A Spatiotemporal Cooperative Guidance Method for Multiple Missiles under Three-Dimensional Complex Motion Constraints

Abstract

This invention discloses a multi-missile spatiotemporal cooperative guidance method under three-dimensional complex motion constraints. Based on the three-dimensional relative motion relationship between the missile and the target, a line-of-sight error angle is constructed and orthogonally decomposed. Adjustable parameters are introduced to reconstruct and control the missile's velocity direction, achieving desired attack angle control while satisfying the seeker's field-of-sight constraints. The remaining time coordination error between each missile and its neighboring missiles is calculated, and a dynamic update law for the adjustment parameters is designed. Based on the desired angle attack guidance law design, the adjustment parameters are adjusted to change the trajectory curvature, adjusting the arrival time without changing the axial velocity thrust, thus achieving coordinated strike time for multiple missiles. This invention is applicable to cooperative attack scenarios involving stationary and moving targets, effectively solving the underactuated control problem under speed constraints and realizing three-dimensional spatiotemporal cooperative strikes by multiple missiles under field-of-sight constraints.

Description

Technical Field

[0001] This invention belongs to the field of missile guidance and control, specifically relating to a spatiotemporal cooperative guidance method for multiple missiles under three-dimensional complex motion constraints. Background Technology

[0002] With the continuous development of aerospace weapon system technology both domestically and internationally, the traditional combat method of relying on a single missile for interception can no longer meet the operational requirements of modern battlefields for high reliability and high success rate. Multiple missiles intercepting targets through coordinated guidance can form effective coordination in time and space, thereby significantly improving the probability of intercepting maneuvering targets. Therefore, this has gradually become an important research direction in the field of missile guidance.

[0003] In multi-missile cooperative guidance research, time coordination is one of the earliest and most systematically studied areas. Related technologies have gradually expanded from two-dimensional engagement models targeting stationary targets to three-dimensional space and maneuvering target scenarios. Building on this foundation, some studies have further incorporated spatial coordination factors into the cooperative guidance framework, considering the seeker's field-of-view constraints and designing constraints on the missile's flight or strike direction, thus forming a spatiotemporal cooperative guidance method that balances attack time and attack angle.

[0004] In multi-missile coordinated interception, common coordination variables are remaining time, target range, and lead angle. Remaining time strategies can not only satisfy the simultaneity of multiple missiles but also achieve coordinated guidance under attack time constraints; however, the accuracy of online estimation of remaining time affects the interception result. Remaining range and lead angle strategies require identifying the lead missile as the tracking target but do not require online estimation of remaining time. In actual combat environments, due to factors such as limited engine thrust adjustment capabilities, changes in aerodynamic drag, and maneuvering overload, the speed characteristics of different missiles vary significantly. In such cases, relying solely on range synchronization is insufficient to guarantee time synchronization, making it difficult to achieve precise salvo attack effects.

[0005] Furthermore, existing research often assumes that the missile's axial velocity is controllable, but this is inconsistent with the limited thrust adjustment capabilities of actual engines. In three-dimensional space, uncontrollable axial velocity leads to underactuated problems in controlling distance and line-of-sight angle. Existing solutions often suffer from complex control laws, decreased stability, and difficulty in balancing angular constraints. Therefore, achieving unified and coordinated control of attack time and attack angle in three-dimensional space under the conditions of uncontrollable missile axial velocity and field-of-sight constraints is a key technical challenge that urgently needs to be solved. Summary of the Invention

[0006] Purpose of the invention: This invention proposes a spatiotemporal cooperative guidance method for multiple missiles under three-dimensional complex motion constraints, which effectively solves the problem of underactuated control under speed constraints and realizes three-dimensional spatiotemporal cooperative strike of multiple missiles under field-of-view constraints.

[0007] Technical solution: The present invention provides a multi-missile spatiotemporal cooperative guidance method under three-dimensional complex motion constraints, comprising the following steps:

[0008] (1) Establish a three-dimensional relative motion model between the missile and the target and a missile dynamics model; the three-dimensional relative motion model is used to describe the relative relationship between the missile and the target, including the missile velocity direction, the target velocity direction, the missile-target line-of-sight direction, the desired missile-target line-of-sight direction, the line-of-sight error angle and its equivalent decomposition; the missile dynamics model describes the mapping relationship between the missile acceleration and the rate of change of velocity direction;

[0009] (2) Under the constraint that the axial velocity of the missile is uncontrollable, an adjustment parameter is introduced to adjust the distribution ratio of the missile velocity direction in the line of sight and the lateral direction, and the desired velocity direction is constructed based on the line of sight error angle and its orthogonal components.

[0010] (3) Combine the convergence condition of the line-of-sight error angle with the field-of-view constraint of the seeker, and solve the feasible domain of the adjustment parameters; while ensuring that the missile continues to fly toward the target, achieve convergence control of the line-of-sight error angle, and ensure that the field-of-view constraint condition is always met during the attack angle adjustment process;

[0011] (4) Based on the line-of-sight distance between the missile and the target, the remaining flight time of each missile is predicted using the Euler method, and the time information is shared through the communication topology network between the missiles;

[0012] (5) Based on the communication topology network, calculate the remaining time coordination error between each missile and its neighboring missiles, and design a dynamic update law for the adjustment parameters; on the basis of the desired angle attack guidance law design, adjust the adjustment parameters to change the ballistic curvature, and adjust the arrival time without changing the axial velocity thrust, so as to achieve multi-missile strike time coordination.

[0013] (6) Calculate the dynamics of the desired velocity direction, and combine the dynamic inverse controller to generate the missile's acceleration command, so as to realize the time and space coordinated guidance of multiple missiles in three-dimensional space.

[0014] Further, in step 1, the three-dimensional relative motion model between the missile and the target is described as follows:

[0015]

[0016] Among them, for missiles , Indicates the distance of the bullet's line of sight. and These represent the speeds of the missile and the target, respectively. and These represent the elevation and azimuth angles of the missile's velocity vector in the line-of-sight coordinate system, respectively. and These represent the elevation and azimuth angles of the target velocity vector in the line-of-sight coordinate system, respectively. and These represent the elevation and azimuth angles of the bullet's line of sight, respectively. and These represent the missile's pitch acceleration and yaw acceleration in the line-of-sight coordinate system, respectively. Indicates missile mass, This indicates the thrust generated by the missile engine. This indicates the aerodynamic drag experienced by the missile. It is the acceleration due to gravity;

[0017] Missile speed direction and the direction of the target velocity The equivalent decomposition in the line-of-sight (LOS) coordinate system is:

[0018] ;

[0019] The line-of-sight vector is defined as The desired line of sight is The line-of-sight error angle is The derivative of the line-of-sight error angle is obtained as follows:

[0020]

[0021] in,

[0022] The relation is obtained as follows:

[0023]

[0024] in, and The projections of the line-of-sight error angle onto two orthogonal directions are considered as decompositions of the error angle; if and only if hour, .

[0025] Furthermore, the missile dynamics model is described as follows:

[0026] The missile velocity direction vector retains only the component perpendicular to the LOS axis in the LOS coordinate system, forming a two-dimensional state vector. This state vector is uniquely determined by the pitch and yaw angles in the missile's velocity direction, and can completely characterize the missile's motion characteristics relative to the LOS. The dynamic equation of the velocity direction vector is: ;

[0027] Missile acceleration command As the control input, and combined with the normalization of the missile's velocity magnitude, the dynamic equations of the velocity direction vector are uniformly reorganized into a standard affine control form. ,in, Represents the control input matrix. This indicates the drift term, in which: .

[0028] Furthermore, the implementation process of step (2) is as follows:

[0029] Introducing adjustment parameters The desired velocity direction is constructed based on the line-of-sight error angle and its orthogonal components. The format is:

[0030]

[0031] in, To avoid the minimum variable introduced by singularity, Indication and adjustment parameters Relevant variables, Indicates target speed With missile speed ratio.

[0032] Furthermore, the implementation process of step (3) is as follows:

[0033] Due to the physical limitations of the missile seeker, the missile's lead angle Maximum field of view constraint must be met ,Right now The adjustment parameters are calculated and solved. Lower bound; convergence condition of the line-of-sight angle error as the missile continuously approaches the target. The adjustment parameters are calculated and solved. Upper boundary;

[0034] Adjust parameters The scope is:

[0035]

[0036] in, , , .

[0037] Furthermore, the implementation process of step (4) is as follows:

[0038] Establish guidance state vector Regarding the distance of the bullet's line of sight dynamic equations ; The distance range from the current moment to the point of impact. Discretize into Equally spaced points; combining Euler's algorithm with trapezoidal integrals for state variables. Update the forecast:

[0039]

[0040] in, Index of iteration steps , , Current line-of-sight distance;

[0041] After the prediction iteration is completed, the prediction termination state is used as a guide. Compared with the initial state The remaining flight time of the missile was calculated. :

[0042]

[0043] Furthermore, the implementation process of step (5) is as follows:

[0044] Remaining Time Coordination Error Designed as follows:

[0045]

[0046] in, Indicates missile The neighboring nodes;

[0047] Adjust parameters The dynamic update law is designed as follows:

[0048]

[0049] in, This is a limiting function used to restrict parameters within the feasible region. Inside; As the driving term, its expression is:

[0050]

[0051] Among them, parameters Used to ensure The increase of parameters Used for adjusting and controlling time errors;

[0052] when At the same time, a simultaneous priority cooperative guidance strategy is adopted, giving equal priority to the strike time and the remaining time error, to ensure that the adjustment parameters achieve a balance between satisfying the strike time of a single missile and the consistency of time coordination among multiple missiles.

[0053] when At that time, a time-accelerated cooperative guidance strategy is adopted to drive the project. The main focus is on the timing of the strike. Its speed accelerates the arrival time of a single missile. .

[0054] Furthermore, the implementation process of step (6) is as follows:

[0055] Acceleration control commands The solution based on the dynamic inverse control method is as follows:

[0056]

[0057] in, To control the input matrix, The current missile velocity direction vector, To control bandwidth gain, This includes the drift matrix caused by coordinate system rotation; It is the total differential of the desired velocity direction vector, including the feedforward compensation term for target maneuver;

[0058] Acceleration command It can be decomposed into space guidance components. and time co-component These are used to eliminate geometric attack angle errors and adjust the remaining flight time, respectively, to achieve time and space coordinated guidance of multiple missiles in three-dimensional space.

[0059] Beneficial effects: Compared with the prior art, the beneficial effects of the present invention are as follows:

[0060] 1. This invention takes into account the uncontrollable axial velocity of actual missiles and various spatiotemporal constraints. By introducing adjustable parameters in the equivalent decomposition of the line of sight, the spatiotemporal coordination problem under underactuated conditions is solved without changing the thrust.

[0061] 2. This invention addresses the problem of field-of-view constraints by establishing an analytical relationship between adjustment parameters and the seeker's field of view, and determining the feasible domain of the adjustment parameters. By restricting commands within the feasible domain, the risk of targets exceeding the field of view due to coordinated maneuvers is avoided from a mechanistic perspective, significantly improving interception reliability.

[0062] 3. Compared with existing technologies that can only control distance synchronization or are limited to stationary targets, this invention achieves precise control of attack time and attack angle in three-dimensional space, and extends from stationary targets to moving targets.

[0063] 4. This invention designs two spatiotemporal cooperative guidance strategies: synchronization priority and time acceleration. This effectively avoids the problem of time cooperative control failure after line-of-sight error is eliminated in the terminal guidance phase. At the same time, the combat system can flexibly switch between pursuing higher time synchronization and faster strike time according to mission requirements, making up for the shortcomings of the existing single cooperative mode. Attached Figure Description

[0064] Figure 1 This is a schematic diagram of the guidance geometry between the aircraft and the target position in this invention;

[0065] Figure 2 This is a design framework diagram of a spatiotemporal synchronization guidance law in this invention, where the axial velocity is uncontrollable and constrained by the field of view.

[0066] Figure 3 This is a comprehensive schematic diagram of the entire guidance process when striking a stationary target using the embodiments of the present invention; wherein, (a) is a schematic diagram of the missile-target interception curve; (b) is a schematic diagram of the missile-target line-of-sight distance; (c) is a schematic diagram of the missile's remaining time; (d) is a schematic diagram of the missile's line-of-sight error angle; and (e) is a schematic diagram of the missile adjustment parameters.

[0067] Figure 4 The following is a diagram showing the missile's state during the entire guidance process when striking a stationary target using the embodiments of the present invention; wherein, (a) is a schematic diagram of the missile's forward angle; (b) is a schematic diagram of the missile's velocity; (c) is a schematic diagram of the missile's forward tilt angle; (d) is a schematic diagram of the missile's forward deflection angle; (e) is a schematic diagram of the missile's line-of-sight pitch acceleration; and (f) is a schematic diagram of the missile's line-of-sight yaw acceleration.

[0068] Figure 5 This is a comprehensive schematic diagram of the entire guidance process when striking a moving target using the embodiments of the present invention; wherein, (a) is a schematic diagram of the missile-target interception curve; (b) is a schematic diagram of the missile-target line-of-sight distance; (c) is a schematic diagram of the missile's remaining time; (d) is a schematic diagram of the missile's line-of-sight error angle; and (e) is a schematic diagram of the missile adjustment parameters.

[0069] Figure 6 The diagram shows the missile's state during the entire guidance process when striking a moving target, as described in this embodiment of the invention. (a) is a schematic diagram of the missile's forward angle; (b) is a schematic diagram of the missile's velocity; (c) is a schematic diagram of the missile's forward tilt angle; (d) is a schematic diagram of the missile's forward deflection angle; (e) is a schematic diagram of the missile's line-of-sight pitch acceleration; and (f) is a schematic diagram of the missile's line-of-sight yaw acceleration. Detailed Implementation

[0070] The present invention will now be described in further detail with reference to the accompanying drawings.

[0071] This invention proposes a spatiotemporal cooperative guidance method for multiple missiles under three-dimensional complex motion constraints. The communication topology of the multi-missile cooperation is undirected and connected, such as... Figure 1 , Figure 2 As shown, the specific steps include:

[0072] Step 1: Establish a three-dimensional relative motion model and a missile dynamics model between the missile and the target. The three-dimensional relative motion model is used to describe the relative geometric relationship between the missile and the target, including: missile velocity direction, target velocity direction, missile-target line-of-sight direction, desired missile-target line-of-sight direction, line-of-sight error angle and its equivalent decomposition. The missile dynamics model describes the mapping relationship between the missile's acceleration and the rate of change of velocity direction.

[0073] Establish the relative motion equations for a missile intercepting a moving target in three-dimensional space:

[0074]

[0075] Among them, for missiles , Indicates the distance of the bullet's line of sight. and These represent the speeds of the missile and the target, respectively. and These represent the elevation and azimuth angles of the missile's velocity vector in the line-of-sight coordinate system, respectively. and These represent the elevation and azimuth angles of the target velocity vector in the line-of-sight coordinate system, respectively. and These represent the elevation and azimuth angles of the bullet's line of sight, respectively. and These represent the missile's pitch acceleration and yaw acceleration in the line-of-sight coordinate system, respectively. Indicates missile mass, This indicates the thrust generated by the missile engine. This indicates the aerodynamic drag experienced by the missile. This is the acceleration due to gravity.

[0076] Establish missile speed direction and the direction of the target velocity Equivalent decomposition in the line-of-sight coordinate system:

[0077]

[0078] Define the line-of-sight vector as The desired line of sight is The line-of-sight error angle is Based on the kinematic model, the derivative of the line-of-sight error angle is obtained as follows:

[0079]

[0080] in:

[0081] Furthermore, we obtain the following relation:

[0082]

[0083] in, and The projections of the line-of-sight error angle onto two orthogonal directions can be considered as a decomposition of the error angle. This applies if and only if... hour, Therefore, the control objective of eliminating line-of-sight errors is equivalent to decomposing line-of-sight errors into quantities. and Control is zero.

[0084] The missile's velocity direction vector retains only the component perpendicular to the LOS axis in the LOS coordinate system, forming a two-dimensional state vector. This state vector is uniquely determined by the pitch and yaw angles in the missile's velocity direction, and can completely characterize the missile's lateral motion characteristics relative to the LOS. The dynamic equation of the velocity direction vector is: Introducing lateral acceleration commands for the missile. As the control input, and combined with the normalization of the missile's velocity magnitude, the dynamic equations of the velocity direction vector are uniformly reorganized into a standard affine control form. ,in, Represents the control input matrix. This represents the drift matrix, where the drift term contains... , .

[0085] Step 2: Under the constraint that the missile's axial velocity is uncontrollable, an adjustment parameter is introduced to adjust the distribution ratio of the missile's velocity direction in the line-of-sight direction and the lateral direction. The desired velocity direction is constructed based on the line-of-sight error angle and its orthogonal components.

[0086] Introducing adjustment parameters Based on the line-of-sight error angle and its orthogonal components, the desired velocity direction is constructed as follows:

[0087]

[0088] in, This refers to a minimum variable to avoid the introduction of singularity. Indication and adjustment parameters Relevant variables, This indicates the bullet-to-target velocity ratio. Specifically, when... In this case, the desired velocity direction for a moving target can be reduced to the desired velocity direction for a stationary target.

[0089] Step 3: By jointly analyzing the convergence condition of the line-of-sight error angle and the field-of-view constraint of the seeker, solve for the feasible region of the adjustment parameters. This ensures that the missile continues to fly towards the target while achieving convergent control of the line-of-sight error angle, and guarantees that the field-of-view constraint is always met during the attack angle adjustment process.

[0090] Based on the relative motion model in step 1 and the guidance law structure in step 2, the relative distance between the projectile and the target is calculated. satisfy:

[0091]

[0092] This ensures that the distance between the missile and the target continues to decrease over time, ensuring that the missile can stably approach the target.

[0093] Define the angle between the missile's velocity direction and the line of sight as the lead angle. Based on the definition of the equivalent decomposition of missile velocity in the line-of-sight coordinate system in step 1, we obtain... According to the physical limitations of the missile seeker, the missile's forward angle must meet the maximum field of view constraint. ,Right now The adjustment parameters are calculated and solved. Lower bound; the rate of change of the line-of-sight angle error for a moving target. Must meet The adjustment parameters are calculated and solved. The upper realm.

[0094] Adjust parameters The scope is:

[0095]

[0096] in, , , .

[0097] Step 4: Based on the line-of-sight distance between the missile and the target, predict the remaining flight time of each missile using the Euler method, and share the time information through the communication topology network between the missiles.

[0098] Define the guidance state vector as follows:

[0099]

[0100] State vector Regarding the distance of the bullet's line of sight The dynamic changes are as follows:

[0101]

[0102] Let the current line-of-sight distance and the state vector be denoted as follows: and To facilitate numerical integration, the continuous independent variable is... In the interval Internal division into There are 1, 2, 3, 4, 5, 6, 12, 13, 14, 16, 17, 18, 19 ... .make Index of iteration steps Initialize the prediction state to the current measurement state: line-of-sight distance. Direction of gaze Missile speed Pitch angle in the direction of missile velocity azimuth angle of missile velocity direction Target location Missile position .

[0103] The prediction time step is Within the stated time step, the target position and missile position are predicted and updated:

[0104]

[0105] Calculate the missile's altitude based on its position, determine the corresponding gravitational acceleration, and then obtain the total acceleration:

[0106]

[0107] Update missile speed:

[0108]

[0109] After the missile position and velocity are predicted, the Euler algorithm and trapezoidal integral are used to analyze the state variables. Update the forecast:

[0110]

[0111] After the prediction iteration is completed, the prediction termination state is used as a guide. Compared with the initial state The remaining flight time of the missile is calculated as follows:

[0112] .

[0113] Step 5: Based on the communication topology network, calculate the remaining time coordination error between each missile and its neighboring missiles, and design a dynamic update law for the adjustment parameters. Building upon the desired angle attack guidance law design, adjust the trajectory curvature by changing the adjustment parameters, thereby adjusting the arrival time without altering the axial velocity thrust, to achieve coordinated strike time among multiple missiles.

[0114] Define time coordination error For its remaining time and neighboring nodes Average remaining time difference:

[0115]

[0116] The dynamic update law for the design adjustment parameters is:

[0117]

[0118] in, Used to force control variables to satisfy feasible region constraints, ensuring the physical feasibility of the system while maintaining dynamic smoothness. This is the driving factor.

[0119] Driver item Designed as follows:

[0120]

[0121] Among them, parameters Used to ensure The increase of parameters Used for adjusting and controlling time errors.

[0122] when At the same time, the spatiotemporal coordinated guidance strategy is a simultaneous priority type (SP-STCG) spatiotemporal coordinated guidance strategy, which simultaneously assigns a time limit for the strike. Coordinate with remaining time error Equal priority. This strategy ensures that the adjustment parameters strike a balance between the time required for a single missile strike and the time coordination consistency among multiple missiles.

[0123] when At that time, the spatiotemporal cooperative guidance strategy is a time-accelerated (TA-STCG) spatiotemporal cooperative guidance strategy, with the driving term... Focus primarily on timing of hits The speed of arrival. This strategy aims to accelerate the arrival time of a single missile. To meet the hit time constraint as quickly as possible.

[0124] During the remaining time adjustable phase, by adjusting the adjustable parameters Through dynamic adjustment, multiple missile systems can achieve consistency in remaining time, thereby realizing time coordination.

[0125] Step 6: Calculate the dynamics of the desired velocity direction, and combine it with the dynamic inverse controller to generate the missile's acceleration command, thereby realizing time and space coordinated guidance of multiple missiles in three-dimensional space.

[0126] Considering the target's motion in the rotating line-of-sight coordinate system, the target velocity vector The derivative includes the target's own acceleration term and the Coriolis term:

[0127]

[0128] When the target acceleration is unknown or difficult to measure accurately, it is assumed that the change in the target velocity direction is mainly caused by the rotation of the line-of-sight coordinate system. Therefore, the following approximation is used for feedforward calculation:

[0129]

[0130] Calculate the coordinated adjustment parameters Dynamic changes:

[0131]

[0132] in, For vectors The first item.

[0133] Define the projection vector of the line-of-sight angle error Combined with step 1 and The rate of change of the line-of-sight angle error projection vector is used to calculate the derivative of the projection vector.

[0134]

[0135] in, , .

[0136] Based on the derivatives of the above components, for the moving target scenario, the feedforward expression for the directional derivative of the missile's desired velocity is calculated:

[0137]

[0138] Among them, when hour, ;when hour, .

[0139] Define the controller tracking error as:

[0140]

[0141] To ensure the closed-loop stability of the system, the desired error dynamics are designed to decay exponentially in the form of a first order, resulting in:

[0142]

[0143] in, To control bandwidth gain.

[0144] Based on the affine control model from step 1 and the desired dynamics from step 2, the acceleration control command is derived by using the inverse dynamics approach:

[0145]

[0146] The acceleration command generated by the dynamic inverse controller is decomposed into spatial and temporal components:

[0147]

[0148] in, Represents the space guidance component, used to eliminate geometric errors. It also compensates for the target's movement to ensure a successful hit. This represents the time-coordinated component, dynamically driven by adjustable parameters, used to eliminate time errors.

[0149] Under this acceleration control command, the system is input-state stable (ISS), and the convergence bound of the tracking error is directly determined by... The amplitude is determined by it.

[0150] Consider a system with four missiles coordinating guidance, and set a maximum field of view constraint. The initial conditions and expected terminal interception conditions for the four missiles are shown in Table 1:

[0151] Table 1 Design of Multi-Missile Cooperative Interception Scenario under Velocity Constraints

[0152]

[0153] The effectiveness and superiority of this invention in striking stationary targets were verified. Based on the initial conditions set in Table 1, simulations were conducted using two strategies proposed in this invention: the synchronization-priority type (SP-STCG) and the time-acceleration type (TA-STCG).

[0154] like Figure 3 As shown in Figure (a), the missile-target interception curves demonstrate that all four missiles successfully intercepted stationary targets under both strategies, proving the accuracy of this invention in striking stationary targets under underactuated conditions. A comparison reveals that the SP-STCG strategy generates a larger trajectory curvature, indicating that the missiles consume energy and time to accommodate the missile with more remaining time to achieve synchronization; while the TA-STCG strategy produces a relatively straight trajectory, reflecting its pursuit of rapid strike. Figure 3 The diagram showing the missile-target line-of-sight distance in (b) illustrates that the line-of-sight distances of each missile monotonically converge to zero, verifying the effectiveness of the guidance law. Figure 3As shown in the remaining time diagram in (c), although the initial remaining flight times of the four missiles differ greatly, under the cooperative mechanism proposed in this invention, the remaining times of each missile rapidly converge in the mid-flight phase, and the overall interception time is significantly shortened under the TA-STCG strategy. Figure 3 The diagram (d) illustrates the line-of-sight error angle. All missiles' line-of-sight error angles effectively converge to 0, achieving strike from the desired line of sight. For example... Figure 3 The diagram in (e) shows the adjustment parameters. The parameters are dynamically adjusted throughout the guidance process and remain within the feasible region. Under the TA-STCG strategy, the adjustment parameters increase rapidly in the initial stage, increasing the tangential velocity component, thereby accelerating the convergence of line-of-sight errors and the flight process.

[0155] like Figure 4 The schematic diagram of the lead angle shown in Figure (a) demonstrates that throughout the entire flight, the lead angle of all missiles remains within the set maximum field of view constraint, strictly meeting the seeker's field of view limit. Figure 4 The missile velocity diagram shown in (b) effectively verifies the algorithm's adaptability to uncontrollable velocities. Figure 4 (c) and Figure 4 The schematic diagram of the missile's forward tilt angle and forward deflection angle shown in diagram (d) shows that the velocity elevation angle and azimuth angle in the line-of-sight coordinate system converge to 0, enabling a strike from the desired line-of-sight direction. Figure 4 (e) and Figure 4 The diagram of line-of-sight pitch and yaw acceleration shown in (f) shows that the line-of-sight pitch and yaw acceleration commands are relatively large in the initial stage to quickly eliminate errors, and gradually converge to zero in the final stage. The control commands are smooth and within a reasonable range.

[0156] Verify the adaptability and robustness of this invention when striking moving targets. Set the target to... The target moves at a constant linear speed, and the other initial conditions are consistent with those for verifying the three-dimensional spatiotemporal cooperative interception of stationary targets. Simulation verification is performed using the two strategies proposed in this invention: synchronization priority type (SP-STCG) and time acceleration type (TA-STCG).

[0157] like Figure 5 As shown in (a), the missile-target interception curves demonstrate that all four missiles successfully intercepted the moving target under both strategies, proving the accuracy of this invention in striking moving targets under underactuated conditions. The SP-STCG strategy generates a trajectory with a larger curvature, while the TA-STCG strategy produces a relatively straight trajectory. Figure 5 The diagram showing the line-of-sight distance between missiles and targets in (b) illustrates that the line-of-sight distance of each missile can still converge to zero, but compared to stationary targets, the convergence process exhibits more significant differences in the middle and later stages. For example... Figure 5 The remaining time diagram shown in (c) illustrates that, under moving target conditions, the remaining times of each missile are consistent during the mid-flight phase, but a significant time error occurs at the terminal stage. In comparison, the SP-STCG strategy exhibits higher time synchronization, while the TA-STCG strategy, due to its accelerated average interception time, has lower time synchronization than SP-STCG. Figure 5 The diagram (d) illustrates the line-of-sight error angle. All missiles' line-of-sight error angles effectively converge to 0, achieving strike from the desired line of sight. For example... Figure 5 The diagram in (e) shows the adjustment parameters. The system was dynamically adjusted throughout the guidance process and remained within the feasible range without any loss of control.

[0158] like Figure 6 The schematic diagram of the lead angle shown in Figure (a) demonstrates that throughout the entire flight, the lead angle of all missiles remains within the set maximum field of view constraint, strictly meeting the seeker's field of view limit. Figure 6 The missile velocity diagram shown in (b) effectively verifies the algorithm's adaptability to uncontrollable velocities. Figure 6 (c) and Figure 6 The diagram (d) shows the missile's forward tilt angle and forward deflection angle. In the line-of-sight coordinate system, both the forward tilt angle and forward deflection angle of the missile's velocity converge to 0, enabling a strike from the desired line-of-sight direction. Figure 6 (e) and Figure 6 The diagram of line-of-sight pitch and yaw acceleration shown in (f) shows that the line-of-sight pitch and yaw acceleration commands are relatively large in the initial stage to quickly eliminate errors, and gradually converge to zero in the final stage. The control commands are smooth and within a reasonable range.

[0159] In summary, the SP-STCG strategy proposed in this invention is suitable for saturation attack missions with extremely high time synchronization accuracy requirements, while the TA-STCG strategy is suitable for penetration missions with high strike speed requirements. Both can achieve efficient three-dimensional spatiotemporal coordinated strikes while satisfying field-of-view constraints and uncontrollable velocity constraints.

[0160] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for spatiotemporal cooperative guidance of multiple missiles under three-dimensional complex motion constraints, characterized in that, Includes the following steps: (1) Establish a three-dimensional relative motion model between the missile and the target and a missile dynamics model; the three-dimensional relative motion model is used to describe the relative relationship between the missile and the target, including the missile velocity direction, the target velocity direction, the missile-target line-of-sight direction, the desired missile-target line-of-sight direction, the line-of-sight error angle and its equivalent decomposition; the missile dynamics model describes the mapping relationship between the missile acceleration and the rate of change of velocity direction; (2) Under the constraint that the axial velocity of the missile is uncontrollable, an adjustment parameter is introduced to adjust the distribution ratio of the missile velocity direction in the line of sight and the lateral direction, and the desired velocity direction is constructed based on the line of sight error angle and its orthogonal components. (3) Combine the convergence condition of the line-of-sight error angle with the field-of-view constraint of the seeker, and solve the feasible domain of the adjustment parameters; while ensuring that the missile continues to fly toward the target, achieve convergence control of the line-of-sight error angle, and ensure that the field-of-view constraint condition is always met during the attack angle adjustment process; (4) Based on the line-of-sight distance between the missile and the target, the remaining flight time of each missile is predicted using the Euler method, and the time information is shared through the communication topology network between the missiles; (5) Based on the communication topology network, calculate the remaining time coordination error between each missile and its neighboring missiles, and design a dynamic update law for the adjustment parameters; on the basis of the desired angle attack guidance law design, adjust the adjustment parameters to change the ballistic curvature, and adjust the arrival time without changing the axial velocity thrust, so as to achieve multi-missile strike time coordination. (6) Calculate the dynamics of the desired velocity direction, and combine the dynamic inverse controller to generate the missile's acceleration command, so as to realize the time and space coordinated guidance of multiple missiles in three-dimensional space.

2. The method for spatiotemporal cooperative guidance of multiple missiles under three-dimensional complex motion constraints according to claim 1, characterized in that, In step 1, the three-dimensional relative motion model between the missile and the target is described as follows: ； Among them, for missiles , Indicates the distance of the bullet's line of sight. and These represent the speeds of the missile and the target, respectively. and These represent the elevation and azimuth angles of the missile's velocity vector in the line-of-sight coordinate system, respectively. and These represent the elevation and azimuth angles of the target velocity vector in the line-of-sight coordinate system, respectively. and These represent the elevation and azimuth angles of the bullet's line of sight, respectively. and These represent the missile's pitch acceleration and yaw acceleration in the line-of-sight coordinate system, respectively. Indicates missile mass, This indicates the thrust generated by the missile engine. This indicates the aerodynamic drag experienced by the missile. It is the acceleration due to gravity; Missile speed direction and the direction of the target velocity The equivalent decomposition in the line-of-sight (LOS) coordinate system is: ； The line-of-sight vector is defined as The desired line of sight is The line-of-sight error angle is The derivative of the line-of-sight error angle is obtained as follows: ； in, The relation is obtained as follows: ； in, and The projections of the line-of-sight error angle onto two orthogonal directions are considered as decompositions of the error angle; if and only if hour, .

3. The method for spatiotemporal cooperative guidance of multiple missiles under three-dimensional complex motion constraints according to claim 1, characterized in that, The missile dynamics model is described as follows: The missile velocity direction vector retains only the component perpendicular to the LOS axis in the LOS coordinate system, forming a two-dimensional state vector. This state vector is uniquely determined by the pitch and yaw angles in the missile's velocity direction, and can completely characterize the missile's motion characteristics relative to the LOS. The dynamic equation of the velocity direction vector is: ; Missile acceleration command As the control input, and combined with the normalization of the missile's velocity magnitude, the dynamic equations of the velocity direction vector are uniformly reorganized into a standard affine control form. ,in, Represents the control input matrix. This indicates the drift term, in which: .

4. The method for spatiotemporal cooperative guidance of multiple missiles under three-dimensional complex motion constraints according to claim 1, characterized in that, The implementation process of step (2) is as follows: Introducing adjustment parameters The desired velocity direction is constructed based on the line-of-sight error angle and its orthogonal components. The format is: ； in, To avoid the minimum variable introduced by singularity, Indication and adjustment parameters Relevant variables, Indicates target speed With missile speed ratio.

5. The method for spatiotemporal cooperative guidance of multiple missiles under three-dimensional complex motion constraints according to claim 1, characterized in that, The implementation process of step (3) is as follows: Due to the physical limitations of the missile seeker, the missile's lead angle Maximum field of view constraint must be met ,Right now The adjustment parameters are calculated and solved. Lower bound; convergence condition of the line-of-sight angle error as the missile continuously approaches the target. The adjustment parameters are calculated and solved. Upper boundary; Adjust parameters The scope is: ； in, , , .

6. The method for spatiotemporal cooperative guidance of multiple missiles under three-dimensional complex motion constraints according to claim 1, characterized in that, The implementation process of step (4) is as follows: Establish guidance state vector Regarding the distance of the bullet's line of sight dynamic equations ; The distance range from the current moment to the point of impact. Discretize into Equally spaced points; combining Euler's algorithm with trapezoidal integrals for state variables. Update the forecast: ； in, Index of iteration steps , , Current line-of-sight distance; After the prediction iteration is completed, the prediction termination state is used as a guide. Compared with the initial state The remaining flight time of the missile was calculated. : 。 7. The method for spatiotemporal cooperative guidance of multiple missiles under three-dimensional complex motion constraints according to claim 1, characterized in that, The implementation process of step (5) is as follows: Remaining Time Coordination Error Designed as follows: ； in, Indicates missile The neighboring nodes; Adjust parameters The dynamic update law is designed as follows: ； in, This is a limiting function used to restrict parameters within the feasible region. Inside; As the driving term, its expression is: ； Among them, parameters Used to ensure The increase of parameters Used for adjusting and controlling time errors; when At the same time, a simultaneous priority cooperative guidance strategy is adopted, giving equal priority to the strike time and the remaining time error, to ensure that the adjustment parameters achieve a balance between satisfying the strike time of a single missile and the consistency of time coordination among multiple missiles. when At that time, a time-accelerated cooperative guidance strategy is adopted to drive the project. The main focus is on the timing of the strike. Its speed accelerates the arrival time of a single missile. .

8. The method for spatiotemporal cooperative guidance of multiple missiles under three-dimensional complex motion constraints according to claim 1, characterized in that, The implementation process of step (6) is as follows: Acceleration control commands The solution based on the dynamic inverse control method is as follows: ； in, To control the input matrix, The current missile velocity direction vector, To control bandwidth gain, This includes the drift matrix caused by coordinate system rotation; It is the total differential of the desired velocity direction vector, including the feedforward compensation term for target maneuver; Acceleration command It can be decomposed into space guidance components. and time co-component These are used to eliminate geometric attack angle errors and adjust the remaining flight time, respectively, to achieve time and space coordinated guidance of multiple missiles in three-dimensional space.

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