time Control Cooperative Guidance Law for UAVs under Time-Varying Velocity

Aiming at the problem that multiple Unmanned Aerial Vehicles (UAVs) attack the stationary target cooperatively under time-varying velocity, the cooperative guidance law with finite time convergence on two-dimensional plan and the three-dimensional cooperative guidance laws with impact time constraint are designed separately in this paper. Firstly, based on the relative motion equation between UAV and target on two-dimensional plane, the time cooperative guidance model of multiple UAVs is established. Then based on the consistency theory and graph theory, a distributed time cooperative guidance law is designed, which can ensure that the impact time of all UAVs can be quickly consistent in a limited time. Next, the cooperative guidance problem is expanded from two-dimensional plane to three-dimensional space, the motion model between UAV and target in three-dimensional space is established and the expression of time-to-go estimation under time-varying velocity is derived. Finally, according to whether there is the communication among UAVs under the condition of time-varying velocity, a multiple UAVs three-dimensional cooperative guidance law based on desired impact time and a multiple UAVs three-dimensional cooperative guidance law based on coordination variables are designed, respectively. The simulation results show that the cooperative guidance law with finite time convergence on two-dimensional plan and the three-dimensional cooperative guidance law with impact time constraint proposed in this paper are effective, which can both realize the saturation attack under the time-varying velocity.

Three-dimensional cooperative guidance strategy and guidance law for intercepting highly maneuvering target

Cooperative interception of the target with strong maneuverability by multiple missiles with weak maneuverability in the three-dimensional nonlinear model is studied. Firstly, the three-dimensional nonlinear model of cooperative guidance is established. The three-dimensional reachable region is represented composed of lateral acceleration and longitudinal acceleration in the two-dimensional coordinate system. Secondly, the problem of the multiple missile's reachable coverage area is transformed into the problem of cooperative coverage. A cooperative coverage strategy is proposed and an algorithm for quickly calculating the number of required missiles is designed. Then, the guidance law based on the cooperative coverage strategy is proposed, and it is proved that cooperative interception of the target can be achieved under the acceleration limit. Moreover, the relations among the number of missiles, the initial array position of terminal guidance and the coverage area of the target’s large maneuver are analyzed. The dynamic adjustment strategy of guidance parameters is proposed to reduce the guidance error. Finally, simulation results show that multiple missiles with low maneuverability can achieve effective interception of target with strong maneuverability through the proposed cooperative strategy and cooperative guidance method.

Target Tracking Enhancement by Three-Dimensional Cooperative Guidance Law Imposing Relative Interception Geometry

The problem that two cooperative missiles intercept a maneuvering target while imposing a desired relative geometry is investigated in the paper. Firstly, a three-dimensional (3D) estimation model for cooperative target tracking is proposed and the observability of the missile-target range measurement is analyzed. In order to enhance the estimation performance, a two-level cooperative interception guidance architecture is proposed which combines a coordination algorithm with a novel 3D fixed-time convergent guidance law considering line of sight (LOS) angle constraints, such that the desired relative geometry can be imposed quickly and steadily by a dynamic strategy. The effectiveness and superiority of the proposed guidance law is evidenced through the numerical simulations comparing with other guidance laws.

Three-dimensional cooperative guidance law for multiple missiles with impact angle constraint

This paper proposes a cooperative guidance law for attacking a ground target with the impact angle constraint based on the motion camouflage strategy in the line-of-sight (LOS) frame. A dynamic model with the impact angle constraint is established according to the relative motion between multiple missiles and the target. The process of cooperative guidance law design is divided into two stages. Firstly, based on the undirected graph theory, a new finite-time consensus protocol on the LOS direction is derived to guarantee relative distances reach consensus. And the value of acceleration command is positive, which is beneficial for engineering realization. Secondly, the acceleration command on the normal direction of the LOS is designed based on motion camouflage and finite-time convergence, which can ensure the missiles reach the target with the desired angle and satisfy the motion camouflage state. The finite-time stability analysis is proved by the Lyapunov theory. Numerical simulations for stationary and maneuver targets have demonstrated the effectiveness of the cooperative guidance law proposed.

A robust three-dimensional cooperative guidance law against maneuvering target

This paper proposes a robust three-dimensional cooperative guidance law (RTCGL) against a maneuvering target. When some missiles are intercepted during the engagement, this RTCGL integrated with a local filtering algorithm can ensure that the rest missiles hit the maneuvering target simultaneously. The pitch acceleration command is designed based on an augmented proportional navigation guidance law and can make the missile’s trajectory fall into its yaw plane. Then the three-dimensional cooperative problem is converted into a planar one. The yaw acceleration command consists of a guidance component for homing and a coordination component for simultaneous arrival. Numerical simulation results are presented to verify the effectiveness of the cooperative guidance law.

Two-stage cooperative guidance strategy using a prescribed-time optimal consensus method

This paper addresses the optimal decentralized three-dimensional cooperative guidance problem for multiple interceptors against a stationary target considering dynamically changing and directed communication topologies. A two-stage cooperative strategy is proposed to achieve simultaneous attack regardless of the information on time-to-go. More specifically, a prescribed-time optimal consensus method is applied in the process of the first-stage distributed cooperative guidance law design to generate desired initial conditions for the latter guidance phase, where the consensus arriving time can be off-line pre-appointed according to interception mission requirements without conservative estimation and is independent of the initial conditions of interceptor's states. Furthermore, the optimal consensus control under directed and periodical switching topologies is also considered in the first guidance phase, and the analytically optimal cooperative guidance law is formulated based on Pontryagin's principle. As for the second guidance phase, all interceptors are switched to typical pure proportional navigation guidance law, and the salvo attack can be achieved eventually. Extensive numerical simulations are performed to validate the effectiveness and superiority of the proposed cooperative guidance scheme.

A Three-Dimensional Cooperative Guidance Law Based on Consensus Theory for Maneuvering Targets

In this paper, a cooperative guidance law based on consensus theory is proposed for multiple flight vehicles against a maneuvering target in a three-dimensional plane. The proposed guidance law has three orientation components: the one along the line-of-sight (LOS) ensures that all flight vehicles reach the target simultaneously, and the other two normal to the LOS in longitudinal and lateral plane guarantee the accurate interception. The target maneuverings are estimated by a finite-time convergence disturbance observer (FTDOB) and are compensated into the kinematic equation to achieve more accurate interception. Using the Lyapunov stability theorem, time-to-go of all flight vehicles’ convergence is proved. Mathematical simulations verify the effectiveness of the proposed cooperative guidance law.

Coverage-based three-dimensional cooperative guidance strategy against highly maneuvering target

A coverage-based cooperative guidance strategy is proposed for multiple missiles to cooperatively intercept a highly maneuvering target. The scenario of interest is that several missiles separate with each other to cooperatively intercept the target at the beginning of terminal guidance phase, and both the interceptors and target are assumed to have limited maneuverability. The guidance goal is formulated to cooperatively cover the target evasion region by coordinating the reachable sets of different interceptors. To achieve this goal, firstly, the concept of virtual aiming points is introduced to bias the reachable set of true proportional navigation guidance law (TPN) as expected. Then, to maximally cover the target maneuvering range, we transform the cooperation problem into an optimization problem to find a set of proper virtual aiming points for different missiles. The main advantage of the proposed guidance strategy is that it enables multiple missiles without maneuverability superiority to intercept a highly maneuvering target. Numerical simulations clearly show the effectiveness of the proposed cooperative strategy.

Three-dimensional cooperative guidance and control law for multiple reentry missiles with time-varying velocities

A three-dimensional partial integrated guidance and control law is proposed for cooperative flight of multiple hypersonic reentry missiles with uncontrollable and time-varying velocities. As for the problem of multiply reentry missiles with varying velocities attacking the target synchronously, a cooperative scheme is presented by adjusting the lateral pre-setting angle of velocity. In addition, a partial integrated guidance and control method with a two-loop controller structure is designed to realize the proposed cooperative scheme. Considering the saturation of the velocity slope angle and the unknown uncertainty, the two-loop three-channel controller of each reentry missile is designed based on dynamic inverse theory, dynamic surface control theory and extended state observer. The stability of the closed-loop system is demonstrated by Lyapunov theory. Simulation results verify the effectiveness and superiority of the proposed guidance and control law.

Three-dimensional cooperative guidance law for multiple missiles with finite-time convergence

For the three-dimensional terminal guidance problem of multiple missiles cooperatively intercepting a maneuvering target, a novel finite-time cooperative guidance law with impact angle constraints is proposed. It is continuous and requires no information on target maneuvers. Firstly, the multiple missiles cooperative guidance model with impact angle constraints is constructed. We subsequently divide the process of cooperative guidance law design into two stages. In the first stage, based on the adaptive super-twisting algorithm and integral sliding mode, a new finite-time consensus protocol, i.e., the acceleration command on the line-of-sight direction, is designed to guarantee that all missiles reach the maneuvering target simultaneously. In the second stage, a new adaptive nonsingular fast terminal sliding mode control law, i.e., the acceleration command on the normal direction of the line-of-sight, is developed to ensure the finite-time convergence of the line-of-sight angular rate and line-of-sight angle between individual missile and the target. Furthermore, the detailed finite-time stability analysis is given based on the Lyapunov theory. Finally, numerical simulations demonstrate the effectiveness of the proposed cooperative guidance law.

Distributed three-dimensional cooperative guidance via receding horizon control

The paper presents a new three-dimensional (3D) cooperative guidance approach by the receding horizon control (RHC) technique. The objective is to coordinate the impact time of a group of interceptor missiles against the stationary target. The framework of a distributed RHC scheme is developed, in which each interceptor missile is assigned its own finite-horizon optimal control problem (FHOCP) and only shares the information with its neighbors. The solution of the local FHOCP is obtained by the constrained particle swarm optimization (PSO) method that is integrated into the distributed RHC framework with enhanced equality and inequality constraints. The numerical simulations show that the proposed guidance approach is feasible to implement the cooperative engagement with satisfied accuracy of target capture. Finally, the computation efficiency of the distributed RHC scheme is discussed in consideration of the PSO parameters, control update period and prediction horizon.

Three-dimensional cooperative guidance laws against stationary and maneuvering targets

This paper presents the cooperative strategies for salvo attack of multiple missiles based on the classical proportional navigation (PN) algorithm. The three-dimensional (3-D) guidance laws are developed in a quite simple formulation that consists of a PN component for target capture and a coordination component for simultaneous arrival. The centralized algorithms come into effect when the global information of time-to-go estimation is obtained, whereas the decentralized algorithms have better performance when each missile can only collect information from neighbors. Numerical simulations demonstrate that the proposed coordination algorithms are feasible to perform the cooperative engagement of multiple missiles against both stationary and maneuvering targets. The effectiveness of the 3-D guidance laws is also discussed.

A Three-Dimensional Cooperative Guidance Law of Multimissile System

In order to conduct saturation attacks on a static target, the cooperative guidance problem of multimissile system is researched. A three-dimensional guidance model is built using vector calculation and the classic proportional navigation guidance (PNG) law is extended to three dimensions. Based on this guidance law, a distributed cooperative guidance strategy is proposed and a consensus protocol is designed to coordinate the time-to-go commands of all missiles. Then an expert system, which contains two extreme learning machines (ELM), is developed to regulate the local proportional coefficient of each missile according to the command. All missiles can arrive at the target simultaneously under the assumption that the multimissile network is connected. A simulation scenario is given to demonstrate the validity of the proposed method.