A waypoint-based multi-missile online cooperative path planning method

Abstract

This invention discloses a multi-missile online cooperative trajectory planning method based on waypoints. It introduces two types of virtual waypoints: cooperative relay points and virtual target points. The former is responsible for spatial cooperative tasks, while the latter is responsible for temporal cooperative tasks. Various complex tasks can be achieved through different combinations of cooperative relay points and virtual target points. Furthermore, transforming the task and trajectory planning problem into a waypoint planning problem effectively reduces computational complexity, enabling the algorithm to execute online. When applied to typical cooperative reconnaissance and strike missions, the terminal guidance activation constraints and detection constraints in the cooperative trajectory planning can be converted into virtual target points, while the synchronous strike and reconnaissance constraints can be converted into cooperative relay points between these virtual target points.

Description

Technical Field

[0001] This invention relates to the field of missile trajectory control technology, and more specifically to a multi-missile online collaborative trajectory planning method based on waypoints. Background Technology

[0002] Cooperative trajectory planning is a problem that, considering environmental factors such as terrain and weather, and under conditions such as inter-missile coordination, operational scenarios, and the constraints of the loitering munition itself, aims to plan the optimal flight state of a loitering munition from its initial spatiotemporal state to its target spatiotemporal state, based on defined mission requirements. Unlike typical trajectory planning problems, cooperative trajectory planning adds temporal and spatial coordination constraints, resulting in complex mathematical descriptions and significant optimization challenges. Traditional optimal control methods for multi-missile cooperative trajectory planning are complex to construct, with solution times typically measured in hours, making them unsuitable for online planning tasks in highly dynamic environments.

[0003] Therefore, how to propose a multi-missile online cooperative trajectory planning method based on a waypoint simplification model is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] In view of this, the present invention provides a method for online collaborative trajectory planning of multiple missiles based on waypoints. In order to complete the online planning of multiple missile penetration and collaborative strike missions, the present invention relaxes the description of the traditional optimal control problem and decomposes the overall optimization task into multiple sub-tasks for optimization.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A multi-missile online cooperative trajectory planning method based on waypoints includes the following steps:

[0007] Terminal guidance activation constraints:

[0008] S11. Update the target motion state and missile motion state in real time according to the target motion state model and missile motion state model respectively;

[0009] S12. Obtain the terminal guidance switching point of the missile in the current state, calculate the remaining range from the current state of the missile to the terminal guidance switching point of the missile and estimate the flight time t, calculate the expected state of the target after the flight time t and calculate the new terminal guidance switching point of the missile.

[0010] S13. Repeat S11-S12, iteratively optimize the terminal guidance switching point of the lead missile using the new terminal guidance switching point of the lead missile, and calculate the terminal guidance switching point of the lead missile based on the terminal guidance switching point of the lead missile after iterative optimization and the expected position of the target, combined with the mission.

[0011] Detection constraints:

[0012] S21. Update the target motion state and missile motion state in real time according to the target motion state model and missile motion state model respectively;

[0013] S22. Obtain the lead missile cooperative detection point in the current state, calculate the remaining distance from the current state of the lead missile to the lead missile cooperative detection point and estimate the flight time t, calculate the expected state of the target after the flight time t and calculate the new lead missile cooperative detection point.

[0014] S23. Repeat S21-S22, iteratively optimize the lead missile cooperative detection point using the new lead missile cooperative detection point, and calculate the follower missile cooperative detection point based on the optimized lead missile cooperative detection point and the expected target position, combined with the mission.

[0015] S24. Extend the line connecting the two sets of cooperative detection points in the middle of the missile cooperative detection point in both directions in opposite directions. Calculate the climb and dive distances based on the difference between the detection altitude and the cruise altitude, the missile's climb and dive capabilities, and the maximum available overload, and determine the two sets of altitude adjustment points.

[0016] Collaborative constraints:

[0017] S31. Based on the missile motion state model, update the missile motion state in real time, place the missile's current position at the head of the waypoint sequence, and insert virtual target points in each mission phase;

[0018] S32. For each virtual target point, calculate the straight-line distance between the adjacent waypoints before and after the virtual target point, keeping the longest trajectory unchanged, and adjust the distance of the remaining trajectories by lateral maneuvering by adjusting the position of the virtual target point, until all virtual target points have been calculated, and output the virtual target points.

[0019] Preferably, in S11 and S21, the specific content of real-time updates to the target motion state and missile motion state based on the target motion state model and missile motion state model respectively includes:

[0020] The system acquires real-time motion data of the target and missile using sensors, preprocesses the acquired real-time motion data using sensor performance models, and updates the target motion state and missile motion state based on the preprocessed motion data.

[0021] Preferably, in S12, the terminal guidance seeker detects and covers a certain state, and calculates the terminal guidance switching point of the missile in the corresponding state.

[0022] Preferably, the specific process of iteratively optimizing the terminal guidance switching point of the leading missile in S13 through the new terminal guidance switching point includes:

[0023] For each new terminal guidance switching point of the lead missile, the flight time t1 of the lead missile from the previous state position to the new terminal guidance switching point is calculated. If the difference between t and t1 is less than the preset error or the number of iterations reaches the maximum value, the terminal guidance switching point of the lead missile after iteration optimization is output.

[0024] Preferably, in S22, the detection sensor coverage location is determined based on a certain state, and the corresponding missile-guided cooperative detection point is calculated.

[0025] Preferably, in S23, the specific process of iteratively optimizing the lead missile cooperative detection point using the new lead missile cooperative detection point includes:

[0026] For each new leader missile cooperative detection point obtained, the flight time t1 of the leader missile moving from the previous state position to the new leader missile cooperative detection point is calculated. If the difference between t and t1 is less than the preset error or the number of iterations reaches the maximum value, the leader missile cooperative detection point after iterative optimization is output.

[0027] Preferably, the method for selecting virtual target points in collaborative constraints is as follows:

[0028] The selection criteria for virtual target p2 are: R 12 +R 23 =R Lw ,

[0029] Where p1 is the forward point of the virtual target, p2 is the virtual target, p3 is the backward point of the virtual target, and R 12 For the journey from p1 to p2, R 23 For the flight distance from p3 to p2, R 13 The flight path is from p1 to p3; the aircraft first flies towards p2, then passes p2 and flies towards p3; R Lw For the expected remaining flight distance;

[0030] Based on the calculation methods for remaining distance and desired course, we can obtain:

[0031]

[0032] In the formula: θ V and φ V Represents the latitude and longitude of the virtual target, ψ 12 The desired heading angle pointing to the virtual target point;

[0033] Let R 12 =R 23 =R Lw / 2, according to the spherical triangle theorem, we can obtain:

[0034]

[0035] In the formula: ψ13 =ψ w This represents the expected heading angle toward the target after passing the virtual target point;

[0036] The location of the virtual target point is:

[0037]

[0038] The height of the virtual target point satisfies:

[0039]

[0040] In the formula, h1 and h3 are the altitudes of waypoints p1 and p3, respectively;

[0041] The virtual target point is p2(φ) V ,θ V ,h V ), and repeatedly update p2 online.

[0042] As can be seen from the above technical solution, compared with the prior art, this invention discloses a multi-missile online cooperative trajectory planning method based on waypoints. This invention introduces two types of virtual waypoints: cooperative relay points and virtual target points. The former is responsible for realizing spatial cooperative tasks, and the latter is responsible for realizing temporal cooperative tasks. Various complex tasks can be achieved through different combinations of cooperative relay points and virtual target points. Furthermore, transforming the task and trajectory online planning problem into a waypoint planning problem effectively reduces computational complexity, enabling the algorithm to execute online.

[0043] When applied to typical cooperative reconnaissance and strike missions, this method converts terminal guidance activation constraints and detection constraints in cooperative trajectory planning into virtual target points, while synchronous strike and reconnaissance constraints can be converted into cooperative relay points between these virtual target points. By segmenting the mission using cooperative relay points, optimization strategies can be designed for each task to reduce optimization complexity. Simultaneously, simplified models of sensor, target motion states, and missile motion states are established to further reduce computational load and achieve online planning. Attached Figure Description

[0044] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0045] Figure 1 The overall workflow diagram of a multi-missile online collaborative trajectory planning method based on waypoints provided by this invention;

[0046] Figure 2This is a circular arc turning design scheme provided in the embodiments of the present invention;

[0047] Figure 3 This is an S-shaped maneuvering turn design scheme provided in the embodiments of the present invention;

[0048] Figure 4 The flowchart of the terminal guidance switching cooperative relay point calculation in the multi-missile online cooperative trajectory planning method based on waypoints provided by the present invention is shown below;

[0049] Figure 5 This invention provides a flowchart of the collaborative detection and collaborative relay point calculation process in a multi-missile online collaborative trajectory planning method based on waypoints.

[0050] Figure 6 A flowchart of virtual target point calculation in a multi-missile online cooperative trajectory planning method based on waypoints provided by this invention;

[0051] Figure 7 A schematic diagram of a lateral maneuver strategy based on a virtual target in a waypoint-based online cooperative trajectory planning method provided by the present invention;

[0052] Figure 8 This is a schematic diagram of the coverage area of ​​the sensor model provided in this embodiment of the invention;

[0053] Figure 9 This is a schematic diagram of the longitudinal section of the sensor model provided in this embodiment of the invention;

[0054] Figure 10 This is a schematic diagram of the height adjustment point provided in an embodiment of the present invention;

[0055] Figure 11 This is a schematic diagram of the target ship's navigation trajectory provided in an embodiment of the present invention;

[0056] Figure 12 This is a schematic diagram of the missile terminal guidance switching point range deviation provided in an embodiment of the present invention;

[0057] Figure 13 This is a schematic diagram of the missile terminal velocity pointing deviation provided in an embodiment of the present invention;

[0058] Figure 14 This is a diagram showing the change of the missile baseline (detection point) provided in an embodiment of the present invention;

[0059] Figure 15 The range deviation (relative to 10km) at the missile terminal guidance switching point provided in this embodiment of the invention;

[0060] Figure 16 This is a diagram showing the maximum lateral overload variation of the missile provided in an embodiment of the present invention;

[0061] Figure 17 This is a diagram showing the maximum total overload variation of the missile provided in this embodiment of the invention;

[0062] Figure 18 This is a schematic diagram of the trajectory of a missile (missile 3) provided in an embodiment of the present invention. Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0064] This invention discloses a multi-missile online cooperative trajectory planning method based on waypoints, such as... Figure 1 As shown in the figure. In this method, real-time motion data of the target and missile are acquired through sensors, the acquired real-time motion data are preprocessed using a sensor performance model, and the target motion state and missile motion state are updated based on the preprocessed motion data.

[0065] In this embodiment, a passive radar seeker is used as an example to illustrate the sensor performance model:

[0066] This passive radar seeker sensor can measure the line-of-sight angle between the target and the sensor, which is used as observation information in target localization. For the i-th missile, the measured quantity is...

[0067]

[0068] In the formula, γ is the elevation angle and η is the azimuth angle.

[0069] The measurement equation is then:

[0070]

[0071] Where v is the measurement noise vector.

[0072]

[0073] In the formula, Let [x] be the transformation matrix from the inertial frame to the sensor's own frame. s,i ,y s,i ,z s,i ] T Let [x] be the coordinates of the i-th sensor in the inertial frame. t ,y t ,z t ] TLet be the coordinates of the target in the inertial frame.

[0074] For simplified sensor performance models, E(R) is generally used. H ,R L ,γ H ,γ L ,η H ,η L Defined as follows, where E∈{0,1} is a sensor performance index, where 0 represents undetectable and 1 represents detectable; R H ,R L For the purpose of detection range constraints, the two values ​​represent the maximum and minimum detection ranges; γ H ,γ L For elevation angle constraints, the two values ​​represent the maximum and minimum visible elevation angles, respectively; η H, η L For azimuth constraints, the two are the maximum and minimum visible azimuth angles, respectively.

[0075] For the target motion state model:

[0076] In many cases, targets do not always move in one direction, but rather constantly change their course along a predetermined route, or change their course according to the battlefield threat situation. Simultaneously, targets may also change their speed. Therefore, it is necessary to model some typical target maneuvering patterns for target state prediction in online cooperative trajectory planning methods. This embodiment only illustrates typical target motion state models:

[0077] Curved maneuvering turn

[0078] like Figure 2 As shown, let the target's maneuver overload be N. T The target speed is V. T The target's current position is a; when the target begins to maneuver, its distance from the next waypoint (denoted as b) is L.

[0079] S-shaped maneuvering turn

[0080] like Figure 3 As shown, to achieve the target S-shaped maneuver, the method adopted is similar to that of the arc maneuver. The baseline ab is divided into two equal segments, and each segment is considered as a circular arc.

[0081] During the maneuver, the target is first instructed to travel with overload N; when the angle between the velocity direction and the baseline ab is θ0, it travels with overload -N; when the angle between the velocity direction and the baseline ab returns to θ0, it travels with overload N again.

[0082] Sine (cosine) motion

[0083] The target performs sine (cosine) maneuvers as follows:

[0084] V = V0 + at (1.4)

[0085]

[0086] Where: N z To control overload, N m For maximum maneuver overload, T jd For the maneuver cycle.

[0087] Missile motion state model

[0088] Based on Newton's second law, the equation of motion of the center of mass of a continuous system of particles with varying mass is:

[0089]

[0090] Where: P, R, mg, F k ′ represent thrust, aerodynamic force, gravity, and inertial force, respectively.

[0091] Choosing the geocentric coordinate system as the reference coordinate system, the equation can be further expressed as:

[0092]

[0093] In the formula: δr / δt is the rate of change of the geocentric radius vector of the anti-ship missile relative to the geocentric coordinate system, δr / δt=V, then the formula can be expressed as:

[0094]

[0095] In the formula: V represents the velocity vector of the anti-ship missile relative to the ground.

[0096] The decomposition of the equation in the position coordinate system results in an overly complex form, placing significant pressure on the real-time operation of the system. For typical cruise missiles, their available overload and total impulse are large, and their flight distance is short; therefore, small quantities can be ignored, and the equation becomes:

[0097]

[0098] Establishing simplified models of the motion states of sensors, targets, and missiles can further reduce the computational load and enable online planning.

[0099] 1. Terminal guidance activation constraints

[0100] Terminal guidance activation constraints include position and heading constraints, defined by two sets of cooperative relay points, referred to as terminal guidance switching points. The calculation process for terminal guidance switching cooperative relay points is as follows: Figure 4 As shown.

[0101] Terminal guidance activation constraints constrain the heading by the relative positions of two sets of cooperative relay points, and constrain the position by the set of cooperative relay points closest to the target. This phase consists of the following three key steps:

[0102] Step 1: Roughly calculate the terminal guidance switching point of the missile.

[0103] The target and missile motion states are updated using current sensor measurement information. The target's current state is used as the required detection coverage position of the terminal guidance seeker, and the terminal guidance switching point is calculated.

[0104] Step 2: Iteratively optimize the terminal guidance switching point of the missile.

[0105] Calculate the remaining range from the current state of the missile leader to the terminal guidance switching point and estimate the flight time using the current speed. Calculate the expected state of the target after that time and use that state as the required detection coverage position for the terminal guidance seeker. Calculate the terminal guidance switching point of the missile leader. Repeat the above steps to iteratively optimize the terminal guidance switching point of the missile leader.

[0106] Step 3: Calculate the switching point from terminal guidance to missile.

[0107] Using the terminal guidance switching point of the missile leader and the expected position of the target, the terminal guidance switching point of the missile leader is calculated in conjunction with the mission.

[0108] 2. Detection Constraints

[0109] The detection constraints include elevation constraints, baseline constraints, and sensor orientation constraints, which are simplified into position constraints and heading constraints, defined by four sets of cooperative relay points, referred to as cooperative detection points. The calculation process for cooperative detection relay points is as follows: Figure 5 As shown.

[0110] Since cooperative detection constraints typically include altitude change requirements, the first and fourth groups of cooperative relay points are altitude adjustment points, set at their cruising altitude; the middle two groups of cooperative relay points are set at their detection altitude, with constraints applied to their heading and position. This phase consists of the following four key steps:

[0111] Step 1: Coarsely solve for the missile-leading cooperative detection point

[0112] Update the target and missile motion status using current sensor measurement information, calculate the lead missile cooperative detection point based on the target's current state and the required detection sensor coverage location.

[0113] Step 2: Iteratively optimize the missile-leading cooperative detection points

[0114] Calculate the remaining range from the current state of the missile leader to the cooperative detection point and estimate the flight time using the current speed. Calculate the expected state of the target after that time and use that state as the required sensor coverage location. Calculate the cooperative detection point for the missile leader. Repeat the above steps to iteratively optimize the cooperative detection point for the missile leader.

[0115] Step 3: Calculate the missile-coordinated detection point

[0116] Using the lead missile's cooperative detection point and the target's expected location, the follower missile's cooperative detection point is calculated in conjunction with mission requirements.

[0117] Step 4: Calculate the height adjustment point

[0118] The lines connecting the two sets of coordinated detection points in the middle are extended in opposite directions in both directions. The climb and dive distances are calculated based on the difference between the detection altitude and the cruise altitude, the missile's climb and dive capabilities, and the maximum available overload, and the two sets of altitude adjustment points are determined.

[0119] 3. Collaboration (Time) Constraints

[0120] Coordination (time) constraints are tasks that need to be executed synchronously, such as simultaneously arriving at the terminal guidance activation point or simultaneously arriving at the cooperative detection starting point. This constraint is satisfied by inserting virtual target points into the existing waypoint sequence and adjusting the total flight path. The virtual target point calculation process is as follows: Figure 6 As shown.

[0121] Virtual target point such as Figure 7 As shown, p1 is the forward waypoint of the virtual target, p2 is the virtual target, and p3 is the backward waypoint of the virtual target. 12 For the journey from p1 to p2, R 23 For the flight distance from p3 to p2, R 13 The flight path is from p1 to p3; the aircraft first flies towards p2, and then flies towards p3 after passing through p2.

[0122] In summary, the key to controlling the remaining range lies in the selection of p2. The selection of the virtual target p2 must satisfy R. 12 +R 23 =R Lw , where R Lw This represents the expected remaining distance. Based on the calculation methods for the remaining distance and expected course, we can obtain:

[0123]

[0124] In the formula: θ V and φ V Represents the latitude and longitude of the virtual target, ψ 12 The desired heading angle pointing towards the virtual target point.

[0125] Let R 12 =R23 =R Lw / 2, according to the spherical triangle theorem, we can obtain:

[0126]

[0127] In the formula: ψ 13 =ψ w This represents the expected heading angle toward the target after passing the virtual target point.

[0128] Therefore, the location of the virtual target point is:

[0129]

[0130] The height of the virtual target point satisfies:

[0131]

[0132] In the formula, h1 and h3 are the altitudes of waypoints p1 and p3, respectively. At this point, the virtual target point p2(φ) is... V ,θ V ,h V () has been fully defined.

[0133] The above method is in R 12 +R 23 =R Lw This was obtained based on the premise that the aircraft instantaneously adjusted its heading angle to ψ when passing p2. 13 However, the heading angle cannot change abruptly; after passing p2, the aircraft will smoothly turn to ψ. 13 The direction is such that the actual remaining range will be greater than R. Lw .

[0134] To address the aforementioned issues, p2 can be updated repeatedly online. As the remaining range decreases, the transition from p1p2 to p2p3 will become increasingly smooth, leading to more precise control over the remaining range. Furthermore, due to interference factors such as deviations in the initial motion state, aerodynamic forces, and atmospheric model biases, the virtual target point must be updated online.

[0135] In this embodiment, the sensor coverage area is calculated based on a typical sensor model, and its coverage area is as follows: Figure 8 As shown.

[0136] The sensor's detection distance is R, and its maximum detection angle is α. max The lowest detection angle is α min The detection half-angle is β. Furthermore, the sensor is assumed to remain horizontal throughout the analysis.

[0137] When calculating the terminal guidance switching point using a sensor model, it is necessary to ensure that the target is within the sensor coverage area when the UAV is at that point. The horizontal constraint on sensor coverage can be achieved by ensuring the heading always points towards the target. The longitudinal profile coverage will be discussed next. Figure 9 As shown. The specific calculation method for the terminal guidance switching point is as follows:

[0138] Define the flight altitude as H1, the target altitude as H0, and the terminal guidance switching distance as D. f Then the final guidance switching point needs to satisfy the following constraints:

[0139]

[0140] If we define the relaxation coefficient α∈(0,1), then the terminal guidance switching distance and flight altitude can be calculated by solving the following system of equations.

[0141]

[0142] At this point, the calculation of the terminal guidance switching point is complete.

[0143] The height adjustment point is calculated after the calculation of the two collaborative detection points is completed. Its horizontal position is located on the extension line connecting the two collaborative detection points, and its longitudinal profile position is as follows: Figure 10 As shown. The specific calculation method for the height adjustment point is as follows:

[0144] The location of the altitude adjustment point needs to meet missile performance constraints. Here, we use climb rate and dive rate as examples to illustrate the calculation method for the altitude adjustment point. Let the detection altitude be H1, the cruise altitude be H0, and the climb distance be D. r The descent distance is D d The maximum climb rate is v r The maximum dive rate is v d If the drone's cruising horizontal speed is v, then the altitude adjustment point needs to satisfy the following constraints:

[0145]

[0146] Define the relaxation coefficient α∈(0,1), then the ascent distance and descent distance can be calculated as follows.

[0147]

[0148] Once the ascent and descent distances are obtained, the positions of the two altitude adjustment points can be calculated.

[0149] The missile's flight path is obtained based on two sets of coordinated detection points and altitude adjustment points.

[0150] The following example illustrates a coordinated attack on a destroyer using three cruise missiles. The target, missile, and trajectory parameters are as follows:

[0151] Table 1. Maneuver parameters of a certain destroyer

[0152]

[0153]

[0154] Table 2 Missile and Track Parameters

[0155]

[0156] The missile performed two climb probes during flight, and finally switched to terminal guidance at the end of the continuous probe phase. The initial target motion was assumed to be: velocity 15 m / s, longitude 75°, latitude 57°, and heading angle -150.68°; the target was assumed to be traveling at a constant speed and without lateral maneuvers (considering Earth's rotation and oblateness). Figure 11 As shown.

[0157] Considering ideal initial conditions, that is, when the three missiles enter the cruise phase, their remaining range from the target is basically equal, their lateral relative distance basically meets the baseline requirements for the first joint detection, and the flight speed of the three missiles is equal and remains stable.

[0158] Table 3 shows the motion states of the three missiles at the start of low-altitude cruise and the basic motion state of the target. In this scenario, the initial remaining ranges of the three missiles are 871.8 km, 874.9 km, and 872.8 km, respectively, with a maximum deviation of 3.1 km; calculated based on the missile's cruise speed of 270 m / s, the time deviation is 11.5 s. Meanwhile, the lateral distances (baselines) between missiles 1-3, 2-3, and 1-2 are 1.11 km, 2.22 km, and 3.33 km, respectively, which are significantly different from the baseline requirement (20 km) for the initial climb-coordinated detection.

[0159] Table 3 Initial conditions for simulation

[0160]

[0161] Meanwhile, interference factors that follow a uniform distribution are set as shown in Table 4, and 500 Monte Carlo target simulations are conducted to verify the results of the cooperative ballistic planning.

[0162] Table 4. Range of Interference and Deviation Experiencing the Missile

[0163]

[0164] like Figure 12 As shown, under the influence of interference factors, the speed of multiple missiles at the terminal stage is basically opposite to the direction of the target's movement, which can satisfy the underwater collaborative detection constraint of the target and achieve underwater collaborative strike against the target.

[0165] like Figure 13 As shown, under the influence of interference factors, multiple missiles can meet the baseline constraints proposed by the collaborative detection mission.

[0166] like Figure 14 As shown, relative to the theoretical terminal guidance switching point (10km from the predicted hit point), the range deviation of each missile at the terminal guidance switching point did not exceed 80m; and when the missile flew at a speed of 150m / s (after deceleration), with a simulated step size of 0.5s, the flight distance of each missile step reached 75m. Therefore, it can be considered that the above-mentioned multi-missile cooperative trajectory planning method is correct and effective.

[0167] at the same time, Figure 15 This indicates that at the moment of terminal guidance switching, the remaining range deviation between the foremost and the last missile is generally less than 20m, further verifying the correctness of the multi-missile cooperative trajectory planning method.

[0168] like Figure 16 , Figure 17 As shown, the missile's normal overload during flight is always within the allowable range because the cooperative trajectory planning algorithm constrains the lateral maneuverability (total normal overload and tilt angle).

[0169] like Figure 18 As shown, Missile 3 employs different lateral maneuver ranges under different initial conditions to compensate for flight time deviations caused by initial position and velocity variations. It can be seen that the missile completes most of its lateral maneuvering before its first climb detection phase. This is because this period accounts for the vast majority of the missile's total flight time (800km–200km), and the cooperative trajectory planning method proposed in this invention also places the turning requirement within this stage.

[0170] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0171] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-missile online cooperative trajectory planning method based on waypoints, characterized in that, Includes the following steps: Terminal guidance activation constraints: S11. Update the target motion state and missile motion state in real time according to the target motion state model and missile motion state model respectively; S12. Obtain the terminal guidance switching point of the missile in the current state, calculate the remaining range from the current state of the missile to the terminal guidance switching point of the missile and estimate the flight time t, calculate the expected state of the target after the flight time t and calculate the new terminal guidance switching point of the missile. S13. Repeat S11-S12, iteratively optimize the terminal guidance switching point of the lead missile using the new terminal guidance switching point of the lead missile, and calculate the terminal guidance switching point of the lead missile based on the terminal guidance switching point of the lead missile after iterative optimization and the expected position of the target, combined with the mission. Detection constraints: S21. Update the target motion state and missile motion state in real time according to the target motion state model and missile motion state model respectively; S22. Obtain the lead missile cooperative detection point in the current state, calculate the remaining distance from the current state of the lead missile to the lead missile cooperative detection point and estimate the flight time t, calculate the expected state of the target after the flight time t and calculate the new lead missile cooperative detection point. S23. Repeat S21-S22, iteratively optimize the lead missile cooperative detection point using the new lead missile cooperative detection point, and calculate the follower missile cooperative detection point based on the optimized lead missile cooperative detection point and the expected target position, combined with the mission. S24. Extend the line connecting the two sets of cooperative detection points in the middle of the missile cooperative detection point in both directions in opposite directions. Calculate the climb and dive distances based on the difference between the detection altitude and the cruise altitude, the missile's climb and dive capabilities, and the maximum available overload, and determine the two sets of altitude adjustment points. Collaborative constraints: S31. Based on the missile motion state model, update the missile motion state in real time, place the missile's current position at the head of the waypoint sequence, and insert virtual target points in each mission phase; S32. For each virtual target point, calculate the straight-line distance between the adjacent waypoints before and after the virtual target point, keep the longest trajectory unchanged, and adjust the distance of the other trajectories by lateral maneuvering by adjusting the position of the virtual target point, until all virtual target points have been calculated, and output the virtual target points; The cooperative detection point is a detection constraint defined by four sets of cooperative relay points; The detection constraints include elevation constraints, baseline constraints, and sensor orientation constraints, which are simplified into position constraints and heading constraints. The cooperative relay point is a set virtual waypoint.

2. The method of claim 1, wherein, In S11 and S21, the specific content of real-time updates to the target motion state and missile motion state based on the target motion state model and missile motion state model respectively includes: The system acquires real-time motion data of the target and missile using sensors, preprocesses the acquired real-time motion data using sensor performance models, and updates the target motion state and missile motion state based on the preprocessed motion data.

3. The multi-missile online cooperative trajectory planning method based on waypoints according to claim 1, characterized in that, In S12, the terminal guidance seeker detects the coverage position of a certain state and calculates the terminal guidance switching point of the missile in the corresponding state.

4. The method of claim 1, wherein, The specific process of iteratively optimizing the terminal guidance switching point of the missile in S13 through the new terminal guidance switching point includes: For each new terminal guidance switching point of the lead missile, the flight time t1 of the lead missile from the previous state position to the new terminal guidance switching point is calculated. If the difference between t and t1 is less than the preset error or the number of iterations reaches the maximum value, the terminal guidance switching point of the lead missile after iteration optimization is output.

5. The method of claim 1, wherein, In S22, the detection sensor coverage location is determined based on a certain state, and the corresponding missile-guided cooperative detection point is calculated for that state.

6. The method of claim 1, wherein, In S23, the specific process of iteratively optimizing the missile-leader cooperative detection point using the new missile-leader cooperative detection point includes: For each new leader missile cooperative detection point obtained, the flight time t1 of the leader missile moving from the previous state position to the new leader missile cooperative detection point is calculated. If the difference between t and t1 is less than the preset error or the number of iterations reaches the maximum value, the leader missile cooperative detection point after iterative optimization is output.

7. The method of claim 1, wherein, The method for selecting virtual target points in collaborative constraints is as follows: Virtual target The selection condition is: , in For the virtual target waypoint, For virtual targets, For the virtual target's waypoint, for arrive The voyage, for arrive The voyage, for arrive The flight range; the aircraft first headed towards Flight, passing Then to flight; For the expected remaining flight distance; Based on the calculation methods for remaining distance and desired course, we can obtain: ； In the formula: and Represents the latitude and longitude of the virtual target. The desired heading angle pointing to the virtual target point; make According to the spherical triangle theorem, we can obtain: ； In the formula: This represents the expected heading angle toward the target after passing the virtual target point; The location of the virtual target point is: ； The height of the virtual target point satisfies: ； wherein the altitude of the waypoint ; Virtual target point is Online repeated update .

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