A method for planning the return trajectory of UAV formations based on the Durbins curve

Abstract

This invention discloses a method for planning the return trajectory of unmanned aerial vehicles (UAVs) in formation based on the Durbins curve, belonging to the field of UAV trajectory planning technology. It can adapt to any initial heading and formation flight heading of the UAVs, automatically adjust the phase of the UAVs relative to the formation, and ensure safety. The method includes the following steps: obtaining the UAV's own position and heading; designing a Durbins return flight path based on the desired return point position and heading; adjusting the UAV's flight altitude to be staggered from the formation flight altitude; calculating the phase difference based on the UAV's arrival time at the return point and the desired return time, and designing a phase adjustment path; adjusting the UAV's flight altitude to match the formation flight altitude, and returning to the formation; ensuring that the UAVs accurately and efficiently reintegrate into the original formation trajectory under safe and collision-free conditions.

Description

Technical Field

[0001] This invention belongs to the field of UAV trajectory planning technology, specifically relating to a method for planning the return trajectory of UAV formations based on the Durbins curve. Background Technology

[0002] The return journey of unmanned aerial vehicles (UAVs) after performing reconnaissance missions within a formation is a crucial step in ensuring the continuity of the formation's mission. When the return point is determined to be a specific location within the formation, trajectory planning faces a series of complex issues, including safety assurance, formation adaptation, and phase alignment. The UAVs must ensure the safety of the return process, avoiding collisions with other formation members still on missions; simultaneously, they need to accurately select the return point to adapt to the formation's dynamic trajectory and formation; and strictly control the return time to ensure that the UAVs are accurately positioned when the formation reaches the rendezvous point, achieving phase alignment.

[0003] However, existing research largely focuses on formation maintenance and cooperative control, and only considers the return of UAVs in static formations, with insufficient research on methods for UAVs to return and re-enter dynamic formations. For example, patent CN117387625A proposes a return planning method based on the Durbins curve, which considers the initial and target headings of the UAV and achieves path smoothing. However, this method has significant limitations; its return point is only considered as geographical coordinates and is not adapted to dynamic formation scenarios. This means that this method cannot solve the core problem of how UAVs accurately dock with dynamic formation structures, i.e., how to achieve precise overlap with the formation in space and time. Existing technologies lack research on this. Moreover, during the process of UAVs re-entering the formation, they need to start from the current position and enter the formation with a specific heading. However, traditional path planning methods often ignore the deviation between the initial heading of the UAV and the heading of the formation, which may lead to improper flight path planning and increase flight risks. Therefore, designing reasonable return trajectories and strategies based on the characteristics of formation return is of vital importance to solving the core problem of UAVs safely, efficiently, and accurately re-entering the original dynamic formation. Summary of the Invention

[0004] This invention provides a method for planning the return trajectory of UAV formations based on the Dubins curve, which can solve the problem in the prior art that it is difficult for UAVs to accurately align with the predetermined position in the formation and achieve phase synchronization when returning from a reconnaissance mission. This ensures that UAVs can accurately and efficiently reintegrate into the original formation trajectory under the premise of safety and no collision.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for planning the return trajectory of UAV formations based on the Durbins curve includes the following steps:

[0007] S1: Obtain the drone's own position and heading, and design the Dubins return route based on the expected return point position and heading;

[0008] S2: Adjust the drone's flight altitude to be different from the formation's flight altitude;

[0009] S3: Calculate the phase difference based on the time the UAV arrives at the return point and the expected return time, and design the phase adjustment route;

[0010] S4: Adjust the drone's flight altitude to match the formation's flight altitude and rejoin the formation.

[0011] In the above steps, the Dubins route described in S1 selects one of the four standard path types LSL (left-straight-left), LSR (left-straight-right), RSL (right-straight-left), or RSR (right-straight-right) according to the actual situation to generate the optimal smooth path from the current position of the UAV to the return point.

[0012] In S3, the phasing flight path length and number of flight circles for the UAV are determined based on the UAV's performance constraints and the difference between the actual arrival time and the expected arrival time; the shortest flight distance... From the time of arrival at the return point Expected arrival time Speed Formation sailing cycle Circular arc segment radius and formation route length The decision is as follows:

[0013]

[0014] in, express right Take the remainder. The value is an adjustable integer and should be selected appropriately. Make The distance is sufficient for phase adjustment, therefore Must meet:

[0015] ,

[0016] at the same time, The distance should be as short as possible so that the drones can re-enter the formation as quickly as possible. At the same time, the following conditions must also be met:

[0017] .

[0018] Further calculations revealed the number of laps the drone needed to make along the phasing path. and straight segment length :

[0019] ,

[0020] in This indicates rounding down to the nearest integer.

[0021] Beneficial effects: This invention provides a method for planning the return trajectory of UAV formations based on the Durbins curve, which has the following advantages compared with the prior art:

[0022] 1. During the re-entry of a UAV into formation, it needs to start from its current position and enter the formation with a specific heading. Traditional path planning methods often ignore the deviation between the UAV's initial heading and the formation heading, which may lead to improper flight path planning and increase flight risks. The method of this invention comprehensively considers the UAV's current heading, the target return point heading, and their dynamic constraints, and uses the Dubins curve to generate a smooth and safe transition route, ensuring the safety and efficiency of the return process.

[0023] 2. Re-entering a formation requires real-time response to the formation's dynamic movements. Existing technologies often rely on adjusting the drone's own speed or coordinating with other members of the formation to match the phase, which not only increases system complexity but may also interfere with the original formation's flight mission. This invention innovatively designs a phase-alignment flight path that adaptively aligns the drone's phase with the formation, thereby achieving a smooth re-entry of the drone without affecting the original formation's flight mission.

[0024] 3. The method of the present invention has low computational load, does not require complex online real-time calculations to determine the current position of the UAV and continuously issue the desired position command, and can adapt to any initial heading of the UAV and formation flight heading, automatically adjust the phase of the UAV with the formation, avoid collisions and ensure safety, and provide a trajectory planning scheme with low computational burden, easy implementation and reliable effect for UAV formation return mission. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the UAV return trajectory planning in an embodiment of the present invention;

[0026] Figure 2 This is a schematic diagram of Durbins curves in different directions in an embodiment of the present invention;

[0027] Figure 3 This is a simulated flight path diagram of the UAV in an embodiment of the present invention;

[0028] Figure 4 This is a time diagram showing the specific flight segments of the UAV in this embodiment of the invention. Detailed Implementation

[0029] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments:

[0030] like Figure 1 As shown, the drones are arranged in formation, evenly distributed along a closed flight path, and travel at a constant speed along a circular trajectory. At a certain moment, one drone breaks away from the formation at the departure point to carry out a reconnaissance mission and enter its mission segment. After completing the reconnaissance mission, it performs Dubins flight path planning from the return starting point with the initial heading, adjusts its flight altitude, enters the return segment, and arrives at the return point with the desired attitude. The Dubins flight path design needs to be based on the actual situation, such as... Figure 2 As shown, select one of the four standard path types: LSL (left-straight-left), LSR (left-straight-right), RSL (right-straight-left), or RSR (right-straight-right) to generate the optimal smooth path from the UAV's current position to the return point.

[0031] Let the initial position coordinates of the UAV be... yaw angle is The coordinates of the return point are The desired yaw angle is Set the radius of the tangent circle at the return starting point to be... The radius of the tangent circle at the return point is Based on geometric relationships, the coordinates of the center of the initial tangent circle can be easily obtained. Coordinates of the center of the circle tangent to the return point .

[0032] When the Dubins curve is RSR or RSL, the coordinates of the center of the initial tangent circle are:

[0033] .

[0034] When the Dubins curve is LSR or LSL, the coordinates of the center of the initial tangent circle are:

[0035] .

[0036] When the Dubins curve is RSR or LSR, the coordinates of the center of the tangent circle at the return point are:

[0037] .

[0038] When the Dubins curve is RSL or LSL, the coordinates of the center of the tangent circle at the return point are:

[0039] .

[0040] Based on the coordinates of the center of the circle and the type of the Dobbins curve, the coordinates of the tangent point are further determined. and heading at the cut-out point and the coordinates of the entry point and heading at the entry point :

[0041] RSR type (with true north as 0 degrees and clockwise as positive):

[0042]

[0043] RSL type:

[0044] ,

[0045] LSR type:

[0046] , LSL type:

[0047] ,

[0048] Calculate and compare the lengths of the four types of Durbins paths, and select the shortest path for navigation.

[0049] Upon entering the return flight segment, the drone adjusts its altitude to avoid collisions with the formation.

[0050] Upon reaching the return point, the drone enters the phasing flight segment, with the phasing route resembling a runway, where the radius of the circular arc segment is... Based on the drone's flight speed and design roll angle The settings are as follows:

[0051] ,

[0052] Where g is the acceleration due to gravity.

[0053] Let the time it takes for the drone to reach the return point directly via the shortest Durbins path be . The expected time for the current drones in the formation to reach the return point is The speed is The formation sailing period is The formation's route length is The shortest flight distance of the UAV on the phase-adjustment route. Based on the above variables and the radius of the circular arc segment route The decision is made jointly, and the expression is:

[0054] ,

[0055] Where mod represents the remainder. To adjust the parameters, appropriate selection is required. Make The distance is sufficient for phase adjustment, therefore Must meet and:

[0056] ,

[0057] at the same time, The distance should be as short as possible so that the drones can re-enter the formation as quickly as possible. At the same time, the following conditions must also be met:

[0058] .

[0059] The expected time for the current drone in the formation to reach the return point. The number of laps the drones need to make along the phasing path is determined by the arrival time of the first drone in the formation and the phase difference between the current drone and the first drone. and straight segment length :

[0060] ,

[0061] in This indicates rounding down to the nearest integer.

[0062] In this embodiment, it is assumed that the total number of drones in the formation is... The current drone's serial number is The phase difference between the current drone and the first drone is:

[0063] .

[0064] Let the expected time for the first drone to reach the return point be... The expected time for the current drone in the formation to reach the return point is:

[0065] .

[0066] Number of flight circles of the UAV in the phasing segment and the length of the straight line segment It is determined by the following relationship:

[0067] ,

[0068] in This indicates rounding down to the nearest integer.

[0069] After the phase adjustment segment, the UAV's flight path is aligned with the formation. By adjusting the flight altitude, it can return to the formation.

[0070] The simulated flight path of the drone is as follows Figure 3 As shown, the specific timeframe for the simulation phase is as follows: Figure 4The simulation results only show the flight path of UAV No. 3. Starting at 725.32s, UAV No. 3 enters a long, closed flight path, evenly distributed along it with the other two UAVs. At 1083.90s, UAV No. 3 leaves the formation to perform a reconnaissance mission. At 1199.03s, the reconnaissance mission ends, and UAV No. 3 flies along the return flight path, entering the phasing phase at 1297.66s. At 1394.71s, it returns to the closed flight path and rejoins the formation. The expected return time of the UAV should be several flight cycles from 725.32s, where the flight cycle... Let the time required for the UAV to travel one revolution along a closed flight path at a speed of 50 m / s be the actual arrival time, and the error between the actual arrival time and the expected arrival time be... The error is less than 1 second.

[0071] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A Dubins curve based trajectory planning method for UAV formation homing, characterized in that, Includes the following steps: S1: Obtain the UAV's own position and heading, and design the Dubins return route based on the expected position and heading of the return point. The Dubins return route is calculated and compared according to one of the four standard path types: LSL, LSR, RSL, and RSR, and the shortest path is selected for navigation. S2: Adjust the drone's flight altitude to be different from the formation's flight altitude; S3: Based on the UAV's arrival time at the return point and the expected return time, calculate the phase difference and design a phase adjustment route. This route is "runway-shaped." The length and number of flight circles of the phase adjustment route are determined based on the UAV's performance constraints and the difference between the actual and expected arrival times. The radius of the circular arc segment of the runway-shaped phase adjustment route... Based on the drone's flight speed and design roll angle The settings are as follows: ， Where g is the acceleration due to gravity; Shortest flight distance of UAV on the phase adjustment route From the time of arrival at the return point Expected arrival time Speed Formation sailing cycle Circular arc segment radius and formation route length The decision is as follows: ， in, express right Take the remainder. An adjustable integer. Must meet: ， The distance should be as short as possible so that the drones can re-enter the formation as quickly as possible. At that time, the following conditions must be met: ； The number of laps the drone needs to make along the phasing path was calculated. and straight segment length : ， in Indicates rounding down; S4: Adjust the drone's flight altitude to match the formation's flight altitude and rejoin the formation.

2. The method for planning the return trajectory of UAV formation based on the Durbins curve according to claim 1, characterized in that, Based on the center coordinates and the type of the Dobbins curve, determine the coordinates of the tangent point and its heading, and the coordinates of the inlet point and its heading. For the RSR type: ， Calculate the Durbins path length; Among them, (x) c0 , y c0 ( ) represents the coordinates of the center of the initial tangent circle. Let the radius of the tangent circle at the starting point of the return journey be _____. Let the radius of the tangent circle at the return point be . Let the coordinates be the center of the circle tangent to the return point. The heading at the cut-out point. The heading at the entry point. The coordinates of the cutting point, These are the coordinates of the entry point.

3. The method for planning the return trajectory of UAV formation based on the Durbins curve according to claim 1, characterized in that, Based on the center coordinates and the type of the Dobbins curve, determine the coordinates of the exit point and the heading at the exit point, and the coordinates of the entry point and the heading at the entry point. For the RSL type: ， Calculate the Durbins path length; Among them, (x) c0 , y c0 ( ) represents the coordinates of the center of the initial tangent circle. Let the radius of the tangent circle at the starting point of the return journey be _____. Let the radius of the tangent circle at the return point be . Let the coordinates be the center of the circle tangent to the return point. The heading at the cut-out point. The heading at the entry point. The coordinates of the cutting point, These are the coordinates of the entry point.

4. The UAV formation return trajectory planning method based on the Durbins curve according to claim 1, characterized in that, Based on the center coordinates and the Dobbins curve type, determine the coordinates of the tangent point and its heading, and the coordinates of the inlet point and its heading. For the LSR type: ， Calculate the Durbins path length; Among them, (x) c0 , y c0 ( ) represents the coordinates of the center of the initial tangent circle. Let the radius of the tangent circle at the starting point of the return journey be _____. Let the radius of the tangent circle at the return point be . Let the coordinates be the center of the circle tangent to the return point. The heading at the cut-out point. The heading at the entry point. The coordinates of the cutting point, These are the coordinates of the entry point.

5. The UAV formation return trajectory planning method based on the Durbins curve according to claim 1, characterized in that, Based on the center coordinates and the Dobbins curve type, determine the coordinates of the tangent point and its heading, and the coordinates of the inlet point and its heading. For the LSL type: ， Calculate the Durbins path length; Among them, (x) c0 , y c0 ( ) represents the coordinates of the center of the initial tangent circle. Let the radius of the tangent circle at the starting point of the return journey be _____. Let the radius of the tangent circle at the return point be . Let the coordinates be the center of the circle tangent to the return point. The heading at the cut-out point. The heading at the entry point. The coordinates of the cutting point, These are the coordinates of the entry point.

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