A distributed time-coordinated guidance method for cruise missile swarms with limited control input

Abstract

The present invention discloses a distributed time-coordinated guidance method for a cruise missile cluster with limited control input, which belongs to the technical field of cruise missile cluster guidance and control. A two-layer cooperative guidance architecture for a cruise missile cluster is established; individuals use the estimated value of remaining flight time as a coordination variable, and exchange their respective estimated values ​​of remaining flight time through inter-missile communication. The coordination variable value expected by each missile is calculated by the coordination strategy and used as the input of the lower-layer time-constrained guidance law; the lower-layer time-constrained guidance law is decomposed into the lateral and longitudinal planes, and the attitude angle and throttle are calculated through the segmented guidance law, which are input into the autopilot as guidance control quantities; the steering amount and throttle amount are obtained according to the input attitude angle and throttle instructions, and the attitude and speed of the cruise missile are controlled to achieve time coordination. The present invention provides a distributed time-coordinated guidance method for a cruise missile cluster with limited control input to solve the problem of simultaneous attack of a cruise missile cluster on a stationary target on the ground when the control input is limited to attitude angle and throttle.

Description

Technical Field

[0001] The present invention relates to the technical field of cruise missile cluster guidance control, and in particular to a cruise missile cluster distributed time collaborative guidance method with limited control input. Background Art

[0002] Cruise missiles are munitions with the characteristics of drones, capable of both loiter and guided strikes. Multiple cruise missiles can leverage their collective strengths through coordinated operations, effectively improving combat effectiveness. Depending on whether the terminal constraint is time or angle, coordinated guidance can be categorized as temporal coordination, spatial coordination, and spatiotemporal coordination. Spatial coordination is mostly open-loop coordination with pre-set attack angle constraints, while closed-loop spatial coordination with information exchange between individuals is often combined with temporal coordination to achieve spatiotemporal coordination. Therefore, time is the most fundamental constraint in multi-missile coordinated guidance scenarios. Against a single target, a simultaneous attack by a swarm of cruise missiles can saturate the target's defense system in a short period of time, increasing the probability of penetration. Against multiple targets, a simultaneous attack by a swarm of cruise missiles can prevent some targets from maneuvering and escaping, achieving a "one-shot kill."

[0003] Time-coordinated guidance method is the key technology to achieve simultaneous strikes. Common time-coordinated guidance methods can be divided into two categories: open-loop coordinated guidance and closed-loop coordinated guidance according to whether there is communication between missiles.

[0004] Open-loop collaborative guidance requires setting the attack time in advance, and time constraints are often introduced based on the following two control methods: (1) Biased proportional guidance law, which adds a time error feedback term to the proportional guidance law. (2) Sliding mode control, which designs the time error of the sliding mode surface to be zero to ensure the motion state converges.

[0005] Closed-loop collaborative guidance achieves coordinated coordination among missiles through communication during the guidance process. Depending on whether a centralized coordination unit is included in the communication topology, closed-loop collaborative guidance can be categorized as centralized or distributed. Compared to centralized coordination, distributed coordination requires less information, enhances cluster robustness, and facilitates cluster expansion. Pre-arrival information on enemy targets is difficult to obtain in real battlefield environments. Distributed coordination strategies coordinate strike times in real time, eliminating the need for pre-determined strike times.

[0006] Most traditional time-coordinated guidance methods fail to consider the autopilot's input constraints and rely solely on acceleration as the autopilot's control input in the guidance loop design. Due to errors in remaining flight time estimation, traditional time-coordinated guidance methods based on remaining flight time have a limited adjustable range. Summary of the Invention

[0007] The purpose of the present invention is to provide a distributed time-coordinated guidance method for a cruise missile cluster with limited control input to solve the problems existing in the background technology.

[0008] To achieve the above objectives, the present invention provides a method for distributed time-coordinated guidance of a cruise missile cluster with limited control input, comprising the following steps:

[0009] S1. Establish a two-layer collaborative guidance architecture for cruise missile swarms, enabling segmented guidance in both the lateral and longitudinal planes. The term "two-layer" refers to the decomposition of the collaborative guidance algorithm into an upper-layer coordination strategy and a lower-layer time-constrained guidance law; it also refers to the collaborative guidance algorithm layer and the cruise missile autopilot control layer.

[0010] S2. Cruise missiles estimate their remaining flight time before striking the target based on their own position information. Cruise missiles communicate with each other to exchange their respective remaining flight time estimates. The coordination strategy calculates the expected coordination variable value for each missile, which serves as the input for the three-stage lateral and two-stage longitudinal coordinated guidance laws.

[0011] S3. A biased proportional guidance law is used in lateral directions, and a lead angle limitation mechanism is used to reduce the remaining flight time estimation error. Longitudinal guidance is decomposed into level flight and dive phases, using total energy control theory and an integral proportional guidance law respectively. The time error is fine-tuned through the level flight to dive switching criterion. The attitude mapping method is used to obtain the attitude angle and throttle command as the control input of the autopilot.

[0012] S4. The inner loop of the cruise missile autopilot obtains the steering amount and throttle amount according to the input attitude angle and throttle command, and controls the attitude and speed of the cruise missile to achieve time coordination.

[0013] Preferably, the double-layer collaborative guidance architecture is applied in the lateral plane and the longitudinal plane respectively.

[0014] Preferably, a three-stage lateral and lateral coordinated guidance law is designed for the lateral plane, including a biased proportional guidance section, a lead angle limitation section, and a pure proportional guidance section. The biased proportional guidance section process is as follows:

[0015] Specify the cruise missile hit time as T d , the cruise missile has flown for t time and has a remaining flight time of t go , then the cruise missile's hit time error e t Expressed as:

[0016] e t =T d -tt go ;

[0017] When each cruise missile hits the target t Equal to 0, achieving the same specified hit time T d Hit the target;

[0018] The bias proportional guidance law expression with time error feedback term is:

[0019] a ITCG =a PNG +Ke t ;

[0020] in, It is a pure proportional guidance law; is the gain coefficient; V is the cruise missile velocity vector, N is the navigation ratio, and R is the missile-target distance;

[0021] The biased proportional guidance law is proposed based on the estimated remaining flight time. The remaining time t go The estimation method is as follows:

[0022]

[0023] Where η is the velocity vector lead angle.

[0024] Preferably, the lead angle limiting stage process is as follows:

[0025] Limit the leading deflection angle to satisfy η h ≤η M ,η M ∈[60°,90°], the rate of change of the leading deflection angle is expressed as:

[0026]

[0027] Among them, R xy 、V xy 、a xy are the relative distance between the missile and the target, the velocity vector of the cruise missile, and the projection of the normal acceleration in the lateral plane; ψ, λ h ,η h They are yaw angle, missile-to-target sight angle and lead angle respectively;

[0028] When the leading deflection angle increases to the upper limit range, the leading deflection angle change rate is set to 0, so that the leading deflection angle no longer increases. The normal acceleration at this time is expressed as:

[0029]

[0030] When the time error e t When converged to 0, the guidance law is switched to pure proportional guidance law;

[0031] The input of the inner loop of the cruise missile autopilot is attitude and throttle. The normal acceleration obtained from the lateral direction is converted into attitude angle through attitude mapping. The cruise missile adopts bank turning control, and the normal acceleration is mapped into the roll command as follows:

[0032]

[0033] Preferably, a longitudinal two-stage cooperative guidance law is designed for the longitudinal plane, including a level flight coordination section and a dive section. The level flight coordination section is before the cruise missile enters a dive, and the time error is coordinated by increasing the track under the control of the lateral cooperative guidance law. The remaining time estimation method adopted assumes that the cruise missile speed is constant, uses the total energy control theory to decouple the altitude and speed control, uses the throttle to control the rate of change of the total energy, and uses the elevator to coordinate the conversion between kinetic energy and potential energy.

[0034] Preferably, the dive phase process is as follows: in the dive phase, the cruise missile rapidly reduces its altitude by controlling the pitch angle and dives toward the target; integrating both sides of the pure proportional guidance law expression, the pure proportional guidance law in integral form is expressed as:

[0035]

[0036] in is the initial value of the line of sight inclination angle when the cruise missile enters a dive; θ0 is the initial value of the pitch angle when entering a dive; the integral form of the proportional guidance law guides the cruise missile to the target.

[0037] Preferably, the longitudinal plane also includes a level flight to dive switching criterion, which is as follows:

[0038] The necessary condition for entering a dive is that the line of sight angle converges to a smaller value, which can be expressed as:

[0039] λ hi <ε1;

[0040] The sight angles of cruise missiles at different altitudes and target distances are different. In order to achieve the earlier entry into the dive of cruise missiles at higher altitudes, the switching criterion is expressed as:

[0041] λ vi <ε2;

[0042] When both equations are satisfied at the same time, the switching criterion for level flight to dive is obtained.

[0043] Preferably, the cooperative guidance laws in the lateral plane and the longitudinal plane are combined to obtain the lower-level time-constrained guidance law. According to the specified hit time in the lateral cooperative guidance law, a distributed coordination strategy is designed to obtain a coordinated hit time to replace the specified hit time T d , the content is as follows:

[0044] The distributed coordination strategy assumes that each missile can obtain the estimated value of the remaining flight time of the adjacent individuals, and increases the weight of the individuals with longer remaining flight time by weighted average method, so that the coordination time t go,i (t) satisfies the individual hit time range [T min ,T max ], the distributed coordination strategy is:

[0045]

[0046] Among them, S i represents the communication topology of cruise missile i; s j represents the number of cruise missiles in its communication topology; k j Represents weight.

[0047] Therefore, the present invention adopts the above-mentioned distributed time-coordinated guidance method for cruise missile clusters with limited control input, which has the following beneficial effects:

[0048] (1) The present invention adds autopilot model constraints to obtain attitude angle and throttle as control inputs of the attitude autopilot, meeting the input restrictions of the tandem wing cruise missile autopilot;

[0049] (2) The distributed coordination strategy coordinates the strike time in real time, avoiding the need to preset the strike time. The present invention adopts a weighted average method to obtain the distributed coordination strategy, so that the coordinated consensus time meets the lower limit of the adjustable range of the cruise missile flight time.

[0050] (3) Based on the concept of segmented guidance, the present invention designs a lead angle limitation mechanism to reduce the remaining flight time estimation error and improve the algorithm adaptability.

[0051] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a flow chart of a distributed time-coordinated guidance method for a cruise missile cluster with limited control input according to the present invention;

[0053] Figure 2 Schematic diagram of a dual-layer collaborative guidance architecture in an embodiment of the present invention;

[0054] Figure 3 This is a flow chart of the three-stage lateral coordinated guidance law according to an embodiment of the present invention;

[0055] Figure 4 This is a flow chart of the lower-level time-constrained guidance law according to an embodiment of the present invention. DETAILED DESCRIPTION

[0056] The following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort shall fall within the scope of protection of the present invention.

[0057] Distributed collaborative guidance algorithms usually build a coordination layer on top of the open-loop collaborative guidance algorithm and apply modern control theory to design collaborative control strategies. Depending on the different coordination variables, they can be divided into the following collaborative methods: (1) Coordination of remaining flight time. Based on the estimated remaining flight time, the control method is designed to coordinate the estimated remaining flight time of each missile to be consistent. (2) Coordination of missile-target distance. The remaining flight time estimation problem is converted into a missile-target distance consistency problem, avoiding the error in the remaining flight time estimation. Most of the time, it is assumed that the speed of each missile is a constant. (3) Coordination of speed. Based on path planning, the speed of each missile is coordinated to achieve coordination.

[0058] Existing methods often use acceleration as control input to the autopilot, without considering the autopilot's input limitations. Cruise missiles, which possess both loiter and guided strike capabilities, often utilize an attitude-based autopilot to maintain stable flight. Autopilot inputs are limited to attitude angle and throttle, requiring a time-coordinated guidance algorithm designed to meet these input limitations, taking into account flight characteristics.

[0059] See also Figure 1 A distributed time-coordinated guidance method for a cruise missile cluster with limited control inputs comprises the following steps:

[0060] S1. Establish a two-layer collaborative guidance architecture for cruise missile clusters, as shown in the attached Figure 2 The "two-layer" design of the collaborative guidance architecture described in this embodiment has two meanings. In algorithm design, the "two-layer" design refers to the decomposition of the collaborative guidance algorithm into an upper-layer coordination strategy and a lower-layer time-constrained guidance law. In control implementation, the "two-layer" design refers to the collaborative guidance algorithm layer and the cruise missile autopilot control layer, corresponding to the guidance loop and control loop, respectively.

[0061] S2. Cruise missiles estimate their remaining flight time before striking the target based on their own position information. Cruise missiles communicate with each other to exchange their respective remaining flight time estimates. The coordination strategy calculates the expected coordination variable value for each missile, which serves as the input for the three-stage lateral and two-stage longitudinal coordinated guidance laws.

[0062] S3. A biased proportional guidance law is used in lateral directions, and a lead angle limitation mechanism is used to reduce the remaining flight time estimation error. Longitudinal guidance is decomposed into level flight and dive phases, using total energy control theory and an integral proportional guidance law respectively. The time error is fine-tuned through the level flight to dive switching criterion. The attitude mapping method is used to obtain the attitude angle and throttle command as the control input of the autopilot.

[0063] S4. The inner loop of the cruise missile autopilot obtains the steering amount and throttle amount according to the input attitude angle and throttle command, and controls the attitude and speed of the cruise missile to achieve time coordination.

[0064] This example primarily outlines a two-layer collaborative guidance architecture from a control implementation perspective. To address the input constraints of the cruise missile's attitude control system, the three-dimensional temporal collaborative guidance problem is decoupled into the lateral and longitudinal planes. Remaining flight time estimates are used as coordination variables to implement a distributed temporal collaborative guidance algorithm. The algorithms for both planes are described in detail below.

[0065] Laterally and upward, the cruise missile estimates the remaining flight time of the individual based on the sight angle between the missile and the target, obtains the estimated remaining flight time of the adjacent individuals through the communication network, obtains the expected remaining flight time by the distributed coordination strategy, and calculates the individual time error.

[0066] Furthermore, under the control of a biased proportional guidance law with a time error feedback term, flight time is coordinated by coordinating the flight path. When the lead angle increases to a limit, the cruise missile flies with a constant normal acceleration, maintaining the lead angle near its maximum value and ensuring the accuracy of the time estimation. When the time error converges, the cruise missile engages the target under the control of the proportional guidance law. The above control methods all calculate the normal acceleration, and the roll angle command is obtained through attitude mapping, which serves as the input to the cruise missile's autopilot.

[0067] (1) Lateral three-stage coordinated guidance law

[0068] In this embodiment, the cruise missile hit time is specified as T d , the cruise missile has flown for t time and has a remaining flight time of t go , then the cruise missile's hit time error e t It can be expressed as:

[0069] e t =T d -tt go ;

[0070] When each cruise missile hits the target t Equal to 0, to achieve the same specified time T d Hit the target.

[0071] The proportional guidance law is simple in form and easy to implement in engineering. The bias proportional guidance law with time error feedback is expressed as:

[0072] a ITCG =a PNG +Ke t ;

[0073] in, It is a pure proportional guidance law. is the gain coefficient, V is the cruise missile velocity vector, N is the navigation ratio, and R is the missile-target distance.

[0074] The above biased proportional guidance law is proposed based on the estimated remaining flight time. The remaining time t go The estimation method of is as follows, where η is the velocity vector leading angle.

[0075]

[0076] This remaining time estimation method is derived under the assumption of a small angle, meaning that the smaller the velocity vector lead angle, the higher the estimation accuracy. After adjustments during the mid-stage guidance phase, the cruise missile's initial velocity vector lead angle is generally small when it enters the terminal guidance phase. However, during the coordination process, the remaining flight time must be coordinated by increasing the flight path, so large lead angles may still occur. To prevent large lead angles from causing inaccurate time estimates and potentially leading to coordination failure during the coordination process, this embodiment incorporates a lead angle limitation mechanism.

[0077] Limit the leading deflection angle to satisfy η h ≤η M ,η M ∈[60°,90°]. The rate of change of the leading deflection angle is expressed as:

[0078]

[0079] Among them, R xy 、V xy 、a xy are the relative distance between the missile and the target, the velocity vector of the cruise missile, and the projection of the normal acceleration in the lateral plane, ψ, λ h ,η h They are yaw angle, missile-target line-of-sight angle and lead angle respectively.

[0080] When the lead angle increases to the upper limit, the rate of change of the lead angle is set to 0, thereby preventing the lead angle from increasing further. The normal acceleration at this time is expressed as:

[0081]

[0082] In addition, in order to ensure accurate strike on the target, when the time error e t When convergence reaches 0, the guidance law is switched to the proportional guidance law.

[0083] The inputs to the inner loop of the cruise missile autopilot are attitude and throttle, so the normal acceleration obtained from the lateral direction needs to be converted into attitude angle through attitude mapping. The cruise missile uses banked turn control, and the normal acceleration is mapped to the roll command as follows:

[0084]

[0085] Therefore, this embodiment designs a three-stage time coordinated guidance algorithm for lateral direction as shown in the attached figure. Figure 3The lateral open-loop collaborative guidance algorithm includes a bias proportional guidance section, a lead angle limitation section, and a pure proportional guidance section.

[0086] In the biased proportional guidance section, the lead angle is less than the maximum lead angle limit. The cruise missile moves away from the target under the control of the biased proportional guidance law, and the flight time is coordinated by increasing the flight track. During this process, the lead angle of the cruise missile gradually increases.

[0087] When the lead angle of the cruise missile increases to its maximum value, it enters the lead angle limitation section. The cruise missile maintains a constant normal acceleration and flies along a logarithmic spiral curve, and the lead angle no longer increases.

[0088] When the calculated time error converges, it enters the proportional guidance phase. The cruise missile switches to the proportional guidance law, the lead angle decreases, and flies towards the target.

[0089] Vertically, the cruise missile's flight phase is divided into a level flight phase and a dive phase, depending on whether it enters a dive. In the level flight phase, altitude and speed control are decoupled based on total energy control theory to generate pitch angle and throttle commands, maintaining stable level flight. The switching criteria for level flight to dive are designed based on lead deflection and lead tilt angles, ensuring that the higher the altitude, the earlier the cruise missile enters a dive. Dive is initiated when the switching criteria are met. The dive phase utilizes integral proportional guidance to directly generate pitch angle commands.

[0090] (2) Longitudinal two-stage coordinated guidance law

[0091] Depending on whether the cruise missile enters a dive, this embodiment divides the longitudinal coordinated guidance law into a level flight coordination section and a dive section.

[0092] 1. Level Flight Coordination Phase: Before the cruise missile enters a dive, time errors are coordinated by increasing the trajectory under the control of the lateral coordinated guidance law. The remaining time estimation method used assumes a constant cruise missile speed. Therefore, to ensure the accuracy of the remaining time estimation during the coordination process, the cruise missile speed must be maintained as much as possible. Total energy control theory is used to decouple altitude and speed control. The core concept is to use the throttle to control the rate of change of total energy and the elevator to coordinate the conversion between kinetic energy and potential energy.

[0093] 2. Dive phase: In the dive phase, the cruise missile rapidly reduces its altitude by controlling the pitch angle and dives towards the target. Integrating both sides of the proportional guidance law expression, the proportional guidance law in integral form is expressed as:

[0094]

[0095] in is the initial value of the line of sight angle when the cruise missile enters a dive, and θ0 is the initial value of the pitch angle when entering a dive. The proportional guidance law in integral form guides the cruise missile to the target.

[0096] 3. "Level Flight to Dive" Switching Criteria: Different cruise missiles have different initial altitudes when entering the dive phase. This embodiment designs a switching criterion for switching from level flight to the dive phase to ensure the coordination of cruise missiles during the dive phase. To ensure guidance accuracy, the necessary condition for entering the dive phase is that the line of sight angle converges to a small value, which can be expressed as:

[0097] λ hi <ε1;

[0098] The sight angles of cruise missiles at different altitudes and target distances are different. In order to make cruise missiles with higher altitudes enter a dive earlier, the switching criterion can be expressed as:

[0099] λ vi <ε2;

[0100] When the above two equations are satisfied at the same time, the switching criterion for level flight to dive is obtained.

[0101] Combining the cooperative guidance laws in the lateral and longitudinal planes, we can obtain the lower-level time-constrained guidance law as shown in the attached figure. Figure 4 As shown. The lateral direction is controlled by the biased proportional guidance law to coordinate the flight of the cruise missile. When the time error e t When it converges to 0, it switches to the proportional guidance law; in the longitudinal direction, the speed and altitude of the cruise missile are maintained by the total energy control theory in the level flight phase. When the switching criteria are met, the cruise missile enters a dive, and in the dive phase, the cruise missile is guided to the target by the integral proportional guidance law.

[0102] In actual combat, the actual hit time is often unpredictable. Therefore, this embodiment designs a distributed coordination strategy to obtain a coordinated hit time to replace the specified hit time T d .

[0103] The distributed coordination strategy assumes that each missile can only obtain the estimated remaining flight time of its neighboring individuals. By using the weighted average method, the weight of the individual with the larger remaining flight time is increased, so that the coordinated time t go,i (t) Satisfy the individual hit time range as much as possible [T min ,T max ]. The distributed coordination strategy is:

[0104]

[0105] Among them S i represents the communication topology of cruise missile i, s j represents the number of cruise missiles in its communication topology, k j Represents weight.

[0106] Finally, the inner loop of the cruise missile autopilot obtains the steering amount and throttle amount according to the input attitude angle and throttle command, and controls the attitude and speed of the cruise missile to achieve time coordination.

[0107] Therefore, the present invention adopts the above-mentioned distributed time collaborative guidance method for a cruise missile cluster with limited control input, and adopts a weighted average method to obtain a distributed coordination strategy, so that the coordinated consensus time meets the lower limit of the adjustable range of the cruise missile flight time, reduces the remaining flight time estimation error, and improves the adaptability of the algorithm.

[0108] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A distributed time-coordinated guidance method for a cruise missile cluster with limited control input, characterized in that: The following steps are involved: S1. Establish a two-layer collaborative guidance architecture for cruise missile swarms, achieving segmented guidance in both the lateral and longitudinal planes. "Two-layer" refers to the decomposition of the collaborative guidance algorithm into an upper-layer coordination strategy and a lower-layer time-constrained guidance law. It also refers to the collaborative guidance algorithm layer and the cruise missile autopilot control layer. S2. Each cruise missile estimates its remaining flight time before striking the target based on its own position information. Through inter-ship communication, the cruise missiles exchange their respective remaining flight time estimates. The coordination strategy then calculates the expected coordination variable value for each missile, which serves as the input for the three-stage lateral and two-stage longitudinal coordinated guidance laws. S3: A biased proportional guidance law is used for lateral guidance, with a lead angle limitation mechanism used to reduce the remaining flight time estimation error. Longitudinal guidance is divided into level flight and dive phases, using total energy control theory and an integral proportional guidance law, respectively. Time error is fine-tuned through a level flight to dive switching criterion. Attitude mapping is used to obtain attitude angles and throttle commands as control inputs for the autopilot. A three-stage coordinated lateral guidance law is designed for the lateral plane, including a biased proportional guidance phase, a lead angle limitation phase, and a pure proportional guidance phase. The biased proportional guidance phase process is as follows: Specify the cruise missile impact time as , the cruise missile has been flying for , the remaining flight time is , then the cruise missile's hit time error is Expressed as: ； When each cruise missile hits its target Equal to 0, to achieve the same specified hit time Hit the target; The bias proportional guidance law expression with time error feedback term is: ； in, , is a pure proportional guidance law; , is the gain coefficient; V is the cruise missile velocity vector, N is the navigation ratio, and R is the missile-target distance; The biased proportional guidance law is proposed based on the estimated remaining flight time. The estimation method is as follows: ； in is the velocity vector leading angle; The process of the lead angle limitation section is as follows: Limit the lead angle to meet , the rate of change of the leading deflection angle is expressed as: ； in, 、 、 are the relative distance between the missile and the target, the velocity vector of the cruise missile, and the projection of the normal acceleration in the lateral plane; 、 、 They are yaw angle, missile-to-target sight angle and lead angle respectively; When the leading deflection angle increases to the upper limit range, the leading deflection angle change rate is set to 0, so that the leading deflection angle no longer increases. The normal acceleration at this time is expressed as: ； When the time error When converged to 0, the guidance law is switched to pure proportional guidance law; The inputs to the inner loop of the cruise missile autopilot are attitude and throttle. The normal acceleration obtained from the lateral direction is converted into attitude angle through attitude mapping. The cruise missile adopts bank turning control, and the normal acceleration is mapped into a roll command expressed as: ； The longitudinal plane also includes the transition criteria from level flight to dive, which are as follows: The necessary condition for entering a dive is that the line of sight angle converges to a smaller value, which can be expressed as: ； The sight angles of cruise missiles at different altitudes and target distances are different. In order to make cruise missiles with higher altitudes enter a dive earlier, the switching criterion is expressed as: ； When both equations are satisfied, the switching criterion for level flight to dive is obtained; The collaborative guidance laws in the lateral and longitudinal planes are combined to obtain the lower-level time-constrained guidance law. A distributed coordination strategy is designed based on the specified hit time in the lateral collaborative guidance law to obtain a coordinated hit time, replacing the specified hit time. , the content is as follows: The distributed coordination strategy assumes that each missile can obtain the estimated value of the remaining flight time of the adjacent individuals, and increases the weight of the individuals with longer remaining flight time by weighted average method, so that the coordinated time is Meet the individual hit time range , the distributed coordination strategy is: ； in, Indicates cruise missile Communication topology; Indicates the number of loitering munitions in its communication topology; represents weight; S4. The inner loop of the cruise missile autopilot obtains the steering amount and throttle amount according to the input attitude angle and throttle command, and controls the attitude and speed of the cruise missile to achieve time coordination.

2. The method for distributed time-coordinated guidance of a cruise missile swarm with limited control input according to claim 1, characterized in that: A two-stage longitudinal cooperative guidance law is designed for the longitudinal plane, including the level flight coordination stage and the dive stage. The level flight coordination stage is before the cruise missile enters the dive, and the time error is coordinated by increasing the track under the control of the lateral cooperative guidance law. The remaining time estimation method adopted assumes that the cruise missile speed is constant, and the total energy control theory is used to decouple the altitude and speed control. The throttle is used to control the rate of change of total energy, and the elevator is used to coordinate the conversion between kinetic energy and potential energy.

3. The method for distributed time-coordinated guidance of a cruise missile cluster with limited control input according to claim 2, characterized in that: The dive phase process is as follows: During the dive phase, the cruise missile rapidly decreases its altitude by controlling the pitch angle and dives toward the target. Integrating both sides of the pure proportional guidance law expression, the integral form of the pure proportional guidance law is: ； in The initial value of the line of sight inclination angle when the cruise missile enters a dive; is the initial pitch angle when entering a dive.

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