Multiple Missiles Research Articles

Cooperative guidance law considering the randomness of the unreliable communication network

The cooperative attack problem of multiple missiles considering the randomness of the unreliable communication network is investigated. Firstly, the stochastic communication network is described by a Bernoulli random model. And the cooperative guidance law with unreliable communication network is proposed, which is composed of the upper consensus algorithm of desired impact time and the local proportional navigation with time-varying navigation gain. Each node of the upper cooperative system uses different update gain to adjust the desired impact time to improve the cooperative performance. Secondly, the mean square stability of the upper cooperative system is analyzed and proved. The explicit necessary and sufficient conditions of the mean square stability are presented for the two-missile cooperative attack system. And the analytic expression of the mean of the cooperative impact time is derived since it influences the attack precision directly and significantly. Thirdly, the effectiveness of the proposed cooperative guidance law with unreliable communication network is verified by simulation. And the influence of the update gain, the communication step, and the mean of link probability on the cooperative attack precision is analyzed.

Distributed cooperative controller design considering guidance loop and impact angle

This paper presents an integrated distributed cooperative guidance and control scheme for multiple missiles to attack a single target simultaneously at desired impact angles. The scheme is divided into two parts: individual part and cooperative part. For the individual part, partial integrated guidance and control method is adopted to generate the elevator deflection (which is a realistic control input) to ensure that the missiles fly along their respective desired line of sight and hit the target; this is in contrast to previous works which analyze only the engagement dynamics and use missile accelerations as the control input, however, the proposed controller also considers the missile dynamics, thus enabling the implementation of an autopilot. For the cooperative part, using only information from adjacent missiles, the proposed distributed cooperative controller can make all missiles hit the target simultaneously. Hence in this scheme, each missile can hit the target at desired angles and at the same time, thus achieving salvo attack. Simulations are performed to verify the effectiveness of the scheme.

3-D impact angle constrained distributed cooperative guidance for maneuvering targets without angular-rate measurements

In this paper, a three-dimensional (3-D) distributed cooperative guidance scheme is presented for multiple missiles to attack a single maneuvering target at pre-specified impact angles. A finite time observer is firstly proposed to provide accurate estimates of full states and disturbances; this is particularly crucial since some system states are not available as they are dependent on the unknown acceleration of the target. Then the guidance law is designed, which consists of two parts: the individual part and cooperative part. In the individual part, each missile is designed separately such that it will fly along the desired line of sight (LOS) after a given time which ensures hit-to-kill attack for the maneuvering target at the desired impact angles. In the cooperative part, the guidance law is designed for each missile using only information from adjacent missiles, to make all missiles hit the target at the same time. Hence it is ensured that all missiles can hit the target simultaneously, as well as at the desired directions (impact angles), then successfully achieving salvo attack. Finally, simulations are performed to verify the effectiveness of the proposed scheme.

Cooperative guidance with multiple constraints using convex optimization

In the existing closed-loop cooperative guidance approaches for salvo attack of multiple missiles, the multiple constraints and time-variant velocity basically cannot be effectively considered. Therefore, two closed-loop cooperative guidance methods are developed in this paper, by employing the efficient convex optimization technique and receding horizon control (RHC) strategy. During each guidance cycle of RHC, the system coordination target is updated and then broadcasted to each missile as a constraint. Subsequently, the convex optimization technique is utilized to solve the multi-constraint optimal proportional guidance problem of each missile online to achieve the consensus on time-to-go among missiles. Simulation results show that for three cases with different conditions of velocity, the cooperative simultaneous attack under multiple constraints can be effectively carried out using each of the two proposed cooperative guidance laws, which verify their effectiveness and feasibility.

Consensus-Based Two-Stage Salvo Attack Guidance

The problem of salvo attack of multiple missiles without time-to-go estimation has been addressed by a two-stage guidance scheme in this correspondence. In the first stage, a simple decentralized control law is designed to provide desired initial conditions (target-missile relative range and velocity lead angle) for the latter stage. As for the second stage, all missiles are governed by classical pure proportional navigation guidance law. Numerical simulations under two-dimensional (2-D) and 3-D cases demonstrate the effectiveness of the proposed formulation.

Improved Spatial Registration and Target Tracking Method for Sensors on Multiple Missiles.

Inspired by the problem that the current spatial registration methods are unsuitable for three-dimensional (3-D) sensor on high-dynamic platform, this paper focuses on the estimation for the registration errors of cooperative missiles and motion states of maneuvering target. There are two types of errors being discussed: sensor measurement biases and attitude biases. Firstly, an improved Kalman Filter on Earth-Centered Earth-Fixed (ECEF-KF) coordinate algorithm is proposed to estimate the deviations mentioned above, from which the outcomes are furtherly compensated to the error terms. Secondly, the Pseudo Linear Kalman Filter (PLKF) and the nonlinear scheme the Unscented Kalman Filter (UKF) with modified inputs are employed for target tracking. The convergence of filtering results are monitored by a position-judgement logic, and a low-pass first order filter is selectively introduced before compensation to inhibit the jitter of estimations. In the simulation, the ECEF-KF enhancement is proven to improve the accuracy and robustness of the space alignment, while the conditional-compensation-based PLKF method is demonstrated to be the optimal performance in target tracking.

A composite impact-time-control guidance law and simultaneous arrival

A new composite impact time control guidance law is proposed for simultaneous attack against a ground target. The guidance strategy is composed of two phases. Specifically, the first phase is to guide the missile to proper switching relative range for the second phase. After which, the second phase will lead the missile to the target with a desired impact time by using the proposed Lyapunov based guidance scheme. The impact time is given in a simple analytical form of initial states and switching relative range, the value of which is determined to control the impact time. The proper range of the switching state is analyzed considering the line of sight angle constraint. And the permissible range for impact time can be calculated corresponding to the proper switching state. Two classes of simultaneous attack are considered to demonstrate the effectiveness of the impact time control. One is the sequential launch, and the other is a salvo launch of multiple missiles from different positions. Numerical simulations are carried out to verify the performance of the proposed methodology.

A joint mid-course and terminal course cooperative guidance law for multi-missile salvo attack

Salvo attacking a surface target by multiple missiles is an effective tactic to enhance the lethality and penetrate the defense system. However, existing cooperative guidance laws in the mid-course or terminal course are not suitable for long- and medium-range missiles or stand-off attacking. Because the initial conditions of cooperative terminal guidance that are generally generated from the mid-course flight may not lead to a successful cooperative terminal guidance without proper mid-course flight adjustment. Meanwhile, cooperative guidance in the mid-course cannot solely guarantee the accuracy of a simultaneous arrival of multiple missiles. Therefore, a joint mid-course and terminal course cooperative guidance law is developed. By building a distinct leader-follower framework, this paper proposes an efficient coordinated Dubins path planning method to synchronize the arrival time of all engaged missiles in the mid-course flight. The planned flight can generate proper initial conditions for cooperative terminal guidance, and also benefit an earliest simultaneous arrival. In the terminal course, an existing cooperative proportional navigation guidance law guides all the engaged missiles to arrive at a target accurately and simultaneously. The integrated guidance law for an intuitive application is summarized. Simulations demonstrate that the proposed method can generate fast and accurate salvo attack.

Cooperative Guidance Law Design for Simultaneous Attack with Multiple Missiles Against a Maneuvering Target

This paper considers the simultaneous attack problem of multiple missiles against a maneuvering target. Different from most of the existing literature in which the simultaneous attack problem is formulated as a consensus problem of missiles’ time-to-go estimates, this paper formulates it as the consensus problem of missiles’ ranges-to-go. Based on this strategy, novel distributed guidance laws are proposed to solve the simultaneous attack problem with the target of unknown maneuverability. Adaptive control method is introduced to estimate the upper bound of the target’s acceleration. The effectiveness of the proposed guidance laws is verified both theoretically and numerically.

Three-dimensional impact angle constrained distributed guidance law design for cooperative attacks

In this paper, a novel cooperative guidance law is proposed to make multiple missiles in the three-dimensional (3-D) space hit simultaneously the same target at pre-specified impact angles. Firstly, the normal accelerations which change the velocity direction (flight-path and heading angle) are designed such that all missiles will fly along the desired line of sight (LOS) after a given time which ensures the hit-to-kill interception at the desired impact angles; then the consensus variable is constructed using available information and can reach consensus under the proposed tangential acceleration which determines the velocity magnitude. Hence simultaneous hit-to-kill attack is achieved. Finally, some simulation studies are performed to verify the effectiveness of the proposed scheme.

Autopilot and guidance law design considering impact angle and time

The authors propose an autopilot based on partial integrated guidance and control for missiles to achieve interception at a pre-specified impact angle and a close approximation of impact time. The scheme has an outer loop comprising the engagement model and slow dynamics (to generate a pitch-rate command that causes the missile to establish a collision course with the target), and an inner loop comprising the fast dynamics (to make the pitch rate track its command signal). The authors divide the missile flight into two phases; in the first phase the controller causes the missile line-of-sight (LOS) angle (impact angle) to converge to the pre-specified value at a pre-specified time, and to remain there thereafter (and hence establishes a collision course at the desired impact angle). In the second phase, the missile will fly along the LOS until interception occurs. The authors also provide an estimated calculation of the impact time and give the factors that influence the estimate, which helps the user systematically choose the missile parameters in order to achieve a certain impact time; this result can be applied to the case of salvo attack of multiple missiles without online data links. Finally, simulations are performed to verify the scheme effectiveness.

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.

Consensus-based impact-time-control guidance law for cooperative attack of multiple missiles

Consensus-based impact-time-control guidance law for cooperative attack of multiple missiles

Impact-Time-Control Guidance Law With Constraints on Seeker Look Angle

An impact-time-control guidance (ITCG) law is required for simultaneous attack of multiple missiles. In application of ITCG, the limit of seeker look angle should be regarded as an important factor in homing engagement scenarios. To avoid the loss of target tracking during engagement, the seeker's look angle should be confined to the seeker's field-of-view limit. This paper suggests a new ITCG law for a realistic situation with constraints on seeker look angle driven by the exact nonlinear equations of motion in plane. The proposed guidance law ensures the seeker's look angle to reduce monotonically from the initial value to zero at the intercept point. The resulting solution is presented in the form of proportional navigation guidance law with a time-varying navigation gain. The closed-form navigation gain can be obtained from information on the current missile-to-target range and heading angle.

Distributed group cooperative guidance for multiple missiles with fixed and switching directed communication topologies

Distributed group cooperative guidance (DGCG) problems for multiple missiles with fixed and switching directed communication topologies are dealt with. In contrast to traditional cooperative guidance utilized to intercept one single target, the group cooperative guidance is applicable to multiple targets. In the group cooperative attack, multi-missile system is classified into multiple subgroups, and each subgroup attacks its respective target. Missiles in the same subgroup are required to reach the target simultaneously, while different subgroups may cooperate successively in terms of the impact time. To realize the group cooperative attack, a two-step guidance strategy is developed. The first step adopts a DGCG law based on local neighboring information for multiple missiles to realize group consensus on range-to-go and leading angle. The second step begins when the group consensus of missiles is achieved. During this step, each missile attacks the target under the proportional navigation guidance law. Derived from feedback linearization and convergence analysis, sufficient conditions for multiple missiles to realize the group cooperative attack with fixed and switching directed communication topologies are proposed, respectively. Finally, numerical examples with two subgroups are given to show the effectiveness of the two-step guidance strategy.

Coverage-based cooperative guidance strategy against highly maneuvering target

Considering highly maneuvering target, a novel cooperative guidance strategy, which aims to make multiple missiles' joint reachable sets cover the target evasion region, is proposed. The assumed engagement scenario is that multiple missiles separate with each other at the beginning of homing phase and then cooperatively intercept the highly maneuvering target which cannot be intercepted by single missile due to insufficient maneuverability. Firstly, for biasing the reachable sets of different missiles to cover different subintervals of target maneuvering range as expected, a biased proportional navigation guidance law (BPN) is designed by introducing the virtual aiming point. Secondly, for the missile-team without communication capability, the minimum relative maneuverability superiority and minimum team size for covering the whole target maneuvering range are derived based on the BPN respectively, and one open-loop cooperative guidance strategy is proposed with an acceptable assumption about the handover errors of midcourse guidance. While for the missile-team with communication capability, a novel coordinating variable is designed and the corresponding closed-loop guidance strategy is proposed. Numerical simulations with different target maneuver modes are presented to verify the guidance performance of the proposed cooperative guidance strategy.

Simultaneous attack strategy against a maneuvering target with unknown acceleration

This paper is concerning the simultaneous attack problem with multiple missiles against a maneuvering target with unknown acceleration. The new guidance protocol, which avoids using the time-to-go information, ensures the simultaneous attack based on the consensus of the range-to-go and the approaching rate of each missile. This strategy is a distributed guidance law where each missile can only get information from neighbors. The consensus of the missiles is shown mathematically as well as with extensive simulations.

Distributed cooperative guidance for multiple missiles with fixed and switching communication topologies

This study investigates cooperative guidance problems for multiple missiles with fixed and switching directed communication topologies. A two-step guidance strategy is proposed to realize the simultaneous attack. In the first step, a distributed cooperative guidance law is designed using local neighboring information for multiple missiles to achieve consensus on range-to-go and leading angle. The second step begins when the consensus of multiple missiles is realized. During the second step, multiple missiles disconnect from each other and hit the target using the proportional navigation guidance law. First, based on the local neighboring communications, a sufficient condition for multiple missiles to realize simultaneous attack with a fixed communication topology is presented, where the topology is only required to have a directed spanning tree. Then, the results are extended to the case of switching communication topologies. Finally, numerical simulations are provided to validate the theoretical results.

Minimum time state consensus for cooperative attack of multi-missile systems

This paper considers the cooperative attack with multiple missiles on a stationary target and a two-step procedure is proposed. First the states of all missiles are guided to achieve minimum time consensus, and then, by using the proportional navigation guidance law with identical navigation gain each missile arrives at the target simultaneously or sequentially. Among which, the strategy to realize state consensus in minimum time is the focus of the issue. In the paper the coordination algorithms are developed based on bang–bang control strategy due to its simply structure, subsequently, it is proved that the time optimal consensus problem can be transformed into a parameter optimization problem. Besides, the proposed schemes are able to significantly reduce the number of parameters to be optimized and finally solve the problem with little computation cost. Different from the impact time control methods, the strategy for state consensus does not demand the information of time-to-go. Meanwhile only the initial values of missiles' states are required for the coordination algorithms which lead to less communication burden. Two different examples are provided to demonstrate the validity and efficiency of our proposed strategy.

Simultaneous attack of a stationary target using multiple missiles: a consensus-based approach

This paper considers the simultaneous attack problem of multiple missiles against a stationary target.Built upon the classic proportional navigation structure, we propose a consensus-based approach to design the cooperative guidance law.Specifically, we present time-varying navigation ratios for the missiles, which exchange the time-to-go estimates between neighboring missilesvia a communication network. For the cases where the communication topology is undirected or in the leader–follower structure with a missile acting as the leader whose navigation ratio cannot be tuned, we show that the proposed cooperative guidance law can solve the simultaneous attack problem. The effectiveness of the theoretical results is finally illustrated by numerical simulations.