Unmanned aerial vehicle path planning method based on bubble collapse thought

Abstract

The application discloses a kind of unmanned aerial vehicle flight path planning methods based on bubble collapse thought, belong to unmanned aerial vehicle flight path planning technical field, unmanned aerial vehicle flight path planning methods based on bubble collapse thought include: construct mathematical model simulation three-dimensional map;Bubble collapse algorithm is initialized, and global flight path optimization function is established;Random parameter of bubble collapse algorithm is generated using Logistics chaos mapping, and improved bubble collapse algorithm is obtained;The surface tension of bubble, transverse external force, similarity, efficiency difference are obtained using global flight path optimization function;Trajectory solution update formula is constructed;According to trajectory solution update formula, optimal flight path is obtained, optimal flight path is smoothed using quadratic Bezier curve, and final flight path is obtained.The application method can realize parameter self-adaptive adjustment, can significantly improve the convergence speed of flight path planning, global search capability and planning precision and efficiency, suitable for unmanned aerial vehicle flight path planning problem under complex environment.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) trajectory planning technology, and in particular to a UAV trajectory planning method based on the concept of bubble collapse. Background Technology

[0002] With the rapid development of UAV technology, UAVs are increasingly widely used in military reconnaissance, disaster relief, environmental monitoring, and other fields. Path planning, as one of the core technologies for autonomous UAV flight, has received widespread attention. The goal of path planning is to design an optimal path for the UAV from its starting point to its destination, enabling it to avoid obstacles, reduce energy consumption, shorten flight time, and ensure flight safety. Currently, path planning algorithms are mainly divided into traditional algorithms (such as A* algorithm and fast exploratory random tree algorithm) and intelligent optimization algorithms (such as genetic algorithms and particle swarm optimization). However, traditional algorithms often struggle to balance global optimization with dynamic environmental adaptability, while intelligent optimization algorithms, although possessing strong global search capabilities, are prone to getting trapped in local optima in complex environments. Summary of the Invention

[0003] The purpose of this application is to overcome the shortcomings of the existing technology and provide a UAV trajectory planning method based on the concept of bubble collapse.

[0004] Firstly, this application provides a UAV trajectory planning method based on the concept of bubble collapse, comprising the following steps: Constructing mathematical models to simulate 3D maps; Initialize the bubble collapse algorithm and establish a global trajectory optimization function; An improved bubble collapse algorithm is obtained by using Logistic chaotic mapping to generate random parameters for the bubble collapse algorithm. The surface tension, lateral force, similarity, and efficiency difference of the bubble are obtained using the global trajectory optimization function. Based on the surface tension, lateral external force, similarity, and efficiency differences of the bubbles, a trajectory solution update formula is constructed. The optimal trajectory is obtained according to the trajectory solution update formula. The optimal trajectory is then smoothed using a quadratic Bézier curve to obtain the final trajectory.

[0005] Optionally, the expression for constructing a mathematical model to simulate a 3D map is as follows: Where n is the number of mountain peaks. Representing the The center coordinates of the mountain peak For the first Topographic parameters of the mountain peak, and The first Mount Tai Axial direction and Attenuation in the axial direction, The x-axis is... The vertical axis is denoted by .

[0006] Optionally, initialize the bubble collapse algorithm and establish a global trajectory optimization function, including: Initialize the bubble collapse algorithm parameters and generate a bubble population; Traverse the bubble population to determine the obstacle collision penalty cost of the flight path; Traverse the bubble population to determine the length cost of the trajectory; Traverse the bubble population to determine the altitude fluctuation cost of the flight path; The global trajectory optimization function is obtained based on the obstacle collision penalty cost, the length cost, and the altitude fluctuation cost of the trajectory.

[0007] Optionally, the global trajectory optimization function The expression is as follows: in, The penalty for collisions with obstacles in the flight path. The cost of the length of the flight path, The cost of altitude fluctuations in the flight path. This is the global trajectory optimization function, i.e., the global trajectory cost.

[0008] Optionally, the surface tension, lateral force, similarity, and efficiency difference of the bubble are obtained using the global trajectory optimization function, including: The individual optimal solution, the global optimal solution, and the fitness value are determined by the global trajectory optimization function. Determine the mean and standard deviation of the fitness values ​​to obtain the normal distribution interval of the fitness values; A suitable solution is obtained based on the normal distribution interval of the fitness values; The surface tension of the current bubble is obtained based on the global trajectory optimization function; The surface tension of the current bubble is normalized to obtain a normalized value of the surface tension. The normalized value of the transverse external force is obtained from the normalized value of the surface tension; Determine the similarity between the current bubble and the global optimal bubble; The performance difference between the current bubble and the global optimal bubble is obtained based on the global trajectory optimization function.

[0009] Optionally, based on the surface tension of the bubbles, lateral external force, similarity, and efficiency differences, a trajectory solution update formula is constructed, including: By comparing the normalized surface tension value of the current bubble with the normalized lateral external force value, the similarity and similarity difference factor between the current bubble and the global optimal bubble, and the efficiency difference and efficiency difference factor between the current bubble and the global optimal bubble, four trajectory solution update formulas are constructed. When the normalized value of surface tension is less than the normalized value of lateral external force, and the similarity between the current bubble and the global optimal bubble is less than the similarity difference factor, and the efficiency difference between the current bubble and the global optimal bubble is less than or equal to the efficiency difference factor, the current bubble is moved one step length toward the direction of the individual optimal solution, and a second step length is added to move it in the random direction to obtain the first trajectory solution update formula. When the normalized value of surface tension is less than the normalized value of lateral external force, and the similarity between the current bubble and the global optimal bubble is less than the similarity difference factor, and the efficiency difference between the current bubble and the global optimal bubble is greater than the efficiency difference factor, the current bubble is moved three steps in the direction of the suitable solution to obtain the second trajectory solution update formula. When the normalized surface tension value is less than the normalized lateral force value, and the similarity between the current bubble and the global optimal bubble is greater than or equal to the similarity difference factor, the current bubble is moved to the global optimal solution by a fourth step to obtain the third trajectory solution update formula. When the normalized value of surface tension is less than the normalized value of lateral external force, the current bubble is moved five steps in a random direction to generate a random solution, and the fourth trajectory solution update formula is obtained.

[0010] Optionally, the random parameter expression for the bubble collapse algorithm is generated using the Logistic chaotic mapping as follows: in, Indicates bubble population The Middle A bubble The random values ​​required during iterative calculations Indicates bubble population The Middle A bubble The Middle The random values ​​required for each sub-variable during iterative computation. This means taking any number from 3.57 to 4.

[0011] Optionally, the update formula for the first path solution is: in, These are random values ​​generated using the Logistic chaotic mapping. This is the current iteration number. For the i-th bubble in the t-th iteration, For the i-th bubble in the (t+1)-th iteration, For the i-th bubble in the t-th cycle The global trajectory optimization function value, The global trajectory optimization function value is generated using random values ​​produced by the Logistic chaotic mapping. For the first step, This is the second step size; The formula for updating the second trajectory solution is: in, This is the current iteration number. For the i-th bubble in the t-th iteration, For the i-th bubble in the (t+1)-th iteration, For a suitable solution, This is the third step length; The formula for updating the third trajectory solution is: in, It is made of bubbles Random values ​​generated using Logistic chaotic mapping are used as the basis. This is the current iteration number. For the i-th bubble in the t-th iteration, For the i-th bubble in the (t+1)-th iteration, For the i-th bubble in the t-th iteration The global trajectory optimization function value, The global trajectory optimization function value is generated using random values ​​produced by the Logistic chaotic mapping. This is the globally optimal solution. This is the fourth step length.

[0012] Optionally, the expression for the random solution is: in, Therefore Random values ​​generated using Logistic chaotic mapping are used as the basis. For the i-th bubble in the t-th iteration, For the fifth step length, The solution is random.

[0013] Optionally, the expression for the quadratic Bézier curve is as follows: in, For parameters, Here, k is the reciprocal of the smoothness control parameter. , , These are the coordinates of three control points, each with [specific coordinates]. , , Corresponding coordinate values ​​on the three coordinate axes , Based on three control points and The curve points are obtained by calculating the values.

[0014] This invention provides a UAV trajectory planning method based on the bubble collapse concept. It improves the randomness generation mechanism of initial bubble parameters through Logistic chaotic mapping, enhancing the global exploration capability of the solution space. Combining the competitive balance principle of surface tension and lateral external forces during bubble collapse, it constructs four types of dynamic update formulas for trajectory solutions, achieving multi-dimensional trajectory optimization. Based on a global trajectory optimization function, it drives the iterative evolution of the bubble state, ultimately generating a three-dimensional optimal trajectory with the lowest energy consumption, highest obstacle avoidance safety, and minimal altitude fluctuation. This method demonstrates significant adaptability in dynamic obstacle environments and multi-constraint task scenarios, providing an innovative solution for autonomous UAV trajectory planning.

[0015] This application provides a UAV trajectory planning method based on the bubble collapse concept. It improves traditional intelligent optimization algorithms by simulating the physical phenomenon of bubble collapse and deeply integrates the bubble collapse concept with a global trajectory optimization function. This addresses the shortcomings of traditional algorithms, such as being prone to getting trapped in local optima and lacking dynamic adaptability, and generates optimal trajectories that balance trajectory length, obstacle avoidance safety, and flight efficiency. Through a dynamic interaction mechanism between bubble surface tension and lateral external force, the update rules for trajectory solutions are adjusted in real time based on the bubble fitness value, achieving a dynamic balance between global search and local optimization, significantly improving the algorithm's convergence accuracy and robustness. It can plan trajectories with the shortest path, reliable obstacle avoidance, and high smoothness, conforming to the kinematic constraints of UAVs, while also meeting the real-time requirements of trajectory planning in complex environments.

[0016] To make the above-mentioned features and advantages of the invention more apparent and understandable, specific embodiments are described below, and detailed descriptions are provided in conjunction with the accompanying drawings. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of a UAV trajectory planning method based on the concept of bubble collapse provided in one embodiment of this application.

[0019] Figure 2 This is a flowchart of step S2 in the UAV trajectory planning method based on the bubble collapse concept provided in one embodiment of this application.

[0020] Figure 3 This is a flowchart of step S5 in a UAV trajectory planning method based on the concept of bubble collapse provided in one embodiment of this application.

[0021] Figure 4 The Benchmark function in the UAV trajectory planning method based on the bubble collapse concept provided in another embodiment of this application. The fitness value changes with the number of iterations after 1000 iterations.

[0022] Figure 5 In another embodiment of this application, the UAV trajectory planning method based on the bubble collapse concept and the particle swarm optimization algorithm are compared in the Benchmark function. A graph showing the change in fitness values ​​after 300 iterations of optimization.

[0023] Figure 6 This is a top view of the optimal trajectory planning of the UAV trajectory planning method based on the bubble collapse idea and the particle swarm algorithm provided in another embodiment of this application after 100 iterations.

[0024] Figure 7 This is a front view of the optimal trajectory planning of the UAV trajectory planning method based on the bubble collapse idea and the particle swarm algorithm provided in another embodiment of this application after 100 iterations.

[0025] Figure 8 This is a side view of the optimal trajectory planning of the UAV trajectory planning method based on the bubble collapse idea and the particle swarm algorithm provided in another embodiment of this application after 100 iterations. Detailed Implementation

[0026] To make the objectives and technical solutions of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the described embodiments of this application without creative effort are within the scope of protection of this application.

[0027] In one embodiment, see Figure 1 This application provides a UAV trajectory planning method based on the bubble collapse concept. The UAV trajectory planning method based on the bubble collapse concept may include the following steps: steps S1 to S6.

[0028] Step S1: Construct a mathematical model to simulate a 3D map.

[0029] Step S2: Initialize the bubble collapse algorithm and establish a global trajectory optimization function.

[0030] Step S3: Use Logistic chaotic mapping to generate random parameters for the bubble collapse algorithm, thus obtaining the improved bubble collapse algorithm.

[0031] Step S4: Use the global trajectory optimization function to obtain the surface tension, lateral external force, similarity, and efficiency difference of the bubble.

[0032] Step S5: Construct the trajectory solution update formula based on the surface tension of the bubble, lateral external force, similarity, and efficiency difference.

[0033] Step S6: Based on the track solution update formula, obtain the optimal track, and use a quadratic Bézier curve to smooth the optimal track to obtain the final track.

[0034] This application presents a UAV trajectory planning method based on the bubble collapse concept. It constructs trajectory solution update formulas for four different scenarios using the bubble collapse algorithm, dynamically balancing trajectory safety and efficiency, and rapidly generating obstacle avoidance paths in complex environments. By optimizing the random parameters of the bubble collapse algorithm through Logistic chaotic mapping, it enhances population diversity and global search capabilities, effectively avoiding the tendency of traditional algorithms to get trapped in local optima. Furthermore, it smooths the trajectory using quadratic Bézier curves, ensuring path continuity and flyability, and reducing the difficulty of UAV attitude adjustment. This method not only effectively balances global search and local optimization capabilities but also overcomes the limitations of traditional intelligent optimization algorithms that are prone to getting trapped in local optima, providing an efficient and robust new solution for UAV trajectory planning.

[0035] In step S1, please refer to Figure 1 In step S1, a mathematical model is constructed to simulate a three-dimensional map.

[0036] As an example, a mathematical model is constructed to simulate a 3D map, which includes obstacles such as mountains and radar. The expression is as follows: Where n is the number of mountain peaks; Representing the The center coordinates of the mountain peak; For the first The topographic parameters of the mountain peak are used to control its height; and The first Mount Tai Axial direction and The attenuation in the axial direction is used to control the slope; The x-axis is the horizontal axis. The vertical axis is denoted by .

[0037] In practice, to avoid collisions with obstacles, the drone's flight path should be kept as far away as possible from mountains and radar obstacles. Mountains and radar are considered areas where drones cannot pass, and drones must avoid collisions with them and need to detour.

[0038] As an example, a data raster method can be used to construct a simulated 3D map of a real environment.

[0039] In step S2, please refer to Figure 1 In step S2, the bubble collapse algorithm is initialized and a global trajectory optimization function is established.

[0040] For example, please refer to Figure 2 Step S2 may include the following steps: Step S21 to Step S25.

[0041] Step S21: Initialize the bubble collapse algorithm parameters and generate a bubble population.

[0042] Step S22: Traverse the bubble population and determine the obstacle collision penalty cost of the trajectory.

[0043] Step S23: Traverse the bubble population and determine the length cost of the trajectory.

[0044] Step S24: Traverse the bubble population and determine the altitude fluctuation cost of the trajectory.

[0045] Step S25: Obtain the global trajectory optimization function based on the obstacle collision penalty cost, trajectory length cost, and trajectory altitude fluctuation cost.

[0046] As an example, the bubble collapse algorithm is an intelligent optimization algorithm based on the physical phenomenon of bubble motion in nature. It is inspired by the fact that during the collapse of a bubble, surface tension drives the bubble's surface area to minimize, while lateral external forces resist this process, ultimately reaching an optimal state through a dynamic balance between the two. The core idea of ​​this algorithm is to map the solution space of the optimization problem to the surface states of a group of bubbles, with each bubble representing a potential solution. By evaluating the surface tension and lateral external forces of the bubbles, and combining the similarity and performance differences between the bubbles and the globally optimal bubble, four different trajectory solution update formulas are constructed. This unique optimization mechanism not only effectively balances global search and local optimization capabilities but also overcomes the limitation of traditional intelligent optimization algorithms that are prone to getting trapped in local optima, providing an efficient and robust new solution for UAV trajectory planning.

[0047] As an example, in step S21, the parameters of the bubble collapse algorithm are initialized, and the parameters of the bubble collapse algorithm may include: the initial radius of the bubble. Surface tension coefficient of bubbles Similarity difference factor Performance Difference Factors Maximum number of loop iterations .

[0048] Furthermore, random generation Bubble population Each bubble represents a possible path solution, then the... The nth bubble (i.e., the first bubble) (Solution to individual flight paths) In the trajectory solution, each sub-variable represents the coordinates of a grid cell in the 3D raster map. The nth subvariable (i.e., the nth subvariable) (number of nodes) In a 3D raster map, the coordinates of a grid cell can be... The initial value of each sub-variable is within the boundary of the search space. This yields an initialized bubble population, providing a foundation for subsequent trajectory optimization.

[0049] It's important to note that each bubble represents a possible trajectory solution; that is, each bubble represents a trajectory. The generation and optimization of the trajectory using the bubble collapse algorithm are accomplished through updates to the bubbles under different conditions in each iteration. Specifically, the bubbles are adjusted in each iteration to tend towards a better solution—a trajectory with shorter length, minimal altitude fluctuation, and obstacle avoidance. Each bubble generates a trajectory by updating the positions of its constituent variables, optimizing the trajectory based on its length, altitude fluctuation, and obstacle avoidance capabilities. Through multiple iterations, the positions of the constituent variables within the bubble are continuously adjusted until the globally optimal trajectory is found.

[0050] Furthermore, in step S22, the bubble population is traversed. For each sub-variable of each trajectory solution, check whether each sub-variable is located within an obstacle. Specifically, for the ... Subvariables That is, the first Nodes If its coordinates If a node is located within an obstacle (i.e., its position in the 3D raster map array M has a value of 1), then the node is recorded as having passed through the obstacle. The number of obstacles encountered in the trajectory solution is counted to obtain the obstacle collision penalty cost of the trajectory. The expression is as follows: in, For bubble population; n is the number of peaks; The first in the representative flight path Each node Coordinates on the axis; The first in the representative flight path Each node Coordinates on the axis; The first in the representative flight path Each node Coordinates on the axis; Here is the obstacle collision penalty function; This means that when the trajectory collides with an obstacle mountain, the penalty cost for the collision with the obstacle mountain is infinitely large, meaning that the trajectory solution is invalid. This is the set of coordinate points that constitute the mountain peaks of the obstacle.

[0051] Further, in step S23, for feasible continuous paths, the total length of the path is calculated to obtain the path length cost, so that shorter paths are preferentially selected during path optimization. Path length cost The expression is as follows: Where n is the number of mountain peaks. The first in the representative flight path Each node Coordinates on the axis The first in the representative flight path Each node Coordinates on the axis The first in the representative flight path Each node Coordinates on the axis The first in the representative flight path Each node Coordinates on the axis The first in the representative flight path Each node Coordinates on the axis The first in the representative flight path Each node Coordinates on the axis.

[0052] Furthermore, in step S24, frequent altitude changes during UAV flight not only increase energy consumption but also raise the probability of risk. Therefore, a better flight path should have low altitude variation fluctuations. This is further optimized by determining the altitude variation cost of the flight path. (Altitude variation cost of the flight path) The expression is as follows: Where n is the number of mountain peaks. The first in the representative flight path Each node Coordinates on the axis The first in the representative flight path Each node Coordinates on the axis This is the penalty coefficient for high degree of variation.

[0053] Furthermore, in step S25, the obstacle collision penalty cost is determined based on the trajectory. The cost of flight path length The cost of altitude fluctuations in flight path The global trajectory optimization function is obtained. Ultimately, the goal is to minimize the global trajectory cost, resulting in an optimal trajectory with the shortest trajectory length, minimal altitude fluctuation, and no obstacle collisions. The global trajectory optimization function is... The expression is as follows: in, The penalty for collisions with obstacles in the flight path. The cost of the length of the flight path, The cost of altitude fluctuations in the flight path.

[0054] In step S3, please refer to Figure 1 In step S3, the random parameters of the bubble collapse algorithm are generated using the Logistic chaotic mapping, resulting in an improved bubble collapse algorithm.

[0055] Specifically, random values ​​are used in solving the bubble collapse algorithm. However, completely random parameter values ​​may reduce the convergence speed of the algorithm. Therefore, the Logistic chaotic mapping can be used to generate the random parameters required in the bubble collapse algorithm. The expression for initializing the bubble population using the Logistic chaotic mapping is as follows: in, It is a bubble population; The first in the bubble population The nth bubble, i.e., the first bubble Solution to each flight path; Indicates bubble population The Middle A bubble The Middle There are 10 sub-variables; N is the number of bubbles; n is the number of sub-variables in each bubble; This represents the first bubble in the bubble population. bubble population The first bubble The Middle Each sub-variable represents a random value taken within the upper and lower boundaries. Indicates the following bubbles Sub-variables in All of them are the same bubble. Corresponding positional sub-variable This is obtained by updating the formula above, based on... Calculated , and then Based on calculations This process is repeated to obtain the initial values ​​for all bubbles; Indicates taking the lower bound and upper limit Any number in the set; This means taking any number from 3.57 to 4.

[0056] Specifically, the expression for the random parameters required by the Logistic chaotic mapping generation algorithm is as follows: in, Indicates bubble population The Middle A bubble The random values ​​required during iterative calculations Indicates bubble population The Middle A bubble The Middle The random values ​​required for each sub-variable during iterative computation. This means taking any number from 3.57 to 4.

[0057] In step S4, please refer to Figure 1 Step S4 involves using a global trajectory optimization function to obtain the surface tension, lateral force, similarity, and performance difference of the bubble. Specifically, this includes: determining the individual optimal solution, the global optimal solution, and the fitness value using the global trajectory optimization function; determining the mean and standard deviation of the fitness value to obtain its normal distribution interval; obtaining a suitable solution based on the normal distribution interval of the fitness value; obtaining the surface tension of the current bubble using the global trajectory optimization function; normalizing the surface tension of the current bubble to obtain a normalized value; obtaining the normalized value of the lateral force based on the normalized surface tension value; determining the similarity between the current bubble and the global optimal bubble; and obtaining the performance difference between the current bubble and the global optimal bubble using the global trajectory optimization function.

[0058] As an example, through the global trajectory optimization function Evaluate the quality of the trajectory represented by each bubble, calculate the fitness value, and update the optimal solutions for individuals in the bubble population. Global optimal solution and population-appropriate solutions It is used to guide the optimization direction of the bubble population.

[0059] As an example, the first In the nth iteration A bubble Individual optimal solution Update using the following formula: in, It is the first In the nth iteration i Individual flight path solution The fitness value.

[0060] As an example, the first In the nth iteration A bubble global optimal solution Update using the following formula: in, For the first In the nth iteration A bubble The individual optimal solution.

[0061] Specifically, determine the mean fitness value corresponding to all track solutions in the current bubble population. and standard deviation The expression is as follows: in, It is the first In the nth iteration Individual flight path solution fitness value, The number of bubbles in the population.

[0062] Furthermore, a normal distribution interval of the fitness values ​​is selected. Used to capture the range of optimal fitness values, and to find all fitness values ​​in the population. Meet the conditions The corresponding trajectory solution, which is a candidate set of suitable solutions for the population. .

[0063] Furthermore, for all bubble populations, a suitable candidate solution set... The mean of the solutions is calculated to obtain the optimal solution for the bubble population. The expression is as follows: in, It is a suitable candidate set of solutions The number of candidate solutions; It is the first i The solution to the trajectory, i.e. the first... i A vector of candidate solutions.

[0064] Further, the surface tension of each bubble is calculated, the first... i A bubble surface tension The expression is as follows: in, Let R be the surface tension coefficient, and R be the radius of the bubble perpendicular to its direction. For the first i The global trajectory optimization function value for each bubble.

[0065] Furthermore, the surface tension is normalized to obtain a normalized value. i A bubble surface tension normalized value The expression is: in, For the first i A bubble Surface tension.

[0066] As an example, all surface tensions acting against the same transverse external force yield a normalized value for the transverse external force. i A bubble normalized value of lateral external force The formula is: in, Indicates the current iteration number. This represents the maximum number of loop iterations.

[0067] Furthermore, the comparison between the current bubble and the globally optimal bubble is calculated. That is, the global optimal solution The similarity. Specifically, the first i A bubble With the global optimal bubble similarity The expression is as follows: Where n is the number of sub-variables in the bubble, For the first i A bubble The Middle Sub-variables, The globally optimal solution The Middle Sub-variables.

[0068] Furthermore, the current bubble and the globally optimal bubble are obtained. The difference in effectiveness. Specifically, the first i A bubble With the global optimal bubble Performance differences The expression is: in, For the first i A bubble The global trajectory optimization function value.

[0069] In step S5, please refer to Figure 1 In step S5, the trajectory solution update formula is constructed based on the surface tension of the bubble, lateral external force, similarity, and efficiency difference.

[0070] For example, please refer to Figure 3 Step S5 may include the following steps: Step S51 to Step S55.

[0071] Step S51: Compare the current... i A bubble normalized surface tension Normalized value of lateral external force The current number i A bubble Similarity to the globally optimal bubble and similarity difference factors The current number i A bubble Performance difference compared to the globally optimal bubble and efficacy difference factors Based on the size of the path, four update formulas for the path solution are constructed.

[0072] Step S52: When and and When the current bubble is moved towards the individual optimal solution, directional movement step size And increase the step size in a random direction. Thus, the update formula for the first trajectory solution is obtained.

[0073] Step S53: When and and At that time, the current bubble is directed towards the suitable solution for the population. directional movement step size Thus, the update formula for the second trajectory solution is obtained.

[0074] Step S54: When and When the current bubble is moved towards the global optimal solution, Movement step size Thus, the update formula for the third trajectory solution is obtained.

[0075] Step S55: When When the time comes, move the current bubble in a random direction by a step size. Generate a random solution Thus, the fourth trajectory solution update formula is obtained.

[0076] As an example, in step S51, the current number is compared. i A bubble normalized surface tension Normalized value of lateral external force The current number i A bubble Similarity to the globally optimal bubble and similarity difference factors The current number i A bubble Performance difference compared to the globally optimal bubble and efficacy difference factors Based on the size of the path, four update formulas for the path solution are constructed.

[0077] As an example, in step S52, when and and At that time, the bubbles Towards the individual optimal solution directional movement step size And increase the step size in a random direction. Then the trajectory solution update formula is: in, These are random values ​​generated using the Logistic chaotic mapping. This is the current iteration number. For the i-th bubble in the t-th iteration, For the i-th bubble in the (t+1)-th iteration, For the i-th bubble in the t-th cycle The global trajectory optimization function value, The global trajectory optimization function value is generated using random values ​​produced by the Logistic chaotic mapping.

[0078] As an example, towards the individual optimal solution directional movement step size The expression is: in, Determines the rate at which the output changes when the cosine similarity changes. This means taking any number from 1 to 2; It is a constant used to adjust the range of output values. This means taking any number between -0.5 and 0.5; The similarity of the individual bubbles is optimal.

[0079] As an example, move the step size in a random direction. The expression is: Further, in step S53, when and and At that time, the bubble group Towards a suitable solution directional movement step size Then the trajectory solution update formula is: in, This is the current iteration number. For the i-th bubble in the t-th iteration, Let i be the i-th bubble in the (t+1)-th iteration.

[0080] As an example, towards a population-appropriate solution directional movement step size The expression is: in, Determines the rate at which the output changes when the cosine similarity changes. This means taking any number from 1 to 2; It is a constant used to adjust the range of output values. This means taking any number between -0.5 and 0.5; To determine the similarity of bubble distributions in a population.

[0081] Further, in step S54, when and At that time, the bubbles Towards the global optimal solution Movement step size Then the trajectory solution update formula is: in, It is made of bubbles Random values ​​generated using Logistic chaotic mapping are used as the basis. This is the current iteration number. For the i-th bubble in the t-th iteration, For the i-th bubble in the (t+1)-th iteration, For the i-th bubble in the t-th iteration The global trajectory optimization function value, The global trajectory optimization function value is generated using random values ​​produced by the Logistic chaotic mapping.

[0082] As an example, towards the global optimal solution Movement step size The expression is: in, Determines the rate at which the output changes when the cosine similarity changes. This means taking any number from 1 to 2; It is a constant used to adjust the range of output values. This means taking any number between -0.5 and 0.5; The similarity of the globally optimal bubbles.

[0083] Further, in step S55, when At that time, the bubbles Move step size in random direction Generate a random solution The expression is: in, Therefore Random values ​​generated using Logistic chaotic mapping are used as the basis. Let i be the i-th bubble in the t-th iteration.

[0084] As an example, move the step size in a random direction. The expression is: in, This is the current iteration number. This represents the maximum number of iterations.

[0085] Furthermore, bubbles can be set. The i-th random solution in the t-th iteration Due to the generated random solutions It may be better than the original solution, or it may be worse than the original solution, so it is necessary to judge each random solution one by one. sub-variables in Is it compared to the sub-variable at the corresponding position in the original solution? To be even better.

[0086] As an example, a random solution can be used. sub-variables in Replace the original solution Sub-variables at corresponding positions A new solution was obtained. The expression is as follows: in, is the current iteration number, and n is the number of sub-variables in the bubble.

[0087] Furthermore, calculate the new solution. Is the trajectory cost better than the original solution? If the trajectory cost is better than that of a random solution, then it indicates that the random solution is better. sub-variables in It is more than the original solution Sub-variables at corresponding positions Even better than the original solution The method uses random solutions sub-variables in And abandon the original solution Sub-variables at corresponding positions This ensures that each search by the algorithm is effective and avoids the algorithm getting stuck in local optima in the later stages. The corresponding formula is as follows: in, Original solution The global trajectory optimization function value, For a new interpretation The global trajectory optimization function value.

[0088] Furthermore, to ensure that all sub-variables of the updated bubble are within the set boundary range, the position of each sub-variable needs to be constrained using a boundary treatment formula, which is as follows: in, Representing the In the nth iteration A bubble The first in Sub-variables, and For the upper and lower bounds of the search space, both have the effect of , , Upper and lower bound constraints on the three coordinate axes, i.e., upper bounds and the lower realm .

[0089] In step S6, please refer to Figure 1 In step S6, the optimal trajectory is obtained according to the trajectory solution update formula. The optimal trajectory is then smoothed using a quadratic Bézier curve to obtain the final trajectory.

[0090] As an example, the optimal trajectory is obtained through step S5. Since the trajectory is composed of discontinuous aircraft points, it will cause the trajectory to be uneven and discontinuous, so further optimization of the trajectory is required. Specifically, it is determined one by one whether there is an obstacle in the line connecting two adjacent aircraft points. If there is, a new trajectory point is inserted between the two nodes to avoid the obstacle.

[0091] Furthermore, quadratic Bézier curves are used to further smooth the trajectory, ensuring its naturalness and continuity. During the quadratic Bézier curve optimization process, calculations are performed... , , Quadratic Bézier curves at three control points The formula is as follows: in, The parameter is in the range of ; This is a smoothness control parameter; the smaller the value, the smoother the curve. Its range is... ; , , These are the coordinates of three control points, each with [specific coordinates]. , , Corresponding coordinate values ​​on the three coordinate axes ; Based on three control points and The curve points are obtained by calculating the values.

[0092] As an example, after obtaining a set of discrete waypoints that meet the constraints through the above steps, a quadratic Bézier curve is used to further smooth the way. The quadratic Bézier curve consists of three control points. , and Define, where It is the starting point. It is the midpoint. Control points determine the shape of the curve. First, the given discrete waypoints are segmented. From the set of discrete waypoints, three points are selected sequentially as a set of control points for each segment of the curve. These three points serve as the start point, control point, and end point, respectively. Simultaneously, it is ensured that the end point of each segment coincides with the start point of the next segment to guarantee the continuity of the curve. For each set of control points... , and , Start from 0 and gradually increase by step size. The value, until For each The value is used to calculate the corresponding coordinates of the quadratic Bézier curve formula. ,according to By connecting the generated curve points in ascending order, the trajectory curve is smoothed.

[0093] As an example, to ensure the algorithm converges within a reasonable time, a maximum number of iterations can be set. As a termination condition, the algorithm terminates and outputs the current optimal trajectory when the preset number of iterations is reached or the change in fitness value falls below a set threshold.

[0094] In one instance, Figure 4 For this application, in the Benchmark function The fitness value change curve after 1000 iterations of optimization is shown in the figure. To verify the effectiveness of the method in this application, the bubble collapse-based method is compared with the traditional intelligent optimization algorithm based on particle swarm optimization. The population size for each algorithm is set to 50, the number of iterations to 100, and the initial and final positions of the UAV are given. Then, each algorithm continuously calculates the optimal trajectory for each step, ultimately obtaining a globally optimal trajectory with the shortest path, minimal altitude fluctuation, and no obstacle collisions. Figure 5 This application combines the bubble collapse concept with traditional intelligent optimization algorithms based on particle swarm optimization in the Benchmark function. A graph showing the change in fitness values ​​after 300 iterations of optimization. Figure 5 As can be seen, the method proposed in this invention based on the idea of ​​bubble collapse has a faster convergence speed and stronger search capability than the traditional particle swarm optimization algorithm.

[0095] In another example, a data raster method can be used to construct a simulated 3D map of a real environment, where the simulation environment is on a scale of 100×100×100 units. Figure 6 , Figure 7 and Figure 8 As shown, the figure simulates nine mountain peaks, including mountain obstacles and radar obstacles from a real environment. The figure is a top-down view of the optimal trajectory planning in 100 iterations for the six applications, based on the bubble collapse approach and the traditional particle swarm optimization method. Figure 7 This is the main view of the optimal trajectory planning in 100 iterations based on the bubble collapse idea and the traditional method based on particle swarm optimization in this application. Figure 8This is a side view comparing the optimal trajectory planning of the bubble collapse-based method and the traditional particle swarm optimization (PSO) method in 100 iterations. As can be seen from the figure, in complex environments, the optimal trajectory length searched by the traditional PSO method is 184.9, while the optimal trajectory length searched by the bubble collapse-based method in this application is 161.8, a reduction of at least 12.5%. Compared to the trajectory planned by the traditional PSO method, this method improves search efficiency, demonstrating a significant advantage in convergence speed and optimization capability.

[0096] This application's UAV trajectory planning method based on the bubble collapse concept improves the random generation mechanism of initial bubble parameters through Logistic chaotic mapping, enhancing the global exploration capability of the solution space. Combining the competitive balance principle of surface tension and lateral external force during bubble collapse, four types of dynamic update formulas for trajectory solutions are constructed to achieve multi-dimensional optimization of the trajectory. Based on the global trajectory optimization function, the bubble state is driven to iteratively evolve, ultimately generating a three-dimensional optimal trajectory with the lowest energy consumption, highest obstacle avoidance safety, and smallest altitude fluctuation. This method enables UAV trajectory planning based on the bubble collapse concept, obtaining a trajectory with the shortest travel distance and no collision with obstacles. It exhibits significant adaptability advantages in dynamic obstacle environments and multi-constraint task scenarios, providing an innovative solution for autonomous UAV trajectory planning.

[0097] It should be understood that although the steps in the flowcharts of the accompanying drawings are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some of the steps in the accompanying drawings may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the sub-steps or stages of other steps.

[0098] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0099] Although this application has been disclosed above with reference to embodiments, it is not intended to limit this application. Anyone skilled in the art may make some modifications and refinements without departing from the spirit and scope of this application. Therefore, the scope of protection of this application shall be determined by the appended claims.

Claims

1. A UAV trajectory planning method based on the concept of bubble collapse, characterized in that, Includes the following steps: Constructing mathematical models to simulate 3D maps; Initialize the bubble collapse algorithm and establish a global trajectory optimization function; An improved bubble collapse algorithm is obtained by using Logistic chaotic mapping to generate random parameters for the bubble collapse algorithm. The surface tension, lateral force, similarity, and efficiency difference of the bubble are obtained using the global trajectory optimization function. Based on the surface tension, lateral external force, similarity, and efficiency differences of the bubbles, a trajectory solution update formula is constructed. The optimal trajectory is obtained according to the trajectory solution update formula. The optimal trajectory is then smoothed using a quadratic Bézier curve to obtain the final trajectory.

2. The UAV trajectory planning method based on the bubble collapse concept according to claim 1, characterized in that, The expression for constructing a mathematical model to simulate a 3D map is as follows: Where n is the number of mountain peaks. Representing the The center coordinates of the mountain peak For the first Topographic parameters of the mountain peak, and The first Mount Tai Axial direction and Attenuation in the axial direction, The x-axis is... The vertical axis is denoted by .

3. The UAV trajectory planning method based on the bubble collapse concept according to claim 1, characterized in that, Initialize the bubble collapse algorithm and establish a global trajectory optimization function, including: Initialize the bubble collapse algorithm parameters and generate a bubble population; Traverse the bubble population to determine the obstacle collision penalty cost of the flight path; Traverse the bubble population to determine the length cost of the trajectory; Traverse the bubble population to determine the altitude fluctuation cost of the flight path; The global trajectory optimization function is obtained based on the obstacle collision penalty cost, the length cost, and the altitude fluctuation cost of the trajectory.

4. The UAV trajectory planning method based on the bubble collapse concept according to claim 3, characterized in that, The global trajectory optimization function The expression is as follows: in, The penalty for collisions with obstacles in the flight path. The cost of the length of the flight path, The cost of altitude fluctuations in the flight path. This is the global trajectory optimization function, i.e., the global trajectory cost.

5. The UAV trajectory planning method based on the bubble collapse concept according to claim 4, characterized in that, The surface tension, lateral force, similarity, and efficiency differences of the bubble are obtained using the global trajectory optimization function, including: The individual optimal solution, the global optimal solution, and the fitness value are determined by the global trajectory optimization function. Determine the mean and standard deviation of the fitness values ​​to obtain the normal distribution interval of the fitness values; A suitable solution is obtained based on the normal distribution interval of the fitness values; The surface tension of the current bubble is obtained based on the global trajectory optimization function; The surface tension of the current bubble is normalized to obtain a normalized value of the surface tension. The normalized value of the transverse external force is obtained from the normalized value of the surface tension; Determine the similarity between the current bubble and the global optimal bubble; The performance difference between the current bubble and the global optimal bubble is obtained based on the global trajectory optimization function.

6. The UAV trajectory planning method based on the bubble collapse concept according to claim 5, characterized in that, Based on the surface tension of the bubbles, lateral external force, similarity, and efficiency differences, a trajectory solution update formula is constructed, including: By comparing the normalized surface tension value of the current bubble with the normalized lateral external force value, the similarity and similarity difference factor between the current bubble and the global optimal bubble, and the efficiency difference and efficiency difference factor between the current bubble and the global optimal bubble, four trajectory solution update formulas are constructed. When the normalized value of surface tension is less than the normalized value of lateral external force, and the similarity between the current bubble and the global optimal bubble is less than the similarity difference factor, and the efficiency difference between the current bubble and the global optimal bubble is less than or equal to the efficiency difference factor, the current bubble is moved one step length toward the direction of the individual optimal solution, and a second step length is added to move it in the random direction to obtain the first trajectory solution update formula. When the normalized value of surface tension is less than the normalized value of lateral external force, and the similarity between the current bubble and the global optimal bubble is less than the similarity difference factor, and the efficiency difference between the current bubble and the global optimal bubble is greater than the efficiency difference factor, the current bubble is moved three steps in the direction of the suitable solution to obtain the second trajectory solution update formula. When the normalized surface tension value is less than the normalized lateral external force value, and the similarity between the current bubble and the global optimal bubble is greater than or equal to the similarity difference factor, the current bubble is moved to the global optimal solution by a fourth step to obtain the third trajectory solution update formula. When the normalized value of surface tension is less than the normalized value of lateral external force, the current bubble is moved five steps in a random direction to generate a random solution, and the fourth trajectory solution update formula is obtained.

7. The UAV trajectory planning method based on the bubble collapse concept according to claim 1, characterized in that, The expression for the random parameters of the bubble collapse algorithm using the Logistic chaotic mapping is as follows: in, Indicates bubble population Middle A bubble The random values ​​required during iterative calculations Indicates bubble population Middle A bubble Middle The random values ​​required for each sub-variable during iterative computation. This means taking any number from 3.57 to 4.

8. The UAV trajectory planning method based on the bubble collapse concept according to claim 7, characterized in that, The update formula for the first trajectory solution is: in, These are random values ​​generated using the Logistic chaotic mapping. This is the current iteration number. For the i-th bubble in the t-th iteration, For the i-th bubble in the (t+1)-th iteration, For the i-th bubble in the t-th cycle The global trajectory optimization function value, The global trajectory optimization function value is generated using random values ​​produced by the Logistic chaotic mapping. For the first step, This is the second step size; The formula for updating the second trajectory solution is: in, This is the current iteration number. For the i-th bubble in the t-th iteration, For the i-th bubble in the (t+1)-th iteration, For a suitable solution, This is the third step length; The formula for updating the third trajectory solution is: in, It is made of bubbles Random values ​​generated using Logistic chaotic mapping are used as the basis. This is the current iteration number. For the i-th bubble in the t-th iteration, For the i-th bubble in the (t+1)-th iteration, For the i-th bubble in the t-th iteration The global trajectory optimization function value, The global trajectory optimization function value is generated using random values ​​produced by the Logistic chaotic mapping. This is the globally optimal solution. This is the fourth step length.

9. The UAV trajectory planning method based on the bubble collapse concept according to claim 7, characterized in that, The expression for the random solution is: in, Therefore Random values ​​generated using Logistic chaotic mapping are used as the basis. For the i-th bubble in the t-th iteration, For the fifth step length, The solution is random.

10. The UAV trajectory planning method based on the bubble collapse concept according to claim 1, characterized in that, The expression for the quadratic Bézier curve is as follows: in, For parameters, Here, k is the reciprocal of the smoothness control parameter. , , These are the coordinates of three control points, each with [specific coordinates]. , , Corresponding coordinate values ​​on the three coordinate axes , Based on three control points and The curve points are obtained by calculating the values.

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