Method and device for planning flight path with appointed arrival time based on preposed angle shaping

Abstract

The invention relates to the technical field of aircraft trajectory planning and control, and provides a specified arrival time flight trajectory planning method and device based on preposed angle shaping. According to the method, under a three-dimensional coordinate system, based on a relative position vector between an aircraft and a fixed target, a kinematics equation used for representing dynamic motion characteristics of the aircraft relative to the fixed target is constructed; deducing a first-order dynamic equation of the preposed angle relative to the dynamic change relation of the relative distance through equality transformation; designing an arbitrary-order polynomial form reference profile of the preposed angle relative to the relative distance; and then, a double-constraint parameter setting strategy is adopted, and a terminal instruction non-divergent time-varying gain proportional guidance type aircraft acceleration instruction is exported in combination with a preposed angle profile and a preposed angle dynamic equation, so that flight path planning is completed based on preposed angle profile high-order shaping and specified arrival time. Dependence on a model linearization and parameter numerical optimization method is avoided, and planning reliability and adaptation capability are improved.

Description

Technical Field

[0001] This application relates to the field of aircraft trajectory planning and control technology, and in particular to a method and apparatus for flight trajectory planning with a specified arrival time based on lead angle shaping. Background Technology

[0002] The core objective of aircraft trajectory planning is to construct the optimal path and achieve precise guidance to the predetermined target point. Conventional designs are constrained by collision avoidance safety and cost control. These types of missions have relatively simple objectives and constraints, and related technical solutions are relatively mature. However, focusing solely on precise rendezvous in planning has significant limitations. In real-world scenarios such as civilian monitoring and inspection, precise logistics delivery, and disaster site surveys, aircraft need to arrive at the target area at specific time points to ensure mission sequence coordination, timely deployment, or rapid emergency response. Using traditional planning models often fails to meet expected time requirements, easily leading to mission process disruptions and consequently affecting overall execution quality.

[0003] Furthermore, most aircraft are prone to terminal control command divergence during actual trajectory planning. This problem not only causes the flight path to deviate from the ideal trajectory but also seriously affects flight stability and safety performance. Simultaneously, in three-dimensional trajectory planning scenarios, due to the strong coupling characteristics of the various dimensions of the motion equations, existing mature two-dimensional trajectory planning schemes are difficult to directly transfer and apply. This has become a key challenge that urgently needs to be overcome in the field. Existing technical solutions often rely on switching strategies, constant rate assumptions, or linearization of the system model, and require extensive parameter tuning, significantly limiting the practical value and applicable scenarios of the technology.

[0004] Therefore, developing aircraft trajectory analysis and planning technology that meets multiple physical constraints is of great significance for improving system adaptability, enhancing mission execution reliability, and simplifying the planning process. Summary of the Invention

[0005] In view of this, embodiments of this application provide a method and apparatus for planning flight trajectories with specified arrival times based on leading angle shaping, in order to solve the problems of poor performance and easy command divergence in the prior art for planning tasks with expected time requirements.

[0006] A first aspect of this application provides a method for planning a flight trajectory at a specified arrival time based on leading angle shaping, comprising:

[0007] In a three-dimensional coordinate system, kinematic equations are constructed to characterize the dynamic motion of the aircraft relative to the fixed target, based on the relative position vector between the aircraft and the fixed target.

[0008] Based on the kinematic equations, the first-order dynamic equation relating the aircraft's velocity lead angle to the relative distance is derived through equation transformations; where the velocity lead angle is the angle between the aircraft's velocity direction and the aircraft's line of sight to the fixed target, and the relative distance is the relative distance between the aircraft and the fixed target.

[0009] A reference profile of arbitrary order polynomial form with respect to the relative distance is constructed, and the reference profile is tuned using a dual-constraint parameter tuning strategy. The dual-constraint parameter tuning strategy includes tuning the reference profile based on the initial state boundary conditions and the terminal state boundary conditions, and tuning the reference profile based on the expected arrival time.

[0010] The flight trajectory planning terminal acceleration command of the aircraft is determined based on the first-order dynamic equation and the reference profile tuning results; wherein, the terminal acceleration command is a time-varying gain proportional guidance command in which the terminal command does not diverge.

[0011] A second aspect of this application provides a flight trajectory planning device for a specified arrival time based on leading angle shaping, comprising:

[0012] The building module is configured to construct kinematic equations in a three-dimensional coordinate system, based on the relative position vector between the aircraft and the fixed target, to characterize the dynamic motion of the aircraft relative to the fixed target.

[0013] The derivation module is configured to derive, based on the kinematic equations, the first-order dynamic equation relating the aircraft's velocity lead angle to the relative distance through equation transformations; where the velocity lead angle is the angle between the aircraft's velocity direction and the aircraft's line-of-sight direction to the fixed target, and the relative distance is the relative distance between the aircraft and the fixed target;

[0014] The tuning module is configured to construct a reference profile of arbitrary order polynomial form with respect to the relative distance, and to tune the reference profile using a dual-constraint parameter tuning strategy. The dual-constraint parameter tuning strategy includes tuning the reference profile based on initial state boundary conditions and terminal state boundary conditions, and tuning the reference profile based on the expected arrival time.

[0015] The planning module is configured to determine the flight trajectory of the aircraft and the terminal acceleration command based on the first-order dynamic equation and the tuning results of the reference profile; wherein, the terminal acceleration command is a time-varying gain proportional guidance command in which the terminal command does not diverge.

[0016] A third aspect of this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method.

[0017] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method.

[0018] The beneficial effects of the embodiments in this application compared with the prior art are:

[0019] This application embodiment constructs kinematic equations to characterize the dynamic motion of the aircraft relative to the fixed target in a three-dimensional coordinate system based on the relative position vector between the aircraft and the fixed target. Through equation transformation, a first-order dynamic equation relating the lead angle to the relative distance is derived. An arbitrary-order polynomial reference profile of the lead angle with respect to the relative distance is designed. Subsequently, a dual-constraint parameter tuning strategy is adopted, and combined with the lead angle profile and the lead angle dynamic equation, a time-varying gain proportional guidance form of aircraft acceleration command with non-divergent terminal commands is derived. This achieves high-order shaping of the lead angle profile and completion of flight trajectory planning based on a specified arrival time, avoiding reliance on model linearization and parameter numerical optimization methods, and improving planning reliability and adaptability. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating a flight trajectory planning method based on pre-angle shaping for a specified arrival time, provided in an embodiment of this application.

[0022] Figure 2 This is a schematic diagram of the motion relationship between an aircraft and a fixed target in three-dimensional space, provided in an embodiment of this application.

[0023] Figure 3 This is a flowchart illustrating another method for planning a flight trajectory based on a specified arrival time using a leading angle shaping method provided in this application embodiment.

[0024] Figure 4 This is a flowchart illustrating another method for planning a flight trajectory based on a specified arrival time using a leading angle shaping, provided in an embodiment of this application.

[0025] Figure 5 This is a schematic diagram of the trajectory planning simulation results for the rendezvous task provided in the embodiments of this application.

[0026] Figure 6This is a schematic diagram of a flight trajectory planning device based on pre-angle shaping for a specified arrival time, provided in an embodiment of this application.

[0027] Figure 7 This is a schematic diagram of the electronic device provided in the embodiments of this application. Detailed Implementation

[0028] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0029] The following will describe in detail, with reference to the accompanying drawings, a method and apparatus for planning a flight trajectory based on a specified arrival time according to an embodiment of this application.

[0030] As mentioned above, in missions where aircraft need to arrive at the target area at specific time points to ensure mission sequence coordination, timely deployment, or rapid emergency response, the traditional planning model often fails to meet the expected time requirements, easily leading to mission process disruptions and affecting overall execution quality. Furthermore, many aircraft are prone to terminal control command divergence during actual trajectory planning.

[0031] In view of this, this application provides a flight trajectory planning method based on leading angle shaping and specified arrival time. In a three-dimensional coordinate system, kinematic equations are constructed based on the relative position vector between the aircraft and a fixed target to characterize the dynamic motion of the aircraft relative to the fixed target. Through equation transformation, a first-order dynamic equation relating the leading angle to the relative distance is derived. An arbitrary-order polynomial reference profile of the leading angle with respect to the relative distance is designed. Subsequently, a dual-constraint parameter tuning strategy is adopted, and combined with the leading angle profile and the leading angle dynamic equation, a time-varying gain proportional guidance form of the aircraft acceleration command with non-divergent terminal commands is derived. This achieves flight trajectory planning based on high-order leading angle profile shaping and specified arrival time, avoiding reliance on model linearization and parameter numerical optimization methods, and improving planning reliability and adaptability.

[0032] Figure 1 This is a flowchart illustrating a flight trajectory planning method based on pre-angle shaping for a specified arrival time, provided in an embodiment of this application. Figure 1 As shown, the method includes the following steps:

[0033] In step S101, in a three-dimensional coordinate system, based on the relative position vector between the aircraft and the fixed target, a kinematic equation is constructed to characterize the dynamic motion of the aircraft relative to the fixed target.

[0034] In step S102, based on the kinematic equations, the first-order dynamic equation relating the aircraft's velocity lead angle to the relative distance is derived through equation transformation.

[0035] Among them, the velocity lead angle is the angle between the direction of the aircraft's velocity and the direction of the aircraft's line of sight to the fixed target, and the relative distance is the relative distance between the aircraft and the fixed target.

[0036] In step S103, a reference profile of arbitrary order polynomial form with respect to the relative distance is constructed, and the reference profile is tuned using a dual-constraint parameter tuning strategy.

[0037] The dual-constraint parameter tuning strategy includes tuning the reference profile based on the initial state boundary conditions and the terminal state boundary conditions, and tuning the reference profile based on the expected arrival time.

[0038] In step S104, the flight trajectory planning terminal acceleration command of the aircraft is determined based on the first-order dynamic equation and the reference profile tuning results.

[0039] Among them, the terminal acceleration command is a time-varying gain ratio guided command in which the terminal command does not diverge.

[0040] In some embodiments of this application, the method may be executed by a server or by a terminal device with certain processing capabilities.

[0041] In some embodiments of this application, kinematic equations can be constructed in a three-dimensional coordinate system based on the relative position vector between the aircraft and the fixed target to characterize the dynamic motion characteristics of the aircraft relative to the fixed target.

[0042] The three-dimensional coordinate system can be, for example, a three-dimensional Cartesian coordinate system, or other three-dimensional coordinate systems; there are no restrictions here. The fixed target can be a stationary target.

[0043] In some embodiments of this application, a first-order dynamic equation relating the aircraft's velocity lead angle to relative distance can be derived from this kinematic equation through equation transformation. Simultaneously, an arbitrary-order polynomial reference profile of the lead angle with respect to relative distance can be constructed, and the reference profile can be tuned using a dual-constraint parameter tuning strategy.

[0044] The dual-constraint parameter tuning strategy includes tuning the reference profile based on initial state boundary conditions and terminal state boundary conditions, and tuning the reference profile based on the expected arrival time. In other words, the leading angle reference profile can be tuned to a form containing only one adjustable parameter based on the initial state boundary conditions and terminal state boundary conditions, and this single adjustable parameter of the reference profile can be tuned based on the expected arrival time.

[0045] In some embodiments of this application, the flight trajectory planning terminal acceleration command of the aircraft can be determined based on the first-order dynamic equation and reference profile tuning results determined above. The terminal acceleration command is a time-varying gain proportional guidance command in which the terminal command does not diverge.

[0046] According to the technical solution provided in the embodiments of this application, kinematic equations are constructed in a three-dimensional coordinate system based on the relative position vector between the aircraft and the fixed target to characterize the dynamic motion characteristics of the aircraft relative to the fixed target; through equation transformation, a first-order dynamic equation relating the leading angle to the dynamic change of relative distance is derived; an arbitrary-order polynomial reference profile of the leading angle with respect to relative distance is designed; subsequently, a dual-constraint parameter tuning strategy is adopted, and combined with the leading angle profile and the leading angle dynamic equation, a time-varying gain proportional guidance form of aircraft acceleration command with non-divergent terminal command is derived. This realizes high-order shaping of the leading angle profile and completion of flight trajectory planning based on specified arrival time, avoiding dependence on model linearization and parameter numerical optimization methods, and improving planning reliability and adaptability.

[0047] Figure 2 This is a schematic diagram illustrating the motion relationship between an aircraft and a fixed target in three-dimensional space, provided in an embodiment of this application. For example... Figure 2 As shown, where and Let A and B represent the aircraft and the fixed target, respectively. Based on the kinematic and dynamic relationships between the aircraft and the fixed target in three-dimensional space, the kinematic equations of the aircraft relative to the fixed target in three-dimensional space are as follows:

[0048] ;

[0049] ;

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] in, The relative distance between the aircraft and the stationary target is the energy in the relative position vector; The rate of change of the relative distance between the aircraft and the stationary target over time; The flight speed of the aircraft The rate of change of the aircraft's speed; and These are the pitch and yaw lead angle components of the aircraft, respectively. and These are the pitch and azimuth components of the aircraft's line-of-sight angle relative to the target point, respectively. and These are the leading angular components and angular rates of the aircraft, respectively. and These are the line-of-sight angular angular components and angular rates of the aircraft relative to the target point; and These are the normal accelerations in the pitch and yaw planes of the aircraft, respectively, and are the control laws that need to be designed. It is the acceleration due to gravity; The thrust generated for the aircraft For aerodynamic drag, , The drag coefficient, Atmospheric density, For the reference area of ​​the aircraft, For the mass of the aircraft.

[0055] And, in three-dimensional space, the forward angle of the aircraft is represented as... ;in, This refers to the forward angle of the aircraft.

[0056] In some embodiments of this application, deriving the first-order dynamic equation relating the aircraft's velocity lead angle to the relative distance based on the kinematic equations through equation transformations may include first calculating the aircraft lead angle expression with respect to time. The derivative of is obtained. Then and Substituting the expression for the aircraft's lead angle into the time derivative expression above, we obtain... Finally, substitute... and Divide both sides of the time derivative expression of the aircraft's forward angle by... By examining both sides of the equation in the expression, we obtain the first-order dynamic equation. .

[0057] In some embodiments of this application, when constructing a reference profile of arbitrary order polynomial form of the leading angle with respect to relative distance, it can be determined that the reference profile of arbitrary order polynomial form of the leading angle with respect to relative distance is a higher-order polynomial function with respect to relative distance. ;in, For the desired leading angle reference profile, This represents the initial relative distance; This is a reference value for the leading angle; , The parameters are those for the profile to be designed. In other words, this higher-order polynomial function can be used as the reference profile for the desired leading angle. Then, a dual-constraint parameter tuning strategy can be used to tune the reference profile.

[0058] When using a dual-constraint parameter tuning strategy to tune a reference profile, the reference profile can be tuned based on both initial state boundary conditions and terminal state boundary conditions.

[0059] At this point, to ensure zero initial convergence error of the flight state with respect to the reference profile, the reference profile can satisfy the following initial state boundary conditions. ;in, Represents the initial angle.

[0060] Then, by solving the initial state boundary conditions, we obtain... .

[0061] Furthermore, to ensure zero miss distance at the end of the flight state with respect to the reference profile, the reference profile can satisfy the following end-state boundary conditions. ;in, Indicates to beg The first derivative is then used to solve the boundary conditions of the terminal state. .

[0062] Next, by combining the solved initial state boundary conditions and the solved terminal state boundary conditions, we obtain the comprehensive expression. .

[0063] Finally, substituting this synthetic expression into the aforementioned higher-order polynomial function, we obtain the forward angle reference profile after tuning based on the initial state boundary conditions and the terminal state boundary conditions. This allows the leading angle reference profile to be obtained. Tuning to include only one adjustable parameter In the form of.

[0064] On the other hand, the reference profile can also be tuned based on the expected arrival time.

[0065] At this point, we can first assume that the speed of the aircraft is constant during flight and denote it as . Approximate calculation of the entire flight time of the spacecraft along the profile from the initial moment to the moment of impact. for .

[0066] Then to The expression is expanded using a series, truncated to fourth-order terms, and only terms about are retained. The second-order term gives:

[0067] ;

[0068] in, This represents the Euler number; other parameters are calculated as follows:

[0069] .

[0070] If the expected arrival time is denoted as ,make Then the profile parameters after tuning the reference profile based on the expected arrival time can be obtained. ;in, The choice of this expected arrival time is used to ensure that the equation has a solution. Since it can be proven... Therefore, this condition This has practical physical significance. This allows for the implementation of this adjustable parameter. The adjustment.

[0071] In some embodiments of this application, determining the flight trajectory planning terminal acceleration command of the aircraft based on the first-order dynamic equation and the reference profile tuning results may include first calculating the lead angle reference profile relative to the relative distance after tuning the reference profile based on the initial state boundary conditions and the terminal state boundary conditions. The first derivative is obtained. .

[0072] Then, based on the first-order dynamic equation, And constructing acceleration commands for aircraft using proportional guidance based on profile parameters tuned to the reference profile according to the expected arrival time. ;in, It is a time-varying proportional gain. .

[0073] Finally, combining L'Hôpital's rule, we obtain the non-divergent terminal proportional gain and acceleration command:

[0074] ;

[0075] ;

[0076] in, For time-varying proportional gain, This is the terminal acceleration command. From this, a non-divergent, time-varying gain proportional guidance form of the terminal acceleration command can be obtained.

[0077] The technical solution provided in this application constructs the leading angle reference profile as a high-order polynomial form of relative distance, and completes the profile parameter tuning by combining the boundary conditions at the initial and terminal times, thereby deriving the analytical profile expression and acceleration control command. The analytical strategy employed by this method does not require linearization of the system model, nor does it require complex profile parameter design and adjustment. It can simultaneously achieve the dual goals of precise arrival time control and bounded terminal control commands, and overcomes the conservative limitations of existing technical solutions while improving adaptability to actual tasks and execution reliability.

[0078] Figure 3 This is a flowchart illustrating another flight trajectory planning method based on pre-angle shaping for a specified arrival time, provided in an embodiment of this application. Figure 3 Steps S301 to S304 in the illustrated embodiment are Figure 1 Steps S101 to S104 in the illustrated embodiment are basically the same and will not be repeated here. Figure 3 As shown, the method also includes the following steps:

[0079] In step S305, during the flight of the aircraft, in response to the determination that the relative position vector between the aircraft and the fixed target has changed, the first-order dynamic equation and the profile parameters after tuning the reference profile based on the updated relative position vector are updated.

[0080] In step S306, the updated flight trajectory planning terminal acceleration command of the aircraft is determined based on the updated first-order dynamic equation and the updated reference profile tuning results.

[0081] In some embodiments of this application, if it is determined that the relative position vector between the aircraft and the fixed target changes during the flight of the aircraft, the first-order dynamic equation and the profile parameters after tuning the reference profile based on the updated relative position vector can be updated. Then, the updated flight trajectory planning terminal acceleration command of the aircraft is determined based on the updated first-order dynamic equation and the updated reference profile tuning result.

[0082] In other words, any current moment can be regarded as the initial moment of the subsequent trajectory, and the adjusted... Calculation formula, after tuning Calculation formulas and parameters , and The initial values ​​in the calculation formula are replaced with real-time values, thereby updating the reference profile in real time during flight, resulting in:

[0083] ;

[0084] ;

[0085] .

[0086] The analytical acceleration command designed in this embodiment can achieve arrival time constraints and ensure that the terminal command does not diverge. Furthermore, this embodiment employs an online planning method based on leading angle profile reshaping, which can update profile parameters in real time according to unexpected situations during flight. This method is characterized by its simplicity, strong applicability, and high reliability.

[0087] Figure 4 This is a flowchart illustrating another flight trajectory planning method based on leading angle shaping for a specified arrival time, provided in an embodiment of this application. Figure 4 As shown, the method includes the following steps:

[0088] In step S1, the kinematic and dynamic equations of the aircraft relative to a fixed target in three-dimensional space can be constructed first. The fixed target can be a stationary target.

[0089] In step S2, the first-order dynamic equation of the aircraft's velocity lead angle with respect to the relative distance is derived.

[0090] In step S3, a higher-order reference profile for the leading angle is constructed using the relative distance as the independent variable, and the parameters are tuned based on the boundary conditions of the initial / terminal states, respectively, to obtain a profile containing only one adjustable parameter. The leading angle reference profile, and the adjustable parameter tuned based on the expected arrival time constraint. .

[0091] In step S4, a method for online updating of the terminal convergence acceleration command and reference profile is designed to obtain the terminal acceleration command for the flight trajectory planning of the aircraft.

[0092] To verify the technical effects of the technical solutions provided in the embodiments of this application, the following experiment was designed:

[0093] Using the scenario of an aircraft arriving at a fixed target at a specified time as a verification scenario, the effectiveness of the online flight trajectory planning method provided in this application embodiment is tested. The experimental parameters are configured as follows: the aircraft speed is set to 250 meters per second (m / s), the initial position coordinates are (0, 0, 0) kilometers (km), the initial target position coordinates are (6, 6, 0) km; the initial lead angle is configured with a pitch component of 10° and a yaw component of 10°; in addition, the aircraft mass is determined to be 90 kilograms (kg), and the reference area is 0.5 square meters (m²).

[0094] The simulation results of trajectory planning for this rendezvous mission are shown in Figure 5. In the simulation, the profile order was set to 3, and the expected arrival times were 35 seconds (s), 40 seconds (s), and 45 seconds (s), respectively. Subplots (a)-(f) in Figure 5 correspond to the aircraft's flight trajectory, relative distance change curve, lead angle change curve, total acceleration command change curve, line-of-sight azimuth angle change curve, and actual pitch angle change curve, respectively. Figure 5 As can be seen, the method provided in this application embodiment can flexibly adjust the arrival time while ensuring accurate arrival, and can ensure that the aircraft control commands converge to a finite value.

[0095] The online flight trajectory planning method proposed in this application effectively fulfills the requirements of specified arrival time and finite terminal command constraints, without relying on model linearization or numerical algorithms, and without requiring adjustment of profile parameters.

[0096] All of the above-mentioned optional technical solutions can be combined in any way to form the optional embodiments of this application, and will not be described in detail here.

[0097] The following are embodiments of the apparatus described in this application, which can be used to execute the embodiments of the method described in this application. For details not disclosed in the apparatus embodiments of this application, please refer to the embodiments of the method described in this application.

[0098] Figure 6 This is a schematic diagram of a flight trajectory planning device based on pre-angle shaping for a specified arrival time, provided in an embodiment of this application. Figure 6 As shown, the device includes:

[0099] Module 601 is configured to construct kinematic equations in a three-dimensional coordinate system, based on the relative position vector between the aircraft and the fixed target, to characterize the dynamic motion of the aircraft relative to the fixed target.

[0100] The derivation module 602 is configured to derive a first-order dynamic equation relating the aircraft's velocity lead angle to the relative distance based on kinematic equations and through equation transformations; where the velocity lead angle is the angle between the aircraft's velocity direction and the aircraft's line of sight to the fixed target, and the relative distance is the relative distance between the aircraft and the fixed target.

[0101] The tuning module 603 is configured to construct a reference profile of arbitrary order polynomial form with respect to the relative distance of the leading angle, and to tune the reference profile using a dual-constraint parameter tuning strategy. The dual-constraint parameter tuning strategy includes tuning the reference profile based on the initial state boundary conditions and the terminal state boundary conditions, and tuning the reference profile based on the expected arrival time.

[0102] The planning module 604 is configured to determine the flight trajectory planning terminal acceleration command of the aircraft based on the first-order dynamic equation and the reference profile tuning results; wherein, the terminal acceleration command is a time-varying gain proportional guidance command in which the terminal command does not diverge.

[0103] According to the technical solution provided in the embodiments of this application, kinematic equations are constructed in a three-dimensional coordinate system based on the relative position vector between the aircraft and the fixed target to characterize the dynamic motion characteristics of the aircraft relative to the fixed target; through equation transformation, a first-order dynamic equation relating the leading angle to the dynamic change of relative distance is derived; an arbitrary-order polynomial reference profile of the leading angle with respect to relative distance is designed; subsequently, a dual-constraint parameter tuning strategy is adopted, and combined with the leading angle profile and the leading angle dynamic equation, a time-varying gain proportional guidance form of aircraft acceleration command with non-divergent terminal command is derived. This realizes high-order shaping of the leading angle profile and completion of flight trajectory planning based on specified arrival time, avoiding dependence on model linearization and parameter numerical optimization methods, and improving planning reliability and adaptability.

[0104] In some implementations, the kinematic equations of the dynamic motion characteristics of the aircraft relative to a fixed target are as follows:

[0105] ;

[0106] ;

[0107] ;

[0108] ;

[0109] ;

[0110] ;

[0111] in, The relative distance between the aircraft and the fixed target. The rate of change of the relative distance between the aircraft and the stationary target over time; The flight speed of the aircraft The rate of change of the aircraft's speed; and These are the pitch and yaw lead angle components of the aircraft, respectively. and These are the pitch and azimuth components of the aircraft's line-of-sight angle relative to the target point, respectively. and These are the leading angular components and angular rates of the aircraft, respectively. and These are the line-of-sight angular angular components and angular rates of the aircraft relative to the target point; and These are the normal accelerations in the pitch and yaw planes of the aircraft, respectively, and are the control laws that need to be designed. It is the acceleration due to gravity; The thrust generated for the aircraft For aerodynamic drag, For the mass of the aircraft.

[0112] And, in three-dimensional space, the forward angle of the aircraft is represented as... ;in, This refers to the forward angle of the aircraft.

[0113] In some implementations, the first-order dynamic equations are determined in the following manner:

[0114] Calculate the aircraft lead angle expression with respect to time. The derivative of is obtained. ;

[0115] Will and Substituting the expression for the aircraft's lead angle into the time derivative expression above, we obtain... ;

[0116] Substitute and Divide both sides of the time derivative expression of the aircraft's forward angle by... By applying the equation to both sides of the expression, we obtain the first-order dynamic equation. .

[0117] In some implementations, the reference profile of the leading angle in arbitrary-order polynomial form with respect to the relative distance is a higher-order polynomial function with respect to the relative distance. ;in, For the desired leading angle reference profile, This represents the initial relative distance; This is a reference value for the leading angle; , These are the profile parameters to be designed.

[0118] In some implementations, the reference profile is tuned based on initial state boundary conditions and terminal state boundary conditions, including:

[0119] To ensure zero initial convergence error of the flight state with respect to the reference profile, the reference profile shall satisfy the following initial state boundary conditions. ;in, Represents the initial angle;

[0120] Solving the initial state boundary conditions yields ;

[0121] To ensure zero miss distance at the end of the flight state with respect to the reference profile, the reference profile must satisfy the following end-state boundary conditions. ;in, Indicates to beg First derivative;

[0122] Solving the terminal state boundary conditions yields ;

[0123] By combining the solved initial state boundary conditions and the solved final state boundary conditions, the comprehensive expression is obtained. ;

[0124] Substituting the synthesized expression into the higher-order polynomial function, we obtain the forward angle reference profile after tuning the reference profile based on the initial state boundary conditions and the terminal state boundary conditions. .

[0125] In some implementations, the reference profile is tuned based on the expected arrival time, including:

[0126] Let the speed of the aircraft be constant during flight and denoted as . Approximate calculation of the entire flight time of the spacecraft along the profile from the initial moment to the moment of impact. for ;

[0127] right The expression is expanded using a series, truncated to fourth-order terms, and only terms about are retained. The second-order term gives:

[0128] ;

[0129] in, This represents the Euler number; other parameters are calculated as follows:

[0130] ;

[0131] Let the expected arrival time be denoted as ,make The profile parameters after tuning the reference profile based on the expected arrival time are obtained by solving. ;in, .

[0132] In some implementations, the flight trajectory planning terminal acceleration command of the aircraft is determined based on the first-order dynamic equations and the reference profile tuning results, including:

[0133] Calculate the leading angle reference profile relative to the relative distance after tuning the reference profile based on the initial state boundary conditions and the terminal state boundary conditions. The first derivative is obtained. ;

[0134] Based on the first-order dynamic equation, And constructing acceleration commands for aircraft using proportional guidance based on profile parameters tuned to the reference profile according to the expected arrival time. ;

[0135] in, It is a time-varying proportional gain. ;

[0136] Combining L'Hôpital's rule, we obtain the non-divergent terminal proportional gain and acceleration command:

[0137] ;

[0138] ;

[0139] in, For time-varying proportional gain, This is the terminal acceleration command.

[0140] In some implementations, it also includes:

[0141] During the flight of the aircraft, in response to the change in the relative position vector between the aircraft and the fixed target, the first-order dynamic equation and the profile parameters after tuning the reference profile based on the updated relative position vector are updated.

[0142] The updated flight trajectory planning terminal acceleration command for the aircraft is determined based on the updated first-order dynamic equations and the updated reference profile tuning results.

[0143] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0144] Figure 7 This is a schematic diagram of the electronic device provided in an embodiment of this application. For example... Figure 7 As shown, the electronic device 7 of this embodiment includes a processor 701, a memory 702, and a computer program 703 stored in the memory 702 and executable on the processor 701. When the processor 701 executes the computer program 703, it implements the steps in the various method embodiments described above. Alternatively, when the processor 701 executes the computer program 703, it implements the functions of each module / unit in the various device embodiments described above.

[0145] Electronic device 7 can be a desktop computer, laptop, handheld computer, cloud server, or other electronic device. Electronic device 7 may include, but is not limited to, processor 701 and memory 702. Those skilled in the art will understand that... Figure 7 This is merely an example of electronic device 7 and does not constitute a limitation on electronic device 7. It may include more or fewer components than shown, or different components.

[0146] The processor 701 can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0147] The memory 702 can be an internal storage unit of the electronic device 7, such as a hard disk or RAM of the electronic device 7. The memory 702 can also be an external storage device of the electronic device 7, such as a plug-in hard disk, Smart Media Card (SMC), Secure Digital (SD) card, Flash Card, etc., equipped on the electronic device 7. The memory 702 can also include both internal and external storage units of the electronic device 7. The memory 702 is used to store computer programs and other programs and data required by the electronic device.

[0148] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0149] If an integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program may include computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. A computer-readable medium may include: any entity or device capable of carrying computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0150] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for planning flight trajectories at a specified arrival time based on pre-arrival angle shaping, characterized in that, include: In a three-dimensional coordinate system, based on the relative position vector between the aircraft and the fixed target, a kinematic equation is constructed to characterize the dynamic motion of the aircraft relative to the fixed target. Based on the kinematic equations, a first-order dynamic equation relating the aircraft's velocity lead angle to the relative distance is derived through equation transformation; wherein, the velocity lead angle is the angle between the aircraft's velocity direction and the aircraft's line-of-sight direction to the fixed target, and the relative distance is the relative distance between the aircraft and the fixed target; A reference profile of arbitrary order polynomial form with respect to the relative distance is constructed, and the reference profile is tuned using a dual-constraint parameter tuning strategy; wherein, the dual-constraint parameter tuning strategy includes tuning the reference profile based on initial state boundary conditions and terminal state boundary conditions, and tuning the reference profile based on the expected arrival time. The flight trajectory planning terminal acceleration command of the aircraft is determined based on the first-order dynamic equation and the reference profile tuning results; wherein, the terminal acceleration command is a time-varying gain proportional guidance command in which the terminal command does not diverge.

2. The method according to claim 1, characterized in that, The kinematic equations of the dynamic motion characteristics of the aircraft relative to the fixed target are as follows: ； ； ； ； ； ； in, The relative distance between the aircraft and the fixed target. The relative distance between the aircraft and the fixed target changes over time. The flight speed of the aircraft The rate of change of the aircraft's speed; and These are the pitch and yaw lead angle components of the aircraft, respectively. and These are the pitch and azimuth components of the aircraft's line-of-sight angle relative to the target point, respectively. and These are the leading angular components and angular rates of the aircraft, respectively. and These are the line-of-sight angular angular components and angular rates of the aircraft relative to the target point; and These are the normal accelerations in the pitch and yaw planes of the aircraft, respectively, and are the control laws that need to be designed. It is the acceleration due to gravity; The thrust generated for the aircraft For aerodynamic drag, For the mass of the aircraft; Furthermore, in three-dimensional space, the forward angle of the aircraft is represented as... ;in, The forward angle of the aircraft is [value missing].

3. The method according to claim 2, characterized in that, The first-order dynamic equations are determined in the following manner: Calculate the aircraft lead angle expression with respect to time. The derivative of is obtained. ; Will and Substituting the expression for the aircraft's lead angle into the time derivative expression above, we obtain... ; Substitute and Divide both sides of the time derivative expression of the aircraft's forward angle by... By examining both sides of the equation in the expression, we obtain the first-order dynamic equation. .

4. The method according to claim 2, characterized in that, The reference profile of the arbitrary-order polynomial form of the preceding angle with respect to the relative distance is a high-order polynomial function with respect to the relative distance. ;in, For the desired leading angle reference profile, This represents the initial relative distance; This is a reference value for the leading angle; , These are the profile parameters to be designed.

5. The method according to claim 4, characterized in that, The reference profile is tuned based on initial state boundary conditions and terminal state boundary conditions, including: To ensure zero initial convergence error of the flight state with respect to the reference profile, the reference profile shall satisfy the following initial state boundary conditions. ;in, Represents the initial angle; Solving the initial state boundary conditions yields ; To ensure zero miss distance at the end of the flight state with respect to the reference profile, the reference profile must satisfy the following end-state boundary conditions. ;in, Indicates to beg First derivative; Solving the terminal state boundary conditions yields ; By combining the solved initial state boundary conditions and the solved final state boundary conditions, the comprehensive expression is obtained. ; Substituting the synthetic expression into the higher-order polynomial function yields the pre-angle reference profile after tuning the reference profile based on the initial state boundary conditions and the terminal state boundary conditions. .

6. The method according to claim 5, characterized in that, Tuning the reference profile based on the expected arrival time includes: Let the speed of the aircraft be constant during flight and denoted as . Approximate calculation of the entire flight time of the spacecraft along the profile from the initial moment to the moment of impact. for ; right The expression is expanded using a series, truncated to fourth-order terms, and only terms about are retained. The second-order term gives: ； in, This represents the Euler number; other parameters are calculated as follows: ； Let the expected arrival time be denoted as ,make The profile parameters, after being tuned based on the expected arrival time, are obtained by solving the problem. ;in, .

7. The method according to claim 6, characterized in that, The flight trajectory planning terminal acceleration command of the aircraft is determined based on the first-order dynamic equation and the reference profile tuning results, including: Calculate the leading angle reference profile relative to the relative distance after tuning the reference profile based on the initial state boundary conditions and the terminal state boundary conditions. The first derivative is obtained. ; According to the first-order dynamic equation, the... The profile parameters, after being tuned to the reference profile based on the expected arrival time, construct a proportional guidance-type aircraft acceleration command. ; in, It is a time-varying proportional gain. ; Combining L'Hôpital's rule, we obtain the non-divergent terminal proportional gain and acceleration command: ； ； in, The time-varying proportional gain is mentioned. This refers to the terminal acceleration command.

8. The method according to claim 1, characterized in that, The method further includes: During the flight of the aircraft, in response to the determination that the relative position vector between the aircraft and the fixed target has changed, the first-order dynamic equation and the profile parameters after tuning the reference profile based on the updated relative position vector are updated. The updated flight trajectory planning terminal acceleration command for the aircraft is determined based on the updated first-order dynamic equations and the updated reference profile tuning results.

9. A flight trajectory planning device based on pre-angle shaping for a specified arrival time, characterized in that, include: The construction module is configured to construct kinematic equations in a three-dimensional coordinate system, based on the relative position vector between the aircraft and the fixed target, to characterize the dynamic motion of the aircraft relative to the fixed target. The derivation module is configured to derive, based on the kinematic equations, a first-order dynamic equation relating the aircraft's velocity lead angle to the relative distance through equation transformations; wherein, the velocity lead angle is the angle between the aircraft's velocity direction and the aircraft's line-of-sight direction to the fixed target, and the relative distance is the relative distance between the aircraft and the fixed target; The tuning module is configured to construct a reference profile of arbitrary order polynomial form with respect to the relative distance of the preceding angle, and to tune the reference profile using a dual-constraint parameter tuning strategy; wherein, the dual-constraint parameter tuning strategy includes tuning the reference profile based on initial state boundary conditions and terminal state boundary conditions, and tuning the reference profile based on the expected arrival time. The planning module is configured to determine the flight trajectory planning terminal acceleration command of the aircraft based on the first-order dynamic equation and the reference profile tuning result; wherein the terminal acceleration command is a time-varying gain proportional guidance command in which the terminal command does not diverge.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 8.

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