Beidou navigation unmanned aerial vehicle inspection path planning method based on simulated annealing algorithm

Abstract

The invention discloses a Beidou navigation unmanned aerial vehicle inspection path planning method based on a simulated annealing algorithm. The method comprises the following steps: S1, reading latitude and longitude data: reading latitude and longitude data of an inspection target point and a base from a file or a database; s2, calculating a distance matrix: calculating an actual distance between any two points according to the longitude and latitude data, and constructing the distance matrix; s3, constructing a solution space: constructing all path sets; s4, selecting an initial solution: selecting an initial path from the path set as a current solution; s5, setting an initial temperature: setting the initial temperature of a simulated annealing algorithm; s6, loop iteration: performing an iteration process of a simulated annealing algorithm; and S7, generating a new solution: generating a new path as the new solution by using a transformation method 2 or a transformation method 3 according to the current solution. The method is used for solving the problem that a genetic algorithm and a particle swarm optimization algorithm are relatively weak in theoretical convergence guarantee, and particularly are possibly difficult to meet theoretical conditions in practical application.

Description

Technical Field

[0001] The invention relates to a Beidou navigation unmanned aerial vehicle inspection path planning method based on a simulated annealing algorithm. Background Art

[0002] In the field of drone inspection path planning, algorithms based on graph theory and optimization algorithms based on certain artificial intelligence are the current mainstream methods. Graph-based algorithms such as the Dijkstra algorithm and the A* algorithm can usually effectively find the shortest path, but these algorithms will encounter problems such as reduced computational efficiency and insufficient real-time performance when dealing with large-scale complex environments. Although they perform well in static and simple scenes, they have poor adaptability in dynamically changing complex environments.

[0003] Some artificial intelligence algorithms, including genetic algorithms and particle swarm optimization, usually require more computing resources. In genetic algorithms, operations such as selection, crossover, and mutation are required, while in particle swarm optimization, the particles of the entire population need to update their positions and velocities in each iteration, which may result in high computational costs in large-scale problems or complex environments. In addition, both genetic algorithms and particle swarm optimization algorithms involve multiple parameters (such as crossover rate, mutation rate, inertia weight, acceleration constant, etc.), and the adjustment of these parameters has a significant impact on the performance of the algorithm, and is often problem-dependent and needs to be carefully tuned to suit specific problems. In particular, in complex optimization calculations, genetic algorithms and particle swarm optimization algorithms may encounter the problem of premature convergence, that is, the algorithm quickly falls into a local optimal solution and stops exploring better solutions. Finally, the theoretical convergence guarantee of genetic algorithms and particle swarm optimization algorithms is weak, especially in practical applications, where it may be difficult to meet the theoretical conditions. Summary of the invention

[0004] The purpose of the present invention is to provide a Beidou navigation UAV inspection path planning method based on a simulated annealing algorithm, which is used to solve the problem that the convergence guarantee of genetic algorithms and particle swarm optimization algorithms is weak in theory, especially that it may be difficult to meet the theoretical conditions in practical applications.

[0005] In order to solve the above problems, the technical solution of the present invention is: The Beidou navigation UAV inspection path planning method based on simulated annealing algorithm includes the following steps; S1: Read longitude and latitude data: Read the longitude and latitude data of the inspection target point and base from the file or database; S2: Calculate the distance matrix: According to the longitude and latitude data, calculate the actual distance between any two points and construct the distance matrix; S3: Construct solution space: construct all path sets; S4: Select initial solution: select an initial path from the path set as the current solution; S5: Set initial temperature: set the initial temperature of the simulated annealing algorithm; S6: loop iteration: perform the iterative process of the simulated annealing algorithm; S7: Generate a new solution: According to the current solution, use the 2-transformation method or the 3-transformation method to generate a new path as a new solution; S8: Calculate the cost function difference: calculate the path length difference between the new solution and the current solution; S9: Acceptance criterion: Determine whether to accept the new solution according to the acceptance criterion. If the cost function difference is less than 0, the new solution is accepted; otherwise, the new solution is accepted with a certain probability; S10: Update the current solution: if the new solution is accepted, the new solution is used as the current solution; S11: Cooling: lowering the temperature according to the cooling coefficient; S12: Determine the end condition: determine whether the temperature reaches the termination temperature. If so, end the iteration; otherwise, continue the iteration. S13: Output the optimal path: output the optimal path found during the iteration process.

[0006] The beneficial effects of the present invention are: 1. Search capability: Simulated annealing algorithm: It can effectively jump out of the local optimal solution and reach the global optimal solution. This algorithm introduces probabilistic factors, and even when encountering a local optimal solution, there is still a certain probability to continue exploring other possible solutions. Graph theory algorithm: It is usually easy to fall into the local optimal solution, especially when there are multiple equal shortest paths, it is difficult to ensure that the global optimal solution is found. Genetic algorithm and particle swarm optimization algorithm: Although they also have the ability to jump out of the local optimal solution, they may converge more slowly than the simulated annealing algorithm, and the parameter adjustment is more complicated.

[0007] 2. Adaptability: Simulated annealing algorithm: Through flexible cooling progress and temperature scheduling, the search range and accuracy can be adaptively adjusted, and it has good adaptability to problems of various sizes. Graph theory algorithm: It requires a complete graph structure to be defined in advance, and it has poor adaptability to dynamically changing environments and it is difficult to adjust the path in real time. Genetic algorithm and particle swarm optimization algorithm: They can adapt to different problem sizes, but they have high computing resource requirements and may require frequent parameter adjustments in practical applications.

[0008] 3. Solution quality: Simulated annealing algorithm: can provide high-quality solutions in a short time, especially under complex multi-constraint conditions. Graph theory algorithm: can quickly find the optimal solution in simple scenarios, but as the scale of the problem increases, the solution time increases significantly, and the quality of the solution cannot be guaranteed. Genetic algorithm and particle swarm optimization algorithm: can find high-quality solutions, but the computational cost is high and the execution efficiency is relatively low.

[0009] 4. Anti-disturbance capability: Simulated annealing algorithm: Through random perturbation and annealing mechanism, it can effectively resist environmental noise and dynamic changes and enhance robustness. Graph theory algorithm: sensitive to environmental noise, once the environment changes, the entire path may need to be recalculated. Genetic algorithm and particle swarm optimization algorithm: have certain anti-disturbance capability, but when facing complex noise, their stability and robustness are not as good as simulated annealing algorithm.

[0010] 5. Flexibility: Simulated annealing algorithm: can flexibly respond to different problem requirements by adjusting parameters such as temperature function and cooling schedule. Graph theory algorithm: relatively fixed, less flexible, and difficult to fine-tune according to actual needs. Genetic algorithm and particle swarm optimization algorithm: although flexible and configurable, parameter selection has a greater impact on the results and requires rich experience to set reasonably.

[0011] In summary, the Beidou navigation UAV inspection path planning method based on simulated annealing algorithm has shown obvious advantages in many key aspects, especially in search capability, adaptability, solution quality, anti-disturbance ability and flexibility. These advantages enable this method to solve complex UAV inspection path planning problems more efficiently and stably in practical applications, providing solid technical support for the widespread application of UAV technology in more fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The present invention will be further described below in conjunction with the accompanying drawings: Figure 1 is a schematic diagram of the inspection path of the present invention, Figure 2 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0013] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0014] The Beidou navigation UAV inspection path planning method based on simulated annealing algorithm includes the following steps; S1: Read longitude and latitude data: Read the longitude and latitude data of the inspection target point and base from the file or database; S2: Calculate the distance matrix: According to the longitude and latitude data, calculate the actual distance between any two points and construct the distance matrix. The method is as follows: Assume that the longitude and latitude of the inspection base are (X, Y). The drone starts from the base, inspects n-2 target points, and then returns to the original base.

[0015] The bases are numbered 1, the target points are numbered 2, 3, ..., n-1, and finally our base is numbered n again. Construct the distance matrix D = (d ij ) n×n , where d ij It represents the distance between two points i and j, i, j = 1, 2, ..., n, and requires a shortest path starting from point 1, going through all the intermediate points and reaching point n.

[0016] The principle of obtaining the actual distance between two points through the Beidou navigation system is: the Beidou navigation system first transmits the geographic coordinates (longitude and latitude) of each target point to the ground base station, and then the base station calculates the actual distance between any two target points to plan the path of the UAV.

[0017] Assume that the geographic coordinates of points A and B are (x1, y1) and (x2, y2) respectively. The length of the minor arc of the great circle passing through points A and B is the actual distance between the two points. A three-dimensional rectangular coordinate system is established with the center of the earth as the coordinate origin O, the equatorial plane as the XOY plane, and the plane where the 0 degree meridian is located as the XOZ plane. Then the rectangular coordinates of points A and B are: A(R cos x1 cos y1, R sin x1 cos y1, R sin y1) B(Rcos x2 cos y2, R sin x2 cos y2, R sin y2)

[0018] Take the radius of the earth as R = 6370km.

[0019] The actual distance d between points A and B is:

[0020] Simplified: d=R arccos[cos(x1-x2)cos y1 cos y2+sin y1 sin y2]; S3: Construct solution space: construct all path sets; The solution space S is represented by the set of cyclic permutations of all fixed starting and ending points of {1,2,…,n-1,n}, that is, S = {(π1,…,π n )|π1=1,(π2,…,π n-1 ) is a cyclic permutation of {2,3,…,n-1}, π n =n}, where each cyclic permutation represents a loop for detecting n-2 target points, π i =j means that during the i-1th inspection of target j, the initial solution can be selected as (1, 2, ..., n), and a better initial solution is obtained using the Monte Carlo method.

[0021] The objective function is the path length for inspecting all target points: S4: Select the initial solution: Select an initial path from the path set as the current solution; S5: Set the initial temperature: Set the initial temperature of the simulated annealing algorithm, for example: room temperature 20°C; S6: Loop iteration: Perform the iterative process of the simulated annealing algorithm; S7: Generate a new solution: According to the current solution, use the 2-opt method or the 3-opt method to generate a new path as the new solution; 2-opt method Arbitrarily select sequence numbers a, b (a < b) and swap the order between a and b. The new path at this time is: π1…π a-1 π b π b-1 …π a+1 π a π b+1 …π n

[0022] 3-opt method Arbitrarily select sequence numbers a, b, and w, and insert the path between a and b after w. The corresponding new path is (assuming a < b < w): π1…π a-1 π b+1 …π w π a …π b π w+1 …π n

[0023] S8: Calculate the cost function difference: Calculate the difference in path length between the new solution and the current solution; For the 2-opt method, the path difference Δf is expressed as:

[0024] S9: Acceptance criterion: Judge whether to accept the new solution according to the acceptance criterion. If the cost function difference is less than 0, accept the new solution; otherwise, accept the new solution with a certain probability. The method for judging the acceptance criterion is:

[0025] If Δf < 0, accept the new path. Otherwise, accept the new path with the probability exp(-Δf / T), that is, accept if exp(-Δf / T) is greater than a random number between 0 and 1. In the formula, P is the acceptance probability and T is the temperature.

[0026] S10: Update the current solution: If the new solution is accepted, use the new solution as the current solution. S11: Cooling: Reduce the temperature according to the cooling coefficient. Cooling is performed using the selected cooling coefficient α, i.e., T←αT, to obtain a new temperature. Here, α = 0.9999 is taken.

[0027] S12: Determine the end condition: Determine whether the temperature has reached the termination temperature. If it has, end the iteration; otherwise, continue the iteration. Use the selected termination temperature e = 10 -40 , and determine whether the annealing process has ended. If T < e, the algorithm ends and the current state is output.

[0028] S13: Output the optimal path: Output the optimal path found during the iteration process.

[0029] Application example: Given the longitudes and latitudes of 100 inspection target points as shown in the following table, and the longitude and latitude of the inspection base are (50, 30), plan the inspection path of the UAV.

[0030]

[0031] The inspection path is as Figure 1 shown, with a length of 43797 km.

[0032] It can be seen from this that the present invention can be applied in: 1. Robot path planning: In an automated production line, the simulated annealing algorithm can be used to optimize the movement path of the robot, reduce the movement time, and improve production efficiency. At the same time, in warehousing and logistics, this algorithm can also plan the optimal route to achieve fast sorting and handling.

[0033] 2. Transportation scheduling: The simulated annealing algorithm can optimize the operation routes and schedules of public transportation vehicles, improving the overall efficiency of the transportation system. For example, in the operation of public transportation such as buses and subways, by adjusting the driving routes and headways, the waiting time of passengers and the empty running rate of vehicles can be reduced.

[0034] 3. Network design optimization: In communication network planning, the simulated annealing algorithm helps to design the most cost-effective network layout, optimize bandwidth allocation and data transmission paths, thereby improving network performance and reliability.

[0035] 4. Supply chain management: In supply chain management, the simulated annealing algorithm can optimize inventory distribution and logistics paths, reduce transportation costs, and improve the response speed and overall efficiency of the supply chain.

[0036] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The protection scope of the present invention should not be regarded as limited to the specific forms described in the embodiments. The protection scope of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A Beidou navigation UAV inspection path planning method based on simulated annealing algorithm, characterized by: The method comprises the following steps: S1: Read longitude and latitude data: Read the longitude and latitude data of the inspection target point and base from the file or database; S2: Calculate the distance matrix: According to the longitude and latitude data, calculate the actual distance between any two points and construct the distance matrix; S3: Construct solution space: construct all path sets; S4: Select initial solution: select an initial path from the path set as the current solution; S5: Set initial temperature: set the initial temperature of the simulated annealing algorithm; S6: loop iteration: perform the iterative process of the simulated annealing algorithm; S7: Generate a new solution: According to the current solution, use the 2-transformation method or the 3-transformation method to generate a new path as a new solution; S8: Calculate the cost function difference: calculate the path length difference between the new solution and the current solution; S9: Acceptance criterion: Determine whether to accept the new solution according to the acceptance criterion. If the cost function difference is less than 0, the new solution is accepted; otherwise, the new solution is accepted with a certain probability; S10: Update the current solution: if the new solution is accepted, the new solution is used as the current solution; S11: Cooling: lower the temperature according to the cooling coefficient; S12: Determine the end condition: determine whether the temperature reaches the end temperature. If so, the iteration ends; otherwise, the iteration continues. S13: Output optimal path: output the optimal path found during the iteration process.

2. The Beidou navigation UAV inspection path planning method based on simulated annealing algorithm according to claim 1 is characterized in that: In step S2, the method for calculating the distance between points A and B is: d = Rarccos[cos(x1-x2)cosy1cosy2+siny1 siny2]; Where d is the distance between two points, (x1, y1) and (x2, y2) are the geographic coordinates of points A and B respectively, and R is the radius of the earth.

3. The Beidou navigation UAV inspection path planning method based on simulated annealing algorithm according to claim 1 is characterized in that: In step S3, the solution space S is represented as a set of cyclic permutations of all fixed starting and ending points of {1,2,…,n-1,n}, that is, S = {(π1,…,π n )|π1=1,(π2,…,π n-1 ) is a cyclic permutation of {2,3,…,n-1}, π n =n}, where each cyclic permutation represents a loop for detecting n-2 target points, π i =j means that during the i-1th inspection of target j, the initial solution is selected as (1, 2,…, n).

4. The Beidou navigation UAV inspection path planning method based on simulated annealing algorithm according to claim 1 is characterized in that: In step S7, the 2-transformation method is as follows: arbitrarily select serial numbers a and b (a < b) and exchange the order between a and b, then the new path is: π1…π a-1 π b π b-1 …π a+1 π a π b+1 …π n 。 5. The Beidou navigation UAV inspection path planning method based on simulated annealing algorithm according to claim 1 is characterized in that: In step S7, the 3-transformation method is as follows: Arbitrarily select serial numbers a, b, and w, and insert the path between a and b after w. The corresponding new path is (assuming a < b < w), then the new path is: π1…π a-1 π b+1 …π w π a …π b π w+1 …π n 。 6. The Beidou navigation UAV inspection path planning method based on simulated annealing algorithm according to claim 1 is characterized by: In step S8, the cost function difference is calculated as follows:

7. The Beidou navigation UAV inspection path planning method based on simulated annealing algorithm according to claim 1 is characterized in that: In step S8, the acceptance criteria judgment method is: If Δf<0, the new path is accepted, otherwise, the new path is accepted with probability exp(-Δf / T), that is, if exp(-Δf / T) is greater than a random number between 0 and 1, it is accepted.

8. The Beidou navigation UAV inspection path planning method based on simulated annealing algorithm according to claim 1 is characterized by: In step S11, the temperature is lowered using the selected temperature reduction coefficient α: T←αT to obtain a new temperature, where α=0.9999.

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