Multi-constrained terminal velocity optimal midcourse guidance method for long-range gliding vehicles

Abstract

The application discloses a kind of multi-constraint terminal velocity optimal midcourse guidance methods suitable for long-range glider, including the following steps: launch platform plans the midcourse guidance trajectory of terminal velocity optimization;Launch platform extracts track point from midcourse guidance trajectory, and passes to aircraft;Aircraft generates midcourse guidance instruction according to received track point;According to midcourse guidance instruction, the flight process of aircraft is controlled.The multi-constraint terminal velocity optimal midcourse guidance method suitable for long-range glider provided by the application can meet time, angle and other terminal constraints simultaneously, and ensures that the kinetic energy loss of midcourse guidance section is minimum, and the maximum gliding distance of aircraft is enhanced.

Description

Technical Field

[0001] This invention relates to a multi-constraint terminal velocity optimal mid-course guidance method applicable to long-range gliders, belonging to the field of guidance and control. Background Technology

[0002] During the mid-course guidance phase, long-range aircraft need to reach the designated airspace within the required time and meet certain angle constraints to provide favorable initial conditions for terminal guidance. Furthermore, it is desirable to minimize the kinetic energy loss of the aircraft during the mid-course guidance phase in order to enhance the maximum glide distance of the aircraft.

[0003] However, the analytical guidance method used in the traditional mid-course guidance phase is generally difficult to meet terminal constraints such as time and angle at the same time, and the kinetic energy loss is relatively large. This results in unfavorable initial conditions and insufficient overload capacity in the terminal guidance phase of the aircraft, which directly reduces the maximum glide distance of the aircraft.

[0004] Existing technologies also include methods for achieving mid-course guidance using numerical optimization, such as the pseudospectral method. Although these methods can plan the optimal trajectory, they require a huge amount of computation and are not suitable for online computation by airborne computers.

[0005] Therefore, it is necessary to study a guidance method that can solve the above problems. Summary of the Invention

[0006] To overcome the above problems, the inventors conducted in-depth research and provided a multi-constraint terminal velocity optimal mid-course guidance method suitable for long-range gliders, comprising the following steps:

[0007] S1. The launch platform plans the trajectory of the medium-speed guided missile with optimal terminal velocity.

[0008] S2. The launch platform extracts the track points from the trajectory of the intermediate-range missile and transmits them to the aircraft.

[0009] S3. The aircraft generates mid-course guidance commands based on the received waypoints;

[0010] S4. Control the flight process of the aircraft according to the guidance commands.

[0011] In a preferred embodiment, in S1, the ballistic trajectory is obtained by establishing a trajectory model and performing multi-constraint numerical optimization on the trajectory model.

[0012] In a preferred embodiment, the multi-constraint application to the trajectory model can be expressed as:

[0013]

[0014] in, Indicates the speed of the aircraft. tf Indicates the predicted interception time. P Indicates engine thrust. α Indicates the balanced angle of attack. β Indicates the balance sideslip angle. m Indicates the mass of the aircraft. D Indicates aerodynamic drag. g Represents gravitational acceleration. Indicates the inclination angle of the flight path. L Indicates lift. Z Indicates lateral force. Indicates the deviation angle of the flight path. Indicates quality per second (QPS). Indicates the velocity of the target point. Indicates the target's tangential acceleration. Indicates the normal acceleration in the vertical plane of the target. Indicates the normal acceleration in the target horizontal plane. Indicates the target track inclination angle. Indicates the target track deflection angle. r Indicates the distance between the aircraft and the target. The vertical component representing the angle between the target velocity and the line-of-sight direction. The horizontal component represents the angle between the target's velocity and the line-of-sight direction. The vertical component representing the angle between the aircraft's velocity and the line of sight. The horizontal component represents the angle between the aircraft's speed and the line of sight. Indicates the aircraft's line-of-sight tilt angle. Indicates the aircraft's line-of-sight deflection angle. This represents the x-coordinate of the spacecraft in the launch coordinate system. This represents the y-coordinate of the spacecraft in the launch coordinate system. This represents the coordinates of the spacecraft on the z-axis of the launch coordinate system. Indicates the maximum flight time of the aircraft. Indicates the aircraft's maximum angle of attack. Indicates the maximum sideslip angle of the aircraft. Indicates the desired terminal velocity angle. Indicates the desired velocity deflection angle at the end. Indicates the desired line-of-sight angle at the end. This indicates the desired line-of-sight deflection angle at the end point.

[0015] In a preferred embodiment, in S3, the waypoints are used as constraints to generate an optimal control problem, and the guidance rate is generated by solving the optimal control problem.

[0016] In a preferred embodiment, in S3, the optimal control problem can be expressed as:

[0017]

[0018] in, t i (i = 0, 2, ..., N+1) This indicates that the missiles arrived at the first... i Time at each waypoint This represents the energy consumed during the guidance process. Represents the integrand variable. Indicates the tangential acceleration of the aircraft. This represents the component of the aircraft's normal acceleration in the vertical plane. This represents the component of the aircraft's normal acceleration in the horizontal plane. This represents the x-coordinate of the spacecraft in the launch coordinate system. This represents the y-coordinate of the spacecraft in the launch coordinate system. This represents the coordinates of the spacecraft on the z-axis of the launch coordinate system. Indicates the first i The x-coordinates of each track point in the launch frame. Indicates the first i The y-coordinate of each track point in the launch frame. Indicates the first i The z-axis coordinates of each track point in the launch system.

[0019] In a preferred embodiment, in S3, the constraint condition further includes minimizing the normal acceleration.

[0020] In a preferred embodiment, the optimal control problem can be expressed as:

[0021]

[0022] in, Indicates the aircraft in the i Zero-control miss distance at each track point a This represents the normal acceleration of the aircraft. t Indicates the current moment. Indicates the expected arrival time. Indicates the aircraft relative to the first i The speed of each waypoint This indicates that the aircraft reached the [number]th [time]. i Remaining flight time for each waypoint.

[0023] In a preferred embodiment

[0024] in, This indicates the aircraft's current speed.

[0025] In a preferred embodiment, the generated guidance command Represented as:

[0026]

[0027] in

[0028]

[0029] ,

[0030] Where n represents the number of the next waypoint the aircraft needs to track, and N represents the total number of waypoints excluding the target point. Indicates the aircraft in the k Zero-control miss distance at each track point.

[0031] In a preferred embodiment

[0032] In S2, the extraction of waypoints includes the following steps:

[0033] S21. Connect the aircraft and the predicted interception point with a straight line, and find the point on the trajectory of the intermediate-range missile that is farthest from the connecting line, and record it as track point 1.

[0034] S22. Use straight lines to connect the aircraft and track point 1, and track point 1 to the predicted interception point in sequence. By connecting these lines, the trajectory of the intermediate-range missile is divided into multiple segments. On each segment of the intermediate-range missile trajectory, find the point that is farthest from the corresponding connecting line, and select the point with the largest distance, which is recorded as track point 2.

[0035] S23. Connect the aircraft, the generated track points, and the predicted interception points with straight lines. Divide the intermediate-range missile trajectory into multiple segments by connecting them. Find the point that is farthest from the corresponding line on each segment of the intermediate-range missile trajectory. Select the point with the largest distance and record it as the next track point.

[0036] S24. Repeat step S23 to generate a preset number of waypoints. Arrange the generated waypoints in spatial order to extract the waypoints.

[0037] In a preferred embodiment, the preset number of waypoints is determined based on the computing power of the aircraft's onboard computer.

[0038] The beneficial effects of this invention include:

[0039] (1) The multi-constraint terminal velocity optimal mid-course guidance method for long-range gliding aircraft provided by the present invention can simultaneously satisfy terminal constraints such as time and angle, providing favorable initial conditions for terminal guidance;

[0040] (2) The multi-constraint terminal velocity optimal mid-course guidance method for long-range gliding aircraft provided by the present invention ensures that the kinetic energy loss in the mid-course guidance phase is minimized and enhances the maximum gliding distance of the aircraft.

[0041] (3) The multi-constraint terminal velocity optimal mid-course guidance method for long-range gliders provided by the present invention adopts the idea of ​​combining trajectory optimization and trajectory tracking, which solves the problem that the onboard computer has insufficient computing power and it is difficult to plan the optimal trajectory. Attached Figure Description

[0042] Figure 1 This diagram illustrates a preferred embodiment of a multi-constraint terminal velocity optimal mid-course guidance method for long-range gliders according to the present invention.

[0043] Figure 2 A schematic diagram of the flowchart of a multi-constraint terminal velocity optimal mid-course guidance method for long-range gliders according to a preferred embodiment of the present invention is shown.

[0044] Figure 3 A schematic diagram of the kinematic model of the center of mass of a long-range glider is shown in a multi-constraint terminal velocity optimal mid-course guidance method applicable to a preferred embodiment of the present invention.

[0045] Figure 4 This diagram illustrates the process of transforming the terminal velocity optimal trajectory tracking problem into a guidance problem with waypoint constraints in a multi-constraint terminal velocity optimal mid-course guidance method for long-range gliders according to a preferred embodiment of the present invention.

[0046] Figure 5 This diagram illustrates a waypoint extraction method in a multi-constraint terminal velocity optimal mid-course guidance method for long-range gliders according to a preferred embodiment of the present invention.

[0047] Figure 6 The flight trajectories of the aircraft during the simulation process of Example 1 and Comparative Example 1 are shown;

[0048] Figure 7 The simulation diagrams of the aircraft speed changes during Example 1 and Comparative Example 1 are shown.

[0049] Figure 8 The diagrams showing the changes in the aircraft's equilibrium angle of attack during simulations of Example 1 and Comparative Example 1 are shown.

[0050] Figure 9 The simulation process of the aircraft in Example 1 and Comparative Example 1 is shown. Change diagram;

[0051] Figure 10 The simulation process of the aircraft in Example 1 and Comparative Example 1 is shown. Change diagram;

[0052] Figure 11 The diagram shows the variation of the mean velocity error obtained from 1000 Monte Carlo simulations in Example 1. Detailed Implementation

[0053] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become clearer and more apparent.

[0054] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0055] The present invention provides a multi-constraint terminal velocity optimal mid-course guidance method suitable for long-range gliders, such as... Figure 1 , 2 As shown, it includes the following steps:

[0056] S1. The launch platform plans the trajectory of the medium-speed guided missile with optimal terminal velocity.

[0057] S2. The launch platform extracts the track points from the trajectory of the intermediate-range missile and transmits them to the aircraft.

[0058] S3. The aircraft generates mid-course guidance commands based on the received waypoints;

[0059] S4. Control the flight process of the aircraft according to the guidance commands.

[0060] In a preferred embodiment, in S1, the ballistic trajectory is obtained by establishing a trajectory model and performing multi-constraint numerical optimization on the trajectory model.

[0061] More preferably, the multi-constraint application to the trajectory model can be expressed as:

[0062]

[0063] refer to Figure 3 The kinematic model of the center of mass of the aircraft shown is as follows, in which, Indicates the speed of the aircraft. t f Indicates the predicted interception time. P Indicates engine thrust. α Indicates the balanced angle of attack. β Indicates the balance sideslip angle. m Indicates the mass of the aircraft. D Indicates aerodynamic drag. g Represents gravitational acceleration. Indicates the inclination angle of the flight path. L Indicates lift. Z Indicates lateral force. Indicates the deviation angle of the flight path. Indicates quality per second (QPS). Indicates the velocity of the target point. Indicates the target's tangential acceleration. Indicates the normal acceleration in the vertical plane of the target. Indicates the normal acceleration in the target horizontal plane. Indicates the target track inclination angle. Indicates the target track deflection angle. r Indicates the distance between the aircraft and the target. The vertical component representing the angle between the target velocity and the line-of-sight direction. The horizontal component represents the angle between the target's velocity and the line-of-sight direction. The vertical component representing the angle between the aircraft's velocity and the line of sight. The horizontal component represents the angle between the aircraft's speed and the line of sight. Indicates the aircraft's line-of-sight tilt angle. Indicates the aircraft's line-of-sight deflection angle. This represents the x-coordinate of the spacecraft in the launch coordinate system. This represents the y-coordinate of the spacecraft in the launch coordinate system. This represents the coordinates of the spacecraft on the z-axis of the launch coordinate system. Indicates the maximum flight time of the aircraft. Indicates the aircraft's maximum angle of attack. Indicates the maximum sideslip angle of the aircraft. Indicates the desired terminal velocity angle. Indicates the desired velocity deflection angle at the end. Indicates the desired line-of-sight angle at the end. This indicates the desired line-of-sight deflection angle at the end point.

[0064] Furthermore, the predicted interception time t f It can be a free variable, obtained directly through trajectory optimization; or it can be a fixed variable, specified based on experience, and is not particularly limited in this invention.

[0065] Trajectory optimization problems are a typical type of Bolza-form optimal control problem. Due to the presence of nonlinear terms and constraints, and the need to consider the complex mechanical environment during the trajectory, it is a complex nonlinear optimization problem. Such problems typically lack analytical solutions and generally require numerical optimization algorithms for resolution. However, while programming optimization algorithms can find the global optimum, their main limitations lie in the enormous computational power required, which is generally beyond the capabilities of onboard computers. Furthermore, the slow generation of guidance commands fails to meet the speed requirements of guidance loops. Therefore, for multi-constraint terminal velocity optimal mid-course guidance problems, it is generally difficult for aircraft to directly employ trajectory optimization algorithms for mid-course guidance.

[0066] In this invention, the guidance command process is divided into two parts: trajectory planning and trajectory tracking, to obtain mid-range guidance. The trajectory planning part is executed by the launch platform, which has strong computing power and can meet the huge computational requirements of trajectory planning, thereby planning the optimal trajectory. The aircraft then performs trajectory tracking to reproduce the planned optimal trajectory.

[0067] In this invention, the optimal trajectory tracking problem is constructed by constraining the flight path points of the aircraft. First, a performance index function is selected according to the characteristics of the optimal guidance problem, and the original trajectory tracking problem is transformed into a multi-path point constrained energy optimal guidance problem. Then, the optimal guidance problem is decoupled in the horizontal and vertical channels, which makes it easier to solve directly using optimal control theory.

[0068] Specifically, in S3, the waypoints are used as constraints to generate an optimal control problem. The guidance rate is then generated by solving this optimal control problem. Figure 4 As shown.

[0069] Figure 4 In this context, PIP stands for Predicted Interception Point. Since the curvature characteristics of the trajectory are mainly determined by its normal overload, if enough points are selected on the trajectory, and the number of selected track points is sufficient to reflect the characteristics of the trajectory, then by designing a suitable guidance law, the aircraft can sequentially pass through the target area. P 0 ~ P n+1 By using waypoints, the aircraft can track the optimal trajectory and reproduce the optimal interception effect obtained from trajectory optimization. Therefore, the original optimal trajectory tracking problem can be transformed into a guidance problem with waypoint constraints.

[0070] In a preferred embodiment, in S3, the optimal control problem can be expressed as:

[0071]

[0072] in, t i (i = 0, 2, ..., N+1)This indicates that the missiles arrived at the first... i Time at each waypoint J This represents the energy consumed during the guidance process. Represents the integrand variable. Indicates the tangential acceleration of the aircraft. This represents the component of the aircraft's normal acceleration in the vertical plane. This represents the component of the aircraft's normal acceleration in the horizontal plane. This represents the x-coordinate of the spacecraft in the launch coordinate system. This represents the y-coordinate of the spacecraft in the launch coordinate system. This represents the coordinates of the spacecraft on the z-axis of the launch coordinate system. Indicates the first i The x-coordinates of each track point in the launch frame. Indicates the first i The y-coordinate of each track point in the launch frame. Indicates the first i The z-axis coordinates of each track point in the launch system.

[0073] The aforementioned optimal control problem allows the missile to pass through the target area sequentially with the minimum total overload. n+1 One waypoint.

[0074] Furthermore, the inventors discovered that the induced drag of an aircraft is mainly generated by normal acceleration, and minimizing normal acceleration is beneficial to reducing the kinetic energy loss of the aircraft.

[0075] Preferably, in S3, the constraint condition further includes minimizing the normal acceleration.

[0076] The inventors discovered that the induced drag of an aircraft is proportional to the square of its normal acceleration. Therefore, minimizing the square of the normal acceleration helps reduce induced drag, thereby indirectly increasing terminal velocity. Assume the remaining track points in the trajectory are... P k to P n+1 ,but:

[0077] More preferably, the optimal control problem can be expressed as:

[0078]

[0079] in, Indicates the aircraft in the i Zero-control miss distance at each track point a This represents the normal acceleration of the aircraft. t Indicates the current moment. Indicates the expected arrival time. Indicates the aircraft relative to the firsti The speed of each waypoint This indicates that the aircraft reached the [number]th [time]. i The remaining flight time at each waypoint. Furthermore, by minimizing the normal acceleration constraint, energy loss during the guidance process of the aircraft is reduced, ensuring minimal kinetic energy loss in the mid-guidance phase and enhancing the maximum glide distance of the aircraft.

[0080] The zero-control miss distance of the aircraft refers to: if the aircraft flies in a straight line without making any maneuvers, at the terminal moment relative to the target distance... P i The off-target distance of the point, reference Figure 3 The kinematic model of the center of mass of the aircraft shown in the figure P i Representing the i indivual( i =1 , 2 ,..., n + 1) Waypoints, which are fixed points extracted from the optimal trajectory. (See diagram) r i Indicates aircraft and the first i The distance between points, σ i Representative aircraft and the first i The line-of-sight angle at each point, η i = γ M -σ i Represents the aircraft relative to P i The velocity of the point leads the angle.

[0081] The zero-control miss distance of the aircraft is expressed as:

[0082]

[0083] The inventors discovered that the aforementioned zero-control miss distance is difficult to measure in engineering. In a preferred embodiment, the inventors provide another representation:

[0084]

[0085] in, This indicates the aircraft's current speed. The line-of-sight angular velocity is included. Based on the aircraft's own motion information and track points P i The position information is directly calculated, which makes it easy for the onboard computer to directly calculate and obtain the zero-control miss distance of the aircraft.

[0086] According to a preferred embodiment of the present invention, the generated guidance command Represented as:

[0087]

[0088] in

[0089]

[0090] ,

[0091] Where n represents the number of the next waypoint the aircraft needs to track, and N represents the total number of waypoints excluding the target point. Indicates the aircraft in the k Zero-control miss distance at each track point.

[0092] Theoretically, the more waypoints extracted from the optimal trajectory, the closer the aircraft's flight path will be to the optimal trajectory, and the closer its performance indicators will be to the optimal value. However, observing the form of the guidance law, it can be seen that selecting too many waypoints will lead to high-dimensional matrix inverse operations, which will place a significant computational burden on the onboard computer. How to achieve efficient representation of the optimal trajectory is a challenge.

[0093] In view of this, according to a preferred embodiment of the present invention, in step S2, the extraction of waypoints includes the following steps:

[0094] S21. Connect the aircraft and the predicted intercept point PIP with a straight line. Find the point on the intermediate-range missile trajectory that is farthest from the connecting line, and denote it as track point 1. The distance of this point from the connecting line is... ,like Figure 5 As shown by the solid line;

[0095] S22, Using a straight line, connect the aircraft and trackpoint 1, trackpoint 1 with the predicted interception point. Connect the points sequentially to divide the trajectory of the medium-range missile into multiple segments. On each segment, find the point furthest from the corresponding connecting line. Select the point with the largest distance and denote it as track point 2. The distance of this point from the connecting line is... d 2， like Figure 5 As shown by the midpoint line;

[0096] S23. Connect the aircraft, the generated track points, and the predicted interception points with straight lines. Divide the intermediate-range missile trajectory into multiple segments by connecting them. Find the point that is farthest from the corresponding line on each segment of the intermediate-range missile trajectory. Select the point with the largest distance and record it as the next track point.

[0097] S24. Repeat step S23 to generate a preset number of waypoints. Arrange the generated waypoints in spatial order to extract the waypoints.

[0098] The aforementioned preferred method for extracting waypoints possesses translation and rotation invariance while also employing iterative calculation, facilitating rapid execution of computer programs and requiring less computing power. This enables the onboard computer to quickly extract waypoints, thereby ensuring the aircraft's tracking effect on the mid-course missile trajectory with optimal terminal velocity planned by the launch platform. Ultimately, this minimizes kinetic energy loss during the mid-course guidance phase and enhances the aircraft's maximum glide distance.

[0099] Furthermore, in this invention, the preset number of waypoints is determined based on the computing power of the onboard computer, and is preferably 4-6.

[0100] Example Example 1

[0101] A simulation experiment was conducted in which the aircraft was launched from the origin and attacked a moving target 150km away. The mid-course guidance process included the following steps:

[0102] S1. Plan the trajectory of a medium-speed missile with optimal terminal velocity;

[0103] S2. Extract the track points from the trajectory of the medium-speed guided missile and transmit them to the aircraft;

[0104] S3. The aircraft generates mid-course guidance commands based on the received waypoints;

[0105] S4. Control the flight process of the aircraft according to the guidance commands.

[0106] In S1, the ballistic trajectory is obtained by establishing a trajectory model and performing multi-constraint numerical optimization on the trajectory model.

[0107] The multiple constraints applied to the trajectory model are represented as follows:

[0108]

[0109] In S3, the waypoints are used as constraints to generate the optimal control problem, and the guidance rate is generated by solving the optimal control problem.

[0110] In S3, the optimal control problem can be expressed as:

[0111]

[0112] In S3, the constraint condition also includes minimizing the normal acceleration, and the optimal control problem can be expressed as:

[0113]

[0114]

[0115] Generated guidance commands Represented as:

[0116]

[0117] in

[0118]

[0119] ,

[0120] In S2, the extraction of waypoints includes the following steps:

[0121] S21. Connect the aircraft and the predicted interception point with a straight line, and find the point on the trajectory of the medium-range missile that is farthest from the connecting line, and record it as track point 1;

[0122] S22. Use straight lines to connect the aircraft and track point 1, and track point 1 to the predicted interception point in sequence. By connecting these lines, the trajectory of the intermediate-range missile is divided into multiple segments. On each segment of the intermediate-range missile trajectory, find the point that is farthest from the corresponding connecting line, and select the point with the largest distance, which is recorded as track point 2.

[0123] S23. Connect the aircraft, the generated track points, and the predicted interception points with straight lines. Divide the intermediate-range missile trajectory into multiple segments by connecting them. Find the point that is farthest from the corresponding line on each segment of the intermediate-range missile trajectory. Select the point with the largest distance and record it as the next track point.

[0124] S24. Repeat step S23 to generate a preset number of waypoints. Arrange the generated waypoints in spatial order to extract the waypoints.

[0125] The preset number of waypoints n was set to 1, 2, and 4, and simulation experiments were conducted respectively.

[0126] Comparative Example 1

[0127] The same experiment as in Example 1 was conducted, except that proportional guidance was used during the mid-course guidance process.

[0128] Figure 6 The simulation results of Example 1 and Comparative Example 1 show the flight trajectories of the aircraft. As can be seen from the figures, the aircraft in Example 1 were able to reach the target interception point, while the aircraft in Comparative Example 1 failed to reach the interception point due to excessive speed loss.

[0129] Figure 7The simulation results for Example 1 and Comparative Example 1 show the velocity changes of the aircraft. It can be seen from the figures that the terminal velocity of the aircraft in Example 1 is close to the optimal value and significantly higher than the terminal velocity of the aircraft in Comparative Example 1. Furthermore, Figure 8 The diagrams showing the changes in the aircraft's equilibrium angle of attack during simulations of Example 1 and Comparative Example 1 are illustrated. Figure 9 The simulation process of the aircraft in Example 1 and Comparative Example 1 is shown. Change diagram Figure 10 The simulation process of the aircraft in Example 1 and Comparative Example 1 is shown. Change diagram, based on Figures 6-10 Comparing the results of different preset numbers of waypoints in Example 1, it can be seen that adding an extra waypoint during the mid-course guidance process can greatly improve the terminal velocity performance of mid-course guidance. As the number of waypoints increases, the guidance method can make the key variables such as the trajectory, speed, and flight time of the aircraft converge to the optimal value. When the number of waypoints increases to more than 4, the terminal velocity of the aircraft is close to the optimal value.

[0130] Furthermore, for Example 1, 1000 Monte Carlo simulations were performed, and the variation law of the mean speed error was obtained as follows: Figure 11 As shown in the figure, as the total number of waypoints increases, the aircraft can not only reach the predicted intercept point, but its terminal velocity also converges to the optimal value rapidly at a similar exponential rate. The simulation results show that the mid-course guidance method in Example 1 only requires a small number of waypoints to ensure the optimal terminal velocity of the aircraft. This feature ensures the speed of mid-course guidance law calculation and facilitates the efficient calculation of guidance commands on the embedded airborne computer.

[0131] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," "outer," "front," and "rear," etc., indicate the orientation or positional relationship based on the orientation or positional relationship in the working state of this invention, and are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. Furthermore, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0132] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal communication between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0133] The present invention has been described above with reference to preferred embodiments; however, these embodiments are merely exemplary and illustrative. Various substitutions and modifications can be made to the present invention based on these embodiments, all of which fall within the scope of protection of the present invention.

Claims

1. A multi-constraint terminal velocity optimal mid-course guidance method suitable for long-range gliders, characterized in that, Includes the following steps: S1. The launch platform plans the trajectory of the medium-speed guided missile with optimal terminal velocity. S2. The launch platform extracts the track points from the trajectory of the intermediate-range missile and transmits them to the aircraft. S3. The aircraft generates mid-course guidance commands based on the received waypoints; S4. Control the flight process of the aircraft according to the guidance commands. In S3, the waypoints are used as constraints to generate the optimal control problem, and the guidance rate is generated by solving the optimal control problem. The optimal control problem can be expressed as: ， in, t i (i = 0, 2, ..., N+1) This indicates that the missiles arrived at the first... i Time at each waypoint This represents the energy consumed during the guidance process. Indicates the integrand variable. Indicates the tangential acceleration of the aircraft. This represents the component of the aircraft's normal acceleration in the vertical plane. This represents the component of the aircraft's normal acceleration in the horizontal plane. This represents the x-coordinate of the spacecraft in the launch coordinate system. This represents the y-coordinate of the spacecraft in the launch coordinate system. This represents the coordinates of the spacecraft on the z-axis of the launch coordinate system. Indicates the first i The x-coordinate of each track point in the launch frame. Indicates the first i The y-coordinate of each track point in the launch frame. Indicates the first i The z-axis coordinates of each track point in the launch system.

2. The multi-constraint terminal velocity optimal mid-course guidance method for long-range gliders according to claim 1, characterized in that, In S1, the ballistic trajectory is obtained by establishing a trajectory model and performing multi-constraint numerical optimization on the trajectory model.

3. The multi-constraint terminal velocity optimal mid-course guidance method for long-range gliders according to claim 2, characterized in that, The multiple constraints applied to the trajectory model can be expressed as follows: ， in, Indicates the speed of the aircraft. t f Indicates the predicted interception time. P Indicates engine thrust. α Indicates the balanced angle of attack. β Indicates the balance sideslip angle. m Indicates the mass of the aircraft. D Indicates aerodynamic drag. g Represents gravitational acceleration. Indicates the inclination angle of the flight path. L Indicates lift. Z Indicates lateral force. Indicates the deviation angle of the flight path. Indicates quality per second (QPS). Indicates the velocity of the target point. Indicates the target's tangential acceleration. Indicates the normal acceleration in the vertical plane of the target. Indicates the normal acceleration in the target horizontal plane. Indicates the target track inclination angle. Indicates the target track deflection angle. Indicates the distance between the aircraft and the target. The vertical component representing the angle between the target velocity and the line-of-sight direction. The horizontal component represents the angle between the target's velocity and the line-of-sight direction. The vertical component representing the angle between the aircraft's velocity and the line of sight. The horizontal component represents the angle between the aircraft's speed and the line of sight. Indicates the aircraft's line-of-sight tilt angle. Indicates the aircraft's line-of-sight deflection angle. This represents the x-coordinate of the spacecraft in the launch coordinate system. This represents the y-coordinate of the spacecraft in the launch coordinate system. This represents the coordinates of the spacecraft on the z-axis of the launch coordinate system. Indicates the maximum flight time of the aircraft. Indicates the aircraft's maximum angle of attack. Indicates the maximum sideslip angle of the aircraft. Indicates the desired terminal velocity angle. Indicates the desired velocity deflection angle at the end. Indicates the desired line-of-sight angle at the end. This indicates the desired line-of-sight angle at the end.

4. The multi-constraint terminal velocity optimal mid-course guidance method for long-range gliders according to claim 1, characterized in that, In S3, the constraint condition also includes minimizing the normal acceleration.

5. The multi-constraint terminal velocity optimal mid-course guidance method for long-range gliders according to claim 4, characterized in that, The optimal control problem can be expressed as: ， in, Indicates the aircraft in the i Zero-control miss distance at each track point a This represents the normal acceleration of the aircraft. t Indicates the current moment. Indicates the expected arrival time. Indicates the aircraft relative to the first i The speed of each waypoint This indicates that the aircraft reached the [number]th [time]. i Remaining flight time for each waypoint.

6. The multi-constraint terminal velocity optimal mid-course guidance method for long-range gliders according to claim 5, characterized in that, ， in, This indicates the aircraft's current speed.

7. The multi-constraint terminal velocity optimal mid-course guidance method for long-range gliders according to claim 5, characterized in that, Generated guidance commands Represented as: ， in ， ， ， Where n represents the number of the next waypoint the aircraft needs to track, and N represents the total number of waypoints excluding the target point. Indicates the aircraft in the k Zero-control miss distance at each track point.

8. The multi-constraint terminal velocity optimal mid-course guidance method for long-range gliders according to claim 1, characterized in that, In S2, the extraction of waypoints includes the following steps: S21. Connect the aircraft and the predicted interception point with a straight line, and find the point on the trajectory of the intermediate-range missile that is farthest from the connecting line, and record it as track point 1. S22. Use straight lines to connect the aircraft and track point 1, and track point 1 to the predicted interception point in sequence. By connecting these lines, the trajectory of the intermediate-range missile is divided into multiple segments. On each segment of the intermediate-range missile trajectory, find the point that is farthest from the corresponding connecting line, and select the point with the largest distance, which is recorded as track point 2. S23. Connect the aircraft, the generated track points, and the predicted interception points with straight lines. Divide the intermediate-range missile trajectory into multiple segments by connecting them. Find the point that is farthest from the corresponding line on each segment of the intermediate-range missile trajectory. Select the point with the largest distance and record it as the next track point. S24. Repeat step S23 to generate a preset number of waypoints. Arrange the generated waypoints in spatial order to extract the waypoints.

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