A hot start trajectory planning method for fixed-wing UAV formations

Abstract

This invention provides a hot-start trajectory planning method based on optimal control and artificial potential field, belonging to the field of three-dimensional trajectory planning for unmanned systems. This planning method addresses the shortcomings of traditional simple models in trajectory planning, combining the advantages of optimal control methods in solving nonlinear systems with complex kinematic constraints, and designs a high-quality initialization solution strategy. First, this invention designs an improved artificial potential field method to eliminate local oscillations, achieve intra-flight cooperation, and satisfy physical constraints, obtaining a high-quality homotopy initial solution. Then, the trajectory planning problem of UAV formation is reconstructed into a standard optimal control problem, which is then discretized and transformed into a nonlinear programming problem. Finally, the obtained initial solution is used for trajectory planning. The proposed planner is applied to the trajectory planning problem of fixed-wing UAV formation. The proposed method is effective and robust, and the designed hot-start strategy significantly contributes to convergence.

Description

Technical Field

[0001] This invention belongs to the field of three-dimensional trajectory planning for unmanned aerial vehicle (UAV) systems, and relates to a method for hot-start trajectory planning of fixed-wing UAV formations, particularly a method for hot-start trajectory planning of fixed-wing UAV formations based on optimal control and artificial potential field method. Background Technology

[0002] With the rapid development of control engineering and sensor technology, drones are playing an increasingly important role in various scenarios, such as express delivery, wireless communication support, and disaster relief. Due to payload limitations, a single drone can hardly carry enough fuel and supplies to complete a mission. Therefore, the current trend is to use multiple drones in formation to enhance mission execution capabilities. In the real world, there are many irregular obstacles (such as buildings, hills, and trees) in three-dimensional space, which can hinder drone flight. Maintaining or changing formation places high demands on the motion control of drone formations. Compared to rotary-wing drones, fixed-wing drones are more difficult to control due to their more complex kinematic equations. Motion planning for fixed-wing drone formations involves finding feasible paths from an initial state to a preset terminal state in the environment. The drones need to satisfy their motion equations, achieve obstacle avoidance, maintain or change their formation, and meet other constraints.

[0003] Traditional UAV motion planning methods can be categorized into geometry-based methods, intelligent optimization algorithms, and optimal control methods. Geometry-based methods generate feasible paths by establishing geometric relationships between the UAV and its environment. These methods typically treat the UAV as a point mass, but fixed-wing UAVs are inherently nonlinear systems with complex motion constraints. Therefore, geometry-based methods are more suitable for rotary-wing UAVs, while fixed-wing UAVs struggle to successfully track paths planned by these methods. Intelligent optimization algorithms are planning methods inspired by natural phenomena. However, the inherent randomness of these methods generates a large number of infeasible solutions during the evolutionary process. While these infeasible solutions can be adjusted during iterative evolution, they impose a high computational burden. These drawbacks hinder their application in scenarios with high efficiency requirements.

[0004] Optimal control methods provide time information, or trajectories, for the path of unmanned aerial vehicles (UAVs). These methods drive the UAV to its target state while satisfying maneuverability and obstacle avoidance requirements. Mathematically, trajectory planning can be modeled as a constrained optimal control problem. Due to the nonlinear motion equations and complex spatial constraints of fixed-wing UAVs, the trajectory planning problem transforms into a large-scale nonlinear problem that cannot be directly solved using software packages. Generally, research can be conducted by designing the problem framework and finding high-quality initial guesses. The solution space is inherently severely nonconvex, and such problems heavily rely on high-quality initialization strategies. Although the application of initial guesses in UAV swarms is relatively limited, they have yielded significant results in fields such as autonomous driving and mobile robotics. Providing high-quality initial guesses would greatly contribute to trajectory planning for UAV swarms. Efficiently planning the trajectories of fixed-wing UAV swarms is of great significance for both military and civilian applications, including express delivery scheduling and unmanned warfare.

[0005] This invention was supported by the National Natural Science Foundation of China (12102077, 12161076) and the Fundamental Research Funds for the Central Universities (DUT22RC(3)010, DUT22LAB305, DUT22QN223). Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of geometry-based methods and intelligent optimization algorithms, and to provide a hot-start trajectory planning method based on optimal control method and artificial potential field method, which can realize trajectory planning of fixed-wing UAV formations.

[0007] The technical solution of the present invention to solve the above problems is as follows:

[0008] A hot-start trajectory planning method for fixed-wing UAV formations is implemented based on optimal control and artificial potential field methods, including the following steps:

[0009] Step 1: Determine the scale N of the fixed-wing UAVs based on the actual mission scenario, and the initial position coordinates of the i-th fixed-wing UAV. Mission target location coordinates (x goal ,y goal ,z goal The scene has M obstacles O = {O1, O2, ..., O2}. m ,…,O M Information;

[0010] Step 2: Real obstacles are irregular objects; this method simplifies them into two categories: cylinders and hemispheres. When obstacle O... m When it is a cylinder, the center and radius of the horizontal circle of the cylinder. and When obstacle O mWhen it is a hemisphere, the center and radius of the hemisphere are respectively and

[0011] Step 3: Preset the parameters for the artificial potential field method, including the gravity factor K. att repulsion factor K rep Internal force factor K int The repulsive force range is d0, the attenuation factor n of the repulsive force field relative to the target point is n, and the oscillation angle threshold is θ.

[0012] Step 4: Calculate the initial guess of the formation trajectory using the improved artificial potential field method; the specific steps are as follows:

[0013] 4.1: Calculate the gravitational field U of the i-th fixed-wing UAV at time t. att-i (t) and the corresponding attractive force F att-i (t):

[0014]

[0015]

[0016] Where, d g It is the distance threshold for segmenting the gravitational field; for the i-th fixed-wing UAV, d V (t) represents the Euclidean distance between the target and the target at time t, and V represents the position of the target point (x). goal ,y goal ,z goal ), P i Indicates its position (x) at time t. i (t),y i (t),z i (t)), Indicated by P i Pointing in the direction of V;

[0017] 4.2: Calculate the repulsive field of the i-th fixed-wing UAV at time t. and the corresponding repulsive force F rep-i (t):

[0018]

[0019]

[0020] in, This indicates that at time t, the i-th fixed-wing UAV interacts with obstacle O. m The Euclidean distance between them, W m Indicates obstacle O m Location; Indicated by W m Point to P i The direction;

[0021] 4.3: To prevent collisions between fixed-wing UAVs, design the internal forces between the UAVs. To improve the artificial potential field method. When the Euclidean distance between the i-th and j-th UAVs is less than a set value. hour, This represents the repulsive force on the i-th drone; when the Euclidean distance between them is greater than a set value. hour; The attractiveness to the i-th fixed-wing UAV is expressed as follows:

[0022]

[0023] in, For the i-th and j-th fixed-wing UAVs This represents their Euclidean distance at time t; This represents the expected distance between them; ρ0 is the distance threshold between fixed-wing UAVs. Indicated by P i Point to P j The direction;

[0024] Therefore, the net force F acting on the i-th fixed-wing UAV at time t is res-i (t):

[0025]

[0026] 4.4: To eliminate potential local oscillations when a fixed-wing UAV passes through a region with multiple obstacles, the resultant forces at two adjacent moments are combined to improve local oscillation performance. The actual resultant force F experienced by the i-th fixed-wing UAV at time t is... prac-i (t) is as follows:

[0027]

[0028]

[0029] Where λ1 and λ2 are weighting factors, satisfying λ1 + λ2 = 1; Δθ is the resultant force F. res-i (t) and the resultant force F res-i The angle between (t-1);

[0030] 4.4: Calculate the heading angle χ of the i-th fixed-wing UAV at time (t+1) under ideal conditions. i (t+1):

[0031]

[0032]

[0033] Where ε=Δt*ω max ω represents the maximum permissible change in the UAV's orientation between two adjacent moments, where Δt is the sampling time interval; max The maximum angular velocity that a fixed-wing drone can withstand; The resultant force F prac-i The direction angle of (t);

[0034] 4.5: Calculate the flight path angle γ of the i-th fixed-wing UAV at time (t+1) under ideal conditions. i (t+1):

[0035]

[0036]

[0037] 4.5: When the heading angle is small, the fixed-wing UAV can accelerate to its maximum speed. When the heading angle is too large, it needs to decelerate. Calculate the speed of the i-th fixed-wing UAV at time (t+1):

[0038]

[0039] Among them, v max and v min ε and Δx1 represent the maximum and minimum acceptable speeds for the fixed-wing UAV, respectively; a is its acceleration; Δx1 and Δx2 are two angular thresholds satisfying Δx1 < Δx2 < ε; v const This indicates the desired speed of a fixed-wing drone;

[0040] 4.6: Calculate the path point of the i-th fixed-wing UAV at time t:

[0041]

[0042] 4.7: Starting from t=0, repeat steps 4.1-4.6 to calculate the path point at each sampling time. Until... ∈ is a constant that measures the proximity of the UAV to the target point. The calculation using the artificial potential field method is then completed, and the sequence of path points calculated by the artificial potential field method is used as the initial guess for the trajectory planning problem.

[0043] Step 5: Reconstruct the trajectory planning problem of fixed-wing UAV formation into an optimal control problem; the specific steps are as follows:

[0044] 5.1: Describe the kinematic equations of the i-th fixed-wing UAV:

[0045]

[0046] Where i = {1, 2, ..., N} represents the i-th fixed-wing UAV; the time domain t ∈ [0, t f ], t f Let x be the flight termination time that needs to be solved. For the i-th UAV, (x... i (t),y i (t),z i (t) represents its three-dimensional position information; v i (t) represents velocity; γ i (t) represents the flight path angle; χ i (t) is the heading angle; T i (t), φ i (t) and n i (t) represents the engine thrust, tilt angle, and load factor of the fixed-wing UAV, respectively; x i (t),y i (t),z i (t),v i (t),χ i (t),γ i The first derivative of (t); g is the acceleration due to gravity; aerodynamic drag D i =αρv i (t)sC D0 +αρv i (t)skC DL Where α is a constant coefficient; ρ is the air density; s is the wing area of ​​the UAV; C D0 The zero resistance coefficient is given by k; k is the coefficient of inductive resistance. L is the lift coefficient, where L i (t)=n i (t)mg is the lift of the UAV, and m is the mass of the fixed-wing UAV.

[0047] For the i-th fixed-wing UAV, the state variable s i (t)=[x i (t),y i (t),z i (t),v i (t),χ i (t),γ i [(t)];Control quantity u i (t)=[T i (t),φ i (t),n i Therefore, its equation of motion can be simply expressed as (t)]. Where f i (·): Let i represent the dynamics of the i-th drone;

[0048] 5.2: For a fixed-wing UAV formation, the state s(t) = [s1(t), s2(t), ..., s N (t)]; control u(t)=[u1(t),u2(t),…,u N (t)];The dynamics of the formation f(t)=[f1,f2,…,f N Therefore, the kinematic equations of the formation are as follows:

[0049]

[0050] 5.3: Establishing the boundary conditions for the optimal control problem. For the trajectory planning problem of a fixed-wing UAV, the focus is on its initial position. and target location (x) goal ,y goal ,z goal The boundary conditions for other state variables are not required. Therefore, the boundary conditions for the i-th fixed-wing UAV are as follows:

[0051]

[0052] 5.4: Determine the physical constraints of the fixed-wing UAV. For the i-th fixed-wing UAV, define the state s i (t) is restricted to the interval s i (t)∈ in and These represent the minimum and maximum values ​​of the state, respectively; similarly, the control u... i (t) is also restricted to the interval [ t ] in and These are the minimum and maximum values ​​that are controlled, respectively.

[0053] For coordinated operation, drones in a fixed-wing drone swarm need to maintain communication; therefore, no two fixed-wing drones can be too far apart. The communication constraints are set as follows:

[0054]

[0055] Among them, D comm This is the maximum communication distance between drones; the specific value depends on the type of drone and the specific application scenario. i,j (t) is the Euclidean distance between the i-th UAV and the j-th UAV at time t;

[0056] To ensure safety, fixed-wing drones in a formation need to maintain a certain distance from each other. The safety constraints are set as follows:

[0057]

[0058] Among them, D safe It is the minimum safe distance between drones, and the specific value is set according to the type of drone and the specific application scenario;

[0059] To enable obstacle avoidance for fixed-wing UAVs, the obstacle constraints are set as follows:

[0060]

[0061] Where β is the distance between the drone and obstacle O. m Minimum distance between; The i-th drone and obstacle O m Euclidean distance between them; r m It is the radius of the obstacle; when the obstacle O m When it is a cylinder, the distance When obstacle O m When it is a hemisphere, the distance

[0062] To ensure that a fixed-wing UAV formation maintains a specific geometric structure during flight, the first fixed-wing UAV is designated as the core UAV, and the other UAVs maintain a specific positional relationship with it. Therefore, the formation constraints are set as follows:

[0063]

[0064] Where i = 2, 3, ..., N; j = 1 is the index of the core machine; This represents the position coordinates of the i-th UAV relative to the core machine;

[0065] 5.5: This method aims to minimize the termination time of fixed-wing UAV formation flight, and sets the objective function as follows:

[0066] 5.6: The trajectory planning problem for fixed-wing UAV formations can be constructed as the following optimal control problem:

[0067]

[0068] Step 6: To improve the efficiency of the solution process, the fixed-wing UAV formation constraints are penalized to the performance index function, and an augmented objective function is constructed. Where b is the relaxation factor;

[0069] Step 7: The optimal control problem (22) can be transformed into the following problem:

[0070]

[0071] Step 8: For the numerical solution problem, apply it to the time domain [0, t f Discretize the problem (9) to transform it into a nonlinear programming problem. Define (N) fe +1) sampling times {t p |p=0,1,…,N fe The sampling times are required to be uniformly distributed in the time domain [0, t]. f ] on, i.e. t p -t p-1 =(t f -0) / N fe =q,p=1,2,…,N fe , where q is in t p-1 and t p The equal time intervals between them. Then introduce the variable {s}. p |p=0,1,…,N fe} and {u p |p=0,1,…,N fe Let} represent s(t) and u(t) respectively;

[0072] Step 9: Use the fourth-order Runge-Kutta method in the interval [t] p ,t p+1 Discretized equations of motion:

[0073]

[0074] Where, k1=f(s) p ,u p ,t p ), k4=f(s p +k3*q,u p ,t p +q); k1 is the kinematic equation of the formation. At time t p s p As a state, with u p To control the obtained solution; k2 is the kinematic equation of the formation. In time Treat As a state, with u p To control the obtained solution; k3 is the kinematic equation of the formation. In time Treat As a state, with u p To control the obtained solution; k4 is the kinematic equation of the formation. At time t p +q is used with s p +k3*q is the state, and u is the state. pTo control the obtained solution;

[0075] Step 10: In all subintervals [t] p ,t p+1 Repeat step 9 to form a nonlinear programming problem:

[0076]

[0077] Among them, G(s) p ,u p ,t f ) represents the set of boundary conditions and physical constraints.

[0078] The solution to the nonlinear programming problem shown in Equation (25) is also a numerical approximation of the continuous-time optimal control problem (23).

[0079] Step 11: Input the high-quality initial guess obtained in step 4 and the problem statement (25) obtained in step 10 into the nonlinear programming solver IPOPT to perform trajectory planning for the UAV formation and obtain the formation flight trajectory.

[0080] The beneficial effects of this invention are as follows:

[0081] (1) The improved artificial potential field method of this invention can overcome many shortcomings of the traditional artificial potential field method, eliminate local oscillations, achieve intra-team coordination and meet physical constraints, and is more practical. Especially when providing initial guesses for trajectory planning problems, it accelerates the convergence of optimal control problems, and the effect is significantly improved.

[0082] (2) This invention first applies an improved artificial potential field method to provide high-quality initial guesses. Secondly, it transforms the trajectory planning problem of fixed-wing UAV formations into an optimal control problem and discretizes it. Finally, it solves the problem using the nonlinear programming solver IPOPT to obtain the flight trajectory of the fixed-wing UAV formation. This invention solves the problems of difficulty in handling complex kinematic constraints based on geometric methods and the high computational burden of intelligent optimization algorithms. The established trajectory planning method for fixed-wing UAV formations can successfully solve the problem in complex three-dimensional scenes with obstacles. The formation can maintain the desired formation during flight and can flexibly pass through narrow gaps. It is computationally simple, efficient, and has high planning efficiency, and can be widely applied in the trajectory planning problem of fixed-wing UAV formations. Attached Figure Description

[0083] Figure 1 This is a flowchart of the trajectory planning process.

[0084] Figure 2 A schematic diagram of the kinematic model of the UAV; where (a) is a side view of the UAV and (b) is a front view of the UAV.

[0085] Figure 3 (a) is the flight trajectory of a fixed-wing UAV formation planned in a complex environment.

[0086] Figure 3 (b) is Figure 3 (a) Detailed unfolded view of point A.

[0087] Figure 3 (c) is Figure 3 (a) Detailed unfolded view of point B. Detailed Implementation

[0088] The following embodiments will further illustrate the present invention with reference to the accompanying drawings.

[0089] A hot-start trajectory planning method for fixed-wing UAV formations based on optimal control and artificial potential field method is proposed. This method is implemented using the artificial potential field method and optimal control method. The trajectory planning process is described below. Figure 1 The method mainly includes formulating the optimal control problem, obtaining a high-quality homotopy initial guess using an improved artificial potential field method, and discretizing the optimal control problem. The specific implementation steps of this invention are as follows:

[0090] Step 1: Determine the scale of the fixed-wing UAVs N=4 based on the actual mission scenario, the initial position coordinates of the fixed-wing UAVs (100m, 10m, 10m), (70m, 30m, 10m), (130m, 10m, 10m) and (80m, 50m, 10m), the position coordinates of the mission target point (800m, 600m, 100m), and the 10 obstacles in the scenario P={O1, O2, ..., O m ,…,O 10 Information;

[0091] Step 2: Real obstacles are irregular objects. This method simplifies them into cylinders and hemispheres. There are 6 cylindrical obstacles with the centers of their horizontal circles being (300m, 200m), (550m, 550m), (500m, 100m), (750m, 450m), (500m, 300m), and (300m, 400m), and the radius of each circle being 80m. There are 4 hemispherical obstacles with the centers and radii of their hemispheres being [(300m, 50m, 0m), 50m], [(700m, 200m, 0m), 70m], [(500m, 300m, 0m), 150m], and [(650m, 500m, 0m), 100m].

[0092] Step 3: Preset the parameters for the artificial potential field method, including the gravity factor K. att =20, repulsion factor K rep =100, internal force factor Kint =20, the repulsive force range is d0=80m, the attenuation factor of the repulsive force field relative to the target point is n=2, and the oscillation angle threshold is θ=4 / π;

[0093] Step 4: Calculate the initial guess of the formation trajectory using the improved artificial potential field method; the specific steps are as follows:

[0094] 4.1: Calculate the gravitational field U of the i-th fixed-wing UAV at time t. att-i (t) and the corresponding attractive force F att-i (t):

[0095]

[0096]

[0097] Where, d g =100m is the distance threshold for segmenting the gravitational field; for the i-th fixed-wing UAV, d V (t) represents the Euclidean distance between the target and the target at time t, V represents the position of the target point (800m, 600m, 100m), and P i Indicates its position (x) at time t. i (t),y i (t),z i (t)), Indicated by P i Pointing in the direction of V;

[0098] 4.2: Calculate the repulsive field of the i-th fixed-wing UAV at time t. and the corresponding repulsive force F rep-i (t):

[0099]

[0100]

[0101] in, This indicates that at time t, the i-th fixed-wing UAV interacts with obstacle O. m The Euclidean distance between them, W m Indicates obstacle O m Location; Indicated by W m Point to P i The direction;

[0102] 4.3: To prevent collisions between drones, design the internal forces between drones. To improve the artificial potential field method. When the Euclidean distance between the i-th and j-th UAVs is less than a set value. hour, This represents the repulsive force on the i-th drone; when the Euclidean distance between them is greater than a set value. hour; The attractiveness to the i-th fixed-wing UAV is expressed as follows:

[0103]

[0104] in, For the i-th and j-th fixed-wing UAVs Represents the Euclidean distance at time t; expected distance The distance threshold between fixed-wing UAVs is ρ0 = 40m. Indicated by P i Point to P j The direction;

[0105] Therefore, the net force F acting on the i-th fixed-wing UAV at time t is res-i (t):

[0106]

[0107] 4.4: To eliminate potential local oscillations when a fixed-wing UAV passes through a region with multiple obstacles, the resultant forces at two adjacent moments are combined to improve local oscillation performance. The actual resultant force F experienced by the i-th fixed-wing UAV at time t is... prac-i (t) is as follows:

[0108]

[0109]

[0110] Where λ1 and λ2 are weighting factors; Δθ is the resultant force F. res-i (t) and the resultant force F res-i The angle between (t-1);

[0111] 4.4: Calculate the heading angle χ of the i-th fixed-wing UAV at time (t+1) under ideal conditions. i (t+1):

[0112]

[0113]

[0114] Where ε=Δt*ω max The maximum permissible change in the UAV's orientation between two adjacent moments is represented by Δt = 0.05 s; the maximum angular velocity ω max =0.3491; The resultant force F prac-i The direction angle of (t);

[0115] 4.5: Calculate the flight path angle γ of the i-th fixed-wing UAV at time (t+1) under ideal conditions. i (t+1):

[0116]

[0117]

[0118] 4.5: When the heading angle is small, the fixed-wing UAV can accelerate to its maximum speed. When the heading angle is too large, it needs to decelerate. Calculate the speed of the i-th fixed-wing UAV at time (t+1):

[0119]

[0120] Among them, v max =15m / s and v min = 10 m / s, which are the maximum and minimum acceptable speeds for a fixed-wing UAV, respectively, and a = 0.5 m / s. 2 It is its acceleration; Δχ1 and Δχ2 are two angular thresholds, satisfying Δχ1 < Δχ2 < ε; v const =10m / s represents the desired speed of a fixed-wing UAV.

[0121] 4.6: Calculate the path point of the i-th fixed-wing UAV at time t:

[0122]

[0123] 4.7: Repeat steps 4.1-4.5 to calculate the path points at each sampling time. Until... The calculations using the artificial potential field method are then completed, and the series of path points calculated by the artificial potential field method are used as the initial guesses for the trajectory planning problem.

[0124] Step 5: Reconstruct the trajectory planning problem of fixed-wing UAV formation into an optimal control problem; the specific steps are as follows:

[0125] 5.1: Describe the kinematic equations of the i-th fixed-wing UAV:

[0126]

[0127] Where i = {1, 2, ..., 4} represents the i-th drone; the time domain t ∈ [0, t f ], t f Let x be the flight termination time that needs to be solved. For the i-th UAV, (x... i (t),y i (t),z i (t) represents its three-dimensional position information; v i(t) represents velocity; γ i (t) represents the flight path angle; χ i (t) is the heading angle; T i (t), φ i (t) and n i (t) represents the engine thrust, tilt angle, and load factor of the UAV, respectively; gravitational acceleration g = 10 m / s². 2 Aerodynamic drag D i =αρv i (t)sC D0 +αρv i (t)skC DL Where α = 0.5; air density ρ = 1.225 kg / m³ 3 The wing area of ​​the UAV is s = 0.2589m². 2 Zero drag coefficient C D0 =0.0163; Inductive resistivity k = 0.11; L is the lift coefficient, where L i (t)=n i (t)mg is the lift of the drone, and the mass of the drone is m = 1.53 kg.

[0128] For the i-th fixed-wing UAV, state s i (t)=[x i (t),y i (t),z i (t),v i (t),χ i (t),γ i (t)];Control u i (t)=[T i (t),φ i (t),n i Therefore, its equation of motion can be simplified to (t)]. Where f i (·): Let represent the dynamics of the i-th UAV. A schematic diagram of the UAV's kinematic model is shown below. Figure 2 ;

[0129] 5.2: For a fixed-wing UAV formation, the state s(t) = [s1(t), s2(t), ..., s N (t)]; control u(t)=[u1(t),u2(t),…,u N (t)];The dynamics of the formation f(t)=[f1,f2,…,f N Therefore, the kinematic equations of the formation are as follows:

[0130]

[0131] 5.3: Establishing Boundary Conditions for the Optimal Control Problem. For the trajectory planning problem of fixed-wing UAVs, focus on the initial positions of the four fixed-wing UAVs. The boundary conditions for the i-th fixed-wing unmanned aircraft are given by [(70m, 30m, 10m), (130m, 10m, 10m), (80m, 50m, 10m)] and the target position (800m, 600m, 100m). No other boundary conditions are required for other state variables. Therefore, the boundary conditions for the i-th fixed-wing unmanned aircraft are as follows:

[0132]

[0133] 5.4: Determine the physical constraints of the UAV. The i-th fixed-wing UAV will have state s i (t) is restricted to the interval in and Similarly, control u i (t) is also restricted to the interval [ t ] in and

[0134] For coordination, the drones in the formation need to maintain communication; therefore, no two drones can be too far apart. The communication constraints are set as follows:

[0135]

[0136] The longest communication distance between drones, D comm =100m,d i,j (t) is the Euclidean distance between the i-th UAV and the j-th UAV at time t;

[0137] To ensure safety, drones in a formation need to maintain a certain distance from each other. The safety constraints are set as follows:

[0138]

[0139] The minimum safe distance D between drones safe =5m;

[0140] To enable obstacle avoidance for fixed-wing UAVs, the obstacle constraints are set as follows:

[0141]

[0142] Where β is the distance between the drone and obstacle O. m Minimum distance between; The i-th drone and obstacle O mThe Euclidean distance between the drone and the obstacle O; m The minimum distance between them is β = 10m; The i-th drone and obstacle O m The Euclidean distance between them; when the obstacle O m When it is a cylinder, the distance When obstacle O m When it is a hemisphere, the distance

[0143] To maintain a specific geometric structure during drone formation flight, the first drone is designated as the core drone, and the other drones maintain a specific positional relationship with it. Therefore, the formation constraints are set as follows:

[0144]

[0145] Where i = 2, 3, ..., 4; j = 1 is the index of the core machine; This represents the position coordinates of the i-th UAV relative to the core machine;

[0146] 5.5: This method aims to minimize the termination time of fixed-wing UAV formation flight, and sets the objective function as follows:

[0147] 5.6: The trajectory planning problem for fixed-wing UAV formations can be constructed as the following optimal control problem:

[0148]

[0149] Step 6: To improve the efficiency of the solution process, the fixed-wing UAV formation constraints are penalized to the performance index function, and an augmented objective function is constructed. Where the relaxation factor b = 0.1;

[0150] Step 7: The original optimal control problem (47) can be transformed into the following problem:

[0151]

[0152] Step 8: For the numerical solution problem, apply it to the time domain [0, t f Discretize the above to transform problem (48) into a nonlinear programming problem. Define 116 sampling times {t}. p |p=0,1,…,115}, requiring these sampling times to be uniformly distributed in the time domain [0,t]. f ] on, i.e. t p -t p-1 =(t f -0) / 115=q,p=1,2,…,115, where q is in t p-1 and t pThe equal time intervals between them. Then introduce the variable {s}. p |p=0,1,…,115} and {u p Let |p=0,1,…,115} represent s(t) and u(t) respectively;

[0153] Step 9: Use the fourth-order Runge-Kutta method in the interval [t] p ,t p+1 Discretized equations of motion:

[0154]

[0155] Where, k1=f(s) p ,u p ,t p ), k4=f(s p +k3*q,u p ,t p +q); k1 is the kinematic equation of the formation. At time t p s p As a state, with u p To control the obtained solution; k2 is the kinematic equation of the formation. In time Treat As a state, with u p To control the obtained solution; k3 is the kinematic equation of the formation. In time Treat As a state, with u p To control the obtained solution; k4 is the kinematic equation of the formation. At time t p +q is used with s p +k3*q is the state, and u is the state. p To control the obtained solution;

[0156] Step 10: In all subintervals [t] p ,t p+1 Repeat step 9 to form a nonlinear programming problem:

[0157]

[0158] Among them, G(s) p ,u p ,t f ) represents the set of boundary conditions and physical constraints.

[0159] The solution to the nonlinear programming problem shown in formula (50) is also a numerical approximation of the continuous-time optimal control problem (48).

[0160] Step 11: Input the high-quality initial guess obtained in Step 4 and the problem statement (50) obtained in Step 10 into the nonlinear programming solver IPOPT to perform trajectory planning for the UAV formation and obtain the formation flight trajectory.

[0161] The following are specific examples of applications:

[0162] The study focuses on a complex three-dimensional space with narrow gaps, containing 10 obstacles. Four fixed-wing UAVs form a formation, with the desired formation being a straight line during flight.

[0163] like Figure 3 As shown, the proposed method successfully plans flight trajectories for a fixed-wing UAV formation. After the mission begins, the four UAVs quickly form the desired formation and maintain it throughout the flight. When encountering narrow gaps that the desired formation cannot pass through, the UAV formation rapidly and proactively disrupts its formation to pass through the area. After passing through, it restores the desired formation until the mission endpoint, which verifies the method's ability to drive UAV formations in complex environments. It can be seen that the proposed method achieves excellent planning results, meaning that this method is suitable for trajectory planning of fixed-wing UAV formations in complex environments.

[0164] Finally, it should be noted that although this specification describes the specific structure of the present invention in detail through specific embodiments, those skilled in the art should understand that the present invention is not limited to the scope of the above embodiments. Various modifications and substitutions made within the substantive scope of this patent should fall within the protection scope of this patent.

Claims

1. A hot-start trajectory planning method for fixed-wing unmanned aerial vehicle (UAV) formations, characterized in that, Includes the following steps: Step 1: Determine the scale of the fixed-wing UAV based on the actual mission scenario. , No. Initial position coordinates of a fixed-wing UAV Mission target location coordinates Scenes include One obstacle Information; Step 2: Simplify real obstacles into two categories: cylinders and hemispheres; when obstacles... When it is a cylinder, the center and radius of the horizontal circle of the cylinder. and ; When obstacles When it is a hemisphere, the center and radius of the hemisphere are respectively and ; Step 3: Preset the parameters of the artificial potential field method, including the gravity factor. repulsive factor Internal force factor Repulsive force range The attenuation factor of the repulsive field relative to the target point Oscillation angle threshold ; Step 4: Calculate the initial guess of the formation trajectory using the improved artificial potential field method; Step 5: Reconstruct the trajectory planning problem of fixed-wing UAV formation into an optimal control problem; Step 6: Constrain and penalize the fixed-wing UAV formation to the performance index function, and construct the augmented objective function. ,in It is a relaxation factor; Step 7: Transform the optimal control problem from Step 5 into the following problem: ； Step 8: For the numerical solution problem, apply it to the time domain. Discretization transforms the problem into a nonlinear programming problem; definition Each sampling time The sampling times are required to be uniformly distributed in the time domain. Above, that is ,in Is and The equidistant time intervals between them; Then introduce variables. and to represent respectively and ; Step 9: Use the fourth-order Runge-Kutta method in the interval Discretized equations of motion: ； in , , , ; The kinematic equations of the formation In time Treat As a state, with To control the obtained solution; The kinematic equations of the formation In time Treat As a state, with To control the obtained solution; The kinematic equations of the formation In time Treat As a state, with To control the obtained solution; The kinematic equations of the formation In time Treat As a state, with To control the obtained solution; Step 10: In all sub-intervals Repeat step 9 to form a nonlinear programming problem: ； in, Represents a set of boundary conditions and physical constraints; The solution to the nonlinear programming problem shown in equation (25) is also a continuous-time optimal control problem. Numerical approximation solution; Step 11: Formulate the high-quality initial guess obtained in Step 4 and the problem obtained in Step 10. Input the data into a nonlinear programming solver to perform trajectory planning for the UAV formation and obtain the formation flight trajectory.

2. The hot-start trajectory planning method for a fixed-wing UAV formation according to claim 1, characterized in that, Step 4 is described in detail below: 4.1: Calculation Time of the first Gravitational field of a fixed-wing drone and corresponding attraction : ； ； in, It is the distance threshold for segmenting the gravitational field; for the th A fixed-wing drone, Indicates in The Euclidean distance between it and the target at any given moment. Indicates the location of the target point , Indicates that it is in Location at any moment , Indicates by point to The direction; 4.2: Calculation Time of the first Repulsive field of a fixed-wing drone and the corresponding repulsive force : ； ； in, Indicates in Time of the first Fixed-wing drones and obstacles Euclidean distance between them Indicates obstacles Location; , , Indicates by point to The direction; 4.3: To prevent collisions between fixed-wing UAVs, design the internal forces between the UAVs. To improve the artificial potential field method; when the first drones and the first The Euclidean distance between the drones is less than the set value hour, Indicates the first The repulsive force between the drones; when the Euclidean distance between them is greater than a set value. hour; Indicates the first The attractiveness of a fixed-wing UAV is calculated as follows: ； in, For the first frame and the first A fixed-wing drone, Indicates that it is in Euclidean distance at time; This represents the expected distance between them; It is the distance threshold between fixed-wing drones. Indicates by point to The direction; Therefore, the first A fixed-wing drone in The combined force at all times : ； 4.4: To eliminate potential local oscillations when a fixed-wing UAV passes through an area with multiple obstacles, the resultant force at two adjacent moments is merged to improve local oscillation performance; A fixed-wing drone in The actual resultant force at any given moment as follows: ； ； in, and It is a weighting factor that satisfies ; It is a combined force With combined force The included angle between them; 4.5: Calculate the first digit under ideal conditions A fixed-wing drone in Heading angle at any moment : ； ； in, This indicates the maximum permissible change in the drone's orientation between two adjacent time points. It is the sampling time interval; The maximum angular velocity that a fixed-wing drone can withstand; Represents resultant force Direction angle; 4.6: Calculate the first digit under ideal conditions A fixed-wing drone in Flight path angle at time : ； ； 4.7: Calculate the first... A fixed-wing drone in Speed ​​of time: ； in, and The maximum and minimum acceptable speeds for fixed-wing drones, It is its acceleration; and There are two angle thresholds that satisfy... ; This indicates the desired speed of a fixed-wing drone; 4.8: Calculate the first... A fixed-wing drone in Path points at time: ； 4.9: From Begin repeating steps 4.1-4.8 to calculate the path points at each sampling time; until... , It is a constant that measures the proximity of the UAV to the target point; the calculation of the artificial potential field method ends, and the series of path points calculated by the artificial potential field method is used as the initial guess for the trajectory planning problem.

3. The hot-start trajectory planning method for a fixed-wing UAV formation according to claim 1, characterized in that, Step 5 is described in detail below: 5.1: Description of the first Kinematic equations of a fixed-wing UAV: ； in, Indicates the first Fixed-wing unmanned aerial vehicles; time domain , Let be the flight termination time that needs to be solved; for the A drone, It is its three-dimensional position information; For speed; Flight path angle; For heading angle; , and These are the engine thrust, tilt angle, and load factor for a fixed-wing UAV, respectively. They are respectively The first derivative; Acceleration due to gravity; aerodynamic drag ,in The coefficient is constant. air density; This refers to the wing area of ​​the drone; Zero drag coefficient; The coefficient of resistance of the induced resistor; is the lift coefficient, where It is the lift of the drone. It refers to the mass of a fixed-wing drone; For the A fixed-wing unmanned aerial vehicle, state variables Control quantity Therefore, its equation of motion can be simply expressed as: ,in Indicates the first The dynamics of a drone; 5.2: For fixed-wing UAV formations, status ;control Formation dynamics Therefore, the kinematic equations of the formation are as follows: ； 5.3: Establish boundary conditions for the optimal control problem; for the trajectory planning problem of a fixed-wing UAV, focus on its initial position. and target location No requirements are made for the boundary conditions of other state quantities; therefore, the first... The boundary conditions for a fixed-wing UAV are as follows: ； 5.4: Determine the physical constraints of the fixed-wing UAV; for the first... Deploy fixed-wing drones to monitor the status Limited to the range ,in and These represent the minimum and maximum values ​​of the state, respectively; similarly, the control... Also limited to a range ,in and These are the minimum and maximum values ​​that are controlled, respectively. For coordination, communication constraints are set as follows: ； in, It is the maximum communication distance between drones, and the specific value is set according to the type of drone and the specific application scenario. Is Time of the first The drone and the first Euclidean distance between drones; To ensure safety, fixed-wing drones in a formation must maintain a certain distance from each other; the safety constraints are set as follows: ； in, It is the minimum safe distance between drones, and the specific value is set according to the type of drone and the specific application scenario; To enable obstacle avoidance for fixed-wing UAVs, the obstacle constraints are set as follows: ； in, It is drones and obstacles Minimum distance between; It is the first Drones and obstacles Euclidean distance between them; It is the radius of the obstacle; when the obstacle When it is a cylinder, the distance , When obstacles When it is a hemisphere, the distance , ; To ensure that fixed-wing UAV formations maintain a specific geometric structure during flight, the first step is to set up... A fixed-wing UAV serves as the core unit, and other fixed-wing UAVs maintain specific positional relationships with it; therefore, the formation constraints are set as follows: ； in, ; It is the core machine's index; Indicates the first The position coordinates of the drone relative to the core machine; 5.5: To minimize the termination time of fixed-wing UAV formation flight, the objective function is set as follows: ; 5.6: The trajectory planning problem for fixed-wing UAV formations can be constructed as the following optimal control problem:

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