Flight path planning method of aircraft based on inertial navigation

Abstract

The invention relates to an aircraft flight path planning method based on inertial navigation, and the method comprises the steps: obtaining the coordinates of M route points on the total flight path of an aircraft, the total flight path of the aircraft comprises the flight path of M + 1 segments, and each segment is provided with a plurality of sub-segments; constructing an independent variable of a target function according to an item representing a remaining voyage corresponding to a point on the track of the segment, an item representing a remaining voyage corresponding to a starting end point of the track of the target segment, and an item representing a remaining voyage corresponding to an ending end point of the track of the target segment; constructing the target function according to the independent variable of the target function, the item representing the coefficient of the segment and the item representing the primary function; according to the coordinates of the M waypoints, based on the inter-segment transition condition of the objective function, solving a total coefficient set including the coefficient set of each segment; and according to the objective function and the total coefficient set, determining a horizontal and vertical coordinate corresponding relation set of each segment so as to determine the track of each segment.

Description

Technical Field

[0001] This application belongs to the field of aircraft navigation technology, and more specifically relates to a method for flight path planning of aircraft based on inertial navigation. Background Technology

[0002] Currently, aircraft, such as low-altitude aircraft, are widely used in civil applications, including urban and intercity transportation. In some scenarios, aircraft need to sequentially reach various waypoints. For example, in intercity transportation, aircraft need to reach various waypoints in sequence to ultimately achieve mission objectives such as minimizing travel time or flight path.

[0003] How to plan the flight path of an aircraft based on multiple waypoints has become a technical problem that needs to be solved. Summary of the Invention

[0004] This application provides an inertial navigation-based aircraft trajectory planning method to solve the problem of how to plan the aircraft's trajectory based on multiple waypoints.

[0005] This application provides a method for flight path planning of an aircraft based on inertial navigation, the method comprising: Obtain the coordinates of M waypoints on the total flight path of the aircraft. The total flight path of the aircraft includes M+1 segments of the flight path, each segment having multiple sub-segments. The independent variables of the objective function are constructed based on the terms representing the remaining distances corresponding to points on the segmented track, the terms representing the remaining distances corresponding to the start and end points of the segmented track, and the terms representing the remaining distances corresponding to the end points of the segmented track. The objective function is also constructed based on the independent variables of the objective function, the terms representing the coefficients of the segments, and the terms representing the basis functions. Based on the coordinates of M waypoints and the inter-segment transition conditions based on the objective function, the total coefficient set including the coefficient set of each segment is solved. The coefficient set of each segment includes the coefficients corresponding to each sub-segment of the segment. Based on the objective function and the total coefficient set, the set of correspondences between the horizontal and vertical coordinates of each segment is determined to determine the trajectory of each segment. The set of correspondences between the horizontal and vertical coordinates of the target segment includes the correspondence between the horizontal and vertical coordinates of each sub-segment of the target segment. The correspondence between the horizontal and vertical coordinates of the target sub-segments of the target segment represents the relationship between the horizontal coordinate of the target point on the target sub-segment and the vertical coordinate of the target point on the target sub-segment. The target segment is any segment, the target sub-segment is any sub-segment of the target segment, and the target point on the target sub-segment is any point on the target sub-segment.

[0006] One possible implementation also includes: dividing the M+1 segments, wherein dividing the target segment includes: dividing the target segment into three equal parts to obtain three sub-segments of the target segment.

[0007] In one possible implementation, the remaining distance corresponding to a point on a segmented track is the product of the x-coordinate of the point on the segmented track and the Earth's radius.

[0008] In one possible implementation, the independent variables of the objective function are constructed based on the terms representing the remaining distance corresponding to points on the segmented track, the terms representing the remaining distance corresponding to the start and end points of the segmented track, and the terms representing the remaining distance corresponding to the end point of the segmented track: Construct a first remaining range difference term, wherein the first remaining range difference term is the term representing the remaining range corresponding to the point on the segmented track minus the term representing the remaining range corresponding to the start and end points of the segmented track; Construct a second remaining range difference term, wherein the second remaining range difference term is the term representing the remaining range corresponding to the end endpoint of the segmented track minus the term representing the remaining range corresponding to the start endpoint of the segmented track; Based on the first remaining range difference term and the second remaining range difference term, construct the independent variables of the objective function, where the independent variables of the objective function are the first remaining range difference term divided by the second remaining range difference term.

[0009] In one possible implementation, the objective function is: Where p(u) represents the objective function, u Let d represent the independent variable of the objective function. k,i+j Φ represents the piecewise coefficient. i Let j represent the basis function, and j represent the sub-segment number of the segment.

[0010] In one possible implementation, the basis functions for different values ​​of i are: One possible implementation also includes: A flight path model for the aircraft is established based on the terms representing the aircraft's speed, heading angle, altitude, latitude, longitude, Earth's radius, turning acceleration perpendicular to the velocity direction, gravitational acceleration, and disturbances caused by the Earth's non-uniform shape, mass distribution, and rotation.

[0011] In one possible implementation, based on the coordinates of M waypoints and the inter-segment transition conditions based on the objective function, the total coefficient set, including the coefficient set of each segment, is solved as follows: Based on the coordinates of M waypoints and the inter-segment transition conditions based on the objective function, a subset of coefficients in the total coefficient set is solved. Using the Tornado algorithm, with the goal of minimizing the total flight time of the aircraft, we solve for another part of the coefficients in the total coefficient set, excluding the aforementioned part of the coefficients.

[0012] In one possible implementation, the individuals in the Tornado algorithm are a set of values ​​that could be used as the other part of the coefficients, and the value of the individual corresponds to the total flight time of the aircraft.

[0013] In one possible implementation, the aircraft is a low-altitude aircraft.

[0014] Beneficial effects: The method provided in this application embodiment enables the planning of an aircraft's trajectory based on multiple waypoints.

[0015] The method provided in this application solves for the coefficient set of each segment, that is, the coefficients corresponding to each sub-segment of each segment. Based on the coefficients corresponding to each sub-segment of each segment, the trajectory of each sub-segment of the aircraft's total trajectory can be determined. The trajectory is planned at a more refined granularity, that is, sub-segments. Finally, the total trajectory of the aircraft is composed of the trajectories of each sub-segment of each segment.

[0016] The method provided in this application uses coefficients for corresponding segments to enable smoother transitions between the trajectory of a corresponding segment and other segments, as well as between the trajectories of two adjacent sub-segments of a corresponding segment. This improves the smoothness of the planned aircraft's overall trajectory. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of this specification or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings.

[0018] Figure 1 This is a flowchart illustrating the flight path planning method for aircraft based on inertial navigation provided in this application embodiment. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. It should be noted that, unless otherwise specified, the implementation methods and features in the implementation methods in this disclosure can be combined, separated, interchanged, and / or rearranged. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0020] The terminology used herein is for the purpose of describing particular embodiments and is not intended to be limiting. As used herein, unless the context clearly indicates otherwise, the singular forms “a” and “the” are intended to include the plural forms as well. Furthermore, when the terms “comprising” and / or “including” and variations thereof are used in this specification, it indicates the presence of the stated features, integrals, steps, operations, parts, components, and / or groups thereof, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, parts, components, and / or groups thereof. It should also be noted that, as used herein, the terms “substantially,” “about,” and other similar terms are used as approximate terms rather than as terms of degree, thus explaining the inherent biases in measurements, calculated values, and / or provided values ​​that would be recognized by one of ordinary skill in the art.

[0021] refer to Figure 1 It shows a flowchart of the flight path planning method for aircraft based on inertial navigation provided in the embodiments of this application.

[0022] The flight path planning method for aircraft based on inertial navigation provided in this application includes steps S101-S104.

[0023] In step S101, the coordinates of M waypoints on the total flight path of the aircraft are obtained. The total flight path of the aircraft includes M+1 segments of the flight path, and each segment of the M+1 segments has multiple sub-segments. In step S102, the independent variables of the objective function are constructed based on the terms representing the remaining distance corresponding to the points on the segmented track, the terms representing the remaining distance corresponding to the start endpoint of the segmented track, and the terms representing the remaining distance corresponding to the end endpoint of the segmented track. The objective function is also constructed based on the independent variables of the objective function, the terms representing the coefficients of the segments, and the terms representing the basis functions. In step S103, based on the coordinates of the M waypoints and the inter-segment transition conditions based on the objective function, the total coefficient set including the coefficient set of each segment is solved, wherein the coefficient set of the segment includes: the coefficients corresponding to each sub-segment of the segment; In step S104, based on the objective function and the total coefficient set, the set of correspondences between the horizontal and vertical coordinates of each segment is determined to determine the trajectory of each segment. The set of correspondences between the horizontal and vertical coordinates of the target segment includes the correspondence between the horizontal and vertical coordinates of each sub-segment of the target segment. The correspondence between the horizontal and vertical coordinates of the target sub-segments of the target segment represents the relationship between the horizontal coordinate of the target point and the vertical coordinate of the target point on the trajectory of the target sub-segment in the trajectory of the target segment. The target segment is any segment among M+1 segments, the target sub-segment is any sub-segment of the target segment, and the target point is any point on the target sub-segment.

[0024] Before the coefficient set of each segment is solved in step S103, the coefficient set of each segment is an unknown.

[0025] In this embodiment of the application, an aircraft trajectory model is established: (1) in, V , ψ , h , and i These represent the aircraft's speed, heading angle, altitude, latitude, and longitude, respectively. R For the Earth's radius, The turning acceleration is perpendicular to the velocity direction. g It represents the acceleration due to Earth's gravity. This refers to disturbances caused by the Earth's non-uniform shape and mass distribution, as well as its rotation. t Indicates time.

[0026] In this embodiment of the application, a function relating to longitude and latitude is designed: (2) According to equation (1), using Divide by This yields the heading in terms of latitude: (3) (4) At this point, as long as you know , and Then it can be calculated in real time. Substituting into equation (1), the required motor acceleration can be calculated. .

[0027] The latitude and longitude of the aircraft's location are: (5) In formula (5), the subscript 0 represents the initial state, and the coordinates of the aircraft represent the position of the aircraft. x,y )express, x The x-coordinate representing the aircraft's position. y The vertical coordinate representing the aircraft's position. x The geocentric angle corresponding to the distance from the aircraft's position to the starting point. y The heading angle is the angle from the starting point to the position of the aircraft.

[0028] It should be noted that, in the embodiments of this application, a point on an aircraft's flight path can refer to a location. The aircraft will pass over this point when flying along the flight path.

[0029] The starting point, ending point, and waypoints on the aircraft's total trajectory are all given points.

[0030] In this embodiment of the application, the waypoints on the total flight path of the aircraft are located between the starting point and the ending point of the total flight path of the aircraft. The starting point, the ending point, and each waypoint on the total flight path of the aircraft are respectively used as nodes on the total flight path of the aircraft. There are M+2 nodes on the total flight path of the aircraft.

[0031] Each of the M+2 nodes on the aircraft's total flight path corresponds to the remaining flight distance.

[0032] (6) in, This represents the remaining range corresponding to a point on the aircraft's flight path. R is the Earth's radius. In this context, x represents the x-coordinate of a point on the aircraft's flight path.

[0033] In this embodiment of the application, for a point on the aircraft's track, the horizontal coordinate of the point can be the geocentric angle corresponding to the distance from the point to the starting point of the aircraft's total track, and the vertical coordinate of the point can be the heading angle from the starting point of the aircraft's total track to the point.

[0034] The first node on the aircraft's total trajectory, i.e., the starting point of the aircraft's total trajectory, and the last node on the aircraft's total trajectory, i.e., the ending point of the aircraft's total trajectory, correspond to respectively , The subscript f indicates the terminal state.

[0035] This represents the remaining distance corresponding to the first node on the aircraft's total trajectory, which is the starting point of the aircraft's total trajectory.

[0036] These represent the remaining distance between the waypoints on the aircraft's total track and the last waypoint on the aircraft's total track.

[0037] This represents the remaining distance corresponding to the last node on the aircraft's total trajectory, which is the end point of the aircraft's total trajectory.

[0038] In this embodiment of the application, there are M waypoints on the total flight path of the aircraft. The two endpoints of the flight path of each segment in the M+1 segments of the total flight path are two adjacent nodes in the node set of the M waypoints, which include the starting point of the total flight path, the ending point of the total flight path of the aircraft, and the starting point of the total flight path of the aircraft.

[0039] Once the trajectory of each of the M+1 segments of the aircraft's total trajectory is determined, the aircraft's total trajectory can be obtained. That is, the aircraft's total trajectory is composed of the trajectories of each of the M+1 segments of its total trajectory. The aircraft flies according to the total trajectory, from its starting point to its ending point. While flying according to the total trajectory, the aircraft sequentially follows the trajectories of each of the M+1 segments of its total trajectory.

[0040] For one of the M+1 segments of the aircraft's total trajectory, the two endpoints of the trajectory of this segment are the start endpoint and the end endpoint of the trajectory of this segment. During the flight of the aircraft according to the trajectory of this segment, the aircraft flies from the start endpoint of the segment to the end endpoint of the segment.

[0041] Each of the M+1 segments of the aircraft's total trajectory has multiple sub-segments. The remaining distances corresponding to the two endpoints of the trajectory of segment k in the M+1 segments of the aircraft's total trajectory are... The remaining distance corresponding to the starting and ending points of the track segment k. The remaining distance corresponding to the end point of the trajectory of segment k. .

[0042] In one possible implementation, the method further includes: dividing the M+1 segments, wherein dividing the target segment includes: dividing the target segment into three equal parts to obtain three sub-segments of the target segment, wherein the target segment is any one of the M+1 segments of the aircraft's total trajectory.

[0043] The starting endpoint of the first sub-segment of the target segment is the starting endpoint of the target segment. The ending endpoint of the first sub-segment of the target segment is the starting endpoint of the second sub-segment of the target segment. The ending endpoint of the second sub-segment of the target segment is the starting endpoint of the third sub-segment of the target segment. The ending endpoint of the third sub-segment of the target segment is the ending endpoint of the target segment.

[0044] The target segment has four endpoints: the starting endpoint of the target segment, the ending endpoint of the target segment, and the two endpoints between the starting and ending endpoints of the target segment.

[0045] Dividing the target segment into three equal parts to obtain the three sub-segments of the target segment means that the difference between the x-coordinates of any two adjacent endpoints in the target segment is the same, that is, the remaining range corresponding to any two adjacent endpoints in the target segment is the same.

[0046] In one possible implementation, the remaining distance corresponding to a point on a segmented track is the product of the x-coordinate of the point on the segmented track and the Earth's radius.

[0047] In one possible implementation, the independent variables of the objective function are constructed based on the terms representing the remaining distance corresponding to points on the segmented track, the terms representing the remaining distance corresponding to the start and end points of the segmented track, and the terms representing the remaining distance corresponding to the end points of the segmented track. This includes: constructing a first remaining distance difference term, where the first remaining distance difference term is the term representing the remaining distance corresponding to points on the segmented track minus the term representing the remaining distance corresponding to the start and end points of the segmented track; constructing a second remaining distance difference term, where the second remaining distance difference term is the term representing the remaining distance corresponding to the end point of the segmented track minus the term representing the remaining distance corresponding to the start and end points of the segmented track; and constructing the independent variables of the objective function based on the first and second remaining distance difference terms, where the independent variables of the objective function are the first remaining distance difference term divided by the second remaining distance difference term.

[0048] The independent variable of the objective function can be expressed as: (7) Where u is the independent variable of the objective function, This represents the remaining distance corresponding to a point on the track of segment k. This represents the remaining distance corresponding to the starting and ending points of the trajectory of segment k. This represents the remaining distance corresponding to the end point of the trajectory of segment k. Segment k can be any one of the M+1 segments of the aircraft's total trajectory.

[0049] The remaining distance for a point on the track of segment k is the product of the x-coordinate of the point on the track of segment k and the Earth's radius. The remaining distance for the starting and ending points of the track of segment k is the product of the x-coordinate of the starting and ending points of the track of segment k and the Earth's radius. The remaining distance for the ending point of the track of segment k is the product of the x-coordinate of the ending point of the track of segment k and the Earth's radius.

[0050] In one possible implementation, the objective function is: in, p ( u ) represents the objective function. u The independent variable represents the objective function. The coefficients representing the segments, Let j represent the basis function, and j represent the sub-segment number of the segment.

[0051] Here, j can be any one of the sets including 0, 1, 2. The number of segments is M+1, and k can be any one of the sets including 0, 1, 2...M.

[0052] When k takes one of the sets including 0, 1, 2...M, p ( u This can be equivalent to a cubic B-spline function. i is the index of the cubic B-spline function used to distinguish the terms involved in the summation.

[0053] For subsegment j of segment k, All of these are coefficients corresponding to sub-segment j of segment k.

[0054] p(u) takes the value of the ordinate of a point on subsegment j of segment k.

[0055] As an example, j is 0 when calculating the ordinate of a point in the first sub-segment of segment k, j is 1 when calculating the ordinate of a point in the second sub-segment of segment k, and j is 2 when calculating the ordinate of a point in the third sub-segment of segment k.

[0056] As an example, when calculating the ordinate of a point in the first sub-segment of the first segment, j is 0 and k is 0; when calculating the ordinate of a point in the second sub-segment of the first segment, j is 1 and k is 0; and when calculating the ordinate of a point in the third sub-segment of the first segment, j is 2 and k is 0.

[0057] The value of u is calculated based on the x-coordinate of the point on the track of sub-segment j of segment k, the Earth radius R, and formula (7). When calculating the value of u, the formula (7) contains... The remaining distance for a point on the track of sub-segment j of segment k is the product of the x-coordinate of the point on the track of sub-segment j of segment k and the Earth's radius R.

[0058] Each coefficient of segment k corresponds to a sub-segment of segment k. All are coefficients of piecewise k. Where, when j is 0, The coefficient corresponding to the first sub-segment of segment k. These are the coefficients corresponding to the first sub-segment of segment k. When j is 1, The coefficient corresponding to the second sub-segment of segment k. These are the coefficients corresponding to the second segment of segment k. When j is 2... This is the coefficient corresponding to the 3rd segment of segment k. These are the coefficients corresponding to the third sub-segment of segment k.

[0059] In the embodiments of this application, the independent variable of the basis function is also u.

[0060] In one possible implementation, the basis functions for different values ​​of i are: In this embodiment of the application, the inter-segment transition condition includes: function y = p ( x The continuity of the first and second derivatives.

[0061] The starting point of the aircraft's total flight path This indicates that the final destination of the aircraft's total flight path utilizes... This indicates that the i-th waypoint on the aircraft's total track, between the origin and the destination, utilizes... The x-coordinate of the starting point of the aircraft's total trajectory is indicated. The ordinate of the starting point of the aircraft's total trajectory is The x-coordinate of the end point of the aircraft's total trajectory is The ordinate of the end point of the aircraft's total flight path is The x-coordinate of the i-th waypoint is The ordinate of the i-th waypoint is .

[0062] The inter-segment transition conditions based on the objective function can be obtained using the following (4) M +2) equations represent: In this embodiment, the aircraft's total trajectory consists of M+1 segments. Each segment has 6 coefficients. All coefficients are denoted as... .

[0063] k=0,1...,M.

[0064] Inter-segment transition conditions serve as constraints for the solution. In step S103, the coefficient set for each segment can be solved based on the inter-segment transition conditions, with the objective of minimizing the total flight distance (i.e., the length of the aircraft's total trajectory) or the total flight time. The total flight time is the time it takes for the aircraft to fly from the starting point to the destination along its total trajectory.

[0065] In step S103, any given optimization objective and constraints can be used. Algorithms that optimize multiple variables, such as the Grey Wolf Algorithm and the Particle Swarm Optimization Algorithm, aim to minimize the total flight distance (i.e., the length of the aircraft's total trajectory) or the total flight time (i.e., the time taken to fly from the starting point to the ending point of the aircraft's total trajectory). Based on the transition conditions between segments, the total set of coefficients is solved.

[0066] The total set of coefficients obtained by solving satisfies the transition conditions between segments.

[0067] For the target segment, the coefficient set of the target segment includes the coefficients corresponding to each sub-segment of the target segment. Each coefficient in the coefficient set of the target segment corresponds to a sub-segment of the target segment.

[0068] The target segment is any one of the M+1 segments of the aircraft's total trajectory.

[0069] The coefficient set of the target segment includes: the coefficient corresponding to the first sub-segment of the target segment, the coefficient corresponding to the second sub-segment of the target segment, and the coefficient corresponding to every three sub-segments of the target segment.

[0070] In this embodiment of the application, in step S104, the set of correspondences between the horizontal and vertical coordinates of each segment is determined according to the objective function and the total set of coefficients, so as to determine the trajectory of each segment.

[0071] The total trajectory of an aircraft consists of M+1 segments of the total trajectory of the aircraft.

[0072] For a target segment, its track is composed of the tracks of all its sub-segments. For a target sub-segment of the target segment, its track is determined based on the correspondence between its horizontal and vertical coordinates. After determining the correspondence between the horizontal and vertical coordinates of the target sub-segment, its track can be obtained.

[0073] The target segment is any one of the M+1 segments of the aircraft's total trajectory. The target sub-segment of the target segment can be any sub-segment of the target segment.

[0074] Step S104, determining the set of horizontal and vertical coordinate correspondences for each segment based on the objective function and the total coefficient set, includes: for a sub-segment j of segment k, determining the horizontal and vertical coordinate correspondences of sub-segment j of segment k based on the coefficients corresponding to sub-segment j in the coefficient set of segment k in the total coefficient set. Specifically, the horizontal and vertical coordinate correspondences of the first sub-segment of segment k can be determined based on the coefficients corresponding to the first sub-segment of segment k and the objective function. The horizontal and vertical coordinate correspondences of the second sub-segment j of segment k can be determined based on the coefficients corresponding to the second sub-segment of segment k and the objective function. The horizontal and vertical coordinate correspondences of the third sub-segment of segment k can be determined based on the coefficients corresponding to the third sub-segment of segment k and the objective function.

[0075] Here, segment k can be any one of the M+1 segments of the aircraft's total trajectory, and sub-segment j can be any one of the sub-segments of segment k.

[0076] Based on the coefficients and objective function corresponding to the j-th sub-segment of segment k, the principle for determining the correspondence between the horizontal and vertical coordinates of sub-segment j of segment k is as follows: The vertical coordinate of a point on sub-segment j of segment k is... Based on the x-coordinates of points on sub-segment j of segment k. The value of u is the x-coordinate of the point on the j-th sub-segment of segment k. The value of u is calculated, and based on the calculated value of u, the coefficient corresponding to the j-th sub-segment of segment k, and the objective function, the y-coordinate of the point on the j-th sub-segment of segment k can be calculated. The value of is the ordinate of the point on the j-th sub-segment of segment k. Therefore, based on the coefficient corresponding to the j-th sub-segment of segment k, the correspondence between the horizontal and vertical coordinates of the sub-segment j of segment k can be determined.

[0077] In one possible implementation, based on the coordinates of M waypoints and the inter-segment transition conditions based on the objective function, the total coefficient set including the coefficient set of each segment is solved. This includes: solving a portion of the coefficients in the total coefficient set based on the coordinates of M waypoints and the inter-segment transition conditions based on the objective function; and using the Tornado algorithm, with the goal of minimizing the total flight time of the aircraft, solving for another portion of the coefficients in the total coefficient set besides this portion.

[0078] Solving the above (4M+2) equations yields a subset of the coefficients in the total coefficient set, namely (4M+2) coefficients. These (4M+2) coefficients include: k =0,1…, M -1 as well as k = M time .in, k =0,1…, M -1 include: k =0 , k =1 … k = M -1 .

[0079] The Tornado algorithm is used to minimize the total flight time of the aircraft. It solves for the remaining coefficients in the total coefficient set, namely (2M+4) coefficients obtained by subtracting (4M+2) from (M+1) - (4M+2). When using the Tornado algorithm, each individual coefficient represents a set of possible values, and the value of each individual corresponds to the total flight time of the aircraft.

[0080] In one possible implementation, the individuals in the Tornado Algorithm are a set of values ​​that could be used as another set of coefficients, and the value of an individual in the Tornado Algorithm corresponds to the total flight time of the aircraft.

[0081] The following describes the process of using the Tornado algorithm to solve for the coefficients in the total coefficient set other than the specified set of coefficients, with the goal of minimizing the total flight time of the aircraft.

[0082] Population initialization is performed to obtain the initial values ​​for each individual in the population, including: setting the total number of storms generated in the atmosphere to n; setting the number of thunderstorms to... n t And set the number of tornadoes to n o , n to = nt + n o Set the number of storms to n ω , n = n to + n ω The population consists of n individuals, each with a randomly generated initial value and a dimension of 2. M +4; Group matrix Y for: in, d To optimize the dimension of the variable, i.e. (2) M +4). Individual y i ( i =1, 2…, n It could be a storm, thunderstorm, or tornado; Set up individuals i The value is fit i The value vector of the group, corresponding to the total flight time of the aircraft, is represented as: Perform multiple iterations, where the t-th iteration includes: Step 1, the storm evolves into a tornado, update. n ω The location of the storm; Step 2, the storm evolves into a thunderstorm, update. n to The location of the storm; Step 3, the thunderstorm evolved into a tornado, update. n to The location of the thunderstorm; Step 4: During the evolution of the storm, its location may change randomly; update. n ω The location of the storm; Step 5, the random process of storms forming thunderstorms, update. n to The location of the storm.

[0083] In step 1, For i=1 to n ω in, Indicates the first i The current position vector of a tornado in generation t. In step 2, For i=1 to n to Forj=1 to In step 3, For i=1 to n to in, In Indicates the direction of a randomly selected thunderstorm: In step 4, For i=1 to n ω ; Step 5, For i=1 to n to Forj=1 to For large-scale atmospheric turbulence that does not move in a straight line, a three-force equilibrium is formed between the Coriolis force, centrifugal force, and pressure gradient force. The gradient storm velocity that produces thunderstorms and tornadoes is: in, i =1, 2…, n ω . t Represents the storm iteration number. It is the new velocity vector of the i-th storm. It is the first i The current velocity vector of the sub-storm, rand It is a random number between [0, 1]. rand A value <0.5 indicates the storm's movement is in the Northern Hemisphere, while a value >0.5 indicates the storm's movement is in the Southern Hemisphere. η = 0.73 is the contraction factor. Other parameters are as follows: in, T represent t The maximum number of iteration indices.

[0084] in, br = . d 1 is a random integer, equal to +1 or -1. oh r It's weight. oh max =4.0, oh min =1.0.

[0085] Where Ω is the Earth's rotational angular velocity.

[0086] in, It is the current position vector of the tornado at a random index. It is the position vector of the storm. g = round ( n o · rand ) is the random index number of the tornado.

[0087] velocity vector Subject to the following constraints: Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0088] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented in hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0089] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this application. It should be understood that the above description is only a specific embodiment of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A trajectory planning method for aircraft based on inertial navigation, characterized in that: The method includes: Obtain the coordinates of M waypoints on the total flight path of the aircraft. The total flight path of the aircraft includes M+1 segments of the flight path, each segment having multiple sub-segments. The independent variables of the objective function are constructed based on the terms representing the remaining distances corresponding to points on the segmented track, the terms representing the remaining distances corresponding to the start and end points of the segmented track, and the terms representing the remaining distances corresponding to the end points of the segmented track. The objective function is also constructed based on the independent variables of the objective function, the terms representing the coefficients of the segments, and the terms representing the basis functions. Based on the coordinates of M waypoints and the inter-segment transition conditions based on the objective function, the total coefficient set including the coefficient set of each segment is solved. The coefficient set of each segment includes the coefficients corresponding to each sub-segment of the segment. Based on the objective function and the total coefficient set, the set of correspondences between the horizontal and vertical coordinates of each segment is determined to determine the trajectory of each segment. The set of correspondences between the horizontal and vertical coordinates of the target segment includes the correspondences between the horizontal and vertical coordinates of each sub-segment of the target segment. The correspondences between the horizontal and vertical coordinates of the target sub-segments of the target segment represent the relationship between the horizontal coordinate of the target point and the vertical coordinate of the target point on the trajectory of the target sub-segment in the trajectory of the target segment. The target segment is any segment, the target sub-segment is any sub-segment of the target segment, and the target point is any point on the target sub-segment.

2. The method according to claim 1, characterized in that: The method further includes: The M+1 segments are divided, wherein dividing the target segment includes dividing the target segment into three equal parts to obtain three sub-segments of the target segment.

3. The method according to claim 1, characterized in that: The remaining distance for a point on a segmented track is the product of the x-coordinate of the point on the segmented track and the Earth's radius.

4. The method according to claim 1, characterized in that: Based on the terms representing the remaining distance corresponding to points on the segmented track, the terms representing the remaining distance corresponding to the start and end points of the segmented track, and the terms representing the remaining distance corresponding to the end point of the segmented track, the independent variables of the objective function are constructed as follows: Construct a first remaining range difference term, wherein the first remaining range difference term is the term representing the remaining range corresponding to the point on the segmented track minus the term representing the remaining range corresponding to the start and end points of the segmented track; Construct a second remaining range difference term, wherein the second remaining range difference term is the term representing the remaining range corresponding to the end endpoint of the segmented track minus the term representing the remaining range corresponding to the start endpoint of the segmented track; Based on the first remaining range difference term and the second remaining range difference term, construct the independent variables of the objective function, where the independent variables of the objective function are the first remaining range difference term divided by the second remaining range difference term.

5. The method according to claim 1, characterized in that: The objective function is: Where p(u) represents the objective function, u The independent variable represents the objective function. The coefficients representing the segments, Let j represent the basis function, and j represent the sub-segment number of the segment.

6. The method according to claim 5, characterized in that: The basis functions for different values ​​of i are: 。 7. The method according to claim 1, characterized in that: The method further includes: A flight path model for the aircraft is established based on the terms representing the aircraft's speed, heading angle, altitude, latitude, longitude, Earth's radius, turning acceleration perpendicular to the velocity direction, gravitational acceleration, and disturbances caused by the Earth's non-uniform shape, mass distribution, and rotation.

8. The method according to claim 1, characterized in that: Based on the coordinates of M waypoints and the inter-segment transition conditions according to the objective function, the total coefficient set, including the coefficient set of each segment, is calculated as follows: Based on the coordinates of M waypoints and the inter-segment transition conditions based on the objective function, a subset of coefficients in the total coefficient set is solved. Using the Tornado algorithm, with the goal of minimizing the total flight time of the aircraft, another part of the coefficients in the total coefficient set is solved, in addition to the aforementioned part of the coefficients.

9. The method according to claim 8, characterized in that: The individual in the Tornado Algorithm is a set of values ​​that can be used as the other part of the coefficients, and the value of the individual in the Tornado Algorithm corresponds to the total flight time of the aircraft.

10. The method according to any one of claims 1-9, characterized in that: The aircraft in question is a low-altitude aircraft.

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