A method for calculating a route point under different turning modes of a route

Abstract

The application provides a method for calculating the coordinates of a waypoint in different turning modes, which comprises the following steps: obtaining the turning mode, heading, flight time, the heading of the previous waypoint and the next waypoint of the waypoint to be calculated, and judging whether the previous waypoint of the waypoint to be calculated is the first waypoint of the route; if the previous waypoint of the waypoint to be calculated is the first waypoint of the route, calculating the coordinates of the waypoint to be calculated in different turning modes; if the previous waypoint of the waypoint to be calculated is not the first waypoint of the route, calculating the center of the arc and the coordinates of the exit point of the previous turning arc of the waypoint to be calculated; and then calculating the coordinates of the waypoint to be calculated in the modes of the straight line turning, the turning around the point, the turning towards the point and the turning on the point. The application calculates the coordinates of the waypoint according to the turning mode, the heading and the flight time of the waypoint to be calculated, and solves the problem of the route planning and production in the case that the coordinates of the waypoint are unknown.

Description

Technical Field

[0001] This invention relates to a method for calculating route extension points, and more particularly to a method for calculating route extension points under different turning patterns at waypoints. Background Technology

[0002] Airport control towers and other command systems frequently display pre-planned flight path information for aircraft. Before flight, aircraft also need to confirm their flight path on their onboard navigation equipment. The flight path includes multiple waypoints, segments (straight sections), turns, and directional arrows at the end of the path. Each turn is determined by its entry point (starting point), center point, exit point (leveling point), and direction. Each segment on the flight path is tangent to the adjacent turn. After reaching a waypoint, the aircraft must turn to align with the next waypoint. Turning methods include approaching a point, heading towards a point, turning around a point, and straight-line turning. A point-to-point turn is when the aircraft flies past a waypoint before turning towards the next waypoint; in this case, the waypoint itself is the entry point of the turn arc. A point-around turn is when the aircraft does not fly directly over the point but uses that point as the center of the turn arc. A point-to-point turn is when the aircraft has already completed the turn while flying past the waypoint; the waypoint is the exit point of the turn arc. For straight turns, it is not necessary to draw a turn arc; in this case, the radius of the turn arc can be considered to be 0, and the entry point, center, and exit point of the turn arc all coincide.

[0003] The heading of a waypoint on a flight path refers to the angle required to rotate clockwise from the origin of the flight segment containing the waypoint, with due north as the starting axis, until it coincides with the flight segment. When a waypoint is used for a point-around turn, since the waypoint is the center of the turning arc and not on the flight segment, the heading of the entry point of the turning arc is taken as the heading of the waypoint. That is, the heading of a waypoint is the same for both point-around and point-intercept turns: it is the angle between the line connecting the exit point of the previous turning arc and the entry point of the current turning arc, and due north, regardless of the next turning arc. Conversely, the heading for a point-to-point turn is the angle between the line connecting the exit point of the current turning arc and the entry point of the next turning arc, and due north, regardless of the previous turning arc.

[0004] Most existing route planning and drawing methods automatically calculate each turning arc and connect them to generate a great circle route given data such as waypoints and turning methods. However, during route planning, there may be situations where the coordinates of waypoints to be added are unknown, the flight time of known segments is known, and the turning methods and headings of other waypoints are also known. In such cases, routes are dynamically generated. How to deduce the coordinates of unknown waypoints in these situations is a shortcoming that existing technologies have not been able to solve. Summary of the Invention

[0005] Purpose of the invention: The technical problem to be solved by the present invention is to provide a method for calculating the route push point under different turning methods of waypoints, in order to overcome the shortcomings of the existing technology.

[0006] To address the aforementioned technical problems, this invention discloses a method for calculating route extension points under different turning modes at waypoints, comprising the following steps:

[0007] Step 1: Obtain the turning mode, heading, and flight time of the waypoint (i.e., the launch point) of the aircraft to be calculated; obtain the heading and coordinates of the previous waypoint; obtain the heading and coordinates of the next waypoint; and obtain unified speed and turning bank angle data for the launch point, the previous waypoint, and the next waypoint. Based on the above data, calculate the flight distance and turning radius of the launch point, that is, calculate the flight distance L of the launch point based on the flight time T and speed V, as follows:

[0008] L = V × T

[0009] Wherein, the flight time T at the launch point is the time it takes for the aircraft to fly from the exit point of a turn arc on the launch point to the entry point of the turn arc on the launch point, and the flight distance L at the launch point is the distance from the exit point of a turn arc on the launch point to the entry point of the turn arc on the launch point.

[0010] The turning radius R is calculated based on the launch point velocity V and the turning slope B, as follows:

[0011] R = V 2 / (gtan(B))

[0012] Where g is the acceleration due to gravity, the velocity and gradient of the waypoint above and below the launch point are the same as those of the launch point, that is, the turning radius of the launch point, the waypoint above the launch point, and the waypoint below the launch point are the same.

[0013] Step 2: Determine whether the previous waypoint of the launch point is the starting point of the route. If so, calculate the coordinates of the entry point of the turning arc where the launch point is located based on the coordinates of the starting point of the route and the heading of the launch point, and calculate the coordinates of the launch point through Step 4. Otherwise, proceed to Step 3.

[0014] The method for calculating the coordinates of the entry point of the turning arc where the exit point is located includes:

[0015] X t1 =X p +L×cos(π / 2-C t1 )

[0016] Y t1 =Y p +L×sin(π / 2-C t1 )

[0017] Among them, (X) p ,Y pC represents the coordinates of the starting point of the flight path. t1 The heading of the entry point of the turning arc where the launch point is located is given by the coordinates of the entry point of the turning arc where the launch point is located (X). t1 ,Y t1 ).

[0018] Step 3: Based on the coordinates and heading of a waypoint at the launch point and the heading of the launch point, calculate the center of a turning arc at the launch point and the coordinates of the exit point under different turning methods, and then proceed to Step 4.

[0019] The calculation of the center of a turning arc at the exit point under different turning modes and the coordinates of the exit point specifically includes: based on the coordinates of a waypoint at the exit point (X... p ,Y p ), heading C p 1. Heading C at the pushback point; 2. Heading C at the entry point of the turn arc where the pushback point is located. t1 And the center (X) of the turning arc at the point derived from the calculation of the turning radius R in step 1. p2 ,Y p2 ) and exit point (X) p3 ,Y p3 The method is as follows:

[0020] Step 3-1, determine the turning direction D of the waypoint above the launch point. p When π > C p -C>0 or CC p When ≥π, the turning direction D of the previous waypoint p For counterclockwise rotation, when 0 ≤ CC p <π or C p When -C≥π, the turning direction at the previous waypoint is D. p Clockwise, where C p Heading to the previous waypoint;

[0021] Step 3-2: Determine whether the waypoint above the exit point is the end point of the route and whether the exit point is a turning point. If the waypoint above the exit point is not the end point of the route and the exit point is a turning point, proceed to step 4; otherwise, proceed to step 3-3.

[0022] Step 3-3: Determine the turning mode of the waypoint at the exit point, and perform the following calculations based on the turning mode:

[0023] When the previous waypoint is a turning point, deduce the center coordinates (X) of the turning arc at that point. p2 ,Y p2 ) and the coordinates of the turning exit point (X p3 ,Y p3 The calculation method is as follows:

[0024] X p2 =Xp +R×cos(θ)

[0025] Y p2 =Y p +R×sin(θ)

[0026] X p3 =X p2 +R×cos(α)

[0027] Y p3 =Y p2 +R×sin(α)

[0028] Among them, the turning direction D at the previous waypoint p When the rotation is counterclockwise, θ is π-C p α is -C t1 The turning direction at the previous waypoint, D. p When the rotation is clockwise, θ is -C. p α is π-C t1 ;

[0029] When the ejection point is the pressure point or a turning point, C t1 That is, C.

[0030] When the previous route involved a turn around a point, the coordinates (X) of the previous route point can be derived. p ,Y p That is, the coordinates (X) of the center of the arc of the turning point at that point. p2 ,Y p2 ), coordinates of the turning exit point (X p3 ,Y p3 The calculation method is the same as that used when the previous waypoint is a turning point.

[0031] When the previous route turned towards the point, the coordinates (X) of the previous route point can be derived. p ,Y p That is, the coordinates of the turning and exit point (X). p3 ,Y p3 ), and deduce the center coordinates (X) of the turning arc at point. p2 ,Y p2 ) by the coordinates of the exit point (X p3 ,Y p3 The calculation method is as follows:

[0032] X p2 =X p3 -R×cos(α)

[0033] Y p2 =Y p3 -R×sin(α)

[0034] The value of α is the same as the value when the previous waypoint is a turning point;

[0035] Steps 3-4: Calculate the coordinates (X) of the entry point of the turning arc where the exit point is located. t1 ,Y t1 The specific method is as follows:

[0036] X t1 =X p3 +L×cos(π / 2-C t1 )

[0037] Y t1 =Y p3 +L×sin(π / 2-C t1 )

[0038] Step 3-5: When the waypoint above the push-out point is the end point of the route, the coordinates (X) of the entry point of the turning arc where the push-out point is located, calculated in Step 3-4, are... t1 ,Y t1 The coordinates of the derivation point are obtained, and the derivation point calculation is completed; otherwise, proceed to step 4.

[0039] Step 4: For different turning methods of the launch point, calculate the coordinates of the launch point based on the center of the turning arc above the launch point, the coordinates of the entry point of the turning arc where the launch point is located, and the heading of the launch point, and complete this launch point calculation.

[0040] The calculation of the coordinates of the derivation point specifically includes:

[0041] Step 4-1: Determine the turning method of the exit point. When the turning method of the exit point is a point-press turn, determine the coordinates (X) of the entry point of the turning arc where the exit point is located. t1 ,Y t1 The coordinates of the derivation point (X) are the coordinates of the desired derivation point. t ,Y t );

[0042] Step 4-2, when the turning method of the exit point is a turn around the point, the coordinates of the exit point (X) are... t ,Y t )for:

[0043] X t =X t1 +R×cos(α)

[0044] Y t =Y t1 +R×sin(α)

[0045] When the turning direction of the launch point is counterclockwise, α is π-C; when the turning direction of the launch point is clockwise, α is -C.

[0046] Step 4-3: When the turning mode of the pushback point is a turn towards the point, calculate the pushback point coordinates (X) by combining the turning modes of the previous waypoint and the next waypoint. t ,Y t ), the specific methods include:

[0047] Step 4-3-1, exit point of the turning arc where the exit point is located (X) t3 ,Y t3 ) and the next turning arc entry point (X) from the exit point n1 ,Y n1 The relationship is as follows:

[0048] X n1 =X t3 +L n ×cos(π / 2-C)

[0049] Y n1 =Y t3 +L n ×sin(π / 2-C)

[0050] Among them, L n It is the exit point of the turning arc where the exit point is located (X) t3 ,Y t3 ) to the exit point, next turning arc entry point (X) n1 ,Y n1 The distance;

[0051] Exit point at the turning arc where the launch point is located (X) t3 ,Y t3 ) and the center of the turning arc where the launch point is located (X) t2 ,Y t2 The relationship is as follows:

[0052] X t3 =X t2 +R×cos(θ)

[0053] Y t3 =Y t2 +R×sin(θ)

[0054] When the turning direction of the launch point is counterclockwise, θ is -C; when the turning direction of the launch point is clockwise, θ is π-C.

[0055] Similarly, the entry point (X) of the next turning arc is derived from the point. n1 ,Y n1 ), the center of the next turning arc after the launch point (X) n2 ,Y n2 ) and the exit point (X) of the next turning arc after the exit point. n3 ,Y n3 The relationship is as follows:

[0056] X n2 =X n1 +R×cos(γ)

[0057] Y n2 =Y n1 +R×sin(γ)

[0058] X n3 =X n2 +R×cos(δ)

[0059] Y n3 =Y n2 +R×sin(δ)

[0060] Among them, C n3 Given the heading of the exit point at the next turning arc from the exit point, and the turning direction at the next waypoint from the exit point being counterclockwise, γ is π-C and δ is -C. n3 When the next waypoint after the derivation point is clockwise, γ is -C and δ is π-C. n3 ;

[0061] Step 4-3-2: Determine the turning method of the waypoint above the exit point. When the waypoint above the exit point is turning towards the exit point:

[0062] (X t2 –X p3 ) 2 +(Y t2 –Y p3 ) 2 =L 2 +R 2

[0063] At this time (X) p3 ,Y p3 ) is the coordinate of a waypoint above the derivation point (X p ,Y p ), when the turning mode is a point-to-point turn, a point-around turn, or a point-to-point turn, the coordinates (X) of the next waypoint after the exit point are... n ,Y n That is, they correspond to (X) respectively. n1 ,Y n1 ), (X n2 ,Y n2 ) and (X n3 ,Y n3 ), and then calculate the ejection point (X). t ,Y t The coordinates of ) are:

[0064]

[0065]

[0066] Where a and b are parameters;

[0067] The calculation methods for parameters a and b are as follows:

[0068] a=(X n1 –R×cos(θ)–X p3 ) 2 +(Y n1 –R×sin(θ)–Y p3 ) 2 -(L 2 +R 2 )

[0069] b=-2×cos(π / 2-C)×(X n1 –R×cos(θ)–X p3 )-2×sin(π / 2-C)×(Y n1 –R×sin(θ)–Y p3 ).

[0070] Step 4-3-3, when the turning method of the waypoint above the exit point is a point-to-point turn or a point-around turn:

[0071] (X t2 –X p2 ) 2 +(Y t2 –Y p2 ) 2 =L 2 +L p 2

[0072] Among them, when the waypoint above the launch point has a different turning direction than the launch point, L p 2 For 4R 2 Otherwise L p 2 =0, where, passing through point (X) p2 ,Y p2 And the point of tangency (X) p3 ,Y p3 The line parallel to the tangent line of point (X), and the point (X) t2 ,Y t2 ), (X t1 ,Y t1 The intersection point of the lines containing (X) is (X) t2 ’ ,Y t2 ’ ), L p For point (X) t2 ’ ,Y t2’ ) to point (X) t2 ,Y t2 The distance; if a waypoint on the deduced point is a turn around the point, then the coordinates of the center of the turning arc on the deduced point (X) are... p2 ,Y p2 ) is the coordinate of a waypoint above the derivation point (X p ,Y p If the turning method at the previous waypoint was a point-to-point turn, then calculate the center coordinates (X, X) of the turning arc at the exit point according to step 3-3. p2 ,Y p2 Then, combining this with step 4-3-1, calculate the coordinates (X) of the ejection point. t ,Y t The calculation method is the same as the calculation method when the waypoint above the exit point in step 4-3-2 is turning towards the point.

[0073] The coordinates (X) of the ejection point are calculated. t ,Y t When (), the parameters a and b are calculated as follows:

[0074] a=(X n1 –R×cos(θ)–X p2 ) 2 +(Y n1 –R×sin(θ)–Y p2 ) 2 -(L 2 +L p 2 )

[0075] b=-2×cos(π / 2-C)×(X n1 –R×cos(θ)–X p2 )-2×sin(π / 2-C)×(Y n1 –R×sin(θ)–Y p2 ).

[0076] Step 4-4: When the turning method at the exit point is a straight turn, calculate the coordinates (X, Y, F) of the exit point according to the pressing point turning method. t ,Y t ), where the radius of the turning arc is 0, and the entry point, center, and exit point of the turning arc coincide.

[0077] The turning direction at the launch point and the turning direction at the next waypoint after the launch point as described in step 4-3-1 are determined using the same method as the turning direction at the previous waypoint as described in step 3-1. p The judgment method is the same.

[0078] Step 5: Calculate each waypoint that needs to be pushed in the aircraft's route in turn to complete the aircraft's route planning.

[0079] Beneficial effects:

[0080] This invention proposes a method for calculating route derivation points under different waypoint turning methods. It can deduce the coordinates of the planned waypoints based on flight segment time and other waypoint turning methods and headings, even when the coordinates of the waypoints to be planned are unknown. This method fully considers various waypoint combinations with different turning methods and directions. Based on different combination requirements and the desired derivation point heading, flight time, turning method, and turning direction, it can accurately solve for the coordinates of the derivation point, meeting the needs of route drawing. Attached Figure Description

[0081] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments, and the advantages of the present invention in the above and / or other aspects will become clearer.

[0082] Figure 1 This is a schematic diagram of the planned route of the present invention.

[0083] Figure 2 This is a schematic diagram of different turning methods at waypoints according to the present invention; wherein, Figure 2 a is a schematic diagram of a turning point. Figure 2 b is a diagram showing the turning point. Figure 2 c is a diagram showing the turning point. Figure 2 d is a diagram of a straight-line turn.

[0084] Figure 3 This is a schematic diagram illustrating the calculation of the push point when the push point is the pressure point and the turning point of the present invention.

[0085] Figure 4 This is a schematic diagram illustrating the calculation of the push point for the present invention, where the push point is a turning point around the point.

[0086] Figure 5 This is a schematic diagram of the push point calculation for the present invention, where the push point is the turning point. Detailed Implementation

[0087] This invention provides a method for calculating waypoint coordinates under different turning modes. It can calculate the coordinates of waypoints based on preset turning modes, headings, and flight times, solving the problem of route planning and creation when the coordinates of waypoints to be added to the route are unknown. The technical solution adopted is as follows:

[0088] A method for calculating route extension points under different turning patterns at waypoints includes the following steps:

[0089] Step 1) Obtain the turning method, heading, and flight time of the desired waypoint, the heading and coordinates of the waypoint preceding the waypoint, the heading and coordinates of the waypoint following the waypoint, and the speed and turning slope data of the waypoint.

[0090] Step 2) Determine whether the previous waypoint of the exit waypoint is the origin of the route. If the previous waypoint of the exit waypoint is the origin of the route, calculate the coordinates of the entry point of the turning arc where the exit waypoint is located based on the coordinates of the origin of the route and the heading of the exit waypoint, and calculate the coordinates of the exit waypoint through Step 4).

[0091] Step 3) If the waypoint preceding the exit point is not the starting point of the route, calculate the center of the turning arc preceding the exit point and the coordinates of the exit point under different turning methods based on the coordinates and heading of the waypoint preceding the exit point and the heading of the exit point, and then proceed to Step 4).

[0092] Step 4) For the push-out waypoint pressing point, bypass point, point-to-point, or straight-line turning mode, calculate the coordinates of the push-out waypoint based on the center of the turning arc on the push-out point, the coordinates of the entry point of the turning arc where the push-out point is located, and the heading of the push-out point.

[0093] Step 1) of the present invention further includes: calculating the flight distance based on the flight time T and speed V of the required exit waypoint, that is, the distance L from the exit point of a turning arc on the exit point to the entry point of the turning arc where the exit point is located.

[0094] L = V × T;

[0095] Calculate the turning radius R based on the waypoint speed V and the turning angle B:

[0096] R = V 2 / (gtan(B));

[0097] In the formula, g is the acceleration due to gravity, g = 9.8 m / s². 2 .

[0098] In step 2) of this invention, the coordinates of the first point of the flight path (X) are used. p ,Y p ), heading C of the entry point on the turning arc where the launch point is located t1 And in step 1), the flight distance L from the launch point is calculated to determine the coordinates of the entry point (X) of the turning arc where the launch point is located. t1 ,Y t1 )for:

[0099] X t1 =X p +L×cos(π / 2-C t1 );

[0100] Y t1 =Y p+L×sin(π / 2-C t1 ).

[0101] In step 3) of this invention, the coordinates (X) of a waypoint above the launch point are used. p ,Y p ), heading C p 1. Heading C at the pushback point; 2. Heading C at the entry point of the turn arc where the pushback point is located. t1 And the turning radius R is calculated to determine the center (X) of the turning arc at the point. p2 ,Y p2 ) and exit point (X) p3 ,Y p3 The method is as follows:

[0102] (1) Determine the turning direction D of the waypoint above the exit point. p When π > C p -C>0 or CC p When ≥π, D p For counterclockwise rotation, when 0 ≤ CC p <π or C p When -C≥π, D p If the direction is clockwise, meaning you can turn clockwise or counterclockwise to reach the target direction, turn in the direction with the smaller turning radius.

[0103] (2) Determine whether the waypoint above the exit point is the end point of the route and whether the exit point is turning towards the point. If the waypoint above the exit point is not the end point of the route and the exit point is turning towards the point, proceed to step 4).

[0104] (3) Otherwise, determine the turning method of the previous waypoint. If the previous waypoint is a point-to-point turn, then...

[0105] X p2 =X p +R×cos(θ);

[0106] Y p2 =Y p +R×sin(θ);

[0107] X p3 =X p2 +R×cos(α);

[0108] Y p3 =Y p2 +R×sin(α);

[0109] When turning counterclockwise from the previous waypoint, θ is π-C. p α is -C t1 When turning clockwise from the previous waypoint, θ is -C. p α is π-C t1When the ejection point is the pressure point or a turning point, C t1 That is, C. When the previous route was a detour around a point, (X) p ,Y p That is (X) p2 ,Y p2 ), (X p3 ,Y p3 The calculation still follows the formula above. When the previous route was a turn towards the point, (X) p ,Y p That is (X) p3 ,Y p3 ), (X p2 ,Y p2 ) by (X p3 ,Y p3 ) is calculated;

[0110] (4) Calculate the coordinates (X) of the exit point on the turning arc above the exit point. p3 ,Y p3 After that, then in step 2), the formula (X) p ,Y p Replace ) with (X p3 ,Y p3 To calculate the coordinates (X) of the entry point of the turning arc where the exit point is located. t1 ,Y t1 );

[0111] (5) When the waypoint above the launch point is the tail point of the route, the calculated (X) t1 ,Y t1 (This is the coordinate of the desired exit waypoint; otherwise, proceed to step 4).

[0112] Step 4 of the present invention: Based on the center (X) of the turning arc at the launch point. p2 ,Y p2 ), the coordinates of the entry point of the turning arc where the exit point is located (X) t1 ,Y t1 ) and the launch point heading C, etc., to calculate the launch waypoint coordinates (X) t ,Y t The method is as follows:

[0113] (1) Determine the turning method of the exit point. When the exit point is a point-to-point turn, determine the coordinates (X) of the entry point of the turning arc where the exit point is located. t1 ,Y t1 The coordinates of the desired exit waypoint are as follows:

[0114] (2) When the exit point is a turning point around the exit point, the coordinates of the exit waypoint (X) are determined. t ,Y t )for:

[0115] Xt =X t1 +R×cos(α);

[0116] Y t =Y t1 +R×sin(α);

[0117] When the launch point turns counterclockwise, α is π-C; when the launch point turns clockwise, α is -C.

[0118] (3) When the exit point is a turning point, the coordinates of the exit waypoint are calculated by combining the turning mode of the waypoint above the exit point and the turning mode of the waypoint below the exit point;

[0119] (4) Otherwise, the waypoint coordinates of the exit point are calculated by straight-line turning. The straight-line turn can be treated as a special case of a turning arc radius of 0, where the entry point, center, and exit point of the turning arc coincide, in order to calculate the coordinates of the exit waypoint.

[0120] In step 4) of this invention, when the launch point is turning towards the launch point, the center (X) of the turning arc at the launch point is considered. p2 ,Y p2 Exit point (X) p3 ,Y p3 ), the coordinates of the entry point of the turning arc where the exit point is located (X t1 ,Y t1 ), center (X) t2 ,Y t2 Exit point (X) t3 ,Y t3 ), the launch point heading C, and the entry point of the next turn arc after the launch point (X). n1 ,Y n1 ), center (X) n2 ,Y n2 Exit point (X) n3 ,Y n3 ), heading C of the next turning arc after the push-out point and the exit point n3 Calculate the coordinates of the exit waypoint (X) t ,Y t The method is as follows:

[0121] (1) Exit point on the turning arc where the exit point is located (X) t3 ,Y t3 ) and the next turning arc entry point (X) from the exit point n1 ,Y n1 )satisfy:

[0122] X n1 =X t3 +L n ×cos(π / 2-C);

[0123] Y n1 =Y t3 +L n ×sin(π / 2-C);

[0124] Among them, L n It is a point (X) t3 ,Y t3 ) to point (X) n1 ,Y n1 The distance to the exit point (X); similarly, the distance to the exit point (X). t3 ,Y t3 ) and the center (X) t2 ,Y t2 )satisfy:

[0125] X t3 =X t2 +R×cos(θ);

[0126] Y t3 =Y t2 +R×sin(θ);

[0127] Wherein, when the exit point turns counterclockwise, θ is -C; when the exit point turns clockwise, θ is π-C; the entry point of the next turning arc from the exit point (X) n1 ,Y n1 ), center (X) n2 ,Y n2 Exit point (X) n3 ,Y n3 The following transformation relationship exists:

[0128] X n2 =X n1 +R×cos(γ);

[0129] Y n2 =Y n1 +R×sin(γ);

[0130] X n3 =X n2 +R×cos(δ);

[0131] Y n3 =Y n2 +R×sin(δ);

[0132] When turning counterclockwise from the launch point to the next waypoint, γ is π-C and δ is -C. n3 When turning clockwise from the exit point to the next waypoint, γ is -C and δ is π-C. n3 ;

[0133] (2) Determine the turning method of the waypoint above the exit point. If the waypoint is a turning point towards the exit point, exit the point (X) by the turning arc above the exit point. p3 ,Y p3 ), the entry point of the turning arc where the exit point is located (X) t1 ,Y t1 ), the center of the turning arc where the launch point is located (X) t2 ,Y t2 The Pythagorean theors for forming right triangles are:

[0134] (X t2 –X p3 ) 2 +(Y t2 –Y p3 ) 2 =L 2 +R 2 ;

[0135] At this time (X) p3 ,Y p3 This refers to the coordinates of a waypoint above the derivation point (X). p ,Y p ), when the next waypoint is at the point of impact, the point of detour, or the point of turning (X) n ,Y n The coordinates of the points are respectively (X) n1 ,Y n1 ), (X n2 ,Y n2 ), (X n3 ,Y n3 Therefore, by combining the equations in (1), L can be calculated simultaneously. n Then, the coordinates of the waypoint are calculated;

[0136] (3) When the waypoint above the exit point is a point of contact or a point of detour, the distance from the center of the turning arc above the exit point to the center of the turning arc at the exit point is given by the Pythagorean theorem:

[0137] (X t2 –X p2 ) 2 +(Y t2 –Y p2 ) 2 =L 2 +L p 2 ;

[0138] Among them, when the waypoint above the launch point has a different turning direction than the launch point, L p 2 For 4R 2 That is, the square of the sum of the radius of the turning arc at the exit point and the radius of the turning arc at the exit point; otherwise, Lp 2 The value is 0, which is the square of the difference between the radius of the turning arc at the exit point and the radius of the turning arc at the exit point; if the previous waypoint is a turn around the point, then (X p2 ,Y p2 This refers to the coordinates of a waypoint above the derivation point (X). p ,Y p Therefore, by combining the various equations in (1), L can be calculated simultaneously for different turning methods at the next waypoint after the launch point. n Then, the coordinates of the exit waypoint are calculated; if the previous waypoint is a turning point, then the coordinates of (X) are calculated according to the formula in step 3). p2 ,Y p2 Then, combining the equations in (1), L can be calculated simultaneously for different turning methods at the next waypoint after the launch point. n Then, the coordinates of the waypoint are calculated.

[0139] Example:

[0140] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific embodiments and accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments described herein. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0141] like Figure 2 As shown, there are four common wayspoint turns: (e.g., point-to-point turns) Figure 2 As shown in a), turning around the point (as shown in a) Figure 2 As shown in b), turn towards the point (as shown in b). Figure 2 (as shown in c) and straight turns (as shown in c) Figure 2 As shown in d), these four turning methods can be freely combined. This invention ensures that when the coordinates of the waypoint to be planned on a route are unknown, but the flight time and heading are known, the coordinates of the waypoint can be correctly calculated regardless of the turning method used.

[0142] Assume the turning arc where the launch point is located on the flight path is A. t Its center coordinates are (X t2 ,Y t2 The coordinates of the entry point are (X) t1 ,Y t1 The exit point coordinates are (X... t3 ,Y t3 ), the turning arc A where the launch point is located tThe next adjacent turning arc is A. p Its center coordinates, entry point coordinates, and exit point coordinates are respectively (X... p2 ,Y p2 ), (X p1 ,Y p1 ), (X p3 ,Y p3 ), the turning arc A where the launch point is located t The next adjacent turning arc is A. n Its center coordinates, entry point coordinates, and exit point coordinates are respectively (X... n2 ,Y n2 ), (X n1 ,Y n1 ), (X n3 ,Y n3 ), the heading of the launch point is C, and the coordinates are (X). t ,Y t The heading of the entry point on the turning arc where the launch point is located is C. t1 The waypoint heading is C. p The coordinates are (X) p ,Y p The turning direction is D. p The heading of the exit point is C, which is the next turning arc after the launch point. n3 The coordinates are (X) n ,Y n The speed, turning angle, and turning radius at the waypoints are represented by V, B, and R, respectively. From point (X... p3 ,Y p3 Fly to point (X) t1 ,Y t1 The flight time of ) is T.

[0143] The method for calculating route extension points under different turning modes provided in this application embodiment includes the following steps:

[0144] Step 1) Obtain various parameters of the waypoint through the waypoint attribute dialog box of the route planning software. These mainly include longitude, latitude, speed, altitude, slope, heading, turning mode, and flight time. Specifically, the turning mode of the desired waypoint is such as a point, the heading is such as 60°, the flight time is such as 100 seconds, the heading, longitude, and latitude of the previous waypoint, the heading, longitude, and latitude of the next waypoint, and the uniform speed of 900 km / h, turning slope of 45°, and altitude of 8000 meters for the waypoint.

[0145] Step 2) Determine whether the previous waypoint of the exit waypoint is the origin of the route. If the previous waypoint of the exit waypoint is the origin of the route, calculate the coordinates of the entry point of the turning arc where the exit waypoint is located based on the coordinates of the origin of the route and the heading of the exit waypoint, and calculate the coordinates of the exit waypoint through Step 4).

[0146] Step 3) If the waypoint preceding the exit point is not the starting point of the route, calculate the center of the turning arc preceding the exit point and the coordinates of the exit point under different turning methods based on the coordinates and heading of the waypoint preceding the exit point and the heading of the exit point, and then proceed to Step 4).

[0147] Step 4) For the push-out waypoint pressing point, bypass point, point-to-point, or straight-line turning mode, calculate the coordinates of the push-out waypoint based on the center of the turning arc on the push-out point, the coordinates of the entry point of the turning arc where the push-out point is located, and the heading of the push-out point.

[0148] Detailed, such as Figure 3 As shown, A p Exit point 3 to A t The distance L from point 3 to point 4 can be calculated using the flight time T and velocity V between points 3 and 4.

[0149] L = V × T;

[0150] Each turning arc A p A t A n The turning radius R can be calculated based on the waypoint speed V and the turning angle B:

[0151] R = V 2 / (gtan(B));

[0152] In the formula, g is the acceleration due to gravity, g = 9.8 m / s². 2 The turning arc A where the launch point is located t Entry point coordinates (X t1 ,Y t1 )for:

[0153] X t1 =X p3 +L×cos(π / 2-C t1 );

[0154] Y t1 =Y p3 +L×sin(π / 2-C t1 );

[0155] When waypoint (X) p ,Y p When (X) is the starting point of the route, p3 ,Y p3 That is (X) p ,Y p ).

[0156] In an embodiment of the present invention, step 3) is based on point (X) p ,Y p), heading C p Heading C, Heading C of the entry point of the turn arc where the push-out point is located t1 And the calculation of turning radius R. p The center of the circle (X) p2 ,Y p2 ) and exit point (X) p3 ,Y p3 The method is as follows:

[0157] (1) Determine A p Turning direction D p When π > C p -C>0 or CC p When ≥π, D p For counterclockwise rotation, when 0 ≤ CC p <π or C p When -C≥π, D p If the direction is clockwise, meaning you can turn clockwise or counterclockwise to reach the target direction, turn in the direction with the smaller turning radius.

[0158] (2) Determine the waypoint (X) p ,Y p Is point (X) the end of the flight path and is the point of departure a turning point? p ,Y p If the point is not the end of the flight path and the point of departure is turning towards the point of departure, proceed to step 4.

[0159] (3) Figure 3 As shown, otherwise judge A. p The turning method, when A p When turning at the pressure point, point (X) p2 ,Y p2 ), (X p1 ,Y p1 ), (X p3 ,Y p3 It can be converted as follows:

[0160] X p2 =X p1 +R×cos(θ2);

[0161] Y p2 =Y p1 +R×sin(θ2);

[0162] X p3 =X p2 +R×cos(θ1);

[0163] Y p3 =Y p2 +R×sin(θ1);

[0164] Among them, (X) p ,Y p That is (X) p1 ,Y p1 ), A p When turning counterclockwise, θ2 is π-C p θ1 is -C t1 A p When turning clockwise, θ2 is -C p θ1 is π-C t1 When the ejection point is the pressure point or a turning point, C t1 That is, C. When A p When turning around a point, (X) p ,Y p That is (X) p2 ,Y p2 ), (X p3 ,Y p3 ) Calculate according to the above formula; when A p When turning towards point (X) p ,Y p That is (X) p3 ,Y p3 ), (X p2 ,Y p2 ) by (X p3 ,Y p3 ) Calculate it, and then we can further calculate A. t Entry point coordinates (X t1 ,Y t1 When waypoint (X) p ,Y p When ) is the tail point of the route, the calculated (X) t1 ,Y t1 The coordinates of the desired waypoint (X) are then obtained. t ,Y t Otherwise, proceed to step 4).

[0165] In an embodiment of the present invention, step 4) targets A. t Calculation of exit waypoint coordinates (X) under different turning methods t ,Y t The method is as follows:

[0166] (1) Determine A t The turning method, when A t When turning at the pressure point, A t Entry point coordinates (X t1 ,Y t1 ) is (X t ,Y t );

[0167] (2) When A tWhen turning around a point, such as Figure 4 As shown, the waypoint coordinates (X) are derived. t ,Y t )for:

[0168] X t =X t1 +R×cos(α);

[0169] Y t =Y t1 +R×sin(α);

[0170] Among them, A t When turning counterclockwise, α is π-C, A t When turning clockwise, α is -C;

[0171] (3) When A t When turning towards point A, combine it with A. p The turning method and A n Calculation of turning method (X) t ,Y t );

[0172] (4) Otherwise A t Calculated using the straight-line turning method (X) t ,Y t This allows for the processing of straight-line turns into point-based turns where the radius of the turning arc is 0, and the entry point, center, and exit point of the turning arc coincide. This is a special case where the turning point is calculated (X). t ,Y t ).

[0173] In embodiments of the present invention, such as Figure 5 As shown, in step 4), when the exit point is turning towards the point, combine with A. p The turning method and A n Turning method calculation (X) t ,Y t The method is as follows:

[0174] (1)A t Exit point (X) t3 ,Y t3 ) and A n Entry point (X) n1 ,Y n1 )satisfy:

[0175] X n1 =X t3 +L n ×cos(π / 2-C);

[0176] Y n1 =Y t3 +L n×sin(π / 2-C);

[0177] Among them, L n It is a point (X) t3 ,Y t3 ) to point (X) n1 ,Y n1 The distance to the exit point (X); similarly, the distance to the exit point (X). t3 ,Y t3 ) and the center (X) t2 ,Y t2 )satisfy:

[0178] X t3 =X t2 +R×cos(θ1);

[0179] Y t3 =Y t2 +R×sin(θ1);

[0180] Among them, A t When turning counterclockwise, θ1 is -C, A t When turning clockwise, θ1 is π-C; A n Entry point (X) n1 ,Y n1 ), center (X) n2 ,Y n2 Exit point (X) n3 ,Y n3 The following transformation relationship exists:

[0181] X n2 =X n1 +R×cos(θ3);

[0182] Y n2 =Y n1 +R×sin(θ3);

[0183] X n3 =X n2 +R×cos(θ4);

[0184] Y n3 =Y n2 +R×sin(θ4);

[0185] Among them, A n When turning counterclockwise, θ3 is π-C and θ4 is -C. n3 A n When turning clockwise, θ3 is -C and θ4 is π-C. n3 ;

[0186] (2) Determine A p The turning method, when A pWhen turning towards point A p Exit point (X) p3 ,Y p3 A) t Entry point (X) t1 ,Y t1 ),

[0187] A t Center (X) t2 ,Y t2 The Pythagorean theors for forming right triangles are:

[0188] (X t2 –X p3 ) 2 +(Y t2 –Y p3 ) 2 =L 2 +R 2 ;

[0189] At this time (X) p3 ,Y p3 This refers to the coordinates of a waypoint above the derivation point (X). p ,Y p ), A n When pressing the point, circling the point, or turning towards the point (X) n ,Y n The coordinates of the points are respectively (X) n1 ,Y n1 ), (X n2 ,Y n2 ), (X n3 ,Y n3 Therefore, by combining the equations in (1), L can be calculated simultaneously. n Then calculate (X) t ,Y t );

[0190] (3) When A p When turning at or around a point, A p From the center of the circle to A t The distance from the center of the circle is given by the Pythagorean theorem:

[0191] (X t2 –X p2 ) 2 +(Y t2 –Y p2 ) 2 =L 2 +L p 2 ;

[0192] Among them, when A p With A t When turning in different directions, Lp 2 For 4R 2 That is, A p radius and A t The radius and the square of L, otherwise L p 2 It is 0, that is, A p radius and A t The square of the difference in radii; if A p If it is a turn around a point, then (X) p2 ,Y p2 That is, A p Waypoint coordinates (X p ,Y p Therefore, combining the various equations in (1), we can apply this to A. n Calculate L by combining the results for different turning patterns. n Then calculate (X) t ,Y t If A p If it is a point-to-turn, then calculate (X) according to the formula in step (3). p2 ,Y p2 Then, by combining the various formulas in (1), we can target A. n Calculate L by combining the results for different turning patterns. n Then calculate (X) t ,Y t The coordinates of ).

[0193] Based on the above method, the calculated planned route is as follows: Figure 1As shown: The speed, gradient, and altitude of each waypoint are uniformly set to 900 km / h, 45°, and 8000 meters, respectively. The coordinates of the lead point 0 are (117°16′11", 24°59′54"), and the coordinates of the trailing point 7 are (117°47′06", 25°07′35"). Selecting the lead point, in the waypoint properties dialog box, enter a flight time of 100 seconds, a heading of 60°, and select "overshoot" as the turn method. Perform the push-out calculation. According to step 1, the flight distance L = 25000 meters and the turning radius R = 6377.55 meters are calculated for the push-out point. At this point, the waypoint above the push-out point is the lead point, and the lead point is an overshoot turn. Therefore, according to steps 2 and 4-1, the coordinates of the push-out point 1 are calculated to be (117°29′05", 25°06′). 38"), the first round of push point calculation is complete; then input the flight time of the next push point 6 as 100 seconds, heading as 100°, and turn mode as "point turn", and execute the second round of push point calculation. Similarly, according to step 1, the flight distance L = 25000 meters and the turning radius R = 6377.55 meters of push point 6 are calculated. At this time, the waypoint above the push point is the push point obtained from the first round of push point calculation, not the first point of the route. The coordinates of the waypoint 1 above the push point are (117°29′05", 25°06′38"), heading as 60°, and turning at the point. The waypoint below the push point is the end point of the route. The coordinates of the waypoint 7 below the push point are (117°47′06", 25°07′35"), heading as 100°, and turning at the point. According to step 3-1, D is calculated. p To proceed clockwise, based on step 3-3, the coordinates of the center point 2 of the turning arc at the exit point and the exit point 3 are calculated to be (117°30′58", 25°03′38") and (117°29′28", 25°00′28"), respectively. Then, step 4-3-3 calculates the coordinates of the exit point 6 as (117°17′58", 25°12′23"). Next, based on the relationship between the exit point and the center of the turning arc at the exit point in step 4-3-1, the coordinates of the center point 5 of the turning arc at the exit point are calculated to be (117°17′18", 25°08′59"). Finally, based on step 3-4, the coordinates of the entry point 4 of the turning arc at the exit point are calculated to be (117°15′48", 25°05′48"). The planning is now complete. Figure 1 The route shown is as shown.

[0194] The above method can be applied to command systems such as airport towers to pre-plan aircraft flight routes.

[0195] In its specific implementation, this application provides a computer storage medium and a corresponding data processing unit. The computer storage medium is capable of storing a computer program, which, when executed by the data processing unit, can run the invention's content regarding a method for calculating route projection points under different turning modes of waypoints, as well as some or all of the steps in various embodiments. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc.

[0196] Those skilled in the art will clearly understand that the technical solutions in the embodiments of the present invention can be implemented using computer programs and their corresponding general-purpose hardware platforms. Based on this understanding, the technical solutions in the embodiments of the present invention, or the parts that contribute to the prior art, can be embodied in the form of computer programs, i.e., software products. These computer program software products can be stored in a storage medium and include several instructions to cause a device containing a data processing unit (which may be a personal computer, server, microcontroller, MUU, or network device, etc.) to execute the methods described in various embodiments or certain parts of the embodiments of the present invention.

[0197] This invention provides a method for calculating route extension points under different turning patterns at waypoints. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A method for calculating route extension points under different turning patterns at waypoints, characterized in that, Includes the following steps: Step 1: Obtain the turning mode, heading, and flight time of the waypoint (i.e., the launch point) of the aircraft to be calculated; obtain the heading and coordinates of the previous waypoint of the launch point; obtain the heading and coordinates of the next waypoint of the launch point; and obtain the unified speed and turning bank angle data of the launch point, the previous waypoint, and the next waypoint; calculate the flight distance and turning radius of the launch point based on the above data. Step 2: Determine whether the previous waypoint of the launch point is the starting point of the route. If so, calculate the coordinates of the entry point of the turning arc where the launch point is located based on the coordinates of the starting point of the route and the heading of the launch point, and calculate the coordinates of the launch point through Step 4. Otherwise, proceed to Step 3. Step 3: Based on the coordinates and heading of a waypoint at the launch point and the heading of the launch point, calculate the center of a turning arc at the launch point and the coordinates of the exit point under different turning methods, and then proceed to Step 4. Step 4: For different turning methods of the launch point, calculate the coordinates of the launch point based on the center of the turning arc above the launch point, the coordinates of the entry point of the turning arc where the launch point is located, and the heading of the launch point, and complete this launch point calculation. Step 5: Calculate each waypoint that needs to be pushed in the aircraft's route in turn to complete the aircraft's route planning; Specifically, calculating the coordinates of the exit point in step 4 includes: Step 4-1: Determine the turning method of the exit point. When the turning method of the exit point is a point-press turn, determine the coordinates (X) of the entry point of the turning arc where the exit point is located. t1 ,Y t1 The coordinates of the derivation point (X) are the coordinates of the desired derivation point. t ,Y t ); Step 4-2, when the turning method of the exit point is a turn around the point, the coordinates of the exit point (X) are... t ,Y t )for: X t = X t1 + R×cos(α) AND t = And t1 + R×sin(α) Step 4-3: When the turning mode of the pushback point is a turn towards the point, calculate the pushback point coordinates (X) by combining the turning modes of the previous waypoint and the next waypoint. t ,Y t ); Step 4-4: When the turning method at the exit point is a straight turn, calculate the coordinates (X, Y, F) of the exit point according to the pressing point turning method. t ,Y t ), where the radius of the turning arc is 0, and the entry point, center, and exit point of the turning arc coincide.

2. The method for calculating route extension points under different turning modes at waypoints according to claim 1, characterized in that, The calculation of the flight distance and turning radius at the launch point, as described in step 1, involves calculating the flight distance L at the launch point based on the flight time T and velocity V. The method is as follows: L=V×T Wherein, the flight time T at the launch point is the time it takes for the aircraft to fly from the exit point of a turn arc on the launch point to the entry point of the turn arc on the launch point, and the flight distance L at the launch point is the distance from the exit point of a turn arc on the launch point to the entry point of the turn arc on the launch point. The turning radius R is calculated based on the launch point velocity V and the turning slope B, as follows: R=V 2 / (gtan(B)) Where g is the acceleration due to gravity, the velocity and gradient of the waypoint above and below the launch point are the same as those of the launch point, that is, the turning radius of the launch point, the waypoint above the launch point, and the waypoint below the launch point are the same.

3. The method for calculating route extension points under different turning modes at waypoints according to claim 2, characterized in that, The specific method for calculating the coordinates of the entry point of the turning arc where the exit point is located, as described in step 2, includes: X t1 = X p + L×cos(π / 2 - C t1 ) Y t1 = Y p + L×sin(π / 2 - C t1 ) Among them, (X) p ,Y p C represents the coordinates of the starting point of the flight path. t1 The heading of the entry point of the turning arc where the launch point is located is given by the coordinates of the entry point of the turning arc where the launch point is located (X). t1 ,Y t1 ).

4. The method for calculating route extension points under different turning modes at waypoints according to claim 3, characterized in that, Step 3, which involves calculating the coordinates of the center of a turning arc at the exit point under different turning modes, specifically includes: based on the coordinates of a waypoint at the exit point (X... p ,Y p ), heading C p 1. Heading C at the pushback point; 2. Heading C at the entry point of the turn arc where the pushback point is located. t1 And the center (X) of the turning arc at the point derived from the calculation of the turning radius R in step 1. p2 ,Y p2 ) and exit point (X) p3 ,Y p3 The method is as follows: Step 3-1, determine the turning direction D of the waypoint above the launch point. p When π > C p -C>0 or C−C p When ≥π, the turning direction D of the previous waypoint p For counterclockwise rotation, when 0 ≤ C−C p <π or C p When -C ≥ π, the turning direction of the previous waypoint is D. p Clockwise, where C p Heading to the previous waypoint; Step 3-2: Determine whether the waypoint above the exit point is the end point of the route and whether the exit point is a turning point. If the waypoint above the exit point is not the end point of the route and the exit point is a turning point, proceed to step 4; otherwise, proceed to step 3-3. Step 3-3: Determine the turning mode of the waypoint at the exit point, and perform the following calculations based on the turning mode: When the previous waypoint is a turning point, deduce the center coordinates (X) of the turning arc at that point. p2 ,Y p2 ) and the coordinates of the turning exit point (X p3 ,Y p3 The calculation method is as follows: X p2 = X p + R×cos(θ) AND p2 = And p + R×sin(θ) X p3 = X p2 + R×cos(α) AND p3 = And p2 + R×sin(α) Among them, the turning direction D at the previous waypoint p When the rotation is counterclockwise, θ is π-C. p α is -C t1 The turning direction at the previous waypoint, D. p When the rotation is clockwise, θ is -C. p α is π-C t1 ; When the ejection point is the pressure point or a turning point, C t1 That is, C; When the previous route involved a turn around a point, the coordinates (X) of the previous route point can be derived. p ,Y p That is, the coordinates (X) of the center of the arc of the turning point at that point. p2 ,Y p2 ), coordinates of the turning exit point (X p3 ,Y p3 The calculation method is the same as that used when the previous waypoint is a turning point. When the previous route turned towards the point, the coordinates (X) of the previous route point can be derived. p ,Y p That is, the coordinates of the turning and exit point (X). p3 ,Y p3 ), and deduce the center coordinates (X) of the turning arc at point. p2 ,Y p2 ) by the coordinates of the exit point (X p3 ,Y p3 The calculation method is as follows: X p2 = X p3 - R×cos(a) AND p2 = And p3 - R×sin(α) The value of α is the same as the value when the previous waypoint is a turning point; Steps 3-4: Calculate the coordinates (X) of the entry point of the turning arc where the exit point is located. t1 ,Y t1 The specific method is as follows: X t1 = X p3 + L×cos(π / 2 - C t1 ) Y t1 = Y p3 + L×sin(π / 2 - C t1 ) Step 3-5: When the waypoint above the push-out point is the end point of the route, the coordinates (X) of the entry point of the turning arc where the push-out point is located, calculated in Step 3-4, are... t1 ,Y t1 The coordinates of the derivation point are obtained, and the derivation point calculation is completed; otherwise, proceed to step 4.

5. The method for calculating route extension points under different turning modes at waypoints according to claim 4, characterized in that, Step 4-3 describes calculating the launch point coordinates (X) by combining the turning patterns of the waypoints preceding and following the launch point. t ,Y t ), the specific methods include: Step 4-3-1, exit point of the turning arc where the exit point is located (X) t3 ,Y t3 ) and the next turning arc entry point (X) from the exit point n1 ,Y n1 The relationship is as follows: X n1 = X t3 + L n ×cos(π / 2 - C) Y n1 = Y t3 + L n ×sin(π / 2 - C) Among them, L n It is the exit point of the turning arc where the exit point is located (X) t3 ,Y t3 ) to the exit point and the next turning arc entry point (X) n1 ,Y n1 The distance; Exit point at the turning arc where the launch point is located (X) t3 ,Y t3 ) and the center of the turning arc where the launch point is located (X) t2 ,Y t2 The relationship is as follows: X t3 = X t2 + R×cos(θ) AND t3 = And t2 + R×sin(θ) When the turning direction of the launch point is counterclockwise, θ is -C; when the turning direction of the launch point is clockwise, θ is π-C. Similarly, the entry point (X) of the next turning arc is derived from the point. n1 ,Y n1 ), the center of the next turning arc after the launch point (X) n2 ,Y n2 ) and the exit point (X) of the next turning arc after the exit point. n3 ,Y n3 The relationship is as follows: X n2 = X n1 + R×cos(γ) AND n2 = And n1 + R×sin(γ) X n3 = X n2 + R×cos(δ) AND n3 = And n2 + R×sin(δ) Among them, C n3 Given the heading of the exit point at the next turning arc from the exit point, and the turning direction at the next waypoint from the exit point being counterclockwise, γ is π-C and δ is -C. n3 When the next waypoint after the derivation point is clockwise, γ is -C and δ is π-C. n3 ; Step 4-3-2: Determine the turning method of the waypoint above the exit point. When the waypoint above the exit point is turning towards the exit point: (X t2 – X p3 ) 2 + (Y t2 – Y p3 ) 2 = L 2 + R 2 At this time (X) p3 ,Y p3 This refers to the coordinates of a waypoint above the derivation point (X). p ,Y p ), when the turning mode is a point-to-point turn, a point-around turn, or a point-to-point turn, the coordinates (X) of the next waypoint after the exit point are... n ,Y n That is, they correspond to (X) respectively. n1 ,Y n1 ), (X n2 ,Y n2 ) and (X n3 ,Y n3 ), and then calculate the ejection point (X). t ,Y t The coordinates of ) are: X t = X n1 - (-b+ ) / 2 × cos(π / 2 - C) AND t = And n1 - (-b+ ) / 2 × sin(π / 2 - C) Where a and b are parameters; Step 4-3-3, when the turning method of the waypoint above the exit point is a point-to-point turn or a point-around turn: (X t2 – X p2 ) 2 + (Y t2 – Y p2 ) 2 = L 2 + L p 2 Among them, when the waypoint above the launch point has a different turning direction than the launch point, L p 2 For 4R 2 Otherwise L p 2 =0, where, passing through point (X) p2 ,Y p2 And the point of tangency (X) p3 ,Y p3 The line parallel to the tangent line of point (X), and the point (X) t2 ,Y t2 ), (X t1 ,Y t1 The intersection point of the lines containing (X) is (X) t2 ’ ,Y t2 ’ ), L p For point (X) t2 ’ ,Y t2 ’ ) to point (X) t2 ,Y t2 The distance; if a waypoint on the deduced point is a turn around the point, then the coordinates of the center of the turning arc on the deduced point (X) are... p2 ,Y p2 This refers to the coordinates of a waypoint above the derivation point (X). p ,Y p If the turning method at the previous waypoint was a point-to-point turn, then calculate the center coordinates (X, X) of the turning arc at the exit point according to step 3-3. p2 ,Y p2 Then, combining this with step 4-3-1, calculate the coordinates (X) of the ejection point. t ,Y t The calculation method is the same as the calculation method when the waypoint above the exit point in step 4-3-2 is turning towards the point.

6. The method for calculating route extension points under different turning modes at waypoints according to claim 5, characterized in that, The turning direction at the push-out point mentioned in step 4 and the turning direction at the next waypoint after the push-out point mentioned in step 4-3-1 are determined using the same method as the turning direction at the previous waypoint after the push-out point mentioned in step 3-1. p The judgment method is the same.

7. The method for calculating route extension points under different turning modes at waypoints according to claim 6, characterized in that, In step 4-2, when the turning direction of the launch point is counterclockwise, α is π-C; when the turning direction of the launch point is clockwise, α is -C.

8. The method for calculating route extension points under different turning modes at waypoints according to claim 7, characterized in that, The calculation methods for parameters a and b mentioned in step 4-3-2 are as follows: a = (X n1 – R×cos(θ) – X p3 ) 2 + (Y n1 – R×sin(θ) – Y p3 ) 2 - (L 2 + R 2 ) b = -2×cos(π / 2-C)×(X n1 – R×cos(θ) – X p3 ) - 2×sin(π / 2-C)×(Y n1 – R×sin(θ) – Y p3 )。 9. The method for calculating route extension points under different turning modes at waypoints according to claim 8, characterized in that, Step 4-3-3 describes calculating the coordinates (X) of the ejection point. t ,Y t When (), the parameters a and b are calculated as follows: a = (X n1 – R×cos(θ) – X p2 ) 2 + (Y n1 – R×sin(θ) – Y p2 ) 2 - (L 2 + L p 2 ) b = -2×cos(π / 2-C)×(X n1 – R×cos(θ) – X p2 ) - 2×sin(π / 2-C)×(Y n1 – R×sin(θ) – Y p2 )。

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