A method and device for coordinated flight vehicle control and guidance

Abstract

This application discloses a method and apparatus for cooperative containment guidance of aircraft, relating to the field of aircraft guidance and control. The method includes acquiring the position, velocity, heading angle, interception time, navigation ratio of the pursuing aircraft, position, velocity, heading angle of the defending aircraft, target position, and target heading angle of the pursuing aircraft; determining the coordinates of the containment point using a geometric programming method; and controlling the target and the defending aircraft using a cooperative guidance method based on the coordinates of the containment point, the navigation ratio of the pursuing aircraft, the position, velocity, heading angle of the pursuing aircraft, the position, velocity, heading angle of the defending aircraft, the target position, and the target heading angle of the defending aircraft, thereby achieving cooperative containment of the pursuing aircraft. This application improves the effectiveness of the cooperative containment guidance strategy and the interception efficiency of the pursuing aircraft.

Description

Technical Field

[0001] This application relates to the field of aircraft guidance and control, and in particular to a method and apparatus for cooperative strait control guidance of aircraft. Background Technology

[0002] With the rapid development of modern defense technologies, precision guidance technologies, represented by proportional guidance, have been widely used, posing a serious threat to the survivability of high-value aircraft. As guidance technology continues to advance, traditional passive defense measures (such as maneuvering evasion and decoy countermeasures) may no longer be sufficient to ensure the safety of high-value aircraft. To overcome this predicament, the concept of active defense has been proposed: when a high-value aircraft detects a pursuing aircraft, it can launch a defensive aircraft for counter-interception, thus forming a dynamic three-body confrontation model involving the pursuing aircraft, the defensive aircraft, and the target.

[0003] In recent years, scholars have conducted extensive research on the three-body antagonism problem. Existing modeling methods exhibit significant discrepancies between kinematic descriptions and actual physical systems, making the results difficult to apply in practice. Furthermore, studies on the three-body antagonism problem under second-order dynamics are all based on linear models, which limits the applicability of guidance laws. Solving the cooperative restraint guidance problem remains a challenge. Summary of the Invention

[0004] The purpose of this application is to provide a method and apparatus for cooperative deterrence guidance of aircraft, which can improve the effectiveness of cooperative deterrence guidance strategies and the interception efficiency of pursuing aircraft.

[0005] To achieve the above objectives, this application provides the following solution.

[0006] In a first aspect, this application provides a method for coordinated containment guidance of aircraft, comprising: acquiring the position, velocity, heading angle, interception time, navigation ratio of the pursuing aircraft, position, velocity, heading angle of the defensive aircraft, target position, and target heading angle of the defensive aircraft; the defensive aircraft is used to intercept the pursuing aircraft to protect the target; the coordinates of the containment point are determined using a geometric programming method based on the position, velocity, heading angle, interception time, position, and velocity of the defensive aircraft; and the target and the defensive aircraft are controlled using a coordinated guidance method based on the coordinates of the containment point, navigation ratio of the pursuing aircraft, position, velocity, heading angle, and heading angle of the pursuing aircraft, position, velocity, heading angle of the defensive aircraft, target position, and target heading angle of the defensive aircraft, thereby achieving coordinated containment of the pursuing aircraft.

[0007] Secondly, this application provides a flight body cooperative restraint guidance device, comprising: a parameter acquisition module, used to acquire the position, speed, heading angle, interception time, navigation ratio of the pursuing flight body, position, speed, heading angle of the defensive flight body, target position, and target heading angle of the defensive flight body; the defensive flight body is used to intercept the pursuing flight body to protect the target; a restraint point determination module, used to determine the coordinates of the restraint point using a geometric programming method based on the position, speed, heading angle, interception time, position, and speed of the defensive flight body; and a cooperative restraint module, used to control the target and the defensive flight body using a cooperative guidance method based on the coordinates of the restraint point, navigation ratio of the pursuing flight body, position, speed, heading angle, position, speed, heading angle of the defensive flight body, target position, and target heading angle of the defensive flight body, to achieve cooperative restraint of the pursuing flight body.

[0008] Based on the specific embodiments provided in this application, the following technical effects are disclosed.

[0009] This application provides a method and apparatus for coordinated control and guidance of flying objects. Based on the position, speed, heading angle, interception time, position, and speed of the defending flying object, the coordinates of the control point are determined using a geometric programming method. This ensures that the flight trajectory of the pursuing flying object passes through the preset control point by maneuvering the target. A coordinated guidance method is used to control the target and the defending flying object to achieve coordinated control of the pursuing flying object. This allows the target and the defending flying object to actively cooperate in a coordinated manner, significantly improving the overall interception efficiency. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is an application environment diagram of a flight body cooperative restraint guidance method in one embodiment of this application.

[0012] Figure 2 This is a flowchart illustrating a flight body cooperative restraint guidance method provided in one embodiment of this application.

[0013] Figure 3 This is a schematic diagram of a three-body confrontation scenario provided in an embodiment of this application.

[0014] Figure 4 A schematic diagram of a cooperative restraint guidance strategy provided in an embodiment of this application.

[0015] Figure 5 This is a schematic diagram of the feasible region of the restraint point provided in an embodiment of this application.

[0016] Figure 6 This is a schematic diagram showing the distribution of the guidance trajectories and restraint points of three moving bodies provided in an embodiment of this application.

[0017] Figure 7 This is a schematic diagram of the leading angle curve of a pursuing flight vehicle provided in an embodiment of this application.

[0018] Figure 8 A schematic diagram of the head-on interception angle error curve of a pursuing flight vehicle provided in an embodiment of this application.

[0019] Figure 9 This is a schematic diagram of the pursuit-defense line-of-sight distance and the pursuit-target line-of-sight distance provided in an embodiment of this application.

[0020] Figure 10 This is a schematic diagram of the acceleration curves of three moving bodies provided in an embodiment of this application.

[0021] Figure 11 This is a schematic diagram of the functional modules of a flight body cooperative restraint and guidance device provided in another embodiment of this application.

[0022] Figure 12 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0023] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0024] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] The flight body cooperative restraint guidance method provided in this application embodiment can be applied to, for example... Figure 1In the application environment shown, terminal 101 communicates with server 102 via a network. A data storage system can store the data that server 102 needs to process. The data storage system can be set up independently, integrated into server 102, or placed in the cloud or on another server. Terminal 101 can send the position, speed, heading angle, interception time, navigation ratio of the pursuing aircraft, position, speed, heading angle of the defending aircraft, target position, and target heading angle of the defending aircraft to server 102. Upon receiving these parameters, server 102 uses a geometric programming method to determine the coordinates of the restraining point based on these parameters, and then uses a cooperative guidance method to control the target and the defending aircraft to achieve cooperative restraint of the pursuing aircraft. Server 102 can provide feedback on the cooperative guidance method for controlling the target and the defending aircraft to terminal 101. Furthermore, in some embodiments, the collaborative restraint guidance method for flight vehicles can also be implemented separately by the server 102 or the terminal 101. For example, the terminal 101 can directly determine the coordinates of the restraint point using a geometric programming method based on the position, speed, heading angle, interception time, navigation ratio of the pursuing flight vehicle, position, speed, heading angle of the defending flight vehicle, target position, and target heading angle of the pursuing flight vehicle. Then, a collaborative guidance method is used to control the target and the defending flight vehicle to achieve collaborative restraint of the pursuing flight vehicle. Alternatively, the server 102 can obtain the position, speed, heading angle, interception time, navigation ratio of the pursuing flight vehicle, position, speed, heading angle of the defending flight vehicle, target position, and target heading angle of the pursuing flight vehicle from the data storage system, determine the coordinates of the restraint point using a geometric programming method, and then use a collaborative guidance method to control the target and the defending flight vehicle to achieve collaborative restraint of the pursuing flight vehicle.

[0026] The terminal 101 can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle devices. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 102 can be implemented using a standalone server or a server cluster composed of multiple servers, or it can be a cloud server.

[0027] In one exemplary embodiment, such as Figure 2 As shown, a method for cooperative restraint guidance of flight vehicles is provided. This method is executed by computer equipment, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking server 102 as an example, the explanation includes the following steps 201 to 203.

[0028] Step 201: Obtain the position, speed, heading angle, interception time, navigation ratio of the pursuing aircraft, position, speed, heading angle of the defending aircraft, target position, and target heading angle. The defending aircraft is used to intercept the pursuing aircraft to protect the target.

[0029] Step 202: Based on the position of the pursuing aircraft, the speed of the pursuing aircraft, the heading angle of the pursuing aircraft, the interception time, the position of the defending aircraft, and the speed of the defending aircraft, the coordinates of the restraining point are determined using a geometric programming method.

[0030] Step 203: Based on the coordinates of the restraining point, the navigation ratio of the pursuing aircraft, the position of the pursuing aircraft, the speed of the pursuing aircraft, the heading angle of the pursuing aircraft, the position of the defending aircraft, the speed of the defending aircraft, the heading angle of the defending aircraft, the position of the target, and the heading angle of the target, a cooperative guidance method is used to control the target and the defending aircraft to achieve cooperative restraint of the pursuing aircraft.

[0031] In one example, based on the three-body adversarial problem in a two-dimensional plane, we obtain the following: Figure 3 The scenario depicts a combat situation. This scenario consists of three moving objects and one virtual point: a pursuing flying object (using...). A (representation), target (using) T (representation), defensive flying bodies (using) D (represented by), a stationary restraint point (using) P (Indicated). In this example, the pursuing aircraft uses proportional guidance to intercept the target, while the defensive aircraft intercepts the pursuing aircraft. Simultaneously, the target uses a sniping point to perform a sniping maneuver to lure the pursuing aircraft, thus creating favorable conditions for the defensive aircraft to intercept it.

[0032] Figure 3 middle, XOY Represents an inertial coordinate system. Moving body. The velocity, acceleration, and heading angle are respectively expressed as , and And the direction of acceleration is always perpendicular to the direction of velocity. and They represent the movement of the body. Pointing to moving body The distance and angle of sight, and . The leading angle is defined as the velocity. With the movement of the body Pointing to moving body The angle between the lines of sight. In this example, all angles are positive in the counterclockwise direction. Therefore, the equation of motion for the moving body in the inertial frame can be obtained as shown in the following equation.

[0033] (1).

[0034] in, Let x be the x-coordinate of the moving body in the inertial coordinate system. for The derivative, Let x and y be the horizontal and vertical coordinates of the moving body in the inertial coordinate system. for The derivative of .

[0035] Before establishing the dynamic equations, this example is based on the following four assumptions.

[0036] Assumption 1: The pursuing, target, and defending aircraft are all simplified as point mass models, and the dynamic response of their seekers and autopilots is fast enough to be ignored.

[0037] Assumption 2: The velocities of the three moving bodies are all constant, and satisfy the following conditions: This means that the pursuing flying vehicle has a speed advantage over the target and defensive flying vehicles.

[0038] Assumption 3: The pursuing aircraft uses a proportional guidance law, and its navigation ratio can be known or quickly identified by the defending aircraft and the target.

[0039] Assumption 4: The target's heading angle is restricted, that is, during the pursuit and defense process, the target's heading angle is limited. Relative to the initial heading angle The deviation cannot be too large, otherwise the pursuit and defense will be meaningless. Let the maximum heading angle deviation of the target be... ,satisfy .

[0040] The above assumptions are reasonable: In Assumption 1, using a point mass model to simplify the analysis can effectively reduce the complexity of the system without significantly affecting the design and verification of the guidance law. Furthermore, current guidance systems possess rapid dynamic response characteristics, and their time delay effects are negligible relative to the critical time scales of the guidance process. In Assumption 2, due to the short duration of terminal guidance and the gradual change in velocity, it can be approximated that each moving body maintains a constant velocity during the pursuit and defense process. Additionally, in real-world scenarios, the pursuing aircraft typically has a high velocity to ensure effective tracking and engagement of the target, while the target (e.g., a drone) typically has a lower velocity than the pursuing aircraft, and the defending aircraft's velocity falls between the two to both intercept the pursuing aircraft and maintain sufficient maneuverability. In Assumption 3, since this example focuses on designing an inverse proportional guidance strategy, it is assumed that the guidance law of the pursuing aircraft can be quickly and collaboratively identified by the target and the defending aircraft, and important parameters such as the navigation ratio can be estimated online with high accuracy using the Kalman filter algorithm. This technical assumption aligns with the real-time processing capabilities of modern computers. In Assumption 4, the target's maneuverability during mission execution is limited by aircraft performance, mission requirements, and strategic constraints. Excessive deviation in the target's heading may cause it to stray from the mission path or expose it to additional threat areas, impacting mission effectiveness. Therefore, considering heading angle limitations in guidance law design is necessary. Based on these assumptions, the relative kinematic equations between the pursuing aircraft and the target are obtained as shown below.

[0041] (2).

[0042] in, To pursue the target within line of sight, for The derivative, For the target speed, In order to catch up with the speed of the flying object, Target - Pursue the front angle, To pursue - the target's forward angle, To pursue the target's line of sight, for The derivative, For the target heading angle, To pursue the heading angle of the flying object.

[0043] Similarly, the relative kinematic equations between the pursuing and defensive aircraft are expressed as follows.

[0044] (3).

[0045] in, To maintain line of sight for pursuit and defense, for The derivative, To defend against the speed of flying objects, For defense-pursuit of the front corner, For pursuit - defense front angle, For pursuit and defense line of sight, for The derivative, To defend against the heading angle of flying objects.

[0046] Considering that the restraining point is stationary, the relative kinematic equations between the pursuing aircraft and the restraining point are expressed as follows.

[0047] (4).

[0048] in, To maintain line-of-sight distance for pursuit and containment, for The derivative, To pursue and control the enemy, the forward angle of the position. To pursue and contain the enemy, for The derivative of .

[0049] Similarly, the relative kinematic equations between the defensive flying body and the restraining point are expressed as follows.

[0050] (5).

[0051] in, For defensive-controlling point line-of-sight distance, for The derivative, As a defensive-control point, the front corner, For defensive-controlling point of view, for The derivative of .

[0052] The dynamic equations of the heading angles of the three moving bodies can be expressed as follows.

[0053] (6).

[0054] in, for The derivative, .

[0055] Since the pursuing aircraft uses proportional guidance to intercept the target aircraft, its acceleration is expressed as follows.

[0056] (7).

[0057] in, N To achieve a good navigation ratio for tracking aircraft, a value of 3-6 is generally used.

[0058] According to formulas (2) and (6), The second derivative with respect to time can be calculated as follows.

[0059] (8).

[0060] in, for The second derivative, Accelerate towards the target Acceleration to pursue the flying object.

[0061] This means that the target's maneuvering will affect the movement of the pursuing aircraft, therefore, the target's maneuvering patterns can be designed to restrain the pursuing aircraft's movement. Based on this, this application proposes... Figure 4 The diagram illustrates a coordinated containment and guidance strategy. The superscripts '' and '' represent the intermediate moment and the moment the pursuing aircraft is intercepted, respectively.

[0062] like Figure 4 As shown, upon sensing the threat of the pursuing aircraft, the target uses a pre-determined strait control point to execute a strait control guidance law, thereby restricting the movement of the pursuing aircraft and causing the rate of change of line of sight to converge to zero before the pursuing aircraft passes the strait control point. Simultaneously, the defensive aircraft launches towards the strait control point and executes a defensive guidance law to intercept the pursuing aircraft, ensuring a successful head-on interception of the pursuing aircraft on the collision path past the strait control point.

[0063] In one example, step 202 above can be replaced by steps 301 to 303.

[0064] Step 301: Based on the position of the pursuing aircraft, the speed of the pursuing aircraft, the heading angle of the pursuing aircraft, and the interception time, an open-loop trajectory prediction method based on state space representation is used to obtain the interception trajectory of the pursuing aircraft.

[0065] Step 302: Based on the position of the defensive flying object, the speed of the defensive flying object, the position of the pursuing flying object, and the speed of the pursuing flying object, the Apollonius circles corresponding to the pursuing flying object and the defensive flying object are determined using analytical geometry methods.

[0066] Step 303: Based on the interception trajectory of the pursuing flight object, determine the coordinates of the restraining point outside the Apollonius circle using a geometric constraint method.

[0067] In one example, the interception trajectory of the pursuing aircraft includes a left interception trajectory line and a right interception trajectory line. The Apollonius circle includes the x-coordinate of the center, the y-coordinate of the center, and the radius. Step 303 above can be replaced by steps 3031 to 3032.

[0068] Step 3031: Based on the left interception trajectory line, the right interception trajectory line, the horizontal coordinate of the circle center, the vertical coordinate of the circle center, and the radius, the feasible region of the restraint point is determined using the following geometric constraints.

[0069] (9).

[0070] (10).

[0071] in, The x-coordinate of the restraint point, The ordinate of the restraint point, The expression for the right intercept trajectory line. The expression for the left intercept trajectory line, Let x be the x-coordinate of the center of the circle. Let be the ordinate of the center of the circle. The radius is given.

[0072] Step 3032: Based on the feasible region of the restraining point, determine the coordinates of the restraining point according to preset rules.

[0073] In this example, in order to reasonably select the location of the restraining point Ensure that the trajectory of the pursuing aircraft passes through this point, and provide a feasible domain for the tethering point based on the target's reachability and the Apollonius circle.

[0074] Given that the target's velocity is constant, its acceleration is bounded, and its maximum value is expressed as: Therefore, the reachable area of ​​the target is also bounded. Furthermore, the heading angle constraint in Assumption 2 is transformed into the following overload constraint.

[0075] (11).

[0076] in, for t The target acceleration at any given moment for t The target heading angle at any given moment, The target heading angle at the initial moment. This represents the maximum change in the target heading angle.

[0077] To facilitate the analysis of the feasible region of the restraining point, the equation of motion is rewritten in the following form.

[0078] (12).

[0079] in for t Constant movement i Location, for t Constant movement i acceleration, for The derivative, This is the state transition function.

[0080] The reachability region of a target is defined by its left boundary (using...). (represented by), the right boundary of the reachable domain (using) (represented) and isochrones (using) The region is enclosed by (represented by), where the left and right boundaries of the reachable domain represent the flight trajectories of the target when performing left and right maneuvers with maximum overload under heading angle constraints. They can be calculated using the following formulas.

[0081] (13).

[0082] in, At the initial moment, For time intervals, for The location of the target at any given time. The initial position of the target. for The location of the target at any given time. for The acceleration of the target at any given moment.

[0083] The isochrones represent the target's path along the shortest Durbins path, starting from the current position. All locations that can be reached after a certain time. In this example, such as... Figure 5 As shown, region 1 is the reachable region of the target. Under overload constraints, the target can perform any maneuver, and its position in the future time will definitely fall within the reachable region.

[0084] In this example, we'll use a proportional guidance law to illustrate the pursuit of a flying object. The mechanism of the proportional guidance law is to eliminate the rate of change in the line of sight between the pursuing flying object and the target through maneuvering. When the target's acceleration increases, the rate of change in the line of sight increases, requiring the pursuing flying object to generate greater acceleration to counteract the target's maneuvering, thus increasing the trajectory curvature of the pursuing flying object. For example... Figure 5 As shown, considering the extreme case where the target performs a maximum overload maneuver, the target's flight trajectory is... and The corresponding intercept trajectory for the pursuing flying object is the right intercept trajectory line. and left intercept trajectory line The expression for the intercepted trajectory is as follows.

[0085] (14).

[0086] in, For the moment of interception, for Constantly tracking the location of the flying object. In order to track the initial position of the flying object, for Constantly tracking the location of the flying object. for Constantly track the acceleration of the flying object.

[0087] Based on the analysis of the target's reachable area, its position is limited when the target performs any maneuver. and Inside, the corresponding intercept trajectory of the pursuing flight object must be located within... and Within the formed interception envelope, according to the strategic requirements of the cooperative guidance method, a strait control point must be selected within the interception envelope. Only in this way can the flight trajectory of the pursuing aircraft be ensured to pass through the preset strait control point by designing the target's maneuvers.

[0088] Furthermore, to prevent singularities in the pre-defined defense guidance law, the sniping point should be chosen outside the Apollonius circle defined by the pursuing and defending aircraft. This ensures that the pursuing aircraft passes the fixed point first and avoids any obstacles before interception. The situation.

[0089] The expressions for the Apollonius circles corresponding to the pursuing and defending flying objects, determined using analytical geometry, are as follows.

[0090] (15).

[0091] (16).

[0092] (17).

[0093] (18).

[0094] (19).

[0095] in, Let x be the x-coordinate of any point on the Apollonius circle. Let be the ordinate of any point on the Apollonius circle. The initial x-coordinate of the defensive flying object. The initial ordinate of the defensive flying object. To determine the initial x-coordinate of the flying object being pursued, To determine the initial vertical coordinate of the pursuing flying object, The speed ratio between defensive and pursuing flying objects.

[0096] Assumption and You can use functions respectively and This can be described as being achieved through polynomial fitting of the interception trajectory. Based on the preceding theoretical analysis, the position of the restraining point must satisfy the following two geometric constraints.

[0097] (1) It should fall on and Within the defined interception trajectory, inequality (9) is satisfied.

[0098] (2) It must be located outside the Apollonius circle determined by the pursuing and defending aircraft, i.e., satisfying inequality (10).

[0099] Through spatial superposition analysis of dual constraints, it is clear that the feasible region of the restraint point is... Figure 5 Region 2 in the diagram visually illustrates the feasible boundary for selecting the restraint point.

[0100] In this example, the preset rules for determining the coordinates of the restraining point based on the feasible region of the restraining point are as follows.

[0101] (1) Considering the predefined time This means that the closer the tethering point is to the pursuing aircraft, the shorter the predefined time. For both the target and the defending aircraft, this requires greater initial control force to quickly correct errors, which is detrimental to the control system. Therefore, the tethering point should be selected as close as possible to the target defense team and as far away as possible from the pursuing aircraft within the feasible domain.

[0102] (2) From the perspective of mission requirements and strategy considerations, the restraining point should be as close as possible to the mission trajectory in order to minimize the deviation of the target from the mission trajectory after performing restraining maneuvers.

[0103] In one example, step 203 above can be replaced by steps 401 to 403.

[0104] Step 401: Calculate the line-of-sight parameters based on the coordinates of the restraining point, the position of the pursuing flying object, the position of the defending flying object, and the target position; the line-of-sight parameters include the pursuit-target line-of-sight distance, the pursuit-target line-of-sight angle, the pursuit-restraining point line-of-sight distance, the pursuit-restraining point line-of-sight angle, the defense-restraining point line-of-sight distance, the defense-restraining point line-of-sight angle, and the pursuit-defense line-of-sight angle.

[0105] Step 402: Calculate guidance parameters based on the line-of-sight parameters, the coordinates of the strait control point, the position of the pursuing aircraft, the navigation ratio of the pursuing aircraft, the speed of the pursuing aircraft, the heading angle of the pursuing aircraft, the speed of the defending aircraft, the heading angle of the defending aircraft, and the heading angle of the target. The guidance parameters include target guidance parameters, pursuit guidance parameters, defense guidance parameters, the remaining flight time of the pursuing aircraft to the strait control point, the interception angle error, the total time of the pursuing aircraft to the strait control point, and the pursuit-strait control point lead angle.

[0106] Step 403: Based on the line-of-sight parameters and the guidance parameters, the target is controlled by an acceleration command using a preset restraint guidance law, and the defensive flight body is controlled by an acceleration command using a preset defense guidance law, so as to achieve coordinated restraint of the pursuing flight body.

[0107] In one example, the target guidance parameters, pursuit guidance parameters, defense guidance parameters, and pursuit-control point lead angle are calculated using the following formulas.

[0108] (20).

[0109] (twenty one).

[0110] (twenty two).

[0111] (twenty three).

[0112] (twenty four).

[0113] (25).

[0114] (26).

[0115] in, For target guidance parameters, In order to track guidance parameters, For defensive guidance parameters, N The navigation ratio of the pursuing flight object. The distance between the target and the line of sight is the distance to be pursued. Target - Pursue the front angle, The target heading angle, The target line-of-sight angle is the angle of pursuit. The speed of the pursuing flying object. To pursue - the target's forward angle, The line-of-sight distance from the pursuit-control point. To pursue and control the enemy, the forward angle of the position. The heading angle of the pursuing flying object. The line-of-sight angle of the pursuit-control point. The line-of-sight distance of the defense-restraint point. As a defensive-control point, the front corner, The heading angle of the defensive flying body. The line-of-sight angle of the defense-restraint point.

[0116] In one example, the remaining flight time of the pursuing flying object to the strait point and the total time of the pursuing flying object to the strait point are calculated using the following formulas.

[0117] (27).

[0118] (28).

[0119] (29).

[0120] in, To determine the total time it takes for the flying object to reach the point of control, t For the current moment, The remaining flight time, The speed of the pursuing flying object. Initial pursuit distance to the target (line of sight). The coordinates of the restraining point are... The initial position of the pursuing flying object.

[0121] In one example, the acceleration command of the preset restraint guidance law is as follows.

[0122] (30)

[0123] in, Accelerate towards the target The target guidance parameters are as follows. m This is the first adjustment parameter. n This is the second adjustment parameter. , and , The remaining flight time, The forward angle of the pursuit-control point, for The derivative, N The navigation ratio of the pursuing flight object. The distance between the target and the line of sight is the distance to be pursued. for The derivative, The speed of the pursuing flying object. The pursuit guidance parameters are as follows. The derivative of the pursuit-target line-of-sight angle is given by... The line-of-sight distance from the pursuit-control point. for The derivative, The derivative of the line-of-sight angle at the pursuit-control point. To determine the total time it takes for the flying object to reach the point of control, t This refers to the current moment.

[0124] The purpose of the acceleration command in the preset restraint guidance law is to restrain the rate of change of the velocity of the pursuing aircraft with respect to the line-of-sight angle at the restraint point, that is, the derivative of the line-of-sight angle between the pursuing and restraint points. This converges to 0, ensuring that the trajectory of the pursuing aircraft passes through the restraint point and then maintains its course. As can be seen from formula (4), Equivalent to Therefore, the task of restraint can be described as: design Make The pursuing flying object converges to 0 before passing the restraint point.

[0125] The following analysis demonstrates that, under the acceleration command of the preset restraint guidance law, the pursuing aircraft will pass through the restraint point, and the rate of change of its line of sight to the restraint point converges to zero before passing through the restraint point. Furthermore, its heading remains unchanged before and after passing through the restraint point. For ease of explanation, the moment when the pursuing aircraft passes through the restraint point under the target's restraint maneuver is defined as... .

[0126] Calculate according to formula (4) The second derivative The following formula is obtained by substituting the acceleration command of the preset restraint guidance law into the formula.

[0127] (31).

[0128] in, for The second derivative, for The derivative of .

[0129] The solution to the above second-order differential equation is as follows.

[0130] (32)

[0131] in, , , where are two constants. Initial time The value, Initial time The derivative value, This is the total time it takes to chase the flying object to the point of control. It can be seen that... time, This means that the speed of the pursuing flying object is directed towards the point of restraint.

[0132] when When, taking the derivative of equation (32) yields the following formula.

[0133] (33)

[0134] Substituting formulas (32) and (33) into formula (30), we obtain the following formula.

[0135] (34).

[0136] In this example, because and The first term of the above expression is in No strange occurrences will occur. Furthermore, according to... and The definition can be used to deduce This means exist The acceleration will not reach zero. Therefore, the target's acceleration will not exhibit singularity issues.

[0137] As shown in formulas (31) and (33), and They are all composed of polynomials. hour, and All are 0, which means and .therefore, , .for ,based on as well as The state at that time can be analyzed to determine the conditions. It always holds true.

[0138] Given ,mean The convergence to zero occurs before the pursuing flying object reaches the containment point. hour, The pursuing flying object will pass through the strait control point and then maintain its course.

[0139] In one example, the acceleration command of the preset defense guidance law is as follows.

[0140] (35)

[0141] in, To defend against the acceleration of flying objects, The defense guidance parameters are as follows. m This is the first adjustment parameter. n This is the second adjustment parameter. The remaining flight time, The interception angle error is... for The derivative, The line-of-sight distance from the pursuit-control point. for The derivative, The derivative of the line-of-sight angle at the pursuit-control point. N The navigation ratio of the pursuing flight object. The speed of the pursuing flying object. The forward angle of the pursuit-control point, The derivative of the pursuit-target line-of-sight angle is given by... The line-of-sight distance of the defense-restraint point. for The derivative, The derivative of the line-of-sight angle at the defense-restraint point. To determine the total time it takes for the flying object to reach the point of control, t For the current moment, The speed of the defensive flying object, The derivative of the pursuit-defense line-of-sight angle.

[0142] The goal of the preset defense guidance law acceleration command design is to enable the defensive aircraft to intercept the pursuing aircraft head-on on the collision path past the restraint point.

[0143] In one example, the interception angle error is calculated using the following formula.

[0144] (36)

[0145] (37)

[0146] in, The interception angle error is... The line-of-sight angle of the pursuit-control point. The line-of-sight angle of the defense-restraint point. For angle correction parameters, For the initial pursuit-control point line of sight, The initial defensive-control point's line of sight.

[0147] Mode This indicates that the pursuing aircraft, the defensive aircraft, and the harassing point are collinear, with the harassing point located between the pursuing and defensive aircraft. The head-on interception mission of the defensive aircraft can be described as the interception angle error. and the rate of change of line of sight (i.e., the derivative of the line of sight angle at the defense-holding point) )exist Previously it converged to zero, and exist The time remains zero until the pursuing flying object is intercepted. This can be achieved through... and To ensure this. Among them, for The derivative of . Therefore, the defense problem can be understood as designing the acceleration of defensive flying objects. This is to achieve stable interception angle error.

[0148] The following analysis demonstrates that, under the influence of the acceleration command of the preset defense guidance law, the interception angle error... and rate of change of sight exist Previously it converged to zero, and exist The time remains at zero until the pursuing aircraft is intercepted, thus ensuring that the defensive aircraft intercepts the pursuing aircraft head-on.

[0149] Based on formula (36), First derivative with respect to time It can be expressed as the following formula.

[0150] (38).

[0151] Substituting formula (35) into formula (38), we obtain the following formula.

[0152] (39)

[0153] in, for The second derivative of .

[0154] The solution to the above differential equation is shown in the following equation.

[0155] (40)

[0156] in, The first defense constant, The second defense constant is determined by the initial value of the interception angle error. The initial value of its derivative Decision, passed and The calculation yields the result. It can be seen from formula (35) that... , and It appears in the denominator. Similar to the analysis of the pre-set constraint guidance law, and The existence of does not lead to the singularity problem. However, for ,when hour The occurrence of this could lead to singularities. By appropriately selecting the location of the restraint point, this situation can be avoided, thereby ensuring that the preset defense guidance law is free of singularities.

[0157] Taking the derivative of formula (40) yields the following formula.

[0158] (41).

[0159] when At that time, based on formulas (40) and (41), we can obtain This means Geometrically speaking, Ensure points and A , D and P Located on a straight line, P Located between the other two points. Reviewing the analysis of the presupposed restraint guidance law, when... hour, and The condition is met. Combining formulas (35) and (41), we obtain... , and Given that when Time conditions If it is established, then .when At that time, based on Status display at time Thus, we can conclude This indicates that the velocity vectors of both the pursuing and defensive aircraft are pointing towards the point of control. Combined with... A , D and P The geometric relationships between them, these conditions can be derived and Further analysis revealed... and Therefore, for all , This holds true consistently. Because the velocity vector of the defensive aircraft points towards the restraint point, and for all... , and Considering Then the defensive flying vehicle will intercept the pursuing flying vehicle on the collision course past the restraint point.

[0160] In one example, the effectiveness of the proposed method is verified through the following three-body adversarial scenario.

[0161] (1) Setting up the flight simulation system.

[0162] The pursuit vehicle uses proportional guidance to intercept the target; the pursuit vehicle's navigation ratio N =5. When the target is located at (10000) m 5000 m When the target is positioned at (0,0), it senses an interception threat from a pursuing aircraft located at (0,0). The initial heading angles of the target and the pursuing aircraft are 180° and 20°, respectively. The target determines the feasible region of the scouting point and ultimately selects a point 5000 meters ahead of its initial heading as the scouting point, launching a defensive aircraft at it. Considering that the interception angle error will jump 180 degrees when the pursuing aircraft passes the scouting point, the following expression is used in this example to represent the head-on interception angle error. .

[0163] (42).

[0164] when When the convergence reaches -180°, it indicates that the pursuing and defensive aircraft have opposite velocity directions. Combined with... This means that the defensive aircraft achieved a head-on interception of the pursuing aircraft. The simulation time step was set to 1. ms When the line-of-sight distance between the pursuing aircraft and the target or defensive aircraft is less than 1 m The simulation ends when the acceleration due to gravity is taken as... .

[0165] (2) Parameter settings.

[0166] The parameter settings are shown in Table 1.

[0167] In this example, such as Figure 6 , Figure 7 and Figure 8 As shown, the pursuing aircraft was successfully intercepted by the defensive aircraft after passing the sniping point. Figure 7 As shown, the forward angle of the pursuing aircraft relative to the choke point converges to zero within a predetermined time, and then jumps to -180° after passing the choke point. Figure 8 As shown, the head-on interception angle error also converges to zero at a predetermined time and remains zero thereafter. Figure 9 and Figure 10As shown, the line-of-sight distance between the defensive and pursuing aircraft converges to zero, and the accelerations of the three moving bodies remain continuous throughout the process. These results validate the effectiveness of the cooperative deterrence guidance method.

[0168] Based on the same inventive concept, this application also provides a flight body cooperative restraint guidance device for implementing the aforementioned flight body cooperative restraint guidance method. The solution provided by this device is similar to the solution described in the above method; therefore, the specific limitations in one or more flight body cooperative restraint guidance device embodiments provided below can be found in the limitations of the flight body cooperative restraint guidance method described above, and will not be repeated here.

[0169] In one exemplary embodiment, such as Figure 11 As shown, a flight body cooperative restraint guidance device is provided, including: parameter acquisition module 001, restraint point determination module 002 and cooperative restraint module 003.

[0170] The parameter acquisition module 001 is used to acquire the position, speed, heading angle, interception time, navigation ratio of the pursuing aircraft, position, speed, heading angle of the defending aircraft, target position, and target heading angle of the defending aircraft. The defending aircraft is used to intercept the pursuing aircraft to protect the target. The restraint point determination module 002 is used to determine the coordinates of the restraint point using a geometric programming method based on the position, speed, heading angle, interception time, position, and speed of the pursuing aircraft. The cooperative restraint module 003 is used to control the target and the defending aircraft using a cooperative guidance method based on the coordinates of the restraint point, navigation ratio of the pursuing aircraft, position, speed, heading angle, position, speed, heading angle of the defending aircraft, heading angle of the defending aircraft, target position, and target heading angle of the defending aircraft, to achieve cooperative restraint of the pursuing aircraft.

[0171] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 12As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs stored in the non-volatile storage media. The database stores information such as the position, speed, heading angle, interception time, target navigation ratio, position, speed, heading angle, target position, and target heading angle of the pursuing aircraft. The I / O interfaces are used for information exchange between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When executed by the processor, the computer program implements a cooperative aircraft control and guidance method.

[0172] Those skilled in the art will understand that Figure 12 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0173] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0174] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0175] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, etc., and are not limited to these.

[0176] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0177] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for cooperative restraint and guidance of flying bodies, characterized in that, The flight body cooperative restraint guidance method includes: Acquire the position, speed, heading angle, interception time, navigation ratio of the pursuing aircraft, position, speed, heading angle of the defending aircraft, target position, and target heading angle of the defending aircraft; the defending aircraft is used to intercept the pursuing aircraft to protect the target; Based on the position of the pursuing aircraft, the speed of the pursuing aircraft, the heading angle of the pursuing aircraft, the interception time, the position of the defending aircraft, and the speed of the defending aircraft, the coordinates of the restraining point are determined using a geometric programming method; Based on the coordinates of the restraining point, the navigation ratio of the pursuing aircraft, the position of the pursuing aircraft, the speed of the pursuing aircraft, the heading angle of the pursuing aircraft, the position of the defending aircraft, the speed of the defending aircraft, the heading angle of the defending aircraft, the position of the target, and the heading angle of the target, a cooperative guidance method is used to control the target and the defending aircraft to achieve cooperative restraint of the pursuing aircraft.

2. The flight body cooperative restraint guidance method according to claim 1, characterized in that, Based on the position, velocity, heading angle, interception time, position, and velocity of the defending aircraft, the coordinates of the restraining point are determined using a geometric programming method, specifically including: Based on the position of the pursuing aircraft, the speed of the pursuing aircraft, the heading angle of the pursuing aircraft, and the interception time, an open-loop trajectory prediction method based on state space representation is used to obtain the interception trajectory of the pursuing aircraft. Based on the position and velocity of the defensive aircraft, the position and velocity of the pursuing aircraft, the Apollonius circles corresponding to the pursuing and defensive aircraft are determined using analytical geometry methods. Based on the interception trajectory of the pursuing aircraft, the coordinates of the restraining point are determined using a geometric constraint method outside the Apollonius circle.

3. The flight body cooperative restraint guidance method according to claim 2, characterized in that, The interception trajectory of the pursuing aircraft includes a left interception trajectory line and a right interception trajectory line; the Apollonius circle includes the horizontal coordinate of the center, the vertical coordinate of the center, and the radius; Based on the interception trajectory of the pursuing aircraft, the coordinates of the restraining point are determined using a geometric constraint method outside the Apollonius circle, specifically including: Based on the left interception trajectory line, the right interception trajectory line, the x-coordinate of the circle center, the y-coordinate of the circle center, and the radius, the feasible region of the restraint point is determined using the following geometric constraints: ； ； in, The x-coordinate of the restraint point, The ordinate of the restraint point, The expression for the right intercept trajectory line. The expression for the left intercept trajectory line, Let x be the x-coordinate of the center of the circle. Let be the ordinate of the center of the circle. The radius is mentioned; Based on the feasible region of the restraining point, the coordinates of the restraining point are determined according to preset rules.

4. The flight body cooperative restraint guidance method according to claim 1, characterized in that, Based on the coordinates of the restraining point, the navigation ratio of the pursuing aircraft, the position of the pursuing aircraft, the speed of the pursuing aircraft, the heading angle of the pursuing aircraft, the position of the defending aircraft, the speed of the defending aircraft, the heading angle of the defending aircraft, the position of the target, and the heading angle of the target, a cooperative guidance method is used to control the target and the defending aircraft to achieve cooperative restraint of the pursuing aircraft, specifically including: Based on the coordinates of the restraining point, the position of the pursuing flying object, the position of the defensive flying object, and the target position, line-of-sight parameters are calculated; the line-of-sight parameters include the pursuit-target line-of-sight distance, the pursuit-target line-of-sight angle, the pursuit-restraining point line-of-sight distance, the pursuit-restraining point line-of-sight angle, the defense-restraining point line-of-sight distance, the defense-restraining point line-of-sight angle, and the pursuit-defense line-of-sight angle. Based on the line-of-sight parameters, the coordinates of the strait control point, the position of the pursuing aircraft, the navigation ratio of the pursuing aircraft, the speed of the pursuing aircraft, the heading angle of the pursuing aircraft, the speed of the defending aircraft, the heading angle of the defending aircraft, and the heading angle of the target, guidance parameters are calculated; the guidance parameters include target guidance parameters, pursuit guidance parameters, defense guidance parameters, the remaining flight time of the pursuing aircraft to the strait control point, interception angle error, the total time of the pursuing aircraft to the strait control point, and the pursuit-strait control point lead angle; Based on the line-of-sight parameters and the guidance parameters, the target is controlled by an acceleration command using a preset restraint guidance law, while the defensive flight body is controlled by an acceleration command using a preset defense guidance law, so as to achieve coordinated restraint of the pursuing flight body.

5. The flight body cooperative restraint guidance method according to claim 4, characterized in that, The acceleration command for the preset restraint guidance law is as follows: ； in, Accelerate towards the target The target guidance parameters are as follows. m This is the first adjustment parameter. n This is the second adjustment parameter. The remaining flight time, The forward angle of the pursuit-control point, for The derivative, N The navigation ratio of the pursuing flight object. The distance between the target and the line of sight is the distance to be pursued. for The derivative, The speed of the pursuing flying object. The pursuit guidance parameters are as follows. The derivative of the pursuit-target line-of-sight angle is given by... The line-of-sight distance from the pursuit-control point. for The derivative, The derivative of the line-of-sight angle at the pursuit-control point. To determine the total time it takes for the flying object to reach the point of control, t This refers to the current moment.

6. The flight body cooperative restraint guidance method according to claim 4, characterized in that, The acceleration command for the preset defense guidance law is as follows: ； in, To defend against the acceleration of flying objects, The defense guidance parameters are as follows. m This is the first adjustment parameter. n This is the second adjustment parameter. The remaining flight time, The interception angle error is... for The derivative, The line-of-sight distance from the pursuit-control point. for The derivative, The derivative of the line-of-sight angle at the pursuit-control point. N The navigation ratio of the pursuing flight object. The speed of the pursuing flying object. The forward angle of the pursuit-control point, The derivative of the pursuit-target line-of-sight angle is given by... The line-of-sight distance of the defense-restraint point. for The derivative, The derivative of the line-of-sight angle at the defense-restraint point. To determine the total time it takes for the flying object to reach the point of control, t For the current moment, The speed of the defensive flying object, The derivative of the pursuit-defense line-of-sight angle.

7. The flight body cooperative restraint guidance method according to claim 4, characterized in that, The target guidance parameters, pursuit guidance parameters, defense guidance parameters, and pursuit-containment point lead angle are calculated using the following formulas: ； ； ； ； ； ； ； in, For target guidance parameters, To track guidance parameters, For defensive guidance parameters, N The navigation ratio of the pursuing flight object. The distance between the target and the line of sight is the distance to be pursued. Target - Pursue the front angle, The target heading angle, The target line-of-sight angle is the angle of pursuit. The speed of the pursuing flying object. To pursue - the target's forward angle, The line-of-sight distance from the pursuit-control point. To pursue and control the enemy, the forward angle of the position. The heading angle of the pursuing flying object. The line-of-sight angle of the pursuit-control point. The line-of-sight distance of the defense-restraint point. As a defensive-control point, the front corner, The heading angle of the defensive flying body. The line-of-sight angle of the defense-restraint point.

8. The flight body cooperative restraint guidance method according to claim 4, characterized in that, The remaining flight time and total time of the pursuing aircraft to reach the strait point are calculated using the following formulas: ； ； ； in, To determine the total time it takes for the flying object to reach the point of control, t For the current moment, The remaining flight time, The speed of the pursuing flying object. Initial pursuit distance to the target (line of sight). The coordinates of the restraining point are... The initial position of the pursuing flying object.

9. The flight body cooperative restraint guidance method according to claim 4, characterized in that, The interception angle error is calculated using the following formula: ； ； in, The interception angle error is... The line-of-sight angle of the pursuit-control point. The line-of-sight angle of the defense-restraint point. For angle correction parameters, For the initial pursuit-control point line of sight, The initial defensive-control point's line of sight.

10. A flight body cooperative restraint and guidance device, characterized in that, The flight body cooperative restraint guidance device includes: The parameter acquisition module is used to acquire the position, speed, heading angle, interception time, navigation ratio of the pursuing aircraft, position, speed, heading angle of the defending aircraft, target position, and target heading angle; the defending aircraft is used to intercept the pursuing aircraft to protect the target; The restraint point determination module is used to determine the coordinates of the restraint point using a geometric programming method based on the position of the pursuing aircraft, the speed of the pursuing aircraft, the heading angle of the pursuing aircraft, the interception time, the position of the defending aircraft, and the speed of the defending aircraft. The cooperative restraint module is used to control the target and the defensive aircraft using a cooperative guidance method based on the coordinates of the restraint point, the navigation ratio of the pursuing aircraft, the position of the pursuing aircraft, the speed of the pursuing aircraft, the heading angle of the pursuing aircraft, the position of the defensive aircraft, the speed of the defensive aircraft, the heading angle of the defensive aircraft, the position of the target, and the heading angle of the target, so as to achieve cooperative restraint of the pursuing aircraft.

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