Unmanned aerial vehicle four-dimensional flight path planning method in complex low-altitude environment

Abstract

The invention discloses an unmanned aerial vehicle four-dimensional flight path planning method in a complex low-altitude environment, and the method comprises the following steps: 1, generating unmanned aerial vehicle initial path points according to a flight starting point and a target point of an unmanned aerial vehicle, and each path point represents an intermediate point in the flight process of the unmanned aerial vehicle; step 2, establishing an unmanned aerial vehicle flight path planning cost function according to the unmanned aerial vehicle flight task and the flight environment characteristics; step 3, taking the route planning cost function as a constraint condition and an optimization target, utilizing a multi-strategy enhanced marine predator algorithm to carry out iterative optimization for multiple times, and continuously updating the position of the path point until a preset termination condition is met; 4, performing post-processing on the generated air route nodes by using a smoothing algorithm to obtain a smoother flight path; and step 5, outputting the finally generated three-dimensional flight path of the unmanned aerial vehicle, and adding a time dimension in combination with a flight plan so as to generate an optimal four-dimensional flight path from the starting point to the target point before the unmanned aerial vehicle flies.

Description

Technical Field

[0001] This invention relates to the field of UAV four-dimensional trajectory planning methods, and in particular to a UAV four-dimensional trajectory planning method in complex low-altitude environments. Background Technology

[0002] Unmanned aerial vehicle (UAV) trajectory planning is one of the core problems in UAV applications, aiming to generate a safe and efficient flight path for the UAV to reach its destination from its starting point. This process must accurately avoid various potential threats within the airspace (such as terrain obstacles, no-fly zones, severe weather, dynamically moving targets, and enemy detection), and collaboratively optimize multiple potentially conflicting objectives while satisfying the aircraft's physical constraints (such as maneuverability and minimum turning radius). Especially in complex environments such as mountainous terrain and densely populated urban areas, the UAV 3D trajectory planning problem exhibits strong nonlinearity, high dimensionality, and multiple constraints, posing significant challenges to the algorithm's real-time performance, robustness, and global optimization capabilities.

[0003] Research on UAV trajectory planning mainly focuses on two categories: traditional classical algorithms and intelligent optimization algorithms. Traditional classical algorithms, such as Dijkstra's algorithm, A* algorithm, artificial potential field method, fast expanding random tree, and simulated annealing algorithm, perform well in planning, but often face challenges such as high computational cost and insufficient path smoothness when dealing with complex 3D terrain. Furthermore, their optimization time increases exponentially with increasing spatial complexity. Therefore, in recent years, research has gradually shifted towards intelligent optimization algorithms inspired by natural phenomena or biological behaviors. These algorithms, employing random operations, are more likely to escape local optima and are widely used in various optimization problems, becoming an important solution for UAV 3D trajectory planning. Among numerous intelligent optimization algorithms, Particle Swarm Optimization (PSO) is widely considered suitable for various environmental structures due to its high convergence speed, robustness to initial conditions, and strong environmental adaptability. The core of the PSO algorithm lies in balancing individual cognition and social behavior, and coordinating local development with global exploration. Therefore, PSO and its improved algorithms have been introduced into UAV trajectory planning to solve multi-objective optimization problems, such as discrete PSO, hybrid PSO, quantum behavior PSO, and spherical vector-based PSO. Besides PSO, various other intelligent optimization algorithms have also been applied to UAV trajectory planning. For example, the gray wolf optimization algorithm and its improved methods, artificial bee colony optimization, and ant colony optimization have been used to solve UAV trajectory planning problems. However, existing research shows that, given the high complexity of trajectory planning problems, no single algorithm has universal applicability; therefore, developing more efficient optimization methods remains a current research hotspot.

[0004] The Marine Predator Algorithm (MPA), proposed by Faramarzi et al. in 2020, is a swarm intelligence optimization algorithm inspired by marine predator-prey foraging strategies and optimal encounter rate mechanisms. MPA and its improved algorithms have been widely applied in task allocation, image segmentation, parameter optimization, and path planning. However, similar to other intelligent optimization algorithms, MPA still faces challenges in handling complex engineering optimization problems (such as nonlinear, multi-constraint 3D UAV trajectory planning), including slow convergence speed, susceptibility to local optima, and an imbalance between global exploration and local exploitation. This paper focuses on the aforementioned shortcomings of MPA in complex environments (especially 3D UAV trajectory planning), proposes a multi-strategy enhanced Marine Predator Algorithm, and applies it to UAV trajectory planning in complex low-altitude environments. Summary of the Invention

[0005] Purpose of the invention: The technical problem to be solved by the present invention is to provide a four-dimensional trajectory planning method for UAVs in complex low-altitude environments, which addresses the shortcomings of the existing technology.

[0006] To address the aforementioned technical problems, this invention discloses a four-dimensional trajectory planning method for unmanned aerial vehicles (UAVs) in complex low-altitude environments, comprising the following steps:

[0007] Step 1: Generate initial path points for the UAV based on its flight start point and target point. Each path point represents an intermediate point during the UAV's flight.

[0008] Step 2: Based on the UAV flight mission and flight environment characteristics, establish the UAV trajectory planning cost function;

[0009] Step 3: Using the trajectory planning cost function as the constraint and optimization objective, the multi-strategy enhanced marine predator algorithm is used for multiple iterative optimizations, continuously updating the position of the waypoints until the preset termination condition is met.

[0010] Step 4: Post-process the generated waypoints using a smoothing algorithm to obtain a smoother flight path;

[0011] Step 5: Output the final generated 3D UAV trajectory and add the time dimension by combining it with the flight plan, thereby generating the optimal 4D trajectory of the UAV from the starting point to the target point before flight.

[0012] The initial path point generation step for the UAV includes:

[0013] Step 2-1: Calculate r = (r1, r2, ..., r k ,…,r d Let r represent a set of d-dimensional random vectors. k Let the k-th value be represented by the following: Where p satisfies The smallest prime number, d represents the dimension of the solution space, and mod[] represents the modulo operation;

[0014] Step 2-2: Construct a set P of N ideal points d (k):

[0015]

[0016] Steps 2-3: Set the best points P d (k) Mapping to the feasible region of the solution space:

[0017] x k (j)=Lb j +(Ub j -Lb j )P d (k)

[0018] Where, x k (j) represents the initial path point of the UAV, Lb j Ub represents the lower bound of the j-th dimension of the optimization problem. j This represents the upper bound of the j-th dimension of the optimization problem.

[0019] The establishment of the UAV trajectory planning cost function includes:

[0020] minF=w1F safe +w2F threat +w3F length +w4F Height +w5F Devi_angle

[0021] +w6F Pitch_angle +w7F No_fly +w8F Tem +w9F Spa

[0022] Where F represents the total cost of the trajectory, F safe Let w1 represent the weighting coefficient of the safety cost, and F represent the safety cost. threat F represents the threat cost, w2 represents the weighting coefficient of the threat cost, and F represents the threat cost. length w3 represents the distance cost, and F represents the weighting coefficient of the distance cost. Height Indicates height cost, w4 represents the weighting coefficient of height cost, F Devi_angle This represents the maximum yaw angle constraint, w5 represents the weighting coefficient of the maximum yaw angle constraint, and F... Pitch_angle This represents the maximum pitch angle constraint, w6 represents the weighting coefficient of the maximum pitch angle constraint, and F No_fly This represents the no-fly zone constraint, w7 represents the weight coefficient of the no-fly zone constraint, and F... Temw8 represents multi-machine time coordination constraints, and F represents multi-machine time coordination constraints. Spa w9 represents the weight coefficient of the multi-machine spatial collaborative constraint.

[0023] The security cost F threat The expression is:

[0024]

[0025] Among them, F threat For drone security costs, S j Let represent the distance from the projection of the j-th waypoint onto the horizontal plane to the center of the obstacle, D represent the radius of the collision zone, U represent the size of the UAV, T represent the risk distance, K represent the total number of obstacles in the UAV's operating airspace, and n represent the number of waypoints.

[0026] The threat cost F threat The expression is:

[0027]

[0028] Among them, F threat Let Γ(i) represent the set of threat areas detected by the drone at waypoint i, where i is the cost of the drone threat. This represents the threat cost of a drone being detected by the j-th threat area at waypoint i.

[0029] Regarding radar threats, The expression is:

[0030]

[0031] in, E represents the distance of the drone from waypoint i to the center of threat j. Radar This represents a radar threat level constant;

[0032] Regarding the threat of artillery The expression is:

[0033]

[0034] Among them, R a,j Indicates the maximum kill radius of the artillery;

[0035] The distance cost F length The expression is:

[0036]

[0037] Among them, F length Indicates the distance cost of drones, l iThis represents the distance from path node i to node i+1, (x s ,y s ,z s (x) represents the starting position coordinates of the drone. d ,y d ,z d The final coordinates of the UAV's location, L EC This represents the geometric distance between the starting point and the target point;

[0038] The high cost F Height The expression is:

[0039]

[0040] Among them, F Height Indicating the high cost of drones, F Height,i h represents the altitude cost of the UAV at waypoint i. max and h min h represents the maximum and minimum permitted flight altitudes for drones, respectively. i This indicates the flight altitude of the UAV at waypoint i;

[0041] The maximum yaw angle constraint F Devi_angle The expression is:

[0042]

[0043] Among them, F Devi_angle α represents the maximum yaw angle constraint of the UAV. i α represents the offset angle of the current track segment relative to the previous track segment. max This indicates the maximum permissible yaw angle for the drone. This represents the projection of the i-th and i+1-th adjacent route nodes onto the horizontal plane. This represents the projection of the (i+1)th and (i+2)th adjacent path nodes onto the horizontal plane;

[0044] The maximum pitch angle constraint F Pitch_angle The expression is:

[0045]

[0046] Among them, F Pitch_angle θ represents the maximum pitch angle constraint of the UAV. i θ represents the pitch angle of the current track segment relative to the previous track segment. max Indicates the maximum allowable pitch angle for the drone. z represents the projected length of the two adjacent route nodes i and i+1 on the horizontal plane. i and z i+1These represent the flight altitudes of the UAVs at the i-th and i+1-th adjacent route nodes, respectively.

[0047] The no-fly zone constraint F No_fly The expression is:

[0048]

[0049] Among them, F No_fly This indicates the restrictions imposed by the no-fly zone. and These represent the lower and upper limits of the no-fly zone in the x-coordinate, respectively. and These represent the lower and upper limits of the no-fly zone in the y-coordinate, respectively;

[0050] The multi-machine time coordination constraint F Tem The expression is:

[0051]

[0052] Among them, F Tem This indicates multi-machine time coordination constraints. and Let t represent the shortest and longest time taken for the i-th drone to reach the destination, respectively. c This indicates the command time for the drone to reach the target destination. and Let L represent the minimum and maximum flight speeds of the i-th drone, respectively. i This represents the distance from the starting point to the target endpoint for the i-th drone;

[0053] The multi-machine spatial collaborative constraint F Spa The expression is:

[0054]

[0055] Among them, F Spa Describing multi-machine spatial coordination constraints, d i d represents the distance between drone path node i and other drones at the same time. safe This indicates the safe distance between drones.

[0056] The implementation process of the multi-strategy enhanced marine predator algorithm includes:

[0057] Step 5-1: Initialize the parameters involved in the algorithm: the number of optimal points (i.e., the population size N), and the maximum number of iterations Max. Iter Parameters k, a, and b; set the current iteration number Iter = 0;

[0058] Step 5-2: If Iter < Max IterProceed to step 5-3 if necessary, otherwise proceed to step 5-11.

[0059] Step 5-3: Calculate fitness, construct the elite matrix, and store the fitness of the trajectory planning.

[0060] Step 5-4: If Iter < Max Iter / 3, proceed to step 5-5; otherwise, proceed to step 5-6.

[0061] Step 5-5: Generate a random number rand. If rand < 0.5, update the prey position (i.e., update the waypoint) according to the following formula, and then proceed to step 5-9.

[0062]

[0063] in, This indicates the algorithm updates the step size. This represents random numbers generated based on the Cauchy distribution. Represents the prey matrix. Represents an elite matrix;

[0064] If rand ≥ 0.5, combining the position update rules of Levi's flight and differential mutation strategy, update the prey position (i.e., update the waypoint) according to the following formula, and then proceed to steps 5-9.

[0065]

[0066] Where i = 1, 2, ..., N, Indicates element-wise multiplication. Let P represent a random vector of Brownian motion that follows a normal distribution, where P = 0.5 is a constant. This represents a random number vector simulating Levi's flight, where subscripts r1, r2, r3, and r4 are indices that are independently and randomly drawn from the prey matrix;

[0067] Steps 5-6: If Proceed to step 5-7; otherwise proceed to step 5-8.

[0068] Steps 5-7: For the first half of the population, update the prey location (i.e., update the trackpoints) according to the following formula, and then proceed to step 5-9.

[0069]

[0070] Where i = 1, 2, ..., N / 2;

[0071] For the second half of the population, update the prey location (i.e., update the trackpoints) according to the following formula, and then proceed to steps 5-9.

[0072]

[0073] Where i = N / 2, ..., N, CF new The adaptive parameter represents the stride length of the predator, and w represents the nonlinear inertial weight value.

[0074] Steps 5-8: If For all populations, update the prey location (i.e., update the trackpoints) according to the following formula, and then proceed to steps 5-9.

[0075]

[0076] Where i = 1, 2, ..., N;

[0077] Steps 5-9: Complete ocean memory storage and elite matrix update, apply the following formula to update FADs effect, and then proceed to step 5-10.

[0078]

[0079] Where FADs = 0.2 represents the probability threshold for triggering the FADs (Fish Aggregating Devices) effect, and the vector... It is a vector with two states (0 or 1) and is generated according to the following rules: a random vector is generated in the interval [0,1]. If the value is less than 0.2, it is set to 0; if it is greater than 0.2, it is set to 1. r is a random number that follows a uniform distribution in [0,1]. and Let r1 and r2 be the lower and upper bounds of the search space, respectively, and let r1 and r2 be the indices that are independently and randomly drawn from the prey matrix.

[0080] Steps 5-10: Iter+=1, go to 5-2;

[0081] Steps 5-11: Return the optimal solution and end.

[0082] The CF mentioned in steps 5-7 new The novel nonlinear adaptive control parameter strategy is expressed as follows:

[0083]

[0084] Among them, CF new The parameters represent adaptive parameters that control the stride length of marine predators, where Iter represents the current iteration number and Max represents the maximum stride length. Iter This indicates the maximum number of iterations, and exp(·) represents the power of the natural logarithm e, which has a value of approximately 2.7182818.

[0085] The w mentioned in steps 5-7 is a nonlinear inertia weighting strategy, and its expression is:

[0086]

[0087] Where w represents the nonlinear inertia weight value, and parameters k, a, and b represent constants that control the change of the inertia weight value.

[0088] Step 5-5 The random number generation strategy based on the Cauchy distribution is expressed as follows:

[0089]

[0090] in, represents a random number generated based on the Cauchy distribution, with a value range of [0,2], while rand represents a random number in the range of [0,1].

[0091] The smoothing algorithm described in step 4 is the B-spline curve method applied to smooth the optimal path, and its expression is:

[0092]

[0093] Where P(u) represents the smoothed output node coordinates, q i (i = 0, 1, ..., n) represents control points, n represents the number of control points, u represents the number of nodes, k represents the order of the B-spline baseline function, and N i,k (u) represents the k-th order normalized B-spline basis function, and its expression is:

[0094]

[0095] The output optimal four-dimensional trajectory consists of three-dimensional spatial coordinates and a time series, represented as (X,Y,Z,T), where X, Y, and Z represent the three-dimensional spatial coordinates of the UAV, and T represents the time series, including the UAV's planned departure time, planned arrival time, and current time.

[0096] Beneficial effects:

[0097] 1. This invention establishes a cost function for UAV trajectory planning that includes safety cost, distance cost, altitude cost, maximum yaw angle constraint, maximum pitch angle constraint, no-fly zone constraint, multi-aircraft time coordination constraint, and multi-aircraft spatial coordination constraint. It comprehensively considers the optimality and safety of UAV flight and accurately characterizes various constraints and optimization objectives in the UAV flight process.

[0098] 2. Within the framework of the standard marine predator algorithm, this invention designs four improved strategies, including novel adaptive parameters, nonlinear inertial weights, random number generation based on Cauchy distribution, and improved position update rules, which improve the convergence speed and model solution accuracy of the algorithm.

[0099] 3. This invention can effectively improve the flight path planning effect of UAVs, accurately plan the flight path from the starting point to the target endpoint for the UAV, and improve the flight safety and efficiency of UAVs. Attached Figure Description

[0100] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention.

[0101] Figure 2 This is a schematic diagram illustrating the safety cost of the drone using the method of the present invention.

[0102] Figure 3 This is a schematic diagram illustrating the altitude cost of the UAV using the method of the present invention.

[0103] Figure 4 This is the implementation flow of the marine predator algorithm of the present invention.

[0104] Figure 5 The curve shows a comparison between the novel adaptive parameters of the present invention and the traditional adaptive parameters.

[0105] Figure 6 The three-dimensional space curve of the UAV flight trajectory generated by the method of the present invention.

[0106] Figure 7 A side view of the UAV flight path generated by the method of the present invention.

[0107] Figure 8 The fitness curve of the UAV flight track generated by the method of the present invention.

[0108] Figure 9 The UAV flight path fitness curve generated using the method of this invention.

[0109] Figure 10 This is a diagram of the experimental area in this embodiment.

[0110] Figure 11 These are the results of a flight experiment. Detailed Implementation

[0111] This invention proposes a four-dimensional trajectory planning method for unmanned aerial vehicles (UAVs) in complex low-altitude environments. This method establishes a multi-objective optimization model that comprehensively considers the optimality and safety of UAV flight. Within the framework of the standard marine predator algorithm, it introduces four innovative mechanisms: novel adaptive parameters, nonlinear inertial weights, random number generation based on Cauchy distribution, and improved position update rules. These improvements enhance the algorithm's convergence speed and model solution accuracy, enabling precise planning of flight trajectories from the starting point to the target endpoint for the UAV. A flowchart of the specific implementation is shown below. Figure 1 As shown.

[0112] A method for four-dimensional trajectory planning of UAVs in complex low-altitude environments includes the following steps:

[0113] Step 1: Generate initial path points for the UAV based on its flight start point and target point. Each path point represents an intermediate point during the UAV's flight.

[0114] Step 2: Based on the UAV flight mission and flight environment characteristics, establish the UAV trajectory planning cost function;

[0115] Step 3: Using the trajectory planning cost function as the constraint and optimization objective, the multi-strategy enhanced marine predator algorithm is used for multiple iterative optimizations, continuously updating the position of the waypoints until the preset termination condition is met.

[0116] Step 4: Post-process the generated waypoints using a smoothing algorithm to obtain a smoother flight path;

[0117] Step 5: Output the final generated 3D UAV trajectory and add the time dimension by combining it with the flight plan, thereby generating the optimal 4D trajectory of the UAV from the starting point to the target point before flight.

[0118] The initial path point generation step for the UAV includes:

[0119] Step 2-1: Calculate r = (r1, r2, ..., r k ,…,r d Let r represent a set of d-dimensional random vectors. k Let the k-th value be represented by the following: Where p satisfies The smallest prime number, d represents the dimension of the solution space, and mod[] represents the modulo operation;

[0120] Step 2-2: Construct a set P of N ideal points d (k):

[0121]

[0122] Steps 2-3: Set the best points P d (k) Mapping to the feasible region of the solution space:

[0123] x k (j)=Lb j +(Ub j -Lb j )P d (k)

[0124] Where, x k (j) represents the initial path point of the UAV, Lb j Ub represents the lower bound of the j-th dimension of the optimization problem. j This represents the upper bound of the j-th dimension of the optimization problem.

[0125] The establishment of the UAV trajectory planning cost function includes:

[0126] minF=w1F safe +w2F threat +w3F length +w4F Height +w5F Devi_angle

[0127] +w6F Pitch_angle +w7F No_fly +w8F Tem +w9F Spa

[0128] Where F represents the total cost of the trajectory, F safe Let w1 represent the weighting coefficient of the safety cost, and F represent the safety cost. threat F represents the threat cost, w2 represents the weighting coefficient of the threat cost, and F represents the threat cost. length w3 represents the distance cost, and F represents the weighting coefficient of the distance cost. Height Indicates height cost, w4 represents the weighting coefficient of height cost, F Devi_angle This represents the maximum yaw angle constraint, w5 represents the weighting coefficient of the maximum yaw angle constraint, and F... Pitch_angle This represents the maximum pitch angle constraint, w6 represents the weighting coefficient of the maximum pitch angle constraint, and F No_fly This represents the no-fly zone constraint, w7 represents the weight coefficient of the no-fly zone constraint, and F... Tem w8 represents multi-machine time coordination constraints, and F represents multi-machine time coordination constraints. Spa w9 represents the weight coefficient of the multi-machine spatial collaborative constraint.

[0129] The security cost F threat The expression is:

[0130]

[0131] Among them, F threat For drone security costs, S j Let represent the distance from the projection of the j-th waypoint onto the horizontal plane to the center of the obstacle, D represent the radius of the collision zone, U represent the size of the UAV, T represent the risk distance, K represent the total number of obstacles in the UAV's operating airspace, and n represent the number of waypoints.

[0132] The threat cost F threat The expression is:

[0133]

[0134] Among them, F threatLet Γ(i) represent the set of threat areas detected by the drone at waypoint i, where i is the cost of the drone threat. This represents the threat cost of a drone being detected by the j-th threat area at waypoint i.

[0135] Regarding radar threats, The expression is:

[0136]

[0137] in, E represents the distance of the drone from waypoint i to the center of threat j. Radar This represents a radar threat level constant;

[0138] Regarding the threat of artillery The expression is:

[0139]

[0140] Among them, R a,j Indicates the maximum kill radius of the artillery;

[0141] The distance cost F length The expression is:

[0142]

[0143] Among them, F length Indicates the distance cost of drones, l i This represents the distance from path node i to node i+1, (x s ,y s ,z s (x) represents the starting position coordinates of the drone. d ,y d ,z d The final coordinates of the UAV's location, L EC This represents the geometric distance between the starting point and the target point;

[0144] The high cost F Height The expression is:

[0145]

[0146] Among them, F Height Indicating the high cost of drones, F Height,i h represents the altitude cost of the UAV at waypoint i. max and h min h represents the maximum and minimum permitted flight altitudes for drones, respectively. i This indicates the flight altitude of the UAV at waypoint i;

[0147] The maximum yaw angle constraint F Devi_angle The expression is:

[0148]

[0149] Among them, F Devi_angle α represents the maximum yaw angle constraint of the UAV. i α represents the offset angle of the current track segment relative to the previous track segment. max This indicates the maximum permissible yaw angle for the drone. This represents the projection of the i-th and i+1-th adjacent route nodes onto the horizontal plane. This represents the projection of the (i+1)th and (i+2)th adjacent path nodes onto the horizontal plane;

[0150] The maximum pitch angle constraint F Pitch_angle The expression is:

[0151]

[0152] Among them, F Pitch_angle θ represents the maximum pitch angle constraint of the UAV. i θ represents the pitch angle of the current track segment relative to the previous track segment. max Indicates the maximum allowable pitch angle for the drone. z represents the projected length of the two adjacent route nodes i and i+1 on the horizontal plane. i and z i+1 These represent the flight altitudes of the UAVs at the i-th and i+1-th adjacent route nodes, respectively.

[0153] The no-fly zone constraint F No_fly The expression is:

[0154]

[0155] Among them, F No_fly This indicates the restrictions imposed by the no-fly zone. and These represent the lower and upper limits of the no-fly zone in the x-coordinate, respectively. and These represent the lower and upper limits of the no-fly zone in the y-coordinate, respectively;

[0156] The multi-machine time coordination constraint F Tem The expression is:

[0157]

[0158] Among them, F Tem This indicates multi-machine time coordination constraints. and Let t represent the shortest and longest time taken for the i-th drone to reach the destination, respectively. c This indicates the command time for the drone to reach the target destination. and Let L represent the minimum and maximum flight speeds of the i-th drone, respectively. i This represents the distance from the starting point to the target endpoint for the i-th drone;

[0159] The multi-machine spatial collaborative constraint F Spa The expression is:

[0160]

[0161] Among them, F Spa Describing multi-machine spatial coordination constraints, d i d represents the distance between drone path node i and other drones at the same time. safe This indicates the safe distance between drones.

[0162] The implementation process of the multi-strategy enhanced marine predator algorithm includes:

[0163] Step 5-1: Initialize the parameters involved in the algorithm: the number of optimal points (i.e., the population size N), and the maximum number of iterations Max. Iter k, a, and b, set the current iteration number Iter = 0;

[0164] Step 5-2: If Iter < Max Iter Proceed to step 5-3 if necessary, otherwise proceed to step 5-11.

[0165] Step 5-3: Calculate fitness, construct the elite matrix, and store the fitness of the trajectory planning.

[0166] Step 5-4: If Iter < Max Iter / 3, proceed to step 5-5; otherwise, proceed to step 5-6.

[0167] Step 5-5: Generate a random number rand. If rand < 0.5, update the prey position (i.e., update the waypoint) according to the following formula, and then proceed to step 5-9.

[0168]

[0169] in, This indicates the algorithm updates the step size. This represents random numbers generated based on the Cauchy distribution. Represents the prey matrix. Represents an elite matrix;

[0170] If rand ≥ 0.5, combining the position update rules of Levi's flight and differential mutation strategy, update the prey position (i.e., update the waypoint) according to the following formula, and then proceed to steps 5-9.

[0171]

[0172] Where i = 1, 2, ..., N, Indicates element-wise multiplication. Let P represent a random vector of Brownian motion that follows a normal distribution, where P = 0.5 is a constant. This represents a vector of random numbers simulating Levi's flight, with subscripts r1, r2, r3, and r4 being indices that are independently and randomly drawn from the prey matrix;

[0173] Steps 5-6: If Proceed to step 5-7; otherwise proceed to step 5-8.

[0174] Steps 5-7: For the first half of the population, update the prey location (i.e., update the trackpoints) according to the following formula, and then proceed to step 5-9.

[0175]

[0176] Where i = 1, 2, ..., N / 2;

[0177] For the second half of the population, update the prey location (i.e., update the trackpoints) according to the following formula, and then proceed to steps 5-9.

[0178]

[0179] Where i = N / 2, ..., N, CF new The adaptive parameter represents the stride length of the predator, and w represents the nonlinear inertial weight value.

[0180] Steps 5-8: If For all populations, update the prey location (i.e., update the trackpoints) according to the following formula, and then proceed to steps 5-9.

[0181]

[0182] Where i = 1, 2, ..., N;

[0183] Steps 5-9: Complete ocean memory storage and elite matrix update, apply the following formula to update FADs effect, and then proceed to step 5-10.

[0184]

[0185] Where FADs = 0.2 represents the probability threshold for triggering the FADs effect, and the vector... It is a vector with two states (0 or 1) and is generated according to the following rules: a random vector is generated in the interval [0,1]. If the value is less than 0.2, it is set to 0; if it is greater than 0.2, it is set to 1. r is a random number that follows a uniform distribution in [0,1]. and Let r1 and r2 be the lower and upper bounds of the search space, respectively, and let r1 and r2 be the indices that are independently and randomly drawn from the prey matrix.

[0186] Steps 5-10: Iter+=1, go to 5-2;

[0187] Steps 5-11: Return the optimal solution and end.

[0188] The CF mentioned in steps 5-7 new The novel nonlinear adaptive control parameter strategy is expressed as follows:

[0189]

[0190] Among them, CF new The parameters represent adaptive parameters that control the stride length of marine predators, where Iter represents the current iteration number and Max represents the maximum stride length. Iter This indicates the maximum number of iterations, and exp(·) represents the power of the natural logarithm e, which has a value of approximately 2.7182818.

[0191] The w mentioned in steps 5-7 is a nonlinear inertia weighting strategy, and its expression is:

[0192]

[0193] Where w represents the nonlinear inertia weight value, and k, a, and b represent constants that control the change of the inertia weight value.

[0194] Step 5-5 The random number generation strategy based on the Cauchy distribution is expressed as follows:

[0195]

[0196] in, represents a random number generated based on the Cauchy distribution, with a value range of [0,2], while rand represents a random number in the range of [0,1].

[0197] The smoothing algorithm described in step 4 is the B-spline curve method applied to smooth the optimal path, and its expression is:

[0198]

[0199] Where P(u) represents the smoothed output node coordinates, q i(i = 0, 1, ..., n) represents control points, N i,k (u) represents the k-th order normalized B-spline basis function, and its expression is:

[0200]

[0201] The output optimal four-dimensional trajectory consists of three-dimensional spatial coordinates and a time series, represented as (X,Y,Z,T), where X, Y, and Z represent the three-dimensional spatial coordinates of the UAV, and T represents the time series, including the UAV's planned departure time, planned arrival time, and current time.

[0202] Example:

[0203] This embodiment uses a real digital elevation model obtained from a LiDAR sensor to evaluate the algorithm's performance. A terrain feature combining land and sea characteristics is selected as the base. By overlaying complexity variables, a test scenario is generated, such as... Figure 6 As shown. Threats in the test scenario are represented by cylinders and spheres. The starting coordinates of the UAV are set to (200, 100, 150) and the ending coordinates are (800, 800, 150). The number of waypoints is set to n = 12, corresponding to 10 flight paths.

[0204] Figure 6 The three-dimensional space map of the UAV flight path generated by the method of the present invention shows that the method of the present invention can plan a smooth and stable flight path for UAVs in complex environments, effectively avoiding threats in the flight space.

[0205] Figure 7 The side view of the UAV flight path generated using the method of this invention shows that the planned flight path is smooth and stable, and the altitude is controlled within a relatively stable range.

[0206] Figure 8 The top-down view of the UAV flight path generated using the method of this invention shows that the planned trajectory successfully avoided obstacle threats and flew close to a straight line, demonstrating excellent trajectory optimization capabilities, further illustrating the effectiveness of the method of this invention.

[0207] Figure 9 The flight path fitness curve generated by the method of this invention shows that the trajectory planning converges quickly and the convergence value is relatively stable, which demonstrates that the method of this invention has good applicability to UAV trajectory planning problems in complex environments.

[0208] To further verify the effectiveness of this invention in actual flight path generation, a real-world verification experiment was conducted using an industrial-grade UAV platform, and automatic flight control was achieved through UAV ground control software. This software integrates the UAV path planning algorithm proposed in this invention, such as... Figure 10 As shown. The experimental area is located in a 1000m × 1000m airspace around 32.0147°N, 118.8771°E. This area contains complex terrain features such as high-rise buildings and no-fly zones, effectively verifying the algorithm's performance in a real-world environment. After loading the 3D map data of the experimental area into the ground control software and setting the UAV's start and end coordinates, the algorithm proposed in this invention generates a planned flight path consisting of a series of waypoints. After coordinate transformation, these waypoints are uploaded to the UAV flight control system via the ground control software, and autonomous flight is executed.

[0209] Figure 11 The flight experiment results are presented, where the yellow line represents the planned path and the red line represents the actual flight trajectory. The high degree of overlap between the two paths indicates that the path generated by the method of this invention can be effectively followed by the UAV. Throughout the flight, the actual trajectory did not cross any no-fly zones, indicating that the path meets the requirements for safe UAV flight. The results of the examples fully demonstrate the effectiveness and reliability of the method of this invention in actual UAV trajectory planning.

[0210] This invention provides a four-dimensional trajectory planning method for unmanned aerial vehicles (UAVs) in complex low-altitude environments. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

Claims

1. A method for four-dimensional trajectory planning of unmanned aerial vehicles (UAVs) in complex low-altitude environments, characterized in that, Includes the following steps: Step 1: Generate initial path points for the UAV based on its flight start point and target point. Each path point represents an intermediate point during the UAV's flight. Step 2: Based on the UAV flight mission and flight environment characteristics, establish the UAV trajectory planning cost function; Step 3: Using the trajectory planning cost function as the constraint and optimization objective, the multi-strategy enhanced marine predator algorithm is used for multiple iterative optimizations, continuously updating the position of the waypoints until the preset termination condition is met. Step 4: Post-process the generated waypoints using a smoothing algorithm to obtain a smoother flight path; Step 5: Output the final generated 3D UAV trajectory and add the time dimension by combining it with the flight plan, thereby generating the optimal 4D trajectory of the UAV from the starting point to the target point before flight.

2. The method for four-dimensional trajectory planning of UAVs in complex low-altitude environments according to claim 1, characterized in that, The initial path point generation step for the UAV includes: Step 2-1: Calculate r = (r1, r2, ..., r k ,…,r d Let r represent a set of d-dimensional random vectors. k Let the k-th value be represented by the following: Where p satisfies The smallest prime number, d represents the dimension of the solution space, and mod[ represents the modulo operation; Step 2-2: Construct a set P of N ideal points d (k): Steps 2-3: Set the best points P d (k) Mapping to the feasible region of the solution space: x k (j)=Lb j +(Ub j -Lb j )P d (k) Where, x k (j) represents the initial path point of the UAV, Lb j Ub represents the lower bound of the j-th dimension of the optimization problem. j This represents the upper bound of the j-th dimension of the optimization problem.

3. The method for four-dimensional trajectory planning of UAVs in complex low-altitude environments according to claim 1, characterized in that, The establishment of the UAV trajectory planning cost function includes: minF=w1F safe +w2F threat +w3F length +w4F Height +w5F Devi_angle +w6F Pitch_angle +w7F No_fly +w8F Tem +w9F Spa Where F represents the total cost of the trajectory, F safe Let w1 represent the weighting coefficient of the safety cost, and F represent the safety cost. threat F represents the threat cost, w2 represents the weighting coefficient of the threat cost, and F represents the threat cost. length w3 represents the distance cost, and F represents the weighting coefficient of the distance cost. Height Indicates height cost, w4 represents the weighting coefficient of height cost, F Devi_angle This represents the maximum yaw angle constraint, w5 represents the weighting coefficient of the maximum yaw angle constraint, and F... Pitch_angle This represents the maximum pitch angle constraint, w6 represents the weighting coefficient of the maximum pitch angle constraint, and F No_fly This represents the no-fly zone constraint, w7 represents the weight coefficient of the no-fly zone constraint, and F... Tem w8 represents multi-machine time coordination constraints, and F represents multi-machine time coordination constraints. Spa w9 represents the multi-machine spatial collaborative constraint, and w9 represents the weight coefficient of the multi-machine spatial collaborative constraint.

4. The method for four-dimensional trajectory planning of UAVs in complex low-altitude environments according to claim 3, characterized in that, The security cost F safe The expression is: Among them, F safe For drone security costs, S j Let represent the distance from the projection of the j-th waypoint onto the horizontal plane to the center of the obstacle, D represent the radius of the collision zone, U represent the size of the UAV, T represent the risk distance, K represent the total number of obstacles in the UAV's operating airspace, and n represent the number of waypoints. The threat cost F threat The expression is: Among them, F threat Let Γ(i) represent the set of threat areas detected by the drone at waypoint i, where i is the cost of the drone threat. This represents the cost of the threat that the drone is detected by the j-th threat area at waypoint i; Regarding radar threats, The expression is: in, E represents the distance of the drone from waypoint i to the center of threat j. Radar This represents a radar threat level constant; Regarding the threat of artillery The expression is: Among them, R a,j Indicates the maximum kill radius of the artillery; The distance cost F length The expression is: Among them, F length Indicates the distance cost of drones, l i This represents the distance from path node i to node i+1, (x s ,y s ,z s (x) represents the starting position coordinates of the drone. d ,y d ,z d The final coordinates of the UAV's location, L EC This represents the geometric distance between the starting point and the target point; The high cost F Height The expression is: Among them, F Height Indicating the high cost of drones, F Height,i h represents the altitude cost of the UAV at waypoint i. max and h min h represents the maximum and minimum permitted flight altitudes for drones, respectively. i This indicates the flight altitude of the UAV at waypoint i; The maximum yaw angle constraint F Devi_angle The expression is: Among them, F Devi_angle α represents the maximum yaw angle constraint of the UAV. i α represents the offset angle of the current track segment relative to the previous track segment. max This indicates the maximum permissible yaw angle for the drone. This represents the projection of the i-th and i+1-th adjacent route nodes onto the horizontal plane. This represents the projection of the (i+1)th and (i+2)th adjacent path nodes onto the horizontal plane; The maximum pitch angle constraint F Pitch_angle The expression is: Among them, F Pitch_angle θ represents the maximum pitch angle constraint of the UAV. i θ represents the pitch angle of the current track segment relative to the previous track segment. max Indicates the maximum allowable pitch angle for the drone. z represents the projected length of the two adjacent route nodes i and i+1 on the horizontal plane. i and z i+1 These represent the flight altitudes of the UAVs at the i-th and i+1-th adjacent route nodes, respectively. The no-fly zone constraint F No_fly The expression is: Among them, F No_fly This indicates the restrictions imposed by the no-fly zone. and These represent the lower and upper limits of the no-fly zone in the x-coordinate, respectively. and These represent the lower and upper limits of the no-fly zone in the y-coordinate, respectively; The multi-machine time coordination constraint F Tem The expression is: Among them, F Tem This indicates multi-machine time coordination constraints. and Let t represent the shortest and longest time taken for the i-th drone to reach the destination, respectively. c This indicates the command time for the drone to reach the target destination. and Let L represent the minimum and maximum flight speeds of the i-th drone, respectively. i This represents the distance from the starting point to the target endpoint for the i-th drone; The multi-machine spatial collaborative constraint F Spa The expression is: Among them, F Spa Describing multi-machine spatial coordination constraints, d i d represents the distance between drone path node i and other drones at the same time. safe This indicates the safe distance between drones.

5. The method for four-dimensional trajectory planning of UAVs in complex low-altitude environments according to claim 1, characterized in that, The implementation process of the multi-strategy enhanced marine predator algorithm includes: Step 5-1: Initialize the parameters involved in the algorithm: the number of optimal points (i.e., the population size N), and the maximum number of iterations Max. Iter k, a, and b, set the current iteration number Iter = 0; Step 5-2: If Iter < Max Iter Proceed to step 5-3 if necessary, otherwise proceed to step 5-11. Step 5-3: Calculate fitness, construct the elite matrix, and store the fitness of the trajectory planning. Step 5-4: If Iter < Max Iter / 3, proceed to step 5-5; otherwise, proceed to step 5-6. Step 5-5: Generate a random number rand. If rand < 0.5, update the prey position (i.e., update the waypoint) according to the following formula, and then proceed to step 5-9. in, This indicates the algorithm updates the step size. This represents random numbers generated based on the Cauchy distribution. Represents the prey matrix. Represents an elite matrix; If rand ≥ 0.5, combining the position update rules of Levi's flight and differential mutation strategy, update the prey position (i.e., update the waypoint) according to the following formula, and then proceed to steps 5-9. Where i = 1, 2, ..., N, Indicates element-wise multiplication. Let P represent a random vector of Brownian motion that follows a normal distribution, where P = 0.5 is a constant. This represents a vector of random numbers simulating Levi's flight, with subscripts r1, r2, r3, and r4 being indices that are independently and randomly drawn from the prey matrix; Steps 5-6: If Proceed to step 5-7; otherwise proceed to step 5-8. Steps 5-7: For the first half of the population, update the prey location (i.e., update the trackpoints) according to the following formula, and then proceed to step 5-9. Where i = 1, 2, ..., N / 2; For the second half of the population, update the prey location (i.e., update the trackpoints) according to the following formula, and then proceed to steps 5-9. Where i = N / 2, ..., N, CF new The adaptive parameter represents the stride length of the predator, and w represents the nonlinear inertial weight value. Steps 5-8: If For all populations, update the prey location (i.e., update the trackpoints) according to the following formula, and then proceed to steps 5-9. Where i = 1, 2, ..., N; Steps 5-9: Complete ocean memory storage and elite matrix update, apply the following formula to update FADs effect, and then proceed to step 5-10. Where FADs represent the probability threshold for triggering the FADs effect, and the vector... It is a vector with binary states (0 or 1) generated according to the following rules: a random vector is generated in the interval [0,1]. If it is less than FADs, it is set to 0; if it is greater than FADs, it is set to 1. r is a random number that follows a uniform distribution in [0,1]. and Let r1 and r2 be the lower and upper bounds of the search space, respectively, and let r1 and r2 be the indices that are independently and randomly drawn from the prey matrix. Steps 5-10: Iter+=1, go to 5-2; Steps 5-11: Return the optimal solution and end.

6. The method for four-dimensional trajectory planning of UAVs in complex low-altitude environments according to claim 5, characterized in that, The CF mentioned in steps 5-7 new The novel nonlinear adaptive control parameter strategy is expressed as follows: Among them, CF new The parameters represent adaptive parameters that control the stride length of marine predators, where Iter represents the current iteration number and Max represents the maximum stride length. Iter This indicates the maximum number of iterations, and exp(·) represents the power of the natural logarithm e, which has a value of approximately 2.7182818.

7. The method for four-dimensional trajectory planning of UAVs in complex low-altitude environments according to claim 5, characterized in that, The w mentioned in steps 5-7 is a nonlinear inertia weighting strategy, and its expression is: Where w represents the nonlinear inertia weight value, and parameters k, a, and b represent constants that control the change of the inertia weight value.

8. The method for four-dimensional trajectory planning of UAVs in complex low-altitude environments according to claim 5, characterized in that, Step 5-5 The random number generation strategy based on the Cauchy distribution is expressed as follows: in, represents a random number generated based on the Cauchy distribution, with a value range of [0,2], while rand represents a random number in the range of [0,1].

9. The method for four-dimensional trajectory planning of UAVs in complex low-altitude environments according to claim 1, characterized in that, The smoothing algorithm described in step 4 is the B-spline curve method, and its expression is: Where P(u) represents the smoothed output node coordinates, q i (i = 0, 1, ..., n) represents control points, n represents the number of control points, u represents the number of nodes, k represents the order of the B-spline baseline function, and N i,k (u) represents the k-th order normalized B-spline basis function, and its expression is:

10. The method for four-dimensional trajectory planning of unmanned aerial vehicles in complex low-altitude environments according to claim 1, characterized in that, The output optimal four-dimensional trajectory consists of three-dimensional spatial coordinates and a time series, represented as (X,Y,Z,T), where X, Y, and Z represent the three-dimensional spatial coordinates of the UAV, and T represents the time series, including the UAV's planned departure time, planned arrival time, and current time.

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