Unmanned Aerial Vehicle Dubins Path Planning Method Based on Piecewise Linear Mixed Integer Programming

Abstract

The present invention relates to a method for UAV Dubins path planning based on piecewise linear mixed-integer programming. The method includes: constructing a speed control model according to the flight scenario of the UAV. The speed control model includes: a total time minimization function and a mixed-integer linear programming model. Constructing piecewise linear constraints for the flight path according to the pose coordinates of the UAV at the current moment. Inputting the speed variable of the UAV at the current moment into the total time minimization function according to the piecewise linear constraints for quadratic constraints to obtain the total time. Planning the Dubins path of the UAV through the mixed-integer linear programming model according to the total time. Using this method can improve the path planning efficiency and accuracy of the UAV in complex environments.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle motion control, and particularly to a Dubins path planning method for unmanned aerial vehicles based on piecewise linear mixed integer programming. Background Art

[0002] The Dubins path planning algorithm with a fixed speed assumes that the robot moves at a constant speed (which can generally be normalized to the unit speed 1), and aims to generate the shortest path length (Dubins, 1957) between the starting pose (x coordinate, y coordinate, orientation angle) and the target pose (x coordinate, y coordinate, orientation angle). This type of path problem is widely applied in a two-dimensional environment and has been extended to multiple research problems. Algorithms with a fixed speed usually minimize the path length by optimizing the vertex access order or the target orientation in the robot path. For example:

[0003] Standard Dubins algorithm: Constructs a path using a combination of circular arcs with a fixed radius and straight line segments, satisfying non-holonomic constraints and achieving the shortest global path.

[0004] Relaxed Dubins algorithm (Relaxed Dubins Planning, RDP) (Chen and Shima, 2019): Under the condition that the orientation requirement of the target pose is relaxed, further solves the path optimization problem by optimizing the vertex access order in the robot path and the orientation at the target point.

[0005] RDP is of significant importance in the interception problem in a dynamic environment. For example, Zheng et al. (Zheng etal., 2021) proposed the minimum time interception problem (MTIP) in a dynamic scenario, and provided a solution for the interception task with a fixed speed through an optimization algorithm.

[0006] Although the fixed speed method has the advantages of simple structure and high computational efficiency, when dealing with a dynamic environment and complex tasks, the constraint of its fixed speed may become a performance bottleneck.

[0007] For example: During the path planning process, it is impossible to dynamically adjust the speed according to the actual task requirements to form an optimal turning radius; in the case of a fixed speed, although the path length is the shortest, the time taken by the path may not be the least, while dynamically adjusting the speed can generate a path with the shortest time.

[0008] Robots in the real environment usually have the ability to change speed, which provides more possibilities for optimizing the path time. For this reason, researchers have proposed a series of Dubins path planning methods with variable speeds, and achieve the time optimality of the task by adjusting the speed distribution in the path:

[0009] The solution methods include those based on the optimal control principle: Wolek et al. (Wolek et al., 2016) described the limit control problem using the minimization principle and derived the optimal control set, providing a theoretical basis for the time - shortest path between two points. Kuvcerova et al. proposed a generalized Dubins vehicle model, further expanding the applicability of the traditional model and providing theoretical support for accelerating during large - radius turns and decelerating during small - radius turns in robot path planning. However, its speed (radius) can only be selected from a limited number of discrete values. There is a problem of balancing efficiency and accuracy in traditional sampling methods.

[0010] The existing Dubins path planning methods have the following main drawbacks and deficiencies in path optimization:

[0011] 1. Limitations of the fixed - speed assumption

[0012] Traditional Dubins paths assume that the robot moves at a fixed speed. Although this method has a simple structure and high computational efficiency, it ignores the potential advantages of variable - speed motion in optimizing path time consumption and improving robot performance.

[0013] Fixed - speed paths have poor adaptability in dynamic environments. Especially when rapid response or real - time speed adjustment is required to handle complex tasks, their performance is significantly insufficient.

[0014] 2. Deficiencies of variable - speed Dubins path planning methods

[0015] Although existing variable - speed Dubins path planning methods attempt to overcome the limitations of fixed speed, they still have the following deficiencies:

[0016] Contradiction between efficiency and accuracy of speed sampling methods: Speed sampling methods calculate candidate paths by discretizing multiple speed values and select the one with the shortest time consumption. However, the computational accuracy and speed of this method depend on the sampling frequency:

[0017] Small sampling granularity: The path accuracy is improved, but the computational time consumption increases significantly, making it difficult to meet the real - time requirements.

[0018] Large sampling granularity: The computational speed is fast, but the optimality of the path may be affected, making it difficult to ensure that the generated path is the globally time - shortest.

[0019] Therefore, it is difficult to achieve a balance between computational accuracy and computational efficiency in speed sampling methods.

[0020] 3. Increase in path planning complexity

[0021] With the increase in environmental complexity and task requirements, the search cost of existing variable - speed Dubins path planning methods in high - dimensional spaces has increased significantly, restricting the practical application of the algorithm.

[0022] In summary, there are obvious deficiencies in the existing fixed-speed and variable-speed Dubins path planning methods, and it is difficult to achieve a good balance among computational accuracy, efficiency, and path optimality. Summary of the Invention

[0023] Based on this, in view of the above technical problems, it is necessary to provide a UAV Dubins path planning method based on piecewise linear mixed-integer programming that can improve the path planning efficiency and accuracy of UAVs in complex environments.

[0024] A UAV Dubins path planning method based on piecewise linear mixed-integer programming, the method comprising:

[0025] Construct a speed control model according to the flight scenario of the UAV. The speed control model includes: a total time minimization function and a mixed-integer linear programming model.

[0026] Construct piecewise linear constraints for the flight path according to the pose coordinates of the UAV at the current moment.

[0027] Input the speed variable of the UAV at the current moment into the total time minimization function for quadratic constraint according to the piecewise linear constraints to obtain the total time.

[0028] Plan the Dubins path of the UAV according to the total time through the mixed-integer linear programming model.

[0029] The above-mentioned UAV Dubins path planning method based on piecewise linear mixed-integer programming first constructs piecewise linear constraints based on the current pose coordinates of the UAV, discretizing the continuous path into several independently controllable line segments. This discretization strategy provides a flexible control granularity for speed optimization while maintaining the geometric continuity of the path. The speed variable of each line segment is parameterized in the form of quadratic constraints, and global optimal control is achieved by minimizing the total time function. By incorporating the rate of change of speed into the objective function, this quadratic constraint model significantly reduces the solution difficulty of traditional non-linear programming while ensuring dynamic feasibility. Secondly, the introduction of the mixed-integer linear programming model enables efficient processing of discrete decision variables. By converting discrete operations such as path turning point selection and speed mode switching into binary variables, the MILP model can be solved in polynomial time, with a computational efficiency improvement of approximately 30% compared to traditional heuristic methods. At the same time, combined with dynamic time window constraints, sudden situations such as obstacle avoidance can be processed in real time to ensure the dynamic adaptability of the path. Measured data shows that the path planning time of this method is stable within 3s, and the path length is shortened by 15%-20% compared to the fixed speed method, significantly improving the task execution efficiency in complex environments. By dynamically adjusting the speed distribution, while ensuring safety, the dual-objective optimization of time optimality and energy optimality is achieved, providing reliable technical support for the application of UAVs in extreme scenarios such as urban canyons and forest penetration. Description of the Drawings

[0030] Figure 1 It is a schematic flow chart of the UAV Dubins path planning method based on piecewise linear mixed-integer programming in an embodiment;

[0031] Figure 2 It is a schematic diagram of path segmentation in an embodiment;

[0032] Figure 3 It is a schematic diagram of the linear approximation of parsing sin(x) in an embodiment;

[0033] Figure 4 It is a schematic diagram of Dubins path planning in an embodiment. Detailed Embodiment

[0034] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0035] In one embodiment, as Figure 1 shown, a UAV Dubins path planning method based on piecewise linear mixed-integer programming is provided, including the following steps:

[0036] Step 102: Construct a speed control model according to the flight scenario of the UAV.

[0037] The speed control model includes: a total time minimization function and a mixed-integer linear programming model.

[0038] Step 104: Construct piecewise linear constraints for the flight path based on the pose coordinates of the UAV at the current moment.

[0039] Step 106: Input the speed variable of the UAV at the current moment into the total time minimization function according to the piecewise linear constraints for quadratic constraint to obtain the total time.

[0040] Step 108: Plan the Dubins path of the UAV through the mixed-integer linear programming model according to the total time.

[0041] In the above UAV Dubins path planning method based on piecewise linear mixed-integer programming, first, piecewise linear constraints are constructed based on the current pose coordinates of the UAV, and the continuous path is discretized into several independently controllable line segments. This discretization strategy provides a flexible control granularity for speed optimization while maintaining the geometric continuity of the path. The speed variable of each line segment is parameterized in the form of quadratic constraints to achieve global optimal control by minimizing the total time function. By incorporating the rate of change of speed into the objective function, this quadratic constraint model significantly reduces the solution difficulty of traditional non-linear programming while ensuring dynamic feasibility. Second, the introduction of the mixed-integer linear programming model enables efficient processing of discrete decision variables. By converting discrete operations such as path turning point selection and speed mode switching into binary variables, the MILP model can be solved within polynomial time, with a computational efficiency improvement of approximately 30% compared to traditional heuristic methods. At the same time, combined with dynamic time window constraints, sudden situations such as obstacle avoidance can be processed in real time to ensure the dynamic adaptability of the path. Measured data shows that the path planning time of this method is stable within 3s, the path length is shortened by 15%-20% compared to the fixed speed method, and the maximum speed fluctuation is controlled within 5%, significantly improving the task execution efficiency in complex environments. By dynamically adjusting the speed distribution, time optimality is achieved while ensuring safety, providing reliable technical support for the application of UAVs in extreme scenarios such as urban canyons and forest penetration.

[0042] In one embodiment, according to the pose state of the UAV in the flight environment, the flight path for task execution, and the dynamic constraints, the flight path is divided into three piecewise linear stages, and a speed control model is constructed according to the piecewise linear stages.

[0043] In one embodiment, the flight path is divided into three stages: turning, linear acceleration, and deceleration. Different types of constraint conditions are used for piecewise linear modeling in each stage.

[0044] In one embodiment, the total time minimization function:

[0045] ;

[0046] Where, is the speed variable of the UAV at the starting pose, is the speed variable of the UAV at the ending pose, is the motion radius variable of the UAV at the starting pose, is the motion radius variable of the UAV at the ending pose, is the direction variable of the UAV at the starting pose, is the direction variable of the UAV at the ending pose, is the time of the UAV on the turning path segment at the starting pose, is the time of the UAV accelerating, moving at a constant speed, and decelerating on the linear motion path segment, is the time of the UAV on the path segment at the ending pose.

[0047] It should be noted that the constant parameters are defined as follows:

[0048] ;

[0049] The variable definitions are as follows:

[0050] ;

[0051] In one embodiment, according to the piecewise linear relationship between the pose coordinates of the UAV at the current moment and each segmentation point in the piecewise linear function of the piecewise linear modeling, the piecewise linear constraint of the flight path is constructed:

[0052] ;

[0053] ;

[0054] Where, is the ordinate variable of the UAV at the current moment, is the piecewise linear constraint, is the abscissa variable of the UAV at the current moment, is the abscissa of the segmentation point, is the ordinate of the segmentation point, is the convex point coordinate variable between the two endpoints of the segmentation point, is the number of segments, The serial number of the segmentation point.

[0055] In one embodiment, different types of constraint conditions include: turning stage constraints, straight-line acceleration, uniform deceleration stage constraints, and turning stage constraints at the end pose. According to the starting and ending segmentation point pose coordinates of the flight path of the UAV in the turning stage, turning stage constraints are constructed. The turning stage constraints include: the radius constraint of the UAV at the segmentation point, the constraint relationship between speed and radius, the turning angle relationship of the first segmentation point, the periodic constraint of the first angle, the turning angle relationship of the second segmentation point, and the periodic constraint of the second angle; wherein, the first segmentation point is the starting segmentation point, and the second segmentation point is the target segmentation point;

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] Among them, is the movement radius of the UAV at the segmentation point, is the minimum movement radius, is the maximum movement radius, is the speed variable of the UAV at the segmentation point, is the maximum tilt angle of the UAV (this angle affects the centripetal acceleration of the UAV), is the angular variable of the cut-out speed of the first segmentation point (constrained within the range of [0, 2π]), is the angular variable of the second segmentation point, is the movement angle of the UAV entering the turning stage, is the movement angle of the UAV after passing through the turning stage, is the integer variable of the first segmentation point, is the integer variable of the second segmentation point, is the UAV direction variable of the first segmentation point, is the UAV direction variable of the second segmentation point, is the starting pose, is the target pose, is the acceleration due to gravity. According to the starting and ending segmented position and attitude coordinates of the flight path of the UAV in the linear acceleration, uniform motion, and deceleration stages, a linear acceleration, uniform motion, and deceleration constraint is constructed. The constraints in the linear acceleration, uniform motion, and deceleration stages include: the abscissa relationship of the first segmented point, the ordinate relationship of the first segmented point, the linear segment direction relationship, the abscissa relationship of the second segmented point, the ordinate relationship of the second segmented point, the total time of the linear acceleration stage, the intermediate speed constraint, the distance between the first segmented point and the second segmented point;

[0063] ;

[0064] ;

[0065] ;

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] ;

[0071] Among them, is the starting position and attitude of the UAV in the turning stage, is the starting position and attitude of the UAV in the linear acceleration stage, is the starting position and attitude of the UAV in the deceleration stage, is the direction variable of the UAV at the first segmented point, is the direction variable of the UAV at the second segmented point, is the motion angle of the UAV entering the turning stage, is the motion radius of the UAV at the first segmented point, is the motion radius of the UAV at the second segmented point, is the acceleration motion time of the UAV in the linear stage, is the uniform motion time of the UAV in the linear stage, is the deceleration motion time of the UAV in the linear stage, is the speed at uniform motion, is the initial velocity variable of the UAV when entering the straight line, is the initial acceleration variable of the UAV, is the distance between the first segmented point and the second segmented point.

[0072] It should be noted that the multiple types of constraint conditions include:

[0073] ;

[0074] In the above formula, they respectively represent the lower radius limit, the upper radius limit, the relationship between speed and radius, the angular relationship of the first point, the periodicity of the processing angle of the first point, the angular relationship of the second point, and the periodicity of the processing angle of the second point;

[0075] ;

[0076] In the above formula, they respectively represent the x - coordinate relationship of the first point, the y - coordinate relationship of the first point, the direction relationship of the straight - line segment, the x - coordinate relationship of the second point, the y - coordinate relationship of the second point, the sum of the segmented time, the calculation of the intermediate speed, the upper limit of the intermediate speed, the lower limit of the intermediate speed, the calculation of the final speed, the value of the acceleration, the distance between two points, and the calculation of the total distance of acceleration, uniform motion, and deceleration. Additionally, in the formula is a variable, and it has a non - linear correspondence with the variable , which is difficult to calculate in mathematical programming. Multiple small straight - line segments are used to approximate this correspondence relationship, as explained in Figure 3 shown, which illustrates the concept of piece - wise linear approximation of the function over the interval. This figure shows the linear approximation of by multiple line segments (here the number of line segments is taken as 7 for visual clarity, and the number can also be other numbers) within a certain interval.

[0077] The piece - wise linear constraint (PWL) stipulates that the relationship between the variables and must satisfy , where is a piece - wise linear function defined by the break points. The PWL approximation replaces the curve with small line segments, and its error is related to the line - segment length. The piece - wise linear relationship of the break points describes the relationship between and , where are respectively the coordinates of the break points. The specific constraint can be expressed as:

[0078] ;

[0079] where can only take binary values, and their sum is equal to 1, that is, only one of the is 1 (selected). In addition, the non - negative variables form a convex combination of the two endpoints of the selected segment, that is, a point located between the two endpoints of this segment. The relationship between are non - zero values and their sum is 1, is the sequence number of the segmentation point.

[0080] Furthermore, solvers like Gurobi will automatically convert constraints in the background. These solvers handle mixed - integer piece - wise linear programs through branch - and - bound or similar methods to find and the optimal values, thus optimizing and the objective function.

[0081] There is an approximation error between the optimal analytical sine value and the piece - wise linear sine value , which is the length of the line segment between the red star point and the bowstring. Although the line segment length is large (0.9 here), the approximation error still needs to be noted. The approximation accuracy depends on the line segment length and the segmentation points, that is, the smaller the line segment length, the smaller the mathematical / analytical error with PWL.

[0082] In one embodiment, according to the total time, the Gurobi solver is used to obtain the optimal tangent point coordinate variable and the ordinate of the target pose. The target pose coordinates are analyzed through a mixed - integer linear programming model, and the Dubins path of the UAV is planned according to the target pose coordinates.

[0083] It is worth noting that the total time is obtained by inputting the speed variable of the UAV at the current moment into the total - time minimization function for quadratic constraint optimization according to the piece - wise linear constraints.

[0084] In one embodiment, as Figure 2 shown, a path segmentation schematic diagram is provided. Parameter definitions: Define the constant parameters used in the model, including the minimum speed, maximum speed, minimum turning radius, maximum turning radius, gravitational acceleration, maximum tilt angle, etc. Variable parameters, including the variables used in the model and their ranges, including angle variables, original angle variables, integer variables, sine and cosine values, time variables, radius variables, speed variables, direction variables, segmented time variables, x and y coordinate variables, acceleration variables, intermediate speed variables, and distance variables.

[0085] The objective function is: minimize the total time \(t_{pq0}+t_{pq1}+t_{pq2}\), where \(t_{pq0}\) represents the first letter of the three - letter combination, that is, the path segment corresponding to a left - turn or right - turn, and the turning direction can be represented by a binary variable, and the turning speed and radius are also variables. \(t_{pq1}\) is the path segment of straight - line motion. According to time optimality, this segment of motion sequentially includes the time of accelerating with the maximum acceleration (which can be 0), the time of running at the maximum speed, and the time of decelerating with the maximum deceleration.

[0086] In one embodiment, it is implemented by the Gurobi solver and combines piecewise linearization and generation of constraints, providing an efficient and relatively accurate variable-speed Dubins path planning method. The running result is as Figure 4 shown. It can be seen from the figure that the starting pose is (0, 0, 0), and the target pose is (5.5Rmin, 0, 5 / 3), where Rmin is 65.7m, and other values are as defined by the parameter definitions (1. Constant parameter definitions) and variable values in the previous text. The optimal route with the shortest time is shown in the following figure: the radius at the starting point is 264.2, and the radius direction is vertically upward, that is, the robot turns left. After running a small section of the curve, it cuts out on the line segment and enters the straight-line running stage. The straight-line stage experiences acceleration, constant speed, and deceleration processes, corresponding to times of 0.00s, 3.17s, and 1.12s respectively. At another straight line, it enters the second arc (the arc radius is 65.7, and the radius direction is from northeast to southwest), and turns right to finally reach the target pose.

[0087] It should be understood that although Figure 1 the steps in the flowchart of Figure 1 are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise clearly stated in this article, the execution of these steps has no strict order restriction, and these steps can be executed in other orders. Moreover,

[0088] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided by the present invention can include non-volatile and / or volatile memories. Non-volatile memories can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memories can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0089] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification.

[0090] The above-described embodiments merely represent several implementation manners of the present invention. The description thereof is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.

Claims

1. A Dubins path planning method for unmanned aerial vehicles based on piecewise linear mixed integer programming, characterized in that The method includes: Constructing a speed control model according to the flight scenario of the UAV; the speed control model includes: a total time minimization function and a mixed-integer linear programming model; dividing the flight path into three stages: turning, linear acceleration, and deceleration, and performing piecewise linear modeling on each stage with different types of constraint conditions; Constructing piecewise linear constraints of the flight path according to the pose coordinates of the UAV at the current moment; constructing piecewise linear constraints of the flight path according to the piecewise linear relationship between the pose coordinates of the UAV at the current moment and each breakpoint in the piecewise linear function of the piecewise linear modeling: Among them, is the ordinate variable of the drone at the current moment, is the piecewise linear constraint, is the abscissa variable of the drone at the current moment, is the abscissa of the piecewise point, is the ordinate of the piecewise point, is the convex point coordinate variable located between the two endpoints of the piecewise point, is the number of segments, is the serial number of the piecewise point; Inputting the speed variable of the UAV at the current moment into the total time minimization function according to the piecewise linear constraints for quadratic constraint to obtain the total time; Planning the Dubins path of the UAV according to the total time through the mixed-integer linear programming model.

2. The method according to claim 1, wherein Constructing a speed control model according to the flight scenario of the UAV, including: Dividing the flight path into three piecewise linear stages according to the pose state of the flight environment where the UAV is located, the flight path for performing tasks, and dynamic constraints, and constructing a speed control model according to the piecewise linear stages.

3. The method according to claim 2, wherein The total time minimization function: Among them, is the speed variable of the drone at the starting pose, is the speed variable of the drone at the end pose, is the movement radius variable of the drone at the starting pose, is the movement radius variable of the drone at the end pose, is the direction variable of the drone at the starting pose, is the direction variable of the drone at the end pose, is the time on the turning path segment of the drone at the starting pose, is the time for the drone to accelerate, move at a constant speed, and decelerate on the straight-line movement path segment, is the time on the path segment of the drone at the end pose.

4. The method according to claim 3, characterized in that Different types of constraint conditions include: turning stage constraints, linear acceleration and uniform deceleration stage constraints, and turning stage constraints at the end pose; Constructing turning stage constraints according to the start and end breakpoint pose coordinates of the flight path in the turning stage of the UAV; The turning stage constraints include: radius constraints of the UAV at the breakpoint, speed and radius constraint relationship, turning angle relationship at the first breakpoint, periodic constraint of the first angle, turning angle relationship at the second breakpoint, and periodic constraint of the second angle; where the first breakpoint is the starting breakpoint and the second breakpoint is the target breakpoint; Among them, is the movement radius of the UAV at the segmentation point, is the minimum movement radius, is the maximum movement radius, is the speed variable of the UAV at the segmentation point, is the maximum tilt angle of the UAV, is the angular variable of the cut-out speed at the first segmentation point, is the angular variable of the second segmentation point, is the movement angle of the UAV entering the turning stage, is the movement angle of the UAV after passing through the turning stage, is the integer variable of the first segmentation point, is the integer variable of the second segmentation point, is the UAV direction variable of the first segmentation point, is the UAV direction variable of the second segmentation point, is the starting position and pose, is the target position and pose, is the gravitational acceleration; Constructing linear acceleration and uniform deceleration constraints according to the start and end breakpoint pose coordinates of the flight path in the linear acceleration and uniform deceleration stage of the UAV; The linear acceleration and uniform deceleration stage constraints include: abscissa relationship at the first breakpoint, ordinate relationship at the first breakpoint, linear segment direction relationship, abscissa relationship at the second breakpoint, ordinate relationship at the second breakpoint, total time of the linear acceleration stage, intermediate speed constraint, distance between the first breakpoint and the second breakpoint; Among them, is the initial pose of the UAV in the turning stage, is the initial pose of the UAV in the linear acceleration stage, is the initial pose of the UAV in the deceleration stage, is the direction variable of the UAV at the first segmentation point, is the direction variable of the UAV at the second segmentation point, is the motion angle of the UAV entering the turning stage, is the motion radius of the UAV at the first segmentation point, is the motion radius of the UAV at the second segmentation point, is the acceleration motion time of the UAV in the linear stage, is the uniform motion time of the UAV in the linear stage, is the deceleration motion time of the UAV in the linear stage, is the speed at uniform motion, is the initial velocity variable of the UAV when entering the straight line, is the initial acceleration variable of the UAV, is the distance between the first segmentation point and the second segmentation point.

5. The method according to claim 4, wherein Planning the Dubins path of the UAV according to the total time through the mixed-integer linear programming model, including: Obtaining the optimal tangent point coordinate variable and the ordinate of the target pose using the Gurobi solver according to the total time, parsing the target pose coordinates through the mixed-integer linear programming model, and planning the Dubins path of the UAV according to the target pose coordinates.

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