A multi-objective A * Algorithm-based urban drone delivery route optimization method

Abstract

A multi-objective A * This invention relates to an algorithm-based method for optimizing urban drone delivery routes, specifically in the field of drone delivery route planning within urban low-altitude logistics, and particularly to a method based on multi-objective A / B algorithms. * This invention presents an algorithm for optimizing urban drone delivery routes. The purpose of this invention is to address the shortcomings of traditional A / B algorithms. * The algorithm's path search is inefficient and prone to generating redundant nodes, failing to adequately consider the problem of multi-target UAV path planning in 3D space. The process is as follows: Step 1, construct an environment model based on 3D space; Step 2, construct the environment model and multi-target A / B path planning based on 3D space. * Algorithm, constructing a mathematical model of path length, a mathematical model of conflict risk, and a mathematical model of turning characteristics; Step 3, based on multi-objective A * The algorithm and the constructed mathematical models of path length, conflict risk, and turning characteristics are used to obtain the overall path quality score; the path with the highest overall path quality score is selected as the drone delivery path.

Description

Technical Field

[0001] This invention relates to the field of drone delivery route planning in urban low-altitude logistics, and particularly to a multi-objective A / B-based approach. * An algorithm for optimizing urban drone delivery routes. Background Technology

[0002] With the acceleration of urbanization, transportation is facing unprecedented challenges. Urban low-altitude logistics using drones as a delivery method is gradually gaining attention as a novel delivery approach. Since flight path planning is a crucial consideration in drone delivery, researching its impact on urban low-altitude logistics is particularly essential. In recent years, drone technology has developed rapidly and is widely used in various fields. With the increasing complexity of drone missions and the expansion of their application scope, path planning, as one of the core technologies for autonomous drone flight, has gradually become a research hotspot. Therefore, designing efficient and safe flight paths has become a major challenge in current technological research.

[0003] Currently, in UAV path planning technology, traditional A * The algorithm is widely used, but in practical applications, its path search efficiency is low, and it is prone to generating redundant nodes and turning points. Therefore, scholars at home and abroad are constantly improving and optimizing A from various perspectives. * While significant progress has been made in the development of algorithms, research on UAV path planning in three-dimensional space is limited. Therefore, it is necessary to design and implement a UAV path planning system for three-dimensional environments, focusing on solving prominent problems such as effectively representing and perceiving obstacles and risk areas in three-dimensional environments, and generating optimal paths that balance distance and safety in three-dimensional environments. Summary of the Invention

[0004] The purpose of this invention is to solve the problem of traditional A * The algorithm's path search is inefficient and prone to generating redundant nodes, failing to adequately consider the problem of multi-target UAV path planning in 3D space. Therefore, a multi-target A / D path planning approach is proposed. * An algorithm for optimizing urban drone delivery routes.

[0005] A multi-objective A * The specific process of the algorithm's urban drone delivery route optimization method is as follows:

[0006] Step 1: Construct an environment model based on three-dimensional space;

[0007] Step 2: Construct an environment model and multi-objective A based on three-dimensional space. * Algorithms are used to construct mathematical models for path length, conflict risk, and turning characteristics.

[0008] Step 3: Based on multi-objective A * The algorithm and the constructed mathematical models of path length, conflict risk, and turning characteristics are used to obtain the overall path quality score.

[0009] The routes with the highest overall route quality score are selected as drone delivery routes.

[0010] The beneficial effects of this invention are as follows:

[0011] 1. The drone delivery path planning method for low-altitude logistics delivery described in this invention fully considers A. * To address the broad applicability of algorithms and the limitations of traditional methods, a multi-objective A-based algorithm was designed and implemented. * The algorithm's UAV 3D path planning method can plan an optimal path for UAVs that balances path length and safety in complex 3D environments.

[0012] 2. The multi-objective A-based method described in this invention * The algorithm is crucial for drone delivery route planning. This method can use a gridded approach to model the 3D environment and introduce an exponential decay risk assessment mechanism to achieve obstacle perception, overcoming the limitations of traditional algorithms. * The algorithm suffers from problems such as low path search efficiency and the tendency to generate redundant nodes, which effectively improves its computational performance.

[0013] 3. The multi-target A described in this invention * The algorithm implements key functions such as weight optimization, path scoring, and turning characteristic analysis, and is also superior to traditional algorithms in terms of security. * The algorithm, especially in high-risk environments, can provide an intuitive 3D visualization interface and real-time interactive functions, making it more suitable for complex urban environments. Attached Figure Description

[0014] Figure 1 This invention is based on multi-objective A. * A roadmap for research on drone delivery route planning algorithms;

[0015] Figure 2 This is the multi-target A described in this invention. * The path graph obtained when the distance weight and risk weight are set to 0.5 during algorithm path optimization;

[0016] Figure 3 This is the multi-target A described in this invention. * The path graph obtained when the algorithm path optimization is set with a distance weight of 0.8 and a risk weight of 0.2;

[0017] Figure 4 This is the multi-target A described in this invention. *Path data graphs planned with different distance weights in algorithm path optimization;

[0018] Figure 5 This is the multi-target A described in this invention. * A schematic diagram of a complex scenario in an algorithm path optimization simulation environment;

[0019] Figure 6 This is the multi-target A described in this invention. * A schematic diagram of a typical scenario in an algorithm path optimization simulation environment;

[0020] Figure 7 This is the multi-target A described in this invention. * A schematic diagram of a simplified scenario in an algorithm path optimization simulation environment;

[0021] Figure 8 This invention is based on multi-objective A. * Algorithm-based drone path planning graph;

[0022] Figure 9 This invention is based on traditional A * The algorithm's drone path planning graph. Detailed Implementation

[0023] Specific Implementation Method 1: This implementation method is based on multi-objective A * The specific process of the algorithm's urban drone delivery route optimization method is as follows:

[0024] Step 1: Construct an environment model based on three-dimensional space;

[0025] Step 2: Construct an environment model and multi-objective A based on three-dimensional space. * Algorithms are used to construct mathematical models for path length, conflict risk, and turning characteristics.

[0026] Step 3: Based on multi-objective A * The algorithm and the constructed mathematical models of path length, conflict risk, and turning characteristics are used to obtain the overall path quality score.

[0027] The routes with the highest overall route quality score are selected as drone delivery routes.

[0028] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that step one involves constructing an environment model based on a three-dimensional spatial structure.

[0029] The specific process is as follows:

[0030] Step 11: Represent the three-dimensional space using a mesh; the specific process is as follows:

[0031] The three-dimensional space environment is divided into N×N×N cube cells, and each cube cell is represented by coordinates (x, y, z) (coordinates (x, y, z) in a spatial rectangular coordinate system).

[0032] The values ​​of x, y, and z are all within the range of [0, N-1].

[0033] This mesh-based modeling approach allows complex 3D spaces to be discretized into a regular, computationally efficient grid. By default, the system divides the space into 100×100×100 cells, with 100 cells in each direction, resulting in a total of 1,000,000 cells. Each cell represents a small region in 3D space, suitable for representing information such as obstacles, paths, and aircraft positions.

[0034] Steps 1 and 2: Obstacles are mainly divided into two categories: buildings and no-fly zones. The modeling method for each type of obstacle is different.

[0035] Buildings are modeled as cubes, defined by their center position (x, y, z) and dimensions (width, depth, height). Specifically, the vertex extent of a building is described by calculating its boundaries along the x, y, and z axes. The width, depth, and height of a building affect its size and position in three-dimensional space, respectively.

[0036] The no-fly zone is modeled as a sphere, determined by the center position (x, y, z) and radius r; any point within the no-fly zone satisfies the geometric equation of the sphere, that is, the distance from the point to the center of the no-fly zone is less than or equal to the radius r;

[0037] First, the three-dimensional space is represented by a mesh method, dividing the space into N×N×N cubic cells. Each cell represents a small region in the three-dimensional space, used to represent relevant information such as obstacles, paths, and aircraft positions. Then, different methods are used to model different obstacles in the spatial environment. Typically, buildings are modeled as cubes, and no-fly zones are modeled as spheres.

[0038] The other steps and parameters are the same as in Specific Implementation Method 1.

[0039] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that, in step two, an environment model and multi-objective A are constructed based on three-dimensional space. * Algorithms are used to construct mathematical models for path length, conflict risk, and turning characteristics.

[0040] The specific process is as follows:

[0041] Step 2.1: Construct a mathematical model for the path length; the specific process is as follows:

[0042] Mathematical modeling of UAV path length mainly involves establishing a path planning model and optimizing the total path length by combining flight environment constraints and performance indicators. When constructing the model, it is necessary to clearly define the flight environment, such as terrain and obstacles, and secondly, the path planning objectives, such as minimizing the total path and prioritizing obstacle avoidance. The three-dimensional space is divided into a grid, where each grid represents a node, and the lines connecting the grids represent feasible paths. The path length is expressed as the sum of the Euclidean distances between the nodes on the path.

[0043]

[0044] in,

[0045] length(S) represents the length of path segment S;

[0046] x p+1 This represents the coordinates of the (p+1)th node on the x-axis; x p This represents the coordinates of the p-th node on the x-axis;

[0047] y p+1 This represents the coordinate of the (p+1)th node on the y-axis; y p This represents the y-coordinate of the p-th node;

[0048] z p+1 This represents the coordinate of the (p+1)th node on the z-axis; z p This represents the coordinates of the p-th node on the z-axis;

[0049] p represents the p-th node, where p = 1, 2, ..., n;

[0050] n represents the total number of nodes on the flight path; n has a minimum of 3 and a maximum of the path segment length divided by 0.5 and then rounded down; n is determined by the path length (S) and the step size.

[0051] Step 22: Construct a mathematical model of conflict risk. The mathematical model of conflict risk includes the building risk R. b ( p No-fly zone risk R n(p) Point risk R(p), path segment risk R(S), continuity risk factor eff_risk(p), and path segment final risk R final (S) and the average risk R of the path avg (path);

[0052] Steps 2 and 3: Construct a mathematical model of steering characteristics (the mathematical model of steering characteristics is the steering radius).

[0053] Other steps and parameters are the same as in specific implementation method one or two.

[0054] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that step two-two involves constructing a conflict risk mathematical model, which includes building risk R. b(p) No-fly zone risk R n(p) Point risk R(p), path segment risk R(S), continuity risk factor eff_risk(p), and path segment final risk R final (S) and the average risk R of the path avg (path);

[0055] The specific process is as follows:

[0056] The construction of a mathematical model for UAV conflict risk needs to comprehensively consider multiple factors such as aircraft dynamics, environmental perception, and obstacle avoidance strategies. It mainly integrates environmental data and flight parameters, including state parameters such as the UAV's position, speed, and acceleration, and combines uncertainties such as GPS error and crosswind disturbance to assess various risks. The conflict risks considered in this invention are mainly seven.

[0057] Step 221: Calculate the building risk R b(p) ; indicates as:

[0058]

[0059] When dist(p,b) < 0.1, R b(p) =1.0 (maximum risk);

[0060] dist(p,b) represents the distance from node p to the building;

[0061] The formula for calculating dist(p,b) is:

[0062]

[0063] B = (max{b x -p x ,0,p x -(b x +width)}) 2

[0064] C = (max{b y -p y ,0,p y -(b y +depth)}) 2

[0065] D=(max{b z -pz ,0,p z -(b z +height)}) 2

[0066] in,

[0067] (p x ,p y ,p z (b) are the coordinates of node p; x ,b y ,b z ) are the coordinates of the building (usually the smallest coordinate point);

[0068] Width represents the building's dimension along the x-axis; depth represents the building's dimension along the y-axis; height represents the building's dimension along the z-axis.

[0069] B, C, and D represent intermediate variables;

[0070] Step 222: Calculate the risk R of the no-fly zone n(p) ; indicates as:

[0071]

[0072] When dist(p,n) < 0.1, R n(p) =1.0 (maximum risk);

[0073] dist(p,n) represents the distance from node p to the no-fly zone;

[0074] The formula for calculating dist(p,n) is:

[0075]

[0076] in,

[0077] (p x ,p y ,p z (n) are the coordinates of node p; x ,n y ,n z ) represents the coordinates of the no-fly zone (usually the smallest coordinate point);

[0078] R represents the radius of the no-fly zone;

[0079] Step 223: Calculate the point risk R(p); expressed as:

[0080] R(p)=max(R b(p) ,R n(p) (4)

[0081] in,

[0082] R b(p) Building risk refers to the risk that an aircraft faces when it approaches a building along its flight path; R n(p) R(p) represents the risk of an aircraft entering a no-fly zone; R(p) represents the point risk, which is the maximum of the building risk and the no-fly zone risk.

[0083] Step 224: Calculate the continuous risk factor eff_risk(p); expressed as:

[0084] eff_risk(p)=min{1.0,R(S p )+acc_risk(p-1)×0.1} (5)

[0085] in,

[0086] R(S p ) represents the risk of node p in path segment S.

[0087] S p Let p be a node representing path segment S; p1 and p2 are the start and end points of the path segment, representing the two endpoints of the path; p is the index of the node, p = 1, 2, ..., n;

[0088] 0.1 is a weighting coefficient, representing the impact of the cumulative risk at the previous point on the current point;

[0089] acc_risk(p-1) represents the cumulative risk of the (p-1)th node, expressed as:

[0090] acc_risk(p)=acc_risk(p-1)×0.5+R(S p )×0.2

[0091] Initially, the cumulative risk acc_risk(0) is determined by the risk R(S1) of the first sampling point:

[0092] acc_risk(0) = R(S1) × 0.5

[0093] S1 represents sampling point 1 of path segment S;

[0094] Step 225: Calculate the path segment risk R(S); expressed as:

[0095]

[0096] Note: The risk calculation for path segment S is achieved by averaging multiple sampling points;

[0097] in,

[0098] R(S) represents the risk of path segment S;

[0099] R(S p The maximum value of ) is denoted as the risk value R in the path segment. max-risk ;

[0100] n has a minimum of 3 and a maximum of the path segment length divided by 0.5 and then rounded down; n is determined by the path length (S) and the step size; length (S) represents the length of path segment S;

[0101] Step 226: Calculate the final risk R of the path segment. final (S);

[0102] The specific process is as follows:

[0103] If the risk value R in the path segment max-risk A value greater than 0.9 indicates a final risk R for the path segment. final (S) is represented as:

[0104] R final (S)=R(S)×0.85+R max-risk ×0.15 (7)

[0105] If the risk value R in the path segment max-risk Less than or equal to 0.9, the final risk R of the path segment final (S) = 0;

[0106] Step 227: Calculate the average risk R of the path. avg (path); is represented as:

[0107]

[0108] in,

[0109] R(S p ) represents the risk of node p in path segment S;

[0110] length(S p ) represents the length of node p in path segment S;

[0111] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0112] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One to Four in that a mathematical model of steering characteristics (the mathematical model of steering characteristics is the steering radius) is constructed in steps two and three.

[0113] The specific process is as follows:

[0114] First, calculate the included angle based on the two flight speeds of the drone before and after the turn. Then, calculate the radian value of the turn based on the included angle. Finally, determine whether the drone has turned based on the radian or included angle. If it has turned, calculate the turning radius according to the existing formula.

[0115] Step 231: Calculate the included angle θ based on the two velocity vectors v1 and v2 of the UAV, cosθ=v1·v2 / (|v1||v2|);

[0116] in,

[0117] • Represents the dot product (length) of vectors;

[0118] |v1| represents the magnitude (length) of velocity vector v1; |v2| represents the magnitude (length) of velocity vector v2;

[0119] |v1||v2| represents the product of the modulus of vector v1|v1 and the modulus of vector v2|v2;

[0120] Step 2: Calculate the radian value of the included angle θ (take the inverse cosine of the cosine value);

[0121] Step 233: When θ≤0.087 radians (approximately 5 degrees), it is determined that the drone has not turned, and the turning radius R=0;

[0122] When θ > 0.087 radians (approximately 5 degrees), the drone is determined to be turning, and the turning radius R is calculated; the process is as follows:

[0123] The turning radius of a drone is a key parameter for ensuring flight safety and mission efficiency. Drones must adhere to the principle of minimum turning radius when turning. Furthermore, in complex terrain, rationally planning the turning radius can shorten the flight range and reduce energy consumption. Therefore, calculating the turning radius plays a crucial role in drone flight. The formula for calculating the turning radius is as follows:

[0124]

[0125] a, b, and c are the side lengths of the triangle formed when the drone turns;

[0126] Z area Z is the area of ​​the triangle. area The calculation formula is

[0127] s is the semi-perimeter of the triangle.

[0128] First, when constructing the mathematical model for path length, the flight environment and path planning objectives must be clearly defined, and flight environment constraints and performance indicators must be considered. Second, when constructing the mathematical model for conflict risk, multiple factors affecting UAV flight must be comprehensively considered, including the aircraft, flight environment, and other uncertainties, and the risks involved should be taken into account as comprehensively as possible. Finally, when establishing the mathematical model for turning characteristics, the parameters for calculating the turning radius and the conditions for turning must be clearly defined, and then the solution can be obtained by following the calculation process.

[0129] The other steps and parameters are the same as those in one of the specific implementation methods one to four.

[0130] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that step three is based on multi-objective A. * The algorithm and the constructed mathematical models of path length, conflict risk, and turning characteristics are used to obtain the overall path quality score; the path with the highest overall path quality score is selected as the drone delivery path.

[0131] The specific process is as follows:

[0132] Step 31: Obtain the distance score (distance_score) based on the path length mathematical model constructed in Step 21;

[0133] Step 32: Based on the conflict risk mathematical model constructed in Step 22, obtain the average risk value avg_risk and the maximum risk value max_risk; based on the average risk value avg_risk and the maximum risk value max_risk, obtain the risk score risk_score.

[0134] Step 33: Based on the mathematical model of steering characteristics constructed in Step 23, obtain the steering radius score (radius_score).

[0135] Steps 3 and 4: Based on the distance score (distance_score), risk score (risk_score), and turning radius score (radius_score), obtain the overall path quality score.

[0136] The other steps and parameters are the same as those in one of the specific implementation methods one to five.

[0137] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that, in step three-one, the distance score (distance_score) is obtained based on the path length mathematical model constructed in step two-one; the specific process is as follows:

[0138] For applications requiring efficient flight time and energy conservation (such as long-duration drone delivery or real-time missions), distance score is a critical metric. It helps optimize flight routes, reduce unnecessary detours, thereby improving flight efficiency and extending flight time.

[0139] The distance score is used to evaluate the impact of path length on the overall score, and the formula is as follows:

[0140]

[0141] Where length represents the total length of the flight path, which is calculated according to formula (1);

[0142] The distance score is inversely proportional; the longer the path, the lower the score. Adding a constant of 10 can prevent division by zero errors when the path length is zero.

[0143] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0144] Specific Implementation Method Eight: This implementation method differs from any of Specific Implementation Methods One to Seven in that, in step three-two, based on the conflict risk mathematical model constructed in step two-two, the average risk value avg_risk and the maximum risk value max_risk are obtained; based on the average risk value avg_risk and the maximum risk value max_risk, the risk score risk_score is obtained.

[0145] The specific process is as follows:

[0146] Risk scores are particularly important for drone missions requiring high safety or operating in complex environments. By selecting routes with lower risk scores, drones can avoid dangerous areas, reduce the likelihood of flight accidents, and ensure mission safety and success rates.

[0147] Step 321: Based on the conflict risk mathematical model constructed in Step 22, obtain the average risk value avg_risk and the maximum risk value max_risk;

[0148] The average risk value avg_risk is:

[0149]

[0150] The maximum risk value, max_risk, is the mathematical model for conflict risk, including building risk R. b(p) No-fly zone risk R n(p) Point risk R(p), path segment risk R(S), continuity risk factor eff_risk(p), and path segment final risk R final (S), average risk of the path R avgThe maximum value in (path);

[0151] The average risk value avg_risk is the average of the seven risks in formulas (2), (3), (4), (5), (6), (7), and (8);

[0152] The maximum risk value max_risk is the maximum value of the seven risks in formulas (2), (3), (4), (5), (6), (7), and (8).

[0153] Step 322: Based on the average risk value avg_risk and the maximum risk value max_risk, obtain the risk score risk_score; the specific process is as follows:

[0154] The calculation rules are as follows:

[0155] If avg_risk<0.1: risk_score=45×(1-avg_risk 0.8 )

[0156] If 0.1≤avg_risk<0.3: risk_score=45×(1-avg_risk 0.9 )

[0157] If 0.3≤avg_risk<0.7: risk_score=45×(1-avg_risk)

[0158] If avg_risk≥0.7: risk_score=max_risk×(1-(avg_risk-0.7)×0.3).

[0159] The other steps and parameters are the same as those in any of the specific implementation methods one to seven.

[0160] Specific Implementation Method Nine: This implementation method differs from Specific Implementation Methods One through Eight in that, in step three-three, the steering characteristic mathematical model constructed in step two-three is used to obtain the steering radius score (radius_score); the specific process is as follows:

[0161] In missions requiring high flight stability and precise control (such as delivery or photography), excessive sharp turns can negatively impact flight smoothness, increase flight time, and even lead to mission failure. Optimizing the turn radius score helps drones maintain a stable flight path, ensuring precise landings, reducing energy consumption, and mitigating aircraft risks, ultimately improving mission efficiency and safety. The turn radius score reflects the turn radius characteristics of the path, as shown in the following formula:

[0162] If the minimum turning radius R is 0: radius_score = 20

[0163] If the minimum turning radius R is greater than 0:

[0164] Where R represents the minimum turning radius.

[0165] Turning radius score is used to reward larger turning radii, as larger turns are generally smoother and more suitable for safer flight.

[0166] The other steps and parameters are the same as those in one of the specific implementation methods one to eight.

[0167] Specific Implementation Method 10: This implementation method differs from Specific Implementation Methods 1 to 9 in that, in steps 3 and 4, the total path quality score is obtained based on the distance score, risk score, and turning radius score.

[0168] total_score=0.35×distance_score+0.45×risk_score+0.2×radius_score

[0169] Here, total_score represents the overall path quality score.

[0170] The other steps and parameters are the same as those in any of the specific implementation methods one to nine.

[0171] The score is usually calculated as a weighted average of the scores mentioned above. The overall score takes into account factors such as route distance, risk, and turning radius, and is a comprehensive indicator of route quality.

[0172] Multi-objective A * The specific process of the algorithm's path planning method is as follows: First, a path generation strategy is proposed, which accurately simulates the complex urban delivery environment through multi-path planning and realizes a closed-loop flight path; then, a weight optimization mechanism is determined, which comprehensively considers distance, risk and turning radius factors and sets different weights.

[0173] A route generation strategy is proposed: the system supports multi-segment route planning, allowing for the setting of starting points and multiple intermediate nodes based on actual needs, as well as the random generation of nodes, accurately simulating complex urban delivery environments. During the planning process, the system utilizes multi-objective A... * The complete path is planned sequentially from the starting point to each intermediate node, and then back to the starting point from the last node, thus realizing a closed-loop flight path.

[0174] The system employs an automatic weight optimization mechanism. This mechanism iteratively calculates the path score by combining different weights (from 0 to 1 with a step size of 0.05) and selects the highest-scoring combination. The path score considers three factors: distance, risk, and turning radius. Existing research indicates that risk is the most important factor with the highest weight, followed by distance with a relatively high weight, and finally the turning radius. Therefore, the typical score consists of a distance score (35 points), a risk score (45 points), and a turning radius score (20 points).

[0175] Example:

[0176] To verify the effectiveness of this invention, different numbers of buildings and no-fly zones were used to simulate real-world urban scenarios, namely complex, normal, and simple scenarios, and were implemented according to... Figure 1 The process of completing the simulation test allows the drone to fly in three different environments, making the experimental results more realistic.

[0177] 1. Constructing an environment model based on three-dimensional space:

[0178] 1) Three-dimensional spatial representation based on meshing methods:

[0179] The 3D environment is modeled using a meshing method, dividing the space into N×N×N cube cells. Each cell is represented by coordinates (x, y, z), where the values ​​of x, y, and z are all within the range of [0, N-1].

[0180] 2), reference Figure 4 The highest-rated path is found by using different distance weights in each iteration of path planning, thus obtaining the optimal weight path. See also... Figure 2 , Figure 3 As you can see, the paths planned under different weights are completely different, for example... Figure 3 With a risk weight of only 0.2, the planned path is closer to areas with a higher concentration of buildings. Figure 2 A risk weight of 0.5 will make it more likely to avoid areas with obstacles.

[0181] 3) Propose modeling methods for different types of obstacles:

[0182] See Figure 5 , Figure 6 , Figure 7Obstacles are mainly divided into two categories: buildings and no-fly zones, each with a different modeling method. Buildings are modeled as cubes, defined by their center position (x, y, z) and dimensions (width, depth, height). Specifically, the vertex extent of a building can be described by calculating its boundaries along the x, y, and z axes, where width, depth, and height affect the building's size and position in three-dimensional space, respectively. No-fly zones are modeled as spheres, defined by their center position (x, y, z) and radius r. Any point within a no-fly zone satisfies the geometric equations of a sphere, meaning the distance from that point to the center of the no-fly zone is less than or equal to the radius r.

[0183] 2. Based on multi-objective A * Algorithm path optimization modeling:

[0184] 1) Construct a mathematical model for path length:

[0185] After fully considering the flight environment of UAVs in complex, ordinary and simple scenarios, and clarifying the path planning objectives, while taking into account the principle of minimizing the total path and prioritizing obstacle avoidance, the flight path length can be obtained according to formula (1).

[0186] 2) Constructing a mathematical model of conflict risk:

[0187] After understanding the flight environment such as buildings and no-fly zones in different scenarios, the maximum risk value of the drone flight can be calculated according to formula (2); the risk of the drone touching buildings during flight can be calculated according to formula (3); the risk of the drone flying into a no-fly zone can be calculated according to formula (4); the continuous risk factor value can be calculated according to formula (5); and the path segment risk value of the drone flight can be calculated according to formula (6). If the maximum risk exceeds 0.9, the path segment risk can be adjusted according to formula (7) and the final risk value of the path segment can be obtained. In addition, the average risk of the path segment can be calculated according to formula (8). By predicting and calculating various risks, the flight strategy can be further optimized and potential risks can be reduced.

[0188] 3) Construct a mathematical model of steering characteristics:

[0189] The turning angle during the flight of the UAV is determined by v1 and v2. This determines whether the UAV is turning during this stage. If it is turning, the turning radius needs to be calculated. The turning radius can be calculated sequentially by referring to formula (9).

[0190] 3. Based on multi-objective A * System evaluation of the path planning algorithm:

[0191] 1) Distance evaluation:

[0192] The path score can be calculated from the total flight path length according to formula (10). The distance score is inversely proportional; the longer the path, the lower the score. Adding a constant of 10 can prevent division by zero errors when the path length is zero.

[0193] 2) Risk assessment:

[0194] The risk score is calculated based on the path's average risk value (avg_risk) and maximum risk value (max_risk). The formula uses a power operation on the average risk value (avg_risk). By using different exponents, different sensitivity adjustments can be made to the path's risk score. The calculation rules are as follows:

[0195] If avg_risk<0.1: risk_score=45×(1-avg_risk 0.8 )

[0196] If 0.1≤avg_risk<0.3: risk_score=45×(1-avg_risk 0.9 )

[0197] If 0.3≤avg_risk<0.7: risk_score=45×(1-avg_risk)

[0198] If avg_risk≥0.7: risk_score=max_risk×(1-(avg_risk-0.7)×0.3)

[0199] Risk scores can be calculated for different situations.

[0200] 3) Turning radius evaluation:

[0201] The turning radius score reflects the turning radius characteristics of the path. If the minimum turning radius is 0, the turning radius score is 20; if the minimum turning radius is greater than 0, the score is calculated using the formula... The minimum turning radius score is calculated. The turning radius score is used to reward larger turning radii, as larger turns are generally smoother and more suitable for safer flight.

[0202] 4) Based on A * The algorithm's overall path quality score:

[0203] See Figure 4The score is usually calculated as a weighted average of the above scores. The total score takes into account factors such as path distance, risk, and turning radius, and is a comprehensive indicator of path quality. The total score of the UAV flight path quality is obtained by the formula total_score = 0.35 × distance_score + 0.45 × risk_score + 0.2 × radius_score.

[0204] 4. Experimental Results and Conclusions:

[0205] See Figure 8 , Figure 9 This shows that multi-objective A * The algorithm (optimal weights) significantly outperforms the traditional A algorithm in overall performance. * The algorithm performs exceptionally well in terms of safety, path optimization efficiency, and overall performance, especially in simple and ordinary scenarios. However, in complex scenarios, due to the presence of numerous buildings and no-fly zones, regardless of the planning method, situations will inevitably arise where the distance to buildings and no-fly zones is relatively short. Therefore, the optimal weight directly disregards the impact of risk and prioritizes reducing distance, failing to leverage the multi-objective Aspect Ratio. * The advantages of optimization are such that the planned path differs from the traditional A * The algorithm is roughly the same as the traditional A * The algorithms struggle to differentiate the algorithms. Detailed data is shown in Table 1.

[0206] Table 1: Multi-objective A * Compared with traditional A * Comparison of planned paths

[0207]

[0208]

[0209] Therefore, in ordinary and simple scenarios, multi-objective A * The algorithm significantly reduces average risk by 11.60% and 30.15% respectively, substantially reducing potential dangers. Maximum risk is reduced by 9.78% and 28.57% respectively, meaning a safer path can be provided even in extreme situations. In complex scenarios, although the maximum risk is the same, the average risk is still slightly better (1.30%), indicating a more balanced overall risk distribution. (Multi-objective A) * The reduction in node count by 12.50% in normal scenarios and 17.14% in simplified scenarios represents multi-objective A. * It requires less computation when searching for paths and converges to the optimal solution faster, making it suitable for systems with high real-time requirements. Multi-objective A *The path length is slightly longer (2.59%-4.24%), but this disadvantage is offset by significant improvements in safety, stability, and overall score. In most practical applications (such as autonomous vehicles and robot navigation), safety and path quality are more important than absolute path length.

[0210] Therefore, in most practical applications, multi-objective A * The algorithm is a better choice, especially suitable for scenarios with high requirements for security and path quality. Future optimizations could further refine the weighting strategy to achieve a better balance between path length and risk.

[0211] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. A multi-objective-based approach The algorithm-based method for optimizing urban drone delivery routes is characterized by: The specific process of the method is as follows: Step 1: Construct an environment model based on three-dimensional space; Step 2: Constructing an environment model and multi-objective systems based on three-dimensional space. The algorithm constructs mathematical models for path length, conflict risk, and turning characteristics; the specific process is as follows: Step 2: Construct a mathematical model for the path length; Step 22: Construct a mathematical model of conflict risk, which includes building risk. No-fly zone risks Point of risk Path segment risks Continuous risk factors Ultimate risk of the path segment and the average risk of the path ; The specific process is as follows: Step 221: Calculate Building Risk ; indicates as: (2) when , ; Represents a node Distance to the building; The calculation formula is: in, It is a node The coordinates; These are the coordinates of the building; Indicates the building is in Dimensions in the axial direction; Indicates the building is in Dimensions in the axial direction; Indicates the building is in Dimensions in the axial direction; , , Indicates intermediate variables; Step 222: Calculate the risk of the no-fly zone ; indicates as: (3) when , ; Represents a node Distance to the no-fly zone; The calculation formula is: in, It is a node The coordinates; These are the coordinates of the no-fly zone; Indicates the radius of the no-fly zone; Steps 2-3: Calculate point risk ; indicates as: (4) in, It is a building risk; It is a no-fly zone risk; It's a bit risky; Step 224: Calculate the continuity risk factor ; indicates as: (5) in, Represents path segment nodes The risk, ; Represents path segment nodes ; and These are the start and end points of the path segment, respectively; It is the index of the node. 0.1 is a weighting coefficient; Indicates the first The cumulative risk of each node is expressed as: Initially, accumulated risk Risk from the first sampling point Decide: Represents path segment Sampling point 1; Step 225: Calculate path segment risk ; indicates as: (6) in, Represents path segment Risks; The maximum value is denoted as the risk value in the path segment. ; Step 226: Calculate the final risk of the path segment The specific process is as follows: If the risk value is in the path segment A value greater than 0.9 indicates the final risk of the path segment. Represented as: (7) If the risk value is in the path segment Less than or equal to 0.9, final risk of the path segment ; Step 227: Calculate the average risk of the path. ; indicates as: (8) in, Represents path segment nodes Risks; Represents path segment nodes Length; Steps two and three: Constructing a mathematical model of steering characteristics; the specific process is as follows: Step 231: Based on the two velocity vectors of the UAV and Calculate the included angle , ; in, Represents the dot product of vectors; Represents the velocity vector The model; Represents the velocity vector The model; Representing vectors model sum vector model The product; Step 2. Calculate the included angle. The radian value; Steps two and three, when When the radius is radian, it is determined that the drone has not turned, and the turning radius is... ; when When the radius is measured in arcs, it is determined that the drone has turned, and the turning radius is calculated. The process is as follows: (9) , , Let the lengths of the three sides of the triangle formed when the drone turns be the lengths of the triangle formed by the drone. Let the area be the triangle. The calculation formula is ; The length of half the perimeter of the triangle. ; Step 3: Based on multiple objectives The algorithm and the constructed mathematical models of path length, conflict risk, and turning characteristics are used to obtain the overall path quality score; the path with the highest overall path quality score is selected as the drone delivery path. The specific process is as follows: Step 31: Obtain the distance score based on the path length mathematical model constructed in Step 21. ; Step 32: Based on the conflict risk mathematical model constructed in Step 22, obtain the average risk value. and maximum risk value Based on average risk value and maximum risk value Obtain a risk score ; Step 33: Based on the steering characteristic mathematical model constructed in Step 23, obtain the steering radius score. ; Steps 3 and 4: Distance-based scoring Risk Score Turning radius score The overall path quality score is obtained.

2. A multi-objective-based method according to claim 1 The algorithm-based method for optimizing urban drone delivery routes is characterized by: In step one, an environment model is constructed based on a three-dimensional spatial structure. The specific process is as follows: Step 11: Represent the three-dimensional space using a mesh; the specific process is as follows: The three-dimensional spatial environment is divided into A set of cube cells, each cube cell is represented by coordinates. To indicate; in The values ​​are all located in Within the range, The values ​​are all located in Within the range, The values ​​are all located in Within the range; Steps 1 and 2: Obstacles are mainly divided into two categories: buildings and no-fly zones; The building is modeled as a cube, passing through the center of the cube. and size To define a building; The no-fly zone is modeled as a sphere, passing through the center of the sphere. and radius Decide.

3. A multi-objective-based method according to claim 2 The algorithm-based method for optimizing urban drone delivery routes is characterized by: Step two, i.e., constructing a mathematical model for path length; the specific process is as follows: The three-dimensional space is divided into a grid, where each grid represents a node, and the lines connecting the grids represent feasible paths. The path length is expressed as the sum of the Euclidean distances between the nodes on the path. (1) in, Represents path segment Length; Indicates the first Each node Coordinates on the axis; Indicates the first Each node Coordinates on the axis; Indicates the first Each node Coordinates on the axis; Indicates the first Each node Coordinates on the axis; Indicates the first Each node Coordinates on the axis; Indicates the first Each node Coordinates on the axis; Indicates the first 1 node ; Indicates flight path Total number of nodes; ; Represents path segment The length.

4. A multi-objective-based method according to claim 3 The algorithm-based method for optimizing urban drone delivery routes is characterized by: In step three, the distance score is obtained based on the path length mathematical model constructed in step two. The specific process is as follows: The formula is as follows: (10) in, This indicates the total length of the flight path.

5. A multi-objective-based method according to claim 4 The algorithm-based method for optimizing urban drone delivery routes is characterized by: In step three-two, based on the conflict risk mathematical model constructed in step two-two, the average risk value is obtained. and maximum risk value Based on average risk value and maximum risk value Obtain a risk score ; The specific process is as follows: Step 321: Based on the conflict risk mathematical model constructed in Step 22, obtain the average risk value. and maximum risk value ; Average risk value for: Maximum risk value Mathematical models for conflict risk include building risk. No-fly zone risks Point of risk Path segment risks Continuous risk factors Ultimate risk of the path segment Average risk of the path The maximum value in the middle; Step 322: Based on average risk value and maximum risk value Obtain a risk score The specific process is as follows: The calculation rules are as follows: like like like like .

6. A multi-objective-based method according to claim 5 The algorithm-based method for optimizing urban drone delivery routes is characterized by: In step three, based on the mathematical model of steering characteristics constructed in step two and three, the steering radius score is obtained. The specific process is as follows: The formula is as follows: If the minimum turning radius =0: If the minimum turning radius Greater than 0: in, This indicates the minimum turning radius.

7. A multi-objective-based method according to claim 6 The algorithm-based method for optimizing urban drone delivery routes is characterized by: In steps three and four, distance-based scoring Risk Score Turning radius score Obtain the overall path quality score; in, This represents the overall path quality score.

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