Low-altitude unmanned aerial vehicle cluster three-dimensional dynamic obstacle avoidance method based on multi-target perception

Abstract

The invention discloses a low-altitude unmanned aerial vehicle cluster three-dimensional dynamic obstacle avoidance method based on multi-target perception, and belongs to the technical field of unmanned aerial vehicle path planning and obstacle avoidance, and the method comprises the following steps: S1, abstracting a static obstacle into an obstacle ellipsoid model, modeling an unmanned aerial vehicle into a protection area ellipsoid model, and constructing a protection area ellipsoid model; the unmanned aerial vehicle safety buffer interval proportion and the unmanned aerial vehicle border crossing conflict probability serve as a dual-target optimization protection area ellipsoid model, the optimal safety buffer interval is determined, and obstacle avoidance is carried out; s2, performing cluster division on the unmanned aerial vehicles for the dynamic obstacle, establishing a cluster ellipsoid, calculating a relative velocity vector between any unmanned aerial vehicle and the cluster ellipsoid, depicting a parameter equation of a straight line where the relative velocity vector is located, and performing multiple sampling based on a Monte Carlo method to obtain a dynamic obstacle; conflict judgment is carried out based on the intersection relation between the obtained coordinate points and the parameter equation, and if the coordinate points intersect with the parameter equation, potential conflicts are judged, and obstacle avoidance is carried out; the method can solve the problems existing in an existing method.

Description

Technical Field

[0001] The present invention belongs to the technical field of UAV path planning and obstacle avoidance, and specifically relates to a three-dimensional dynamic obstacle avoidance method for low-altitude UAV clusters based on multi-target perception. Background Art

[0002] A drone is an unmanned aircraft that is controlled by radio remote control equipment and its own program control device, and is widely used in low-altitude airspace.

[0003] As the scale of drone operations in low-altitude airspace continues to expand, their high-density operation characteristics have led to increasingly prominent problems such as flight path intersection and route overlap, and the risk of potential conflicts has increased significantly. Therefore, it is particularly important to study conflict identification and prediction during drone operations.

[0004] Currently, there are two main types of conflicts involved in the operation of drones. One is the conflict between drones and static obstacles, and the other is the conflict between drones and dynamic obstacles, including drone clusters.

[0005] Currently, the solution generally adopted for conflicts between drones and static obstacles is macro-path planning. This method does not fully consider the spatial distribution characteristics of obstacles in urban low-altitude airspace, resulting in difficulty in ensuring the accuracy and efficiency of conflict identification in complex environments.

[0006] Currently, the commonly used solution to conflicts between drones and dynamic obstacles, including those between drone clusters, is to use a spherical model to approximate the drone protection zone. This method results in an overly large protection range, which in turn causes unnecessary trajectory adjustments, affecting the accuracy and efficiency of conflict identification. At the same time, the computational complexity of the pairwise conflict detection method increases quadratically with the number of drones, making it difficult to meet the real-time requirements of large-scale cluster flight and unable to effectively cope with dynamic obstacle cluster flight scenarios.

[0007] In view of this, a three-dimensional dynamic obstacle avoidance method for low-altitude UAV cluster based on multi-target perception is designed to solve the above problems. Summary of the Invention

[0008] To solve the problems raised in the above background technology, the present invention provides a three-dimensional dynamic obstacle avoidance method for low-altitude UAV clusters based on multi-target perception, which has the characteristics of solving the problem of conflict recognition between UAVs and static obstacles and dynamic obstacles.

[0009] To achieve the above objectives, the present invention provides the following technical solution: a three-dimensional dynamic obstacle avoidance method for a low-altitude UAV cluster based on multi-target perception, comprising the following steps:

[0010] S1: For static obstacles, the geometric shape of the static obstacle is abstracted into an obstacle ellipsoid model, and the drone protection zone is modeled as a protection zone ellipsoid model. The protection zone ellipsoid model is optimized with the drone safety buffer interval ratio and the drone cross-border conflict probability as dual objectives to determine the optimal safety buffer interval between the drone and the static obstacle, and obstacle avoidance is based on the optimal safety buffer interval;

[0011] S2: For dynamic obstacles, the drones are clustered based on their parameters, including speed, heading, and optimal safety buffer interval. A three-dimensional optimized ellipsoid protection zone model, i.e., the cluster ellipsoid, is established for each cluster. The relative velocity vector between any drone and the cluster ellipsoid is calculated, and the parametric equation of the line containing the relative velocity vector is described. Multiple sampling is performed based on the Monte Carlo method, and conflict judgment is performed based on the intersection relationship between the obtained coordinate points and the parametric equation. If the two intersect, it is determined to be a potential conflict, and obstacle avoidance is based on potential conflicts.

[0012] Furthermore, the specific steps of step S1 include:

[0013] For static obstacles:

[0014] Abstract the geometric shape of static obstacles into obstacle ellipsoid models;

[0015] The drone protection zone is modeled as a protection zone ellipsoid model, where the major axis U x Coplanar with the velocity direction of the drone;

[0016] Based on the obstacle ellipsoid model, the protection zone ellipsoid model is superimposed on the obstacle ellipsoid model as an extended part to establish the obstacle extended protection zone model;

[0017] Based on the obstacle extension protection zone model, the optimal safety buffer interval for drones is constructed by taking the proportion of drone safety buffer interval and the probability of drone crossing the boundary conflict as a dual-objective optimization function.

[0018] The expression of the drone safety buffer interval ratio function is:

[0019]

[0020] Where: f percentage The ratio of the safety buffer interval of the drone; are the lengths of the semi-axes of the geometric volume ellipsoid of the static obstacle; They are the safety buffer intervals in each axis direction of the UAV;

[0021] The expression of the UAV cross-border conflict probability function is:

[0022]

[0023] Where: f conflict is the probability of UAV crossing the boundary conflict; P is the probability of position uncertainty conflict; is a 0-1 decision variable; The total number of all speed and acceleration value combinations;

[0024] constraint:

[0025] Where: are the lengths of the semi-axes of the extended protection zone of the obstacle; are the standard deviations of the positioning errors of the UAV in each axis direction; They are the safety buffer intervals in each axis direction of the UAV; are the random positioning errors of each axis of the UAV;

[0026]

[0027] Where: are the lengths of the semi-axes of the geometric volume ellipsoid of the static obstacle; They are the safety buffer intervals in each axis direction of the UAV;

[0028]

[0029] Where: They are the safety buffer intervals in each axis direction of the UAV;

[0030]

[0031] Where: d x , d y , d z The minimum braking distances of the drone in the x, y, and z axes respectively;

[0032]

[0033] Where: U x 、U y 、U z Axial component; are the components in each axis direction respectively;

[0034]

[0035] Where: is the speed; is the vertical deflection angle of the UAV; is the horizontal deflection angle of the UAV;

[0036]

[0037] Where: is the magnitude of acceleration;

[0038]

[0039] Where: m is the total number of slices in the velocity range; n is the total number of slices in the acceleration range;

[0040] Optimal safety buffer interval obstacle avoidance based on UAV.

[0041] Furthermore, in step S2, the specific steps of clustering to establish a three-dimensional optimized ellipsoid protection zone model include:

[0042] The average value of the positions of all drones in the cluster is taken as the geometric center of the cluster, that is, the cluster centroid;

[0043] The cluster centroid expression is:

[0044]

[0045] Where: is the coordinate of the centroid of the cluster ellipsoid; is the position coordinate of the UAV; n is the number of UAVs in the cluster;

[0046] According to the combined velocity direction angle of the UAVs in the cluster, the rotation angle of the cluster protection zone is determined, including the horizontal deflection angle and the vertical deflection angle;

[0047] The expression is:

[0048]

[0049] Where: is the resultant velocity vector of the cluster ellipsoid; They are Components in the x, y and z axes; are the x, y, and z axis components respectively; n is the number of drones in the cluster;

[0050]

[0051] Where: is the magnitude of the combined velocity of the cluster ellipsoid; is the speed of the drone;

[0052] The expression of horizontal deflection angle is:

[0053]

[0054] Where: is the horizontal deflection angle of the cluster ellipsoid; and They are In the x- and y-axis directions;

[0055] The vertical deflection angle expression is:

[0056]

[0057] Where: is the vertical deflection angle of the cluster ellipsoid; They are Components in the x, y and z axes;

[0058] To minimize U x 、U y and U z The method of summing the lengths of the three directions of the axis to solve the centroid of the cluster ellipsoid along U x 、U y and U z Semi-axis length of the axis and

[0059] To ensure that the semi-axis lengths of the cluster ellipsoid are all positive, three new optimization variables u, v, and w are introduced. They are directly related to the semi-axis lengths of the cluster ellipsoid and are guaranteed to be positive to meet the physical constraints of the model. The simplified optimization objective is defined as:

[0060]

[0061] Where:

[0062] The constraints are defined as:

[0063] Each ellipsoid is contained in the optimized cluster ellipsoid, that is, for each ellipsoid in the cluster, a point inside or on the boundary is randomly selected so that the point is translated and rotated from the global coordinates to the local coordinates and the result of the solution to the cluster ellipsoid equation is less than or equal to 1;

[0064] Based on the cluster centroid and cluster ellipsoid centroid along U x 、U y and U z Semi-axis length of the axis and A three-dimensional optimized ellipsoid protection zone model of the UAV cluster, namely the cluster ellipsoid, is established.

[0065] Furthermore, in step S2, the relative velocity vector expression between any UAV and the cluster ellipsoid is calculated as:

[0066]

[0067] Where: For drone cluster 1 and choose drone n The relative velocity vector.

[0068] Furthermore, in step S2, the parametric equation describing the line where the relative velocity vector lies is expressed as follows:

[0069]

[0070] Where: is the position coordinate of UAV n, and s is an arbitrary real value.

[0071] Furthermore, in step S2, the specific steps of performing conflict judgment based on the obtained intersection relationship between the coordinate points and the parametric equation include:

[0072] The Monte Carlo method is used to sample the cluster ellipsoid surface;

[0073] Substitute the coordinates of the sampling point into the given parametric equation, calculate the corresponding parameter value for each coordinate component, and compare them. If the parameter values obtained by each coordinate component are consistent, it means that the point is on the trajectory of the straight line. Otherwise, the point is not on the straight line. At the same time, if the unit vector component of a certain coordinate direction is zero, check whether the coordinates of the point in this coordinate direction are consistent with the coordinates of the starting point. If they are consistent, the point can still be considered to be on the straight line.

[0074] If the sampling point is located on the straight line described by the relative velocity vector, there is an intersection, which is determined to be a potential conflict.

[0075] Compared with the prior art, the present invention has the following beneficial effects:

[0076] For static obstacles, the present invention proposes a dynamic protection zone model based on the dual-objective optimization of the drone cross-border conflict rate and the safety buffer interval ratio. It not only fully takes into account the spatial distribution characteristics of obstacles in urban low-altitude airspace, but also can effectively achieve a balance between safety and resource efficiency in the buffer zone, significantly reduce the airspace waste caused by over-conservative protection zones, and improve the accuracy and efficiency of conflict identification; for dynamic obstacles, a drone cluster optimization protection zone model is proposed to avoid unnecessary trajectory adjustments caused by excessively large protection ranges. At the same time, by dividing a single drone into multiple clusters, the computational complexity can be significantly reduced, avoiding the problem of the quadratic increase in the computational complexity with the number of drones in the current method, so that it can meet the real-time requirements of large-scale cluster flight and effectively cope with dynamic obstacle cluster flight scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1This is an abstract model diagram of the geometric shape of a static obstacle in the present invention;

[0078] Figure 2 This is the ellipsoid model diagram of the drone protection zone of the present invention;

[0079] Figure 3 This is a model diagram of the obstacle extension protection zone of the present invention;

[0080] Figure 4 This is a three-dimensional optimized ellipsoid protection zone model diagram of the drone cluster of the present invention;

[0081] Figure 5 This is the improved VO model diagram of the conflict between drones and swarms in the present invention;

[0082] Figure 6 It is the distribution diagram of the Pareto optimal solution set of the present invention;

[0083] Figure 7 The relationship diagram between the buffer interval in each direction and the dual targets of the present invention is shown in Figure 1, where (a) is With dual-target relationship, (b) is With the dual-target relationship, (c) is and dual-target relationships;

[0084] Figure 8 This is the cluster ellipsoid pose information diagram of the present invention, where (a) is the cluster ellipsoid The pose information of (b) is the cluster ellipsoid The pose information of

[0085] Figure 9 This is the pose information diagram of the cluster ellipsoid in each axis direction of the present invention, where (a) is the cluster ellipsoid in U x Axis direction pose information, (b) is the cluster ellipsoid in U y Axis direction pose information, (c) is the cluster ellipsoid in U z Axis direction pose information, (d) is the cluster ellipsoid in U x Axis direction pose information, (e) is the cluster ellipsoid in U y Axis direction pose information, (f) is the cluster ellipsoid in U z Axis direction pose information;

[0086] Figure 10 The drone cluster of the present invention With drones Pose information graph;

[0087] Figure 11This is a conflict detection experiment diagram of the Monte Carlo combined with the improved VO algorithm of the present invention. DETAILED DESCRIPTION

[0088] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. 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 making creative efforts are within the scope of protection of the present invention.

[0089] The present invention provides the following technical solution: a three-dimensional dynamic obstacle avoidance method for a low-altitude UAV cluster based on multi-target perception, comprising the following steps:

[0090] S1: For static obstacles, the geometric shape of the static obstacle is abstracted into an obstacle ellipsoid model, and the drone protection zone is modeled as a protection zone ellipsoid model. The protection zone ellipsoid model is optimized with the drone safety buffer interval ratio and the drone cross-border conflict probability as dual objectives to determine the optimal safety buffer interval between the drone and the static obstacle, and obstacle avoidance is based on the optimal safety buffer interval;

[0091] S2: For dynamic obstacles, the drones are clustered based on their parameters, including speed, heading, and optimal safety buffer interval. A three-dimensional optimized ellipsoid protection zone model, i.e., the cluster ellipsoid, is established for each cluster. The relative velocity vector between any drone and the cluster ellipsoid is calculated, and the parametric equation of the line containing the relative velocity vector is described. Multiple sampling is performed based on the Monte Carlo method, and conflict judgment is performed based on the intersection relationship between the obtained coordinate points and the parametric equation. If the two intersect, it is determined to be a potential conflict, and obstacle avoidance is based on potential conflicts.

[0092] Specifically, the specific steps of step S1 include:

[0093] For static obstacles:

[0094] The geometric shape of the static obstacle is abstracted into an obstacle ellipsoid model. Figure 1 ;

[0095] The drone protection zone is modeled as a protection zone ellipsoid model, where the major axis U x Coplanar with the speed direction of the drone, see attached Figure 2 ;

[0096] Based on the obstacle ellipsoid model, the protection zone ellipsoid model is superimposed on the obstacle ellipsoid model as an extended part to establish the obstacle extended protection zone model. Figure 3 ;

[0097] Based on the obstacle extension protection zone model, the optimal safety buffer interval for drones is constructed by taking the proportion of drone safety buffer interval and the probability of drone crossing the boundary conflict as a dual-objective optimization function.

[0098] The drone safety buffer interval ratio is defined as the ratio of the safety buffer interval volume to the obstacle extended protection area volume. The expression of the drone safety buffer interval ratio function is:

[0099]

[0100] Where: f percentage The ratio of the safety buffer interval of the drone; are the lengths of the semi-axes of the geometric volume ellipsoid of the static obstacle; They are the safety buffer intervals in each axis direction of the UAV;

[0101] The probability of a drone crossing the boundary conflict is assessed by accurately quantifying the comprehensive conflict risk of a drone entering the boundary of an abstract model of a static obstacle geometry under multiple complex factors. This probability is determined by the product of the conflict frequency ratio and the position uncertainty conflict probability. The conflict frequency ratio is the ratio of the number of conflicts to the number of simulations. The calculation is based on the value range of the safety buffer interval. The expression of the drone crossing the boundary conflict probability function is:

[0102]

[0103] Where: f conflict is the probability of UAV crossing the boundary conflict; P is the probability of position uncertainty conflict; is a 0-1 decision variable; The total number of all speed and acceleration value combinations;

[0104] constraint:

[0105] Where: are the lengths of the semi-axes of the extended protection zone of the obstacle; are the standard deviations of the positioning errors of the UAV in each axis direction; They are the safety buffer intervals in each axis direction of the UAV; are the random positioning errors of each axis of the UAV;

[0106]

[0107] Where: are the lengths of the semi-axes of the geometric volume ellipsoid of the static obstacle; They are the safety buffer intervals in each axis direction of the UAV;

[0108]

[0109] Where: They are the safety buffer intervals in each axis direction of the UAV;

[0110]

[0111] Where: d x , d y , d z The minimum braking distances of the drone in the x, y, and z axes respectively;

[0112]

[0113] Where: U x 、U y 、U z Axial component; are the components in each axis direction respectively;

[0114]

[0115] Where: is the speed; is the vertical deflection angle of the UAV; is the horizontal deflection angle of the UAV;

[0116]

[0117] Where: is the magnitude of acceleration;

[0118]

[0119] Where: m is the total number of slices in the velocity range; n is the total number of slices in the acceleration range;

[0120] Specifically:

[0121] This probability is determined by the product of the conflict ratio and the position uncertainty conflict probability, where the conflict ratio is the ratio of the number of conflicts to the number of simulations, and the calculation is based on the value range of the safety buffer interval.

[0122] Randomly set different safety buffer intervals and simulate the deceleration process of the drone to obtain the conflict frequency;

[0123] The NSGA-II algorithm is used to initialize a set of variable values within the safety buffer interval;

[0124] For each set of solutions, perform the following process:

[0125] Quantify the number of times the drone decelerates, set the range of speed and acceleration, take m speed values and n acceleration values at equal intervals, and obtain all combinations of speed and acceleration. The number of combinations is the total number of experiments.

[0126] Randomly select horizontal and vertical deflection angles within the range of 0-360°, calculate the corresponding braking distance, and compare it with the safety buffer interval. If the braking distance in any direction is greater than the obstacle protection zone interval in the corresponding direction, it is determined that a conflict has occurred and the number of conflicts is accumulated. Otherwise, there is no conflict.

[0127] The braking distance is calculated based on the drone's speed, acceleration, and braking capability (e.g., emergency braking or return). It represents the minimum distance required to stop the drone. This distance is calculated based on the braking distance along the three axes of the global coordinate system, along the direction of the drone's speed. The buffer interval is then delineated in a new coordinate system centered on the drone, taking into account the drone's motion characteristics.

[0128] After multiple experiments and analyses, the braking distance of the global coordinate system was used as a reference to determine the reasonable settings of the buffer ranges for each axis, optimize the protection zone design, and ensure safety and reliability.

[0129] During the optimization process, the NSGA-II algorithm uses crossover and mutation operations to generate new solutions and retains the optimal solution through selection operations. In each generation of optimization, the algorithm dynamically updates the solution set according to the objective function value.

[0130] The calculation of the position uncertainty conflict probability comprehensively considers the UAV positioning error, assuming that the error follows a normal distribution;

[0131] Model bias refers to the constant bias due to the inherent characteristics of the sensor system;

[0132] Random positioning error originates from model randomness, such as GPS error and environmental interference, and reflects the average offset between the actual position and the ideal position. The standard deviation of the positioning error is used to characterize the fluctuation range of the error and reflect the degree of dispersion of the error relative to the average offset, thereby describing the distribution characteristics and dispersion range of the positioning error.

[0133] Optimal safety buffer interval obstacle avoidance based on UAV.

[0134] Specifically, in step S2, the specific steps of clustering to establish a three-dimensional optimized ellipsoid protection zone model include:

[0135] The average value of the positions of all drones in the cluster is taken as the geometric center of the cluster, that is, the cluster centroid;

[0136] The cluster centroid expression is:

[0137]

[0138] Where: is the coordinate of the centroid of the cluster ellipsoid; is the position coordinate of the UAV; n is the number of UAVs in the cluster;

[0139] According to the combined velocity direction angle of the UAVs in the cluster, the rotation angle of the cluster protection zone is determined, including the horizontal deflection angle and the vertical deflection angle;

[0140] The expression is:

[0141]

[0142] Where: is the resultant velocity vector of the cluster ellipsoid; They are Components in the x, y and z axes; are the x, y, and z axis components respectively; n is the number of drones in the cluster;

[0143]

[0144] Where: is the magnitude of the combined velocity of the cluster ellipsoid; is the speed of the drone;

[0145] The expression of horizontal deflection angle is:

[0146]

[0147] Where: is the horizontal deflection angle of the cluster ellipsoid; and They are In the x- and y-axis directions;

[0148] The vertical deflection angle expression is:

[0149]

[0150] Where: is the vertical deflection angle of the cluster ellipsoid; They are Components in the x, y and z axes;

[0151] To minimize U x 、U y and U z The method of summing the lengths of the three directions of the axis to solve the centroid of the cluster ellipsoid along U x 、U y and U z Semi-axis length of the axis and

[0152] To ensure that the semi-axis lengths of the cluster ellipsoid are all positive, three new optimization variables u, v, and w are introduced. They are directly related to the semi-axis lengths of the cluster ellipsoid and are guaranteed to be positive to meet the physical constraints of the model. The simplified optimization objective is defined as:

[0153]

[0154] Where:

[0155] The constraints are defined as:

[0156] Each ellipsoid is contained in the optimized cluster ellipsoid, that is, for each ellipsoid in the cluster, a point inside or on the boundary is randomly selected so that the point is translated and rotated from the global coordinates to the local coordinates and the result of the solution to the cluster ellipsoid equation is less than or equal to 1;

[0157] Based on the cluster centroid and cluster ellipsoid centroid along U x 、U y and U z Semi-axis length of the axis and Establish a three-dimensional optimized ellipsoid protection zone model for the UAV cluster, namely the cluster ellipsoid, see the attached Figure 4 .

[0158] Specifically, in step S2, the relative velocity vector between any UAV and the cluster ellipsoid is calculated. Figure 5 , the expression is:

[0159]

[0160] Where: For drone cluster 1 and choose drone n The relative velocity vector of

[0161] Here we take UAV 5 as an example, so the attached Figure 5 The expression is:

[0162]

[0163] Specifically, in step S2, the parametric equation of the line where the relative velocity vector is located is described, see the attached Figure 5 , the expression is:

[0164]

[0165] Where: is the position coordinate of the UAV n, s is any real value;

[0166] Here we take UAV 5 as an example, so the attached Figure 5 The expression is:

[0167]

[0168] Specifically, in step S2, the specific steps of performing conflict judgment based on the intersection relationship between the obtained coordinate points and the parametric equation include:

[0169] The Monte Carlo method is used to sample the cluster ellipsoid surface;

[0170] Substitute the coordinates of the sampling point into the given parametric equation, calculate the corresponding parameter value for each coordinate component, and compare them. If the parameter values obtained by each coordinate component are consistent, it means that the point is on the trajectory of the straight line. Otherwise, the point is not on the straight line. At the same time, if the unit vector component of a certain coordinate direction is zero, check whether the coordinates of the point in this coordinate direction are consistent with the coordinates of the starting point. If they are consistent, the point can still be considered to be on the straight line.

[0171] If the sampling point is located on the straight line described by the relative velocity vector, there is an intersection, which is determined to be a potential conflict.

[0172] Example

[0173] Taking the UAV Wingcopter178HeavyLiftA as the research object, the relevant parameters in fixed-wing mode are shown in Table 1:

[0174] Table 1: Wingcopter 178 Heavy Lift A UAV parameter information

[0175]

[0176] Parameters are defined as: obstacle geometry

[0177] During the flight of the drone, considering that the risk in the speed direction is more significant and the safety buffer distance may vary, the safety buffer interval range is set to

[0178] The UAV positioning error factor is introduced into the analysis, and the error parameter is defined as: Their standard deviations are

[0179] After comprehensive analysis, the performance parameters of the drone are: speed acceleration

[0180] The NSGA-II algorithm is used to optimize three decision variables and two objective functions (UAV safety buffer interval ratio and cross-border conflict probability). The parameters of the optimization algorithm are set as follows: the population size is 100, the crossover operation uses the simulated binary crossover (SBX) operator with a crossover probability of 90% and a shape parameter of 15, and the mutation operation uses the polynomial mutation (PM) operator with a shape parameter of 20.

[0181] The calculation of objective function 2 involves triple integrals and high-dimensional variable operations, resulting in long computation time and low efficiency. To improve computational efficiency, based on the variable independence assumption, the cumulative distribution function (CDF) of the multivariate normal distribution is converted into the product of the CDFs of each one-dimensional normal distribution. This avoids the computational complexity of the triple integral and significantly improves computational efficiency.

[0182] The optimization results of the UAV flight safety buffer interval are shown in the attached Figure 6 As shown in the figure, the dual-objective trade-off relationship between the proportion of drone safety buffer interval (objective 1) and the probability of drone cross-border conflict (objective 2) is revealed. It can be seen that when objective 1 is low, about 0.5 (50%), objective 2 is close to 1, indicating that the safety buffer interval is not enough to ensure flight safety. When objective 1 increases from 0.5 (50%) to 0.8 (80%), objective 2 decreases rapidly, with the largest decrease. When objective 1 is close to 1, objective 2 tends to be flat, and the marginal effect decreases, indicating that continuing to increase objective 1 has limited effect on reducing objective 2.

[0183] The annotated data further verifies the characteristics of different solutions, e.g. When , target 1 is close to 0.9 (90%), target 2 is lower, but target 1 is too high and takes up more space resources, which is suitable for high-security mission scenarios. In contrast, Located in the middle of the Pareto frontier, objective 1 is moderate and objective 2 is low, reflecting a balance between safety and resource efficiency;

[0184] The Pareto front distribution is concentrated in the higher target 1 area, indicating that the optimization algorithm effectively reduces target 2. The results show that the relationship between target 1 and target 2 is nonlinear. When the ratio is moderate (0.6 (60%) to 0.8 (80%)), target 2 decreases the fastest, which is the key interval for optimization design;

[0185] The dual-objective optimization results demonstrate the need to strike a balance between safety and resource efficiency based on specific application scenarios. The experiments validate the effectiveness of the algorithm in complex environments and provide theoretical support for path planning and safety buffer design for UAVs in low-altitude urban airspace.

[0186] From the overall trend, as the safety buffer interval increases, the indicators of goal 1 rise rapidly and tend to stabilize, while the indicators of goal 2 show a continuous downward trend, but the specific decline rate and performance vary from figure to figure;

[0187] Detailed perspective as attached Figure 7 As shown, the impact of the safety buffer interval on different objectives is analyzed:

[0188] Depend on Figure 7 (a) It can be seen that the indicators of goal 1 are It quickly reaches the maximum value of 1.0 (100%) near , and then maintains a high level with almost no significant change, which shows that a smaller safety buffer interval can fully optimize the performance of goal 1. At the same time, the indicator of goal 2 is The rate of decrease is faster when After that, the rate of decline gradually slowed down and finally tends to be stable and maintains at a lower level;

[0189] Depend on Figure 7 (b) It can be seen that the overall trend of change is consistent with Figure 7 (a) Similar, but with some differences. Target 1 is also within a smaller safety buffer. It reaches a saturation value of 1.0 (100%) and remains constant thereafter, whereas the rate of decrease for target 2 is slower, especially at When the index decreases significantly, it indicates that the safety buffer interval The negative impact on target 2 is relatively mild, which shows a safety buffer interval While optimizing objective 1, there is little interference with objective 2, which has certain advantages in achieving multi-objective optimization;

[0190] More complex nonlinear trends are caused by Figure 7 As shown in (c), it can be seen that the indicator of target 1 (f1) is It rises rapidly to a maximum value of 1.0 (100%) and then , indicating that further increase in the safety buffer interval may have a negative impact on the performance of Objective 1. In addition, the indicators of Objective 2 It remains stable when the safety buffer interval increases, indicating that the increase in the safety buffer interval has limited impact on target 2. After that, the indicators of target 2 dropped rapidly, indicating that the larger safety buffer interval had a significant adverse effect on target 2. It is worth noting that Nearby, the curves of target 1 and target 2 intersect, indicating that the performance of the two may be relatively balanced. Therefore, compared with Figure 7 (a) and Figure 7 (b) Figure 7 (c) The complexity of the nonlinear impact of the safety buffer on Objectives 1 and 2 is more prominently revealed, indicating that a larger safety buffer range may have adverse effects on both Objectives 1 and 2 simultaneously;

[0191] A comprehensive analysis of the three figures shows that increasing the safety buffer interval significantly improves the performance of target 1, but has a negative impact on the performance of target 2. This impact also exhibits different characteristics as the safety buffer interval changes. Overall, target 1's sensitivity to the safety buffer interval is mainly concentrated in a smaller range (<20m), while target 2's sensitivity decreases significantly within a smaller safety buffer interval range. When the safety buffer interval is larger (>50m), its performance degradation tends to stabilize or even stagnate. Figure 7 (a) and Figure 7 In (b), the larger safety buffer has relatively little effect on target 2, while Figure 7 (c) shows that a too large safety buffer interval may cause the performance of Objective 1 to degrade and Objective 2 to drop significantly. Based on the characteristics of the three figures, it is recommended to control the safety buffer interval within the range of [20,50]m. Within this range, the performance requirements of Objective 1 and Objective 2 can be effectively balanced, achieving a relative balance between the two.

[0192] Given 6 drones with similar flight characteristics, their pose information is shown in Table 2:

[0193] Table 2: Position information of 6 large drones

[0194]

[0195] The clustering conditions are that the speed difference does not exceed 100 km / h, the horizontal deflection angle difference does not exceed 30°, the vertical deflection angle difference does not exceed 30°, and the shortest straight-line distance is not less than 12 km. The drones that meet the conditions are defined as a cluster;

[0196] To characterize the cluster, an optimization model is used to solve the cluster ellipsoid boundary, and further analyze the key characteristics of the cluster, including parameters such as center of mass position, movement direction, and speed, providing an important basis for revealing cluster flight path planning, conflict detection and resolution;

[0197] like Figure 8 As shown, the target objects are divided into two clusters, namely cluster and clusters

[0198] In the cluster The cluster ellipsoid parameters obtained by the ellipsoid optimization model are as follows: the center of mass coordinates are [21.67, 23.33, 5.67] km, the rotation matrix is: [0.95, -0.28, 0.15, 0.28, 0.96, 0.02, -0.15, 0.02, 0.99], the unit vector in the direction of the resultant velocity is [0.95, 0.28, -0.15], and the lengths of each axis are and The results show that cluster It has large spatial expansion and shows obvious anisotropy in each axis direction, especially in U y The expansion in the axial direction is most significant;

[0199] In the cluster In the , the optimized cluster ellipsoid parameters are: center of mass coordinates [48.33, 7.00, 52.33] km, the rotation matrix is: [0.99, -0.16, 0.06, 0.16, 0.99, 0.00, -0.06, 0.00, 0.99], the unit vector in the direction of the resultant velocity is [0.99, 0.16, -0.06], and the lengths of each axis are and With cluster In contrast, cluster Presenting a more compact space structure, especially in U x Axis and U y The expansion in the axial direction is smaller, indicating that the cluster The spatial distribution of

[0200] In order to intuitively demonstrate the adaptability of the optimized ellipsoid in various directions, a three-dimensional visualization analysis of the optimized ellipsoids of the two groups of clusters is performed. The figure shows the clusters With cluster The optimized ellipsoid parameters are presented, focusing on the center of mass position, rotation matrix and the difference in the direction vector of the resultant velocity;

[0201] For six drones, when performing pairwise conflict judgment, the theoretical number of judgments required is C(n,2). For six individuals, according to the combination formula C(6,2), a total of 15 judgments are required. However, if these individuals are divided into two clusters, only one inter-cluster conflict judgment is required, which significantly reduces the computational complexity. As the number of individuals in each cluster increases, the complexity of airspace judgment is further reduced, and the number of conflict judgments is also reduced accordingly. This method has significant advantages in scenarios with highly dense drones, because it can effectively reduce the amount of calculation and improve computing efficiency through cluster division.

[0202] like Figure 9 As shown, from multiple angles (such as U x Axis and U y Axis, Ux Axis and U z Axis, U y Axis and U z Axis) shows in detail the spatial relationship between the optimized ellipsoid and the small ellipsoid, and calculates the x Axis, U y Axis and U z The point on the surface of the small ellipsoid in the axial direction is the farthest from the centroid of the cluster ellipsoid, and the corresponding points are marked with red dots, green triangles and blue squares respectively. The spatial distribution characteristics of the optimized ellipsoid and the small ellipsoid are intuitively presented using visualization at different angles.

[0203] From the optimization results of the two clusters, it can be observed that the optimized ellipsoid completely surrounds all small ellipsoids in all directions, indicating that the model reasonably adjusts the size and direction of the ellipsoid to ensure that the farthest point is completely included, thereby achieving the goal of minimizing the ellipsoid volume;

[0204] This optimization significantly improves the spatial compactness and utilization of clusters, verifying the effectiveness of the ellipsoid optimization model in describing the spatial distribution of clusters. The optimized ellipsoid achieves the expected results in terms of spatial compactness and cluster description.

[0205] Based on the precise characterization and analysis of UAV swarms, a conflict detection and resolution method that treats swarms as individuals is proposed, combined with an improved speed barrier method for conflict avoidance. This method effectively improves the accuracy and effectiveness of low-altitude UAV conflict avoidance and enhances the predictive capabilities of UAVs during flight, providing a scientific basis for management and scheduling, especially in high-altitude swarm flight environments.

[0206] By characterizing the flight characteristics of swarms in detail, flight trends can be accurately predicted, providing theoretical support for the development of autonomous obstacle avoidance technology for drones. This technology demonstrates broad application potential, particularly in multi-drone collaborative flight and high-dynamic, low-altitude flight environments.

[0207] Based on the above theoretical analysis, a conflict detection experiment was conducted between a UAV swarm and a randomly selected single UAV by treating the swarm as a whole.

[0208] The representative UAV cluster 1 and the randomly selected UAV 5 were selected to perform conflict detection by combining the improved speed barrier method with the Monte Carlo method, thereby verifying the effectiveness and reliability of the model in practical applications;

[0209] The position information of UAV 5 is accurately modeled and its center position is set is (10,10,-15), and the semi-axis lengths of each axis are and Speed 250km / h, horizontal deflection angle 30, vertical deflection angle is 10;

[0210] The motion state of the ellipsoid in three-dimensional space is simulated, and its interaction with the large ellipsoid surface is demonstrated through relative velocity analysis and Monte Carlo sampling techniques, such as Figure 10 As shown;

[0211] The results are as follows Figure 11 As shown, the Monte Carlo method is used to analyze the relative velocity vector and possible conflicts between cluster 1 and UAV 5. The direction of the relative velocity is calculated to be [0.67236685, -0.80233718, 7.74430205]. This direction vector represents the relative motion between cluster 1 and UAV 5. Based on this relative velocity direction, the Monte Carlo sampling method is further applied to analyze the relative position between the UAV and the cluster.

[0212] To analyze potential conflicts, the Monte Carlo method generated 50,000 sampling points, which were evenly distributed on the ellipsoid surface where UAV 5 was located. The distribution of the sampling points simulated possible encounter locations in space. Finally, by setting a distance tolerance threshold of 0.2, it was determined whether there was an intersection with the sampling points, that is, whether a conflict would occur.

[0213] The experimental results show that based on the direction of this relative speed, a conflict is eventually detected. This result means that under the given relative speed direction and sampling conditions, the relative motion of cluster 1 and drone 5 will cause the two to encounter each other, thus triggering a conflict;

[0214] Furthermore, the entire computation took 1.8459 seconds, which is relatively short for a computation involving 50,000 sampling points. This demonstrates the efficiency of the Monte Carlo method in handling such spatial encounter problems. Despite the large number of samples, computational time was effectively controlled thanks to efficient computational methods and parallel processing strategies.

[0215] Overall, the experiments demonstrate the effectiveness and feasibility of the Monte Carlo method in UAV conflict detection, and that it can quickly assess potential conflict risks under different conditions. This method provides a powerful tool for future conflict prediction and avoidance in multi-UAV systems, especially in path planning and obstacle avoidance in high-density and complex environments.

[0216] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A three-dimensional dynamic obstacle avoidance method for low-altitude UAV clusters based on multi-target perception, characterized by: The following steps are involved: S1: For static obstacles, the geometric shape of the static obstacle is abstracted into an obstacle ellipsoid model, and the drone protection zone is modeled as a protection zone ellipsoid model. The protection zone ellipsoid model is optimized with the drone safety buffer interval ratio and the drone cross-border conflict probability as dual objectives to determine the optimal safety buffer interval between the drone and the static obstacle, and obstacle avoidance is based on the optimal safety buffer interval; S2: For dynamic obstacles, the drones are clustered based on their parameters, including speed, heading, and optimal safety buffer interval. A three-dimensional optimized ellipsoid protection zone model, i.e., the cluster ellipsoid, is established for each cluster. The relative velocity vector between any drone and the cluster ellipsoid is calculated, and the parametric equation of the line containing the relative velocity vector is described. Multiple sampling is performed based on the Monte Carlo method, and conflict judgment is performed based on the intersection relationship between the obtained coordinate points and the parametric equation. If the two intersect, it is determined to be a potential conflict, and obstacle avoidance is based on potential conflicts.

2. The three-dimensional dynamic obstacle avoidance method for low-altitude UAV clusters based on multi-target perception according to claim 1 is characterized by: The specific steps of step S1 include: For static obstacles: Abstract the geometric shape of static obstacles into obstacle ellipsoid models; The drone protection zone is modeled as a protection zone ellipsoid model, where the major axis U x Coplanar with the velocity direction of the drone; Based on the obstacle ellipsoid model, the protection zone ellipsoid model is superimposed on the obstacle ellipsoid model as an extended part to establish the obstacle extended protection zone model; Based on the obstacle extension protection zone model, the optimal safety buffer interval for drones is constructed by taking the proportion of drone safety buffer interval and the probability of drone crossing the boundary conflict as a dual-objective optimization function. The expression of the drone safety buffer interval ratio function is: Where: f percentage The ratio of the safety buffer interval of the drone; are the lengths of the semi-axes of the geometric volume ellipsoid of the static obstacle; They are the safety buffer intervals in each axis direction of the UAV; The expression of the UAV cross-border conflict probability function is: Where: f conflict is the probability of UAV crossing the boundary conflict; P is the probability of position uncertainty conflict; is a 0-1 decision variable; The total number of all speed and acceleration value combinations; Where: are the lengths of the semi-axes of the extended protection zone of the obstacle; are the standard deviations of the positioning errors of the UAV in each axis direction; They are the safety buffer intervals in each axis direction of the UAV; are the random positioning errors of each axis of the UAV; Where: are the lengths of the semi-axes of the geometric volume ellipsoid of the static obstacle; They are the safety buffer intervals in each axis direction of the UAV; Where: They are the safety buffer intervals in each axis direction of the UAV; Where: d x , d y , d z The minimum braking distances of the drone in the x, y, and z axes respectively; Where: U x 、U y 、U z Axial component; are the components in each axis direction respectively; Where: is the speed; is the vertical deflection angle of the UAV; is the horizontal deflection angle of the UAV; Where: is the magnitude of acceleration; Where: m is the total number of slices in the velocity range; n is the total number of slices in the acceleration range; Optimal safety buffer interval obstacle avoidance based on UAV.

3. The three-dimensional dynamic obstacle avoidance method for low-altitude UAV clusters based on multi-target perception according to claim 2 is characterized by: In step S2, the specific steps of clustering to establish a three-dimensional optimized ellipsoid protection zone model include: The average value of the positions of all drones in the cluster is taken as the geometric center of the cluster, that is, the cluster centroid; The cluster centroid expression is: Where: is the coordinate of the centroid of the cluster ellipsoid; is the position coordinate of the UAV; n is the number of UAVs in the cluster; According to the combined velocity direction angle of the UAVs in the cluster, the rotation angle of the cluster protection zone is determined, including the horizontal deflection angle and the vertical deflection angle; The expression is: Where: is the resultant velocity vector of the cluster ellipsoid; They are Components in the x, y and z axes; are the x, y, and z axis components respectively; n is the number of drones in the cluster; Where: is the magnitude of the combined velocity of the cluster ellipsoid; is the speed of the drone; The expression of horizontal deflection angle is: Where: is the horizontal deflection angle of the cluster ellipsoid; and They are In the x- and y-axis directions; The vertical deflection angle expression is: Where: is the vertical deflection angle of the cluster ellipsoid; They are Components in the x, y and z axes; To minimize U x 、U y and U z The method of summing the lengths of the three directions of the axis to solve the centroid of the cluster ellipsoid along U x 、U y and U z Semi-axis length of the axis and To ensure that the semi-axis lengths of the cluster ellipsoid are all positive, three new optimization variables u, v, and w are introduced. They are directly related to the semi-axis lengths of the cluster ellipsoid and are guaranteed to be positive to meet the physical constraints of the model. The simplified optimization objective is defined as: Where: The constraints are defined as: Each ellipsoid is contained in the optimized cluster ellipsoid, that is, for each ellipsoid in the cluster, a point inside or on the boundary is randomly selected so that the point is translated and rotated from the global coordinates to the local coordinates and the result of the solution to the cluster ellipsoid equation is less than or equal to 1; Based on the cluster centroid and cluster ellipsoid centroid along U x 、U y and U z Semi-axis length of the axis and A three-dimensional optimized ellipsoid protection zone model of the UAV cluster, namely the cluster ellipsoid, is established.

4. The three-dimensional dynamic obstacle avoidance method for low-altitude UAV clusters based on multi-target perception according to claim 3 is characterized by: In step S2, the relative velocity vector expression between any UAV and the cluster ellipsoid is calculated as: Where: For drone cluster 1 and choose drone n The relative velocity vector.

5. The three-dimensional dynamic obstacle avoidance method for low-altitude UAV clusters based on multi-target perception according to claim 4 is characterized by: In step S2, the parametric equation describing the line on which the relative velocity vector lies is expressed as follows: Where: is the position coordinate of UAV n, and s is an arbitrary real value.

6. The three-dimensional dynamic obstacle avoidance method for low-altitude UAV clusters based on multi-target perception according to claim 5 is characterized by: In step S2, the specific steps of performing conflict judgment based on the obtained intersection relationship between the coordinate points and the parametric equation include: The Monte Carlo method is used to sample the cluster ellipsoid surface; Substitute the coordinates of the sampling point into the given parametric equation, calculate the corresponding parameter value for each coordinate component, and compare them. If the parameter values obtained by each coordinate component are consistent, it means that the point is on the trajectory of the straight line. Otherwise, the point is not on the straight line. At the same time, if the unit vector component of a certain coordinate direction is zero, check whether the coordinates of the point in this coordinate direction are consistent with the coordinates of the starting point. If they are consistent, the point can still be considered to be on the straight line. If the sampling point is located on the straight line described by the relative velocity vector, there is an intersection, which is determined to be a potential conflict.

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