A single-route virtual lead aircraft formation method for geometric constraint rules

Abstract

The present invention proposes a method for a single-route virtual lead aircraft formation with geometric constraint rules, which is as follows: For the lateral position control in the route flight mode, the expected reference points of the virtual formation are obtained according to the geometric constraint rules, and then the expected reference points of the formation UAVs are deduced. The line-of-sight guidance law is used to obtain the roll angle commands for each formation UAV to maintain the formation. For the lateral position control in the route switching mode, the virtual formation calculates the position in real time according to the circular arc route, and the formation UAVs use the virtual formation as the expected reference point to obtain the roll angle commands for formation maintenance. For the longitudinal position and altitude control of the formation UAVs, a longitudinal position maintenance controller is designed based on the following deviation between the formation UAVs and the virtual formation to obtain the throttle command, and the elevator command is obtained based on the altitude deviation between the formation UAVs and the virtual formation. The present invention can achieve precise formation maintenance and route tracking control of multiple formation UAVs, does not rely on a high-bandwidth networking radio communication link, and is easy to implement in engineering.

Description

Technical Field

[0001] The present invention relates to the technical field of autonomous formation flight control of aircraft, and particularly to a single-route virtual leader formation method with geometric constraint rules. Background Art

[0002] The unmanned aerial vehicle (UAV) industry has developed rapidly and has been widely applied in military and civilian fields. Due to the inherent limitations of a single aircraft, complex tasks cannot be completed. Therefore, people have started to complete tasks that a single aircraft cannot perform through the cooperation and coordination of multiple aircraft. Among them, the formation control problem is the basis and difficulty of multi-aircraft cooperation, and it is also a research hotspot in the current aircraft field. When multiple UAVs perform cooperative flight tasks, they generally form a formation according to a pre-designed task formation. How to form a predetermined formation and fly along a preset route requires the intervention of a formation control method.

[0003] Currently, the common control methods mainly include the following three: the leader-follower method, the behavior-based method, and the virtual structure method. The leader-follower method has a simple principle and is easy to implement. It is the most classic and earliest control method in multi-UAV formations. However, when the leader is damaged or loses communication with the leader due to external environmental interference, the positions of all UAVs need to be recalculated, and in severe cases, the formation may collapse. The behavior-based method is a bio-inspired control method that simulates the collective behavior patterns of biological communities in nature and has good robustness. When the aircraft in formation flight is disturbed by external environmental factors, the formation can be quickly adjusted through the behavior mode. However, it is difficult to define the behavior of subsystems in the behavior-based method, the design is complex, and it requires the formation system to establish an accurate mathematical model, otherwise the formation control accuracy will be reduced. The virtual structure method improves the risk resistance ability of the formation and is easy to specify the behavior of the aircraft group. However, the traditional virtual structure method has a large amount of calculation and requires high communication quality, and it is difficult to achieve in engineering. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and provide a single-route virtual leader formation method with geometric constraint rules. The present invention is suitable for the condition of a single planned route, determines the virtual formation structure with a virtual leader, and guides multiple UAVs to track the corresponding virtual aircraft to achieve multi-aircraft formation control. This method has high control accuracy and is easy to achieve in engineering.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A single-route virtual leader formation method with geometric constraint rules according to the present invention includes the lateral position control in the route flight mode and the lateral position control in the route switching mode, wherein,

[0007] Pre-design the formation flight route;

[0008] Lateral position control in the en-route flight mode:

[0009] In the en-route flight mode, according to the position of the virtual leader, the expected reference points of the virtual formation are generated on the route according to the geometric constraint rules, and then the expected reference points of the formation UAVs are calculated. According to the expected reference points of the formation UAVs, the roll angle commands for each formation UAV to maintain the formation are obtained by using the line-of-sight guidance law;

[0010] Lateral position control in the route switching mode:

[0011] When the expected reference point of the virtual leader reaches the end of each section of the route, arc route flight is adopted, and the position of the virtual formation is calculated in real time according to the arc route; in the route switching mode, the expected reference point is switched, and the formation UAVs generate the roll angle commands for formation keeping with the virtual formation as the expected reference point, and the position of the virtual leader and the track angle of the formation UAVs are used as the modal washout conditions.

[0012] As a further optimization scheme of the single-route virtual leader formation method with geometric constraint rules of the present invention, it further includes the control of the longitudinal position of the formation. The control of the longitudinal position of the formation means that the following deviation calculation method is divided into two parts: en-route flight and switching mode, and a longitudinal position keeping controller is designed with the following deviation as the input quantity.

[0013] As a further optimization scheme of the single-route virtual leader formation method with geometric constraint rules of the present invention, in step 1,

[0014] The formation flight route includes K sections of routes, where K is an integer greater than or equal to 2. The virtual formation P is composed of virtual aircraft, P = {PV i , i = 1, 2, 3...I}, where I is the number of virtual aircraft and also the number of formation UAVs. PV i is the virtual aircraft of the i-th formation UAV. PV1 is selected as the virtual leader. In the en-route flight stage, according to the position of the virtual leader, the position coordinates of the virtual formation are generated through geometric constraint rules. The position coordinates of PV i are:

[0015]

[0016]

[0017] Among them, PV 1N , PV 1E are the components of the virtual leader coordinates in the N and E directions. The north direction is the N direction, and the east direction is the E direction. PV iN , PV iE are the components of the PV i coordinates in the N and E directions. d fiis the formation spacing of the i-th formation UAV, α fi is the formation angle of the i-th formation UAV. When the i-th formation UAV is on the right side of the virtual lead aircraft, α fi is positive, and vice versa, α fi is negative, ψ segk is the angle between the k-th flight path segment and the north direction, where k is an integer and 1 ≤ k ≤ K, and K is the total number of flight path segments, ψ segk The expression is:

[0018]

[0019] where WP k,N and WP k,E are the components of the starting point coordinates of the k-th flight path segment in the N and E directions, and WP k+1,N and WP k+1,E are the components of the ending point coordinates of the k-th flight path segment in the N and E directions;

[0020] Furthermore, the expected reference point T i of PV i is obtained:

[0021] T iN = PV iN + l f cosψ segk (4)

[0022] T iE = PV iE + l f sinψ segk (5)

[0023] where T iN and T iE are the components of T i in the N and E directions respectively, and l f is the tracking distance of the virtual formation relative to T i ;

[0024] The expected reference point T Ui of the i-th formation UAV is calculated through the expected distance D between the virtual formation and the formation UAV:

[0025]

[0026] where T UiN and T UiE are the components of T Ui in the N and E directions respectively;

[0027] The ground speed V g of the formation UAV, the track angle Ω, and the angle β Ui between the position and the expected reference point Tf , substituting into the line-of-sight guidance law, the lateral position of the formation UAV is calculated to obtain the roll angle command for maintaining the position.

[0028] As a further optimization scheme of the single-route virtual leader formation method with geometric constraint rules described in the present invention, when k = K, it is determined that the formation UAV has completed all route flight tasks and no longer performs route switching mode flight; when k is an integer between 1 and K - 1, the formation UAV performs route switching mode flight, and the cut-in condition for the route switching mode is:

[0029] When T1 reaches the end point WP of the k-th route k+1 , it enters the route switching mode. At this time, the virtual leader is located at the mode cut-in point A. Through the WP k+1 coordinates, the included angle ψ k —WP k+1 between the k-th route WP segk and the north direction, the included angle ψ k+1 —WP k+2 between the (k + 1)-th route WP segk+1 and the north direction, and the tracking distance l f , the coordinates of point A (A N , A E ), and the coordinates of the mode washout point B (B N , B E ) are obtained. WP k is the starting point of the k-th route, WP k+1 is the end point of the k-th route and at the same time the starting point of the (k + 1)-th route, WP k+2 is the end point of the (k + 1)-th route. A N , A E , and B N , B E are the components of points A and B in the N and E directions respectively. The expressions are:

[0030]

[0031]

[0032] WP k+2,N , WP k+2,E are the components of the coordinates of the end point of the (k + 1)-th route in the N and E directions.

[0033] As a further optimization scheme of the single-route virtual leader formation method with geometric constraint rules described in the present invention, the calculation of the roll angle command for maintaining the formation during the route switching mode:

[0034] The virtual leader performs circular arc route flight during route switching, and its real-time position (PV 1N , PV 1E)It is obtained from the arc geometric constraint rules that:

[0035] PV 1N = O N + R1 sin(δ + ξ) (9)

[0036] PV 1E = O E - R1 cos(δ + ξ) (10)

[0037] Among them, O N 、O E are the components of the in - center O of the inscribed circles of the two flight paths WP k —WP k+1 、WP k+1 —WP k+2 in the N and E directions. R1 is the radius of the inscribed circle of the virtual lead aircraft, and δ is the angle between the line connecting the virtual lead aircraft at point A and the center of the circle and the E direction. The expression is:

[0038] δ = arctan((A N - O N ),(A E - O E )) (11)

[0039] The central angle ξ corresponding to the flight path of the virtual lead aircraft is obtained from the speed V0 of the virtual lead aircraft and the flight time t when entering the flight path switching mode:

[0040]

[0041] ξ = ωt (13)

[0042] Among them, ω is the angular velocity of the virtual lead aircraft flying along the arc route. At this time, the PVi coordinates are still obtained according to the straight - line segment calculation formulas (1) and (2);

[0043] In the arc segment, the angle between the arc tangent between the k - th and the (k + 1) - th flight paths and the north direction is ψ′ segk ,

[0044] ψ′ segk = δ + ξ (14)

[0045] In the flight path switching mode, the formation UAVs use PV i as the expected reference point. Substitute the calculation result of formula (14) into formulas (1) and (2) to obtain the coordinates of PV i in the flight path switching mode segment, and then obtain the roll - angle commands required for each formation UAV to maintain the formation shape in the flight path switching mode.

[0046] As a further optimization scheme of the single - route virtual lead aircraft formation method with geometric constraint rules of the present invention, the wash - out judgment condition for the route - switching mode:

[0047] The wash - out conditions for the route - switching mode are specifically as follows:

[0048] According to the first condition, if it is judged that the virtual lead aircraft has completed the circular - route flight, it will continue to fly along the next section of the route;

[0049] After the first condition is satisfied, according to the second condition, it is judged when each formation UAV will switch the desired reference point from PV i to T Ui ;

[0050] If both the first condition and the second condition are satisfied, then the route - switching mode is washed out, and it switches to the route - flight mode for formation flight of the next section of the route;

[0051] The first condition is:

[0052]

[0053] Among them, is the vector from the center O to the virtual lead aircraft PV1, is the modulus of is the vector from WP k+1 to WP k+2 ; is the modulus of;

[0054] The second condition is:

[0055] |ψ i -ψ segk+1 | < ρ f (16)

[0056] When the difference between the track angle of the formation UAV and the route angle of the next section of the route is less than ρ f , it is judged that the route - switching mode is washed out; among them, ρ f is the wash - out threshold, and ψ i is the flight track angle of the i - th formation UAV.

[0057] As a further optimization scheme of the single - route virtual lead aircraft formation method with geometric constraint rules of the present invention, the following - following deviation between the formation UAV and the virtual formation is used as the input quantity to design a longitudinal - position - maintaining controller, and the calculation process of the following - following deviation is as follows:

[0058] (1) The following - following deviation in the route - flight mode

[0059] The i - th formation UAV and the virtual machine PV of the i - th formation UAVi The actual distance D between i is:

[0060]

[0061] where U iN , U iE are the components of the real-time position of the i-th formation UAV in the N and E directions, and PV iN , PV iE are the components of the PV i coordinates in the N and E directions. Then the distance following deviation e Di of the i-th formation UAV is:

[0062] e Di = D i - D(18)

[0063] In this mode, the virtual formation speeds are all the same as the speed V0 of the virtual lead aircraft. Therefore, the speed following deviation e vi of the i-th formation UAV is:

[0064] e Vi = V0 - V i (19)

[0065] where V i is the flight speed of the i-th formation UAV;

[0066] (2) Waypoint switching mode following deviation

[0067] In this mode, an arc waypoint is adopted, and the formation UAVs will perform turning flights. The speed deviation is calculated based on the flight radius and the speed V0 of the virtual lead aircraft;

[0068] Except for the virtual lead aircraft, the difference between the arc radius R i of PV i and the inscribed circle radius R1 of the virtual lead aircraft is ΔR:

[0069] ΔR = d fi sinα fi (20)

[0070] where d fi is the formation spacing of the i-th formation UAV, and α fi is the formation angle of the i-th formation UAV;

[0071] ① Turn left along the waypoint flight direction, and the i-th formation UAV is on the left side of the virtual lead aircraft; or turn right along the waypoint flight direction, and the i-th formation UAV is on the right side of the virtual lead aircraft;

[0072] R i = R1 - ΔR (21)

[0073] ② Turn right along the flight direction of the route, and the i-th formation UAV is located on the left side of the virtual lead aircraft; or turn left along the flight direction of the route, and the i-th formation UAV is located on the right side of the virtual lead aircraft;

[0074] R i = R1 + ΔR (22)

[0075] The distance following deviation in the route switching mode is the same as that in the route flight mode. The expected speed V of the formation UAV icmd is:

[0076] V icmd = V0(R i / R1) (23)

[0077] The speed following deviation e vi is:

[0078] e Vi = V icmd -V i (24).

[0079] Compared with the prior art, the present invention adopts the above technical solutions and has the following technical effects:

[0080] (1) Only a single route of the virtual lead aircraft needs to be provided, and the flight routes of all aircraft can be generated through the formation geometry constraint rules, reducing the data communication volume and being easy to implement in engineering;

[0081] (2) Generate the expected reference points for formation control based on the virtual formation, improve the formation stability, and reduce the risk of formation collapse;

[0082] (3) When switching the route, fly along an arc route and switch the expected reference points of the aircraft to reduce the formation control error;

[0083] (4) The present invention designs a simple, engineering-implementable and stable formation control method to reduce the system's demand for high-bandwidth networking radio communication, increase the system's stability, improve the formation control accuracy, and obtain satisfactory formation flight effects. Description of the Drawings

[0084] Figure 1 is the flight control flow chart of the formation UAV;

[0085] Figure 2a is the multi-aircraft formation topology structure diagram;

[0086] Figure 2b is the topology structure information transmission diagram;

[0087] Figure 3It is a geometric schematic diagram of a multi-aircraft "V" formation;

[0088] Figure 4 It is a geometric schematic diagram of a formation in the en-route flight mode;

[0089] Figure 5 It is a schematic diagram of the en-route switching judgment conditions;

[0090] Figure 6 It is a geometric schematic diagram of a formation in the en-route switching mode;

[0091] Figure 7 It is a schematic diagram of the washout conditions in the en-route switching mode;

[0092] Figure 8 It is a schematic diagram of the following deviation in the en-route flight mode;

[0093] Figure 9 It is a schematic diagram of the following deviation in the en-route switching mode;

[0094] Figure 10 It is a formation flight route map;

[0095] Figure 11 It is a curve graph of the change in the horizontal distance between the formation unmanned aircraft and UAV1;

[0096] Figure 12 It is a curve graph of the change in the altitude of the formation unmanned aircraft. Specific implementation manners

[0097] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0098] A single - route virtual leader formation method based on geometric constraint rules updates the position of the virtual leader in real - time on a pre - planned single route. According to the geometric constraint rules, the virtual formation is deduced from the position of the virtual leader. In the straight - line segment, the formation UAVs generate expected reference points based on the virtual formation. In the switching segment, an arc route is adopted, and the virtual formation is used as the expected reference point to achieve formation flight. In terms of formation lateral position control, in the route flight mode, the expected reference points of the virtual formation on the route are calculated by the geometric constraint rules, and then the expected reference points of the formation UAVs are deduced. The expected reference points are substituted into the line - of - sight guidance law to obtain the roll - angle commands required for each aircraft to maintain the formation. In the route switching mode, to reduce the formation control error and improve the formation stability, the virtual formation calculates the position in real - time according to the arc route, and the formation UAVs perform the switching of expected reference points, and use the virtual formation as the expected reference point to generate the roll - angle commands for formation maintenance. In terms of formation longitudinal position control, this method designs a longitudinal position - maintaining controller with the following deviation between the formation UAVs and the virtual formation as the input quantity. To reduce the longitudinal position error caused by different arc radii, the calculation of the following deviation is still divided into two parts: the route flight mode and the route switching mode.

[0099] In the method of the present invention, the aircraft formation generates expected reference points by combining pre - designed geometric constraint rules with the line - of - sight guidance law. Adopting the way of virtual - leader navigation, only a single route of the virtual leader needs to be provided to complete the formation - shape - maintaining control. The virtual - leader formation has high reliability in maintaining the formation, does not depend on a high - bandwidth networking radio communication link, can realize the accurate formation - shape maintenance and route - tracking control of multiple aircraft, and is easy to be implemented in engineering. The aircraft realizes the formation - shape maintenance and route - tracking control during the flight process.

[0100] This embodiment describes a single - route virtual leader formation method based on geometric constraint rules, and its flow chart is as Figure 1 shown. The formation UAVs obtain the roll - angle commands φ for lateral position maintenance, the speed commands δ for longitudinal position maintenance T , and the elevator commands δ for altitude maintenance θ through the method of the present invention according to the pre - planned route information, and realize the formation - shape control and complete the tracking of the route. The specific implementation method is as follows:

[0101] Multi - aircraft formation topology

[0102] Update the position of the virtual leader in real - time on a pre - planned single route. According to the geometric constraint rules, deduce the virtual formation from the position of the virtual leader. In the straight - line segment, the formation UAVs generate expected reference points based on the virtual formation. In the switching segment, adopt an arc route and use the virtual formation as the expected reference point to achieve formation flight.

[0103] As Figure 2a 、 Figure 2bAs shown in the figure, the topological structure of the formation flight method proposed by the present invention is as follows: Define the virtual formation as consisting of virtual machines, denoted as P, where P = {PV i , i = 1, 2, 3… I}, I is the number of virtual machines and also the number of formation UAVs. PV i is the virtual machine of the i-th formation UAV. Select PV1 as the virtual lead aircraft, and update the position of the virtual lead aircraft in real time on the pre-planned single flight path. According to the geometric constraint rules, calculate the virtual formation from the position of the virtual lead aircraft, and then obtain the expected reference point T i of the virtual formation. The formation UAV UAV i receives the position, speed information of the virtual formation and the coordinate information of point T i in real time, and calculates the expected reference point T Ui of the formation UAV.

[0104] Lateral position keeping method for en-route flight mode

[0105] Taking the multi-aircraft "V" formation of Figure 3 as an example, the control method is designed. As Figure 4 shown, in the en-route flight mode, the steps for the formation UAV UAV1 and the formation UAV UAV2 (the remaining formation UAVs can be obtained similarly from UAV2) to solve the roll angle command required for formation lateral position keeping are as follows:

[0106] (1) Select PV1 in the virtual machine as the virtual lead aircraft, which flies along the flight path at a constant speed V0 in the en-route flight mode. Its position in the NED coordinate system is (PV 1N , PV 1E ). PV2 flies in formation synchronization with it at a distance d f2 and an included angle of α f2 (when the formation UAV is on the right side of the virtual lead aircraft, α f2 is positive, and vice versa, α f2 is negative). Then the position of PV2 can be obtained from the geometric constraint rules:

[0107] PV 2N = PV 1N - d f2 cos(ψ seg1 - α f2 ) (25)

[0108] PV 2E = PV 1E - d f2 sin(ψ seg1 - α f2 ) (26)

[0109] where PV 1N , PV 1Eare the components of the virtual lead aircraft coordinates in the N and E (northward is the N axis, eastward is the E axis) directions, PV 2N , PV 2E are the components of PV2 in the N and E directions, ψ seg1 In the straight-line segment, it is the angle between the first flight path and the northward direction, and the expression is:

[0110]

[0111] Among them, WP 1,N , WP 1,E are the components of the coordinates of the starting point WP1 of the first flight path in the N and E directions, WP 2,N , WP 2,E are the components of the coordinates of the ending point WP2 of the first flight path in the N and E directions.

[0112] (2) Calculate the expected reference point of the virtual formation on the flight path WP1 - WP2:

[0113]

[0114] Among them, T 1N , T 1E are the components of the expected reference point T1 of PV1 in the N and E directions respectively, T 2N , T 2E are the components of the expected reference point T2 of PV2 in the N and E directions respectively, l f is the tracking distance of the virtual formation relative to the expected reference point.

[0115] The expected reference point of the formation UAVs is calculated through the expected distance D between the virtual formation and the formation UAVs:

[0116]

[0117] Among them, T U1N , T U1E are the components of the expected reference point T U1 of the formation UAVs in the N and E directions respectively, T U2N , T U2E are the components of the expected reference point T U2 of the formation UAVs in the N and E directions respectively.

[0118] (3) Substitute the ground speed V g , track angle Ω, and the angle β Ui between the position and the expected reference point T f into the line-of-sight guidance law to calculate the lateral position maintaining roll angle command of the formation UAVs. The position of the formation UAV UAV1 is U1(U 1N , U 1E ), U 1N , U1E is the component of the UAV1 position in the N and E directions, and the components of the flight speed in the NED coordinate system are (V 1N , V 1E ), V 1N , V 1E are the components of the UAV1 flight speed in the N and E directions:

[0119]

[0120] Ω1 = arctan(V 1E , V 1N ) (31)

[0121] β f1 = arctan((T U1E - U 1E ), (T U1N - U 1N )) (32)

[0122] ε1 = β f1 - Ω1 (33)

[0123] Then the desired roll angle φ1 of UAV1 is:

[0124]

[0125] where g is the acceleration due to gravity, and l′ f is the length of the UAV i tracking T Ui . According to the position U2(U 2N , U 2E ), U 2N , U 2E are the components of the UAV2 position in the N and E directions, and the flight speed (V 2N , V 2E ), V 2N , V 2E are the components of the UAV2 flight speed in the N and E directions. Similarly, the desired roll angle φ2 of UAV2 can be obtained:

[0126]

[0127] Ω2 = arctan(V 2E , V 2N ) (36)

[0128] β f2 = arctan((T U2E - U 2E ), (T U2N - U 2N )) (37)

[0129] ε2 = β f2 -Ω2 (38)

[0130]

[0131] Lateral position holding method during route switching phase

[0132] (1) Cut-in conditions for the route switching mode:

[0133] As Figure 5 shown, when the T1 point reaches the end point WP2 of the first route segment, the route switching mode is entered. At this time, the virtual lead aircraft is located at the mode cut-in point A. Through the WP2 coordinates, the included angle ψ between the first route segment WP1 - WP2 and the north direction seg1 , the included angle ψ between the second route segment WP2 - WP3 and the north direction seg2 and the tracking distance l f are used to obtain the coordinates of point A (A N , A E ), the coordinates of point B, the mode washout point (B N , B E ). A N , A E and B N , B E are the components of points A and B in the N and E directions respectively, and the expressions are:

[0134]

[0135] where ψ seg2 is the included angle between the second route segment and the north direction:

[0136]

[0137] (2) Calculation of the roll angle command for formation keeping during the route switching mode::

[0138] As Figure 6 shown, the virtual lead aircraft flies along an arc route during route switching. The position (PV 1N , PV 1E ) is obtained from the arc geometric constraint rules:

[0139] PV 1N = O N + R1 sin(δ + ξ) (42)

[0140] PV 1E = O E - R1 cos(δ + ξ) (43)

[0141] where O N , O EThe components of the in - center O of the inscribed circles of the two flight routes WP1 - WP2 and WP2 - WP3 in the N and E directions, R1 is the radius of the inscribed circle of the virtual lead aircraft, and δ is the angle between the line connecting the virtual lead aircraft at point A and the center of the circle and the E direction. The expression is:

[0142] δ = arctan((A N - O N ),(A E - O E )) (44)

[0143] The central angle ξ corresponding to the flight path of the virtual lead aircraft is obtained from the speed V0 of the virtual lead aircraft and the flight time t when entering the route switching mode:

[0144]

[0145] ξ = ωt (46)

[0146] Among them, ω is the angular velocity of the virtual lead aircraft flying along the circular arc route. At this time, the coordinates of the virtual formation PV2 are still obtained according to the straight - line segment calculation formulas (25) and (26), and ψ′ seg1 is the angle between the circular arc tangent between the first and the second flight routes and the north direction. Its formula is:

[0147] ψ′ seg1 = δ + ξ (47)

[0148] In the route switching mode, the formation UAVs will use PV1 and PV2 as the desired reference points. Substitute formula (47) into formulas (25) and (26) to obtain the coordinates of PV i in the route switching mode section, and then obtain the roll - angle commands required for each formation UAV to maintain the formation.

[0149] (3) Wash - out judgment conditions for the route switching mode:

[0150] The wash - out conditions for the route switching mode are divided into two steps:

[0151] According to the first condition, if it is judged that the virtual lead aircraft has completed the circular arc route flight, it will continue to fly along the next flight route;

[0152] After the first condition is satisfied, according to the second condition, judge when each formation UAV will switch the desired reference point from PV i to T Ui ;

[0153] If both the first condition and the second condition are satisfied, then the route switching mode is washed out, and it switches to the route flight mode for the formation flight of the next flight route;

[0154] As Figure 7 shown, the first condition is:

[0155]

[0156] Among them, is the vector from the center O to the virtual lead aircraft PV1, is the modulus value, is the vector from waypoint WP2 to WP3, is the modulus value.

[0157] The second condition is:

[0158] |ψ i -ψ seg2 | < ρ f (49)

[0159] When the difference between the track angle of each formation UAV and the route angle of the next section of the route is less than ρ f , it is judged that the washout of the route switching mode. Among them, ρ f is the washout threshold, and ψ i is the flight track angle of the i-th formation UAV.

[0160] Longitudinal position keeping control method

[0161] Taking the following deviation between the formation UAV and the virtual formation as the input quantity, a longitudinal position keeping controller is designed. The calculation process of the following deviation is as follows. To reduce the longitudinal position error caused by different radii during circular flight, the method design in this section is still divided into two parts: the route flight mode and the route switching mode.

[0162] (1) Following deviation in the route flight mode

[0163] As Figure 8 shown, the actual distance D i between the formation UAV and PV i is:

[0164]

[0165] Among them, U iE , U iE (i = 1, 2, 3…I, I is the number of virtual machines) are the components of the real-time position of the i-th formation UAV in the N and E directions, and PV iN , PV iE are the components of the PV i coordinates in the N and E directions. Then the distance following deviation of the i-th formation UAV is:

[0166] e Di = D i - D (51)

[0167] In this mode, the virtual formation speeds are all consistent with the speed V0 of the virtual lead aircraft. Therefore, the speed following deviation of the i-th formation UAV is:

[0168] e Vi = V0 - V i (52)

[0169] where V i is the flight speed of each formation UAV.

[0170] (2) Following deviation in the route switching mode

[0171] In this mode, an arc route is adopted, and the formation UAVs will perform turning flights. The speed deviation is calculated based on the flight radius and the speed V0 of the virtual lead aircraft. The schematic diagram for solving the deviation in this mode is as Figure 9 shown.

[0172] Except for the virtual lead aircraft, the difference between the arc radius R i of PV i and the inscribed circle radius R1 of the virtual lead aircraft is ΔR:

[0173] ΔR = d fi sinα fi (53)

[0174] ① Turn left along the route flight direction, and the i-th formation UAV is located on the left side of the virtual lead aircraft; or turn right along the route flight direction, and the i-th formation UAV is located on the right side of the virtual lead aircraft;

[0175] R i = R1 - ΔR (54)

[0176] ② Turn right along the route flight direction, and the i-th formation UAV is located on the left side of the virtual lead aircraft; or turn left along the route flight direction, and the i-th formation UAV is located on the right side of the virtual lead aircraft;

[0177] R i = R1 + ΔR (55)

[0178] The distance following deviation in the route switching mode is the same as that in the route flight mode. The expected speed V icmd of the formation UAVs is:

[0179] V icmd = V0(R i / R1) (56)

[0180] (3) Longitudinal position holding controller

[0181] The input of the longitudinal position holding controller, e x is:

[0182] ex = k D e Di + k V e Vi (57)

[0183] The longitudinal position holding controller is as follows:

[0184]

[0185] δ T is the throttle control amount, and k D , k V , k px , k ix , k dx are fixed parameters, thereby achieving the longitudinal position holding control of formation flight.

[0186] Formation altitude holding control method

[0187] The altitude holding of the formation UAV is divided into two parts: the altitude outer loop and the pitch angle inner loop. The input of the altitude loop is the deviation e h :

[0188] e h = PV iD - U iD (59)

[0189] The desired pitch angle command θ d is calculated by the altitude outer loop, and its expression is:

[0190]

[0191] k ph , k ih , k dh are the proportional, integral, and derivative gains of the altitude outer loop respectively. The input of the pitch angle inner loop is the deviation between the desired pitch angle and the actual pitch angle θ i , and its expression is:

[0192] e θ = θ i - θ (61)

[0193] The elevator control amount δ θ is calculated to achieve the altitude holding of the formation, and its expression is:

[0194]

[0195] k pθ , k iθ , k dθ are the proportional, integral, and derivative gains of the pitch angle inner loop respectively.

[0196] Simulation test verification

[0197] To verify the effectiveness of the formation flight control method proposed by the present invention, a simulation test is carried out on the existing non-linear model of a certain type of fixed-wing UAV. According to the flight performance of the UAV, the simulation parameters are set as follows: where d fi = 100m, α fi = 45°, the flight speed of the virtual lead aircraft V0 = 40m / s, the tracking length l f = 400m, the tracking length l' of the UAV f = 150m, the expected distance D between the PV i and the formation UAV is 150m, and the single planned route is WP1 = (500,0,-200)m, WP2 = (3000,0,-200)m, WP3 = (4500,1500,-200)m. The simulation results are as Figures 10 - 12 shown. The initial positions of the five formation UAVs are randomly distributed. During the flight process from 0 to 40s, the five formation UAVs gradually complete the formation; at 62s, the formation UAVs enter the route switching mode. At this time, the actual relative distance between the formation UAVs slightly deviates from the ideal formation distance. The formation control errors of UAV2 and UAV3 are within 10m, and the formation control errors of UAV4 and UAV5 are within 16m. Among them, since UAV4 has the smallest turning radius during the circular flight, its deceleration amplitude is the largest, resulting in a height error of about 2m, but it can still maintain a good formation flight; during the flight process from 90 to 112s, the formation UAVs have completed the route switching, and the relative distance of the formation UAVs tracks the ideal formation distance. Thus, it can be seen that the formation flight control method proposed by the present invention has higher accuracy in route tracking. When the route is switched, the formation control accuracy is better, thereby verifying the effectiveness of the present invention.

[0198] As mentioned above, it is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A single - route virtual lead - aircraft formation method based on geometric constraint rules, characterized in that, Including the lateral position control of the en-route flight mode and the lateral position control of the en-route switching mode, where Pre-design the formation flight route; Lateral position control of the en-route flight mode: In the en-route flight mode, according to the position of the virtual leader and the geometric constraint rules, generate the expected reference point of the virtual formation on the route, and then calculate the expected reference point of the formation UAVs. According to the expected reference point of the formation UAVs, use the line-of-sight guidance law to obtain the roll angle command for each formation UAV to maintain the formation; Lateral position control of the en-route switching mode: When the expected reference point of the virtual leader reaches the end of each section of the route, fly along an arc route. The virtual formation calculates the position in real time according to the arc route; the en-route switching mode performs the switching of the expected reference point. The formation UAVs generate the roll angle command for formation maintenance with the virtual formation as the expected reference point, and use the virtual leader position and the track angle of the formation UAVs as the mode washout conditions; It also includes the control of the formation longitudinal position. The control of the formation longitudinal position means: divide the following deviation calculation method into two parts: en-route flight and switching mode, and design a longitudinal position maintenance controller with the following deviation as the input quantity; The formation flight route includes K segments of routes, where K is an integer greater than or equal to 2. The virtual formation P consists of virtual aircraft, and P = {PV i , i = 1, 2, 3… I}, where I is the number of virtual aircraft and also the number of formation UAVs. PV i is the virtual aircraft of the i-th formation UAV. PV1 is selected as the virtual lead aircraft. During the route flight phase, according to the position of the virtual lead aircraft, the position coordinates of the virtual formation are generated through geometric constraint rules. The position coordinates of PV i are as follows: Among them, PV 1N and PV 1E are the components of the virtual lead aircraft coordinates in the N and E directions. The north direction is the N direction, and the east direction is the E direction. PV iN and PV iE are the components of PV i coordinates in the N and E directions. d fi is the formation spacing of the i-th formation UAV. α fi is the formation angle of the i-th formation UAV. When the i-th formation UAV is on the right side of the virtual lead aircraft, α fi is positive, otherwise α fi is negative. ψ segk is the angle between the k-th route segment and the north direction. k is an integer and 1 ≤ k ≤ K, where K is the total number of route segments. The expression of ψ segk is as follows: Among them, WP k,N and WP k,E are the components of the starting point coordinates of the k-th flight path in the N and E directions, and WP k+1,N and WP k+1,E are the components of the ending point coordinates of the k-th flight path in the N and E directions; Furthermore, the expected reference point T of PV is obtained. i i :​ T iN = PV iN + l f cosψ segk (4) T iE = PV iE + l f sin ψ segk (5) Among them, T iN and T iE are the components of T i in the N and E directions respectively, and l f is the tracking distance of the virtual formation relative to T i ; The expected reference point T of the i-th formation UAV is calculated through the expected distance D between the virtual formation and the formation UAVs Ui : Among them, T UiN and T UiE are the components of T Ui in the N and E directions respectively; The ground speed V of the formation UAV g , the track angle Ω, and the angle β Ui between the position and the desired reference point T f are substituted into the line-of-sight guidance law to calculate the roll angle command for maintaining the lateral position of the formation UAV; When k = K, it is determined that the formation UAVs have completed all en-route flight tasks and no longer perform en-route switching mode flight; when k is an integer between 1 and K - 1, the formation UAVs perform en-route switching mode flight. The cut-in condition of the en-route switching mode is: When T1 reaches the end point WP of the k-th route segment k+1 it enters the route switching mode. At this time, the virtual lead aircraft is located at the mode cut-in point A. Through the WP k+1 coordinates, the included angle ψ k —WP k+1 between the k-th route segment WP segk —WP k+1 and the north direction, the included angle ψ k+2 between the (k + 1)-th route segment WP segk+1 —WP f and the north direction, and the tracking distance l N , the coordinates of point A (A E ), and the coordinates of the mode washout point B (B N , B E ) are obtained. WP k is the starting point of the k-th route segment, WP k+1 is the end point of the k-th route segment and at the same time serves as the starting point of the (k + 1)-th route segment, WP k+2 is the end point of the (k + 1)-th route segment. A N , A E , B N , and B E are the components of points A and B in the N and E directions respectively. The expressions are as follows: WP k+2,N 、WP k+2,E are the components of the end point coordinates of the (k + 1)-th route segment in the N and E directions; Calculation of the roll angle command for formation maintenance in the en-route switching mode: The virtual host performs an arc route flight during the airway handover, and its real-time position (PV 1N , PV 1E ) is obtained from the arc geometric constraint rules: PV 1N = O N + R1sin(δ + ξ) (9) PV 1E = O E -R1cos(δ + ξ) (10) Among them, O N and O E are the components of the in - center O of the two flight paths WP k —WP k+1 , WP k+1 —WP k+2 in the N and E directions. R1 is the radius of the in - circle of the virtual lead aircraft, and δ is the angle between the line connecting the virtual lead aircraft at point A and the center of the circle and the E direction. The expression is as follows: δ=arctan((A N -O N ),(A E -O E )) (11) The central angle ξ corresponding to the flight route of the virtual leader is obtained from the virtual leader speed V0 and the flight time t when entering the en-route switching mode: ξ = ωt (13) where ω is the angular velocity of the virtual leader flying along the arc route. At this time, the PVi coordinates are still obtained according to the straight-line segment calculation formulas (1) and (2); In the arc segment, the included angle between the arc tangent line between the k-th and the (k + 1)-th navigation routes and the north direction is ψ′ segk , ψ′ segk = δ + ξ (14) In the route switching mode, the formation UAVs use PV i as the desired reference point, substitute the calculation result of formula (14) into formulas (1) and (2) to obtain the coordinates of PV i in the route switching mode section, and then obtain the roll angle commands required for each formation UAV to maintain the formation in the route switching mode; Washout judgment condition of the en-route switching mode: The washout conditions of the en-route switching mode are specifically as follows: According to the first condition, judge that if the virtual leader has completed the arc route flight, then continue to fly along the next section of the route; After the first condition is satisfied, determine when each formation UAV will switch the desired reference point from PV i to T Ui ; If both the first condition and the second condition are satisfied, then the en-route switching mode is washed out and switched to the en-route flight mode for formation flight of the next section of the route; The first condition is: Among them, is the vector from the center O to the virtual lead aircraft PV1, is the modulus of, is the vector from WP k+1 to WP k+2 ; is the modulus of; The second condition is: |ψ i -ψ segk+1 |<ρ f (16) When the difference between the track angle of the formation UAV and the route angle of the next section of the route is less than ρ f , it is judged that the washout of the route switching mode; where ρ f is the washout threshold, and ψ i is the flight track angle of the i-th formation UAV.

2. A method for forming a virtual lead aircraft formation with a single route based on geometric constraint rules according to claim 1, characterized in that, Design a longitudinal position maintenance controller with the following deviation between the formation UAVs and the virtual formation as the input quantity. The following deviation calculation process is as follows: (1) Following deviation in the en-route flight mode The actual distance D between the i-th formation UAV and the virtual machine PV of the i-th formation UAV i is i as follows: where U iN and U iE are the components of the real-time position of the i-th formation UAV in the N and E directions, PV iN and PV iE are the components of the PV i coordinates in the N and E directions, then the distance following deviation e Di of the i-th formation UAV is: e Di = D i - D (18) In this mode, the virtual formation speeds are all consistent with the speed V0 of the virtual lead aircraft. Therefore, the speed following deviation e of the i-th formation UAV vi is as follows: e Vi = V0 - V i (19) Among them, V i is the flight speed of the i-th formation UAV; (2) Following deviation in the en-route switching mode In this mode, an arc route is adopted, and the formation UAVs will perform turning flight. Calculate the speed deviation according to the flight radius and the virtual leader speed V0; PV except for the virtual host i The arc radius R i The difference ΔR from the inscribed circle radius R1 of the virtual host is: ΔR = d fi sinα fi (20) Among them, d fi is the formation spacing of the i-th formation UAV, and α fi is the formation angle of the i-th formation UAV; ① Turn left along the flight direction of the route, and the ith formation UAV is on the left side of the virtual leader; or turn right along the flight direction of the route, and the ith formation UAV is on the right side of the virtual leader; R i = R1 - ΔR (21) ② Turn right along the flight direction of the route, and the ith formation UAV is on the left side of the virtual leader; or turn left along the flight direction of the route, and the ith formation UAV is on the right side of the virtual leader; R i = R1 + ΔR (22) The distance following deviation in the route switching mode is the same as that in the route flight mode, and the expected speed V of the formation UAVs icmd is as follows: V icmd = V0(R i / R1) (23) Velocity following deviation e vi is as follows: e Vi = V icmd - V i (24).

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