A four-dimensional flight path generation and guidance integrated method for flight management system

Abstract

The application provides a four-dimensional flight path generation and guidance integrated method for a flight management system, which adopts a four-order polynomial to segmentally fit a flight trajectory based on a flight path point and a flight section reference speed in a flight plan, updates a flight section distance and an estimated arrival time through iterative optimization, and generates a four-dimensional trajectory function containing time dimension information; a vector field composed of a convergence term and a transfer term is constructed based on the trajectory function, expected attitude, speed parameters and errors are calculated in combination with real-time positions and states of the aircraft, a proportional guidance control law is designed, pitch angle speed, yaw angle speed and flight acceleration instructions are output, and the aircraft is driven to track the four-dimensional trajectory with high precision. The spatial precision and time accuracy of trajectory tracking are improved, the calculation complexity is low, the engineering practicability is high, the method can meet the needs of advanced aviation operation concepts such as continuous descent operation and four-dimensional trajectory operation, and is suitable for flight management systems of various fixed-wing aircrafts.

Description

Technical Field

[0001] This invention belongs to the field of flight management technology, specifically relating to an integrated method for four-dimensional trajectory generation and guidance in flight management systems. Background Technology

[0002] As a core component of avionics systems, the Flight Management System (FMS) directly impacts the accuracy, safety, and efficiency of flight through its trajectory generation and guidance functions. Trajectory generation requires providing feasible flight paths based on waypoints in the flight plan, while trajectory guidance involves sending guidance commands to the aircraft's automatic flight control system to ensure the aircraft reaches its target location at the designated time.

[0003] With the development of the global civil aviation transportation industry and the widespread application of advanced operational concepts such as four-dimensional trajectory operation (TBO), higher requirements have been placed on the accuracy and coordination of trajectory generation and guidance. However, in traditional flight management systems, trajectory generation and trajectory guidance functions are usually decoupled, ignoring the coupling relationship between the two, which limits the overall trajectory tracking performance. For example, some existing technologies decompose the functions into independent modules such as horizontal trajectory planning, vertical trajectory planning, vertical navigation guidance, and horizontal navigation guidance. Although this reduces the complexity of engineering implementation, it does not consider the coupling effect between the horizontal and vertical dimensions and the strong correlation between trajectory planning and guidance tasks.

[0004] Existing four-dimensional trajectory generation methods mainly fall into four categories: heuristic search, rule iteration, optimization solution, and function fitting. Heuristic search methods require time backtracking to correct arrival times; rule iteration methods rely on flight rules to calculate the trajectory step by step; optimization solution methods often employ nonlinear programming techniques but are prone to computational complexity or infeasible solutions; while function fitting methods can characterize flight paths, some schemes cannot guarantee arrival time accuracy and trajectory curvature. Regarding trajectory guidance, existing technologies using guidance laws directly constructed based on waypoints struggle to guarantee arrival time and trajectory details; some vector field guidance methods, while capable of path tracking, do not fully incorporate time constraints, failing to meet the time accuracy requirements of four-dimensional trajectory operation. Furthermore, some methods considering time constraints suffer from high computational complexity and are unsuitable for airborne implementation, making them difficult to apply to real-world flight scenarios.

[0005] In summary, existing technologies lack an integrated solution for four-dimensional trajectory generation and guidance that balances trajectory smoothness, time accuracy, and engineering practicality, and therefore cannot meet the high-performance requirements of advanced aviation operation concepts for flight management systems. Summary of the Invention

[0006] This invention provides an integrated method for four-dimensional trajectory generation and guidance in flight management systems, aiming to solve the problems of insufficient tracking performance, poor time accuracy, and poor trajectory flexibility caused by the decoupling of flight trajectory generation and guidance in existing flight management systems.

[0007] This invention provides an integrated method for four-dimensional trajectory generation and guidance in a flight management system, comprising the following steps: S1. Based on the preset track points and their speeds, obtain the estimated arrival time of each track point; S2. Based on the estimated arrival time of each track point, obtain the piecewise polynomial coefficients of each track on different coordinate axes to obtain the four-dimensional track. S3. Based on the four-dimensional track, update the estimated arrival time of each track point, and then update the polynomial coefficients again. Determine whether the loop calculation should stop based on the estimated arrival times of the old and new track points. If yes, proceed to S4; otherwise, proceed to S2. S4. According to the guidance cycle, determine the time segment and trajectory function to which the aircraft currently belongs. Based on the aircraft's current coordinates, trajectory function, current propagation gain coefficient, and derivative of the trajectory function, obtain the trajectory function guidance vector field. Based on the trajectory function guidance vector field, calculate the flight guidance control commands until the flight ends.

[0008] Optionally, based on the estimated arrival time of each waypoint, the piecewise polynomial coefficients of each waypoint on different coordinate axes are obtained to obtain the four-dimensional waypoint, including: Using formula Obtain the piecewise polynomial coefficients of each track on the coordinate axes x, y and z; Obtain four-dimensional trajectory , , ; in, ; , , The tracks are respectively in x , y , z Polynomial coefficients on the axis; for T i For the first i Estimated arrival time of each waypoint, T i+1 =T i +t i T1=0, , n Number of waypoints t i For the first i Flight time for the segment; x i , yi , z i Indicates waypoints P i The coordinates; , , No. i The speed corresponding to each waypoint is x , y , z Velocity components on the axis.

[0009] Optionally, obtain the trajectory function guiding vector field, including: (1) Calculate the propagation term of the vector field using the derivative of the trajectory function. ,as follows:

[0010] (2) Using the aircraft's current coordinates Calculate the trajectory function, propagation gain coefficient, and convergence term of the vector field. ; (3) Through the formula , thus obtaining the trajectory function guiding vector field.

[0011] Optionally, based on the trajectory function guidance vector field, flight guidance control commands are calculated, including: Through formula and This allows us to obtain the direction and velocity of the guiding vector field. Through formula and Calculate the target pitch and yaw angles in the trajectory guidance vector field; Through formula , and Calculate the errors between the current attitude and the attitude required by the trajectory guidance vector field, and between the current velocity and the speed required by the trajectory guidance vector field; Based on the proportional controller gain parameters k θ , k ψ and k a Through formula , and Receive flight guidance instructions; in, , , These are the guiding vector fields in x axis, y axis, z Reference direction of the axis The reference speed for guiding the vector field.

[0012] Optionally, based on preset waypoints and their speeds, the estimated arrival time for each waypoint is obtained, including: (1) Calculate the first number using the following formula. Segment distance:

[0013] (2) Calculate the flight segment using the following formula. Average speed:

[0014] (3) Calculate the flight segment using the following formula. Flight time:

[0015] (4) For waypoints The estimated arrival time of a waypoint can be calculated using the following formula: T i =T i-1 +t i-1 , T1=0.

[0016] Optionally, prior to S2, the method further includes: (1) For waypoints Calculate the velocity vector of waypoint 1 using the following formula:

[0017] (2) For waypoints When the waypoint i This is not a straight flight segment; the calculation is based on the direction and speed of adjacent waypoints.

[0018] in, , It is a unit vector in the direction of velocity; (3) For waypoints When the waypoint i When the flight segment is a straight line, it can be calculated separately using the following methods: a) Waypoint i Belongs to the starting point of a straight flight segment

[0019] b) Waypoints i End of a straight flight segment

[0020] (4) Calculate the waypoints using the following formula. n velocity vector: .

[0021] Optionally, based on the four-dimensional track, update the estimated arrival time of each waypoint, including: (1) During the arrival time interval [T i T i+1 Take evenly m The time points are as follows: ,in , ; (2) Calculate each using the following formula. Flight segment distance :

[0022] (3) Based on the segment distance, recalculate the segment flight time and estimated arrival time using the following formula: ; T i+1 =T i +t i .

[0023] Optionally, the loop calculation can be stopped based on the estimated arrival times of the old and new waypoints, including: The evaluation index is obtained through the following formula. ; judge E time (k) Is it less than a preset threshold? If E time (k) If the value is less than a preset threshold, the loop calculation terminates; otherwise, it continues. in, k This represents the number of loop iterations.

[0024] This invention provides an integrated method for four-dimensional trajectory generation and guidance in flight management systems. It achieves sequential computation of trajectory generation and guidance functions, ensuring high-precision tracking of the desired trajectory by the aircraft in both spatial and temporal dimensions, while reducing computational complexity and meeting airborne implementation requirements. The beneficial effects are: This invention employs an integrated design for trajectory generation and guidance, fully considering the coupling relationship between the two to avoid performance loss caused by decoupling design, significantly improving the spatial and temporal accuracy of trajectory tracking. Based on a fourth-order polynomial iterative fitting method, it ensures the trajectory smoothly passes through all waypoints, while continuously correcting the estimated arrival time through iterative optimization, improving temporal accuracy. Furthermore, it has low computational complexity, making it suitable for airborne implementation. The vector field guidance method, through the synergistic effect of convergence and propagation terms, can quickly guide the aircraft to converge to the desired trajectory while ensuring stable flight along the trajectory direction, exhibiting strong robustness to trajectory deviations. Linear constraints can be set to correct trajectory segments with excessive fluctuations, making the generated trajectory more consistent with aircraft flight characteristics, improving flight safety and comfort. The entire method has a clear flow, low engineering implementation difficulty, and strong compatibility, making it applicable to the upgrade and transformation of flight management systems for various fixed-wing aircraft. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 A schematic diagram of the data flow of the proposed method in the flight control system; Figure 2 A schematic diagram illustrating the integrated four-dimensional trajectory generation and guidance system; Figure 3 The result of track generation; Figure 4 For flight guidance results; Figure 5 The coordinates, speed, and constraints of the flight path points in the simulation example are shown. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0028] The features and illustrative embodiments of various aspects of the present invention will now be described in detail. Numerous specific details are set forth in the following detailed description to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that the invention may be practiced without requiring some of these specific details. The following description of embodiments is merely intended to provide a better understanding of the invention by illustrating examples of the invention. The invention is by no means limited to any specific setups and methods set forth below, but covers any improvements, substitutions, and modifications to structures, methods, and devices without departing from the spirit of the invention. Well-known structures and techniques are not shown in the drawings and the following description to avoid unnecessarily obscuring the invention.

[0029] In the description of this invention, it should be noted that the directions or positional relationships indicated by terms such as "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer" are based on the directions or positional relationships shown in the accompanying drawings and are only for the convenience of describing and simplifying the invention, and should not be construed as limiting the invention. Furthermore, the use of ordinal numbers (e.g., "first and second," etc.) is for distinguishing objects and is not limited to this order, and should not be construed as indicating or implying relative importance.

[0030] 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, encompassing both direct connection and indirect connection via an intermediate medium. Those skilled in the art can understand the specific meaning of these terms in this invention based on the specific circumstances.

[0031] It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other, and the various embodiments can be referenced and cited in each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0032] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0033] Specifically, see Figure 1 The diagram shows the data flow of the proposed method in the flight control system.

[0034] Taking the three-degree-of-freedom motion model of a fixed-wing aircraft as an example, its mathematical expression is as follows:

[0035] in, These are the coordinates of the aircraft. It is velocity, θ(t) is pitch angle, ψ(t) is yaw angle, v θ(t) is the pitch angular velocity, v ψ (t) is the yaw rate. a v (t) It refers to flight acceleration. The waypoints, waypoint speeds, and straight-line constraints in the simulation example are given as follows: Figure 5 As shown, the initial coordinates of the aircraft are [-200,0,0].

[0036] See Figure 2 As shown in the simulation embodiment, a four-dimensional trajectory generation and guidance integrated method for flight management systems includes the following steps: Step 1: Obtain the waypoints required for calculation ,in , n The number of waypoints; the speed corresponding to each waypoint is obtained. ,in ; Obtain the flight segment that needs to be set as a straight line; Calculate the segment distance, average segment speed, segment flight time, and estimated arrival time of waypoints as follows: (1) Calculate using the following formula 1,...,n-1 Segment distance:

[0037] (2) Calculate the flight segment using the following formula. 1,...,n-1 Average speed:

[0038] (3) Calculate the flight segment using the following formula. 1,...,n-1 Flight time:

[0039] (4) For waypoints The estimated arrival time of the waypoint is calculated using the following formula: T i =T i-1 +t i-1 T1=0 Step 2: Calculate the velocity vectors of the waypoints sequentially, including: (1) Calculate the velocity vector of track point 1 using the following formula:

[0040] (2) For waypoints When the waypoint i This is not a straight flight segment; the calculation is based on the direction and speed of adjacent waypoints.

[0041] in, , It is a unit vector in the direction of velocity.

[0042] (3) For waypoints When the waypoint i When the flight segment is a straight line, it can be calculated separately using the following methods: a) Waypoint i For routes originating from a straight segment, the calculation formula is as follows:

[0043] b) Waypoints i If it falls at the end of a straight flight segment, the calculation formula is as follows:

[0044] (4) Calculate the waypoints using the following formula. n velocity vector:

[0045] Step 3: Based on the waypoint coordinates and estimated arrival time, calculate and obtain the following in sequence. The piecewise polynomial coefficients of the trajectory on different coordinate axes are calculated using the following formula:

[0046] in, ; , , These are the polynomial coefficients of the trajectory on the x, y, and z coordinate axes, respectively. We obtain... Track function , , .

[0047] Step 4: Calculate sequentially using the track function The flight segment distances are as follows: (1) During the arrival time interval [T i T i+1 Take evenly m The time points are as follows: ,in , .

[0048] (2) Calculate each using the following formula. Flight segment distance :

[0049] (3) Based on the segment distance, recalculate the segment flight time and estimated arrival time using the following formula: ; T i+1 =T i +t i .

[0050] Step 5: Calculate the termination criteria for the end of the loop step to determine whether the loop calculation should stop, including: (1) The termination criterion for loop calculation can be calculated and obtained by the following formula:

[0051] in, k Represents the number of loops. E time (k) For evaluation indicators.

[0052] (2) Judgment E time (k) Is it less than the preset threshold?

[0053] a) E time (k) If the threshold is not met, proceed to steps 2, 3, and 4.

[0054] b) E time (k) If the threshold value is less than the preset threshold, the loop terminates and step 6 is executed.

[0055] Step 6: Obtain the aircraft's current coordinates and current time t ; Obtain the aircraft's current pitch angle θ(t), yaw angle ψ(t), and airspeed v(t); Obtain the propagation gain coefficient [k x , k y , k z ]; Obtain the proportional controller gain coefficient k θ k ψ and k a .

[0056] Step 7: Obtain the current time segment and track function, including: via T i <t<T i+1 Determine the condition by iterating through the time periods {1,…,n-1} in sequence to determine [T]. i ,T i+1 For each time period, select the corresponding trajectory function. , , .

[0057] Step 8: Calculate and obtain the trajectory function guiding vector field, including: (1) The propagation term of the vector field is calculated using the derivative of the trajectory function, as follows:

[0058] (2) Calculate the convergence term of the vector field using the aircraft's current coordinates, trajectory function, and propagation gain coefficient, as follows:

[0059] (3) The trajectory function guiding vector field is calculated and obtained using the following formula:

[0060] (4) The direction and velocity of the guiding vector field are calculated and obtained using the following formula:

[0061]

[0062] in, , , These are the guiding vector fields in x axis, y axis, z Reference direction of the axis The reference speed for guiding the vector field.

[0063] Step 9: Calculate flight guidance and control commands, pitch angular velocity v θ (t), yaw angular velocity v ψ (t), flight acceleration a v (t) ,Include: (1) The target pitch angle and yaw angle of the track guidance vector field are calculated using the following formulas:

[0064]

[0065] (2) The errors between the current attitude and the attitude required by the trajectory guidance vector field, and between the current speed and the speed required by the trajectory guidance vector field, are calculated using the following formulas:

[0066]

[0067]

[0068] (3) According to k θ , k ψ and k a The proportional controller gain parameter is used to calculate the flight guidance command using the following formula:

[0069]

[0070]

[0071] Step 10: Send flight guidance command v θ (t), v ψ (t), a v (t) Send the command to the aircraft autopilot to execute, and determine whether the mission is complete, using the following method: a) The current time t exceeds the maximum time T of the trajectory function. n Then the guidance task ends.

[0072] b) The current time t has not exceeded the maximum time T of the trajectory function. n If so, proceed to step 6.

[0073] Finally, the trajectory generation results for this simulation embodiment are as follows: Figure 3 As shown, the flight guidance results are as follows: Figure 4 As shown.

[0074] The above detailed embodiments are a description of the present invention. It should not be considered that the specific embodiments of the present invention are limited to these descriptions. For those skilled in the art, several simple deductions and substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the protection scope of the present invention.

Claims

1. A method for integrated four-dimensional trajectory generation and guidance in a flight management system, characterized in that, Includes the following steps: S1. Based on the preset track points and their speeds, obtain the estimated arrival time of each track point; S2. Based on the estimated arrival time of each track point, obtain the piecewise polynomial coefficients of each track on different coordinate axes to obtain the four-dimensional track. S3. Based on the four-dimensional track, update the estimated arrival time of each track point, and then update the polynomial coefficients again. Determine whether the loop calculation should stop based on the estimated arrival times of the old and new track points. If yes, proceed to S4; otherwise, proceed to S2. S4. According to the guidance cycle, determine the time segment and trajectory function to which the aircraft currently belongs. Based on the aircraft's current coordinates, trajectory function, current propagation gain coefficient, and derivative of the trajectory function, obtain the trajectory function guidance vector field. Based on the trajectory function guidance vector field, calculate the flight guidance control commands until the flight ends.

2. The integrated method for four-dimensional trajectory generation and guidance for flight management systems according to claim 1, characterized in that, Based on the estimated arrival time of each waypoint, the piecewise polynomial coefficients of each waypoint on different coordinate axes are obtained to obtain the four-dimensional waypoint, including: Using formula Obtain the piecewise polynomial coefficients of each track on the coordinate axes x, y and z; Obtain four-dimensional trajectory , , ; in, ; , , The tracks are respectively in x , y , z Polynomial coefficients on the axis; for T i For the first i Estimated arrival time of each waypoint, T i+1 =T i +t i T1=0, , n Number of waypoints t i For the first i Flight time for the segment; x i , y i , z i Indicates waypoints P i The coordinates; , , No. i The speed corresponding to each waypoint is x , y , z Velocity components on the axis.

3. The integrated method for four-dimensional trajectory generation and guidance for flight management systems according to claim 2, characterized in that, Obtain the trajectory function guiding vector field, including: (1) Calculate the propagation term of the vector field using the derivative of the trajectory function. ,as follows: (2) Using the aircraft's current coordinates Calculate the trajectory function, propagation gain coefficient, and convergence term of the vector field. ; (3) Through the formula , thus obtaining the trajectory function guiding vector field.

4. The integrated method for four-dimensional trajectory generation and guidance for flight management systems according to claim 3, characterized in that, Based on the trajectory function guidance vector field, calculate the flight guidance and control commands, including: Through formula and This allows us to obtain the direction and velocity of the guiding vector field. Through formula and Calculate the target pitch and yaw angles in the trajectory guidance vector field; Through formula , and Calculate the errors between the current attitude and the attitude required by the trajectory guidance vector field, and between the current velocity and the speed required by the trajectory guidance vector field; Based on the proportional controller gain parameters k θ , k ψ and k a Through formula , and Receive flight guidance instructions; in, , , These are the guiding vector fields in x axis, y axis, z Reference direction of the axis The reference speed for guiding the vector field.

5. The integrated method for four-dimensional trajectory generation and guidance for flight management systems according to claim 2, characterized in that, Based on preset waypoints and their speeds, obtain the estimated arrival time for each waypoint, including: (1) Calculate the first number using the following formula. Segment distance: (2) Calculate the flight segment using the following formula. Average speed: (3) Calculate the flight segment using the following formula. Flight time: (4) For waypoints The estimated arrival time of a waypoint can be calculated using the following formula: T i =T i-1 +t i-1 ,T1=0.

6. The integrated method for four-dimensional trajectory generation and guidance for flight management systems according to claim 5, characterized in that, Prior to S2, the method further includes: (1) For waypoints Calculate the velocity vector of waypoint 1 using the following formula: (2) For waypoints When the waypoint i This is not a straight flight segment; the calculation is based on the direction and speed of adjacent waypoints. in, , It is a unit vector in the direction of velocity; (3) For waypoints When the waypoint i When the flight segment is a straight line, it can be calculated separately using the following methods: a) Waypoint i Belongs to the starting point of a straight flight segment b) Waypoints i End of a straight flight segment (4) Calculate the waypoints using the following formula. n velocity vector: 。 7. The integrated method for four-dimensional trajectory generation and guidance in a flight management system according to claim 1, characterized in that, Based on the four-dimensional track, update the estimated arrival time of each waypoint, including: (1) During the arrival time interval [T i T i+1 Take evenly m The time points are as follows: ,in , ; (2) Calculate each using the following formula. Flight segment distance : (3) Based on the segment distance, recalculate the segment flight time and estimated arrival time using the following formula: ； T i+1 =T i +t i 。 8. The integrated method for four-dimensional trajectory generation and guidance in a flight management system according to claim 1, characterized in that, The loop calculation is stopped based on the estimated arrival times of the old and new waypoints, including: The evaluation index is obtained through the following formula. ; judge E time (k) Is it less than a preset threshold? If E time (k) If the value is less than a preset threshold, the loop calculation terminates; otherwise, it continues. in, k This represents the number of loop iterations.

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