Urban low altitude-oriented unmanned aerial vehicle three-dimensional dynamic obstacle avoidance method

Abstract

The invention discloses an unmanned aerial vehicle three-dimensional dynamic obstacle avoidance method for urban low altitude, and belongs to the technical field of unmanned aerial vehicle path planning, and the method comprises the following steps: S1, constructing a variable three-dimensional ellipsoid protection area model based on the characteristics of an unmanned aerial vehicle; s2, establishing a relative conflict area RCC and an absolute conflict area ACC; s3, segmenting the absolute conflict area ACC into a plurality of triangular sections, and carrying out conflict detection on the unmanned aerial vehicle through a Moller-Tembert-Ricker algorithm in combination with a dynamic characteristic limiting condition of the unmanned aerial vehicle; s4, solving the release speed and the release course of the unmanned aerial vehicle; according to the method, the three-dimensional ellipsoid protection area model is constructed based on dynamic characteristics such as position information, speed, acceleration and the like of the unmanned aerial vehicle to accurately reflect the motion state and space occupation of the unmanned aerial vehicle in the flight process, and a more accurate conflict detection and release strategy is realized by combining an improved speed obstacle method and a Moller-Tembert-Ricker algorithm, so that the conflict detection and release efficiency of the unmanned aerial vehicle is improved. The system is especially suitable for a complex flight environment in a low-altitude airspace.

Description

Technical Field

[0001] The present invention belongs to the technical field of unmanned aerial vehicle path planning, and particularly relates to a three-dimensional dynamic obstacle avoidance method for unmanned aerial vehicles facing urban low altitude. Background Art

[0002] An unmanned aerial vehicle refers to an unpiloted aircraft controlled by a radio remote control device and a self-contained program control device, and is widely used in the low altitude airspace.

[0003] The low altitude airspace has the characteristics of high airspace density and dynamic obstacles including buildings, other aircraft and meteorological factors. These characteristics make the unmanned aerial vehicle need to cope with more uncertainties and risks when performing tasks. Therefore, how to ensure flight safety in a complex and dynamically changing low altitude airspace environment, especially to effectively avoid obstacles and resolve conflicts, has become an important problem to be solved urgently in the field of unmanned aerial vehicles.

[0004] Traditional unmanned aerial vehicle obstacle avoidance methods generally rely on the velocity obstacle method. The velocity obstacle method depends on a two-dimensional circular protection area model based on geometric principles. It avoids collisions with obstacles by defining a safety interval for the aircraft, but the two-dimensional circular protection area model cannot accurately depict the dynamic behavior of unmanned aerial vehicles in three-dimensional space and cannot adapt to the dynamic obstacle avoidance of unmanned aerial vehicles with high density and multiple dynamically changing targets in the low altitude airspace environment.

[0005] In view of this, a three-dimensional dynamic obstacle avoidance method for unmanned aerial vehicles facing urban low altitude is designed to solve the above problems. Summary of the Invention

[0006] To solve the problems raised in the above background art, the present invention provides a three-dimensional dynamic obstacle avoidance method for unmanned aerial vehicles facing urban low altitude, which has the characteristics of being applicable to complex flight environments in low altitude airspace.

[0007] To achieve the above object, the present invention provides the following technical solution: A three-dimensional dynamic obstacle avoidance method for unmanned aerial vehicles facing urban low altitude, comprising the following steps:

[0008] S1: Collect and analyze the dynamic characteristics, pose information and position uncertainty of the unmanned aerial vehicle, and construct a three-dimensional ellipsoidal protection area model variable based on the characteristics of the unmanned aerial vehicle;

[0009] The expression of the three-dimensional ellipsoidal protection area model is:

[0010]

[0011] In the formula: represents the center coordinate of the unmanned aerial vehicle; R i represents the rotation matrix after the horizontal deflection angle and vertical deflection angle of the unmanned aerial vehicle are rotated, respectively represent the distances along U from the center of the ellipsoidx , U y and U z The semi - axis length of the U - axis;

[0012] S2: Based on the improved velocity obstacle method of the 3D ellipsoidal protection area model constructed by the unmanned aerial vehicle, establish the relative conflict area RCC and the absolute conflict area ACC;

[0013] The expression of the relative conflict area RCC is:

[0014]

[0015] In the formula: Represents the velocity vector of the unmanned aerial vehicle 1; Represents the 3D inflated ellipsoidal protection area of the unmanned aerial vehicle 2;

[0016] The expression of the absolute conflict area ACC is:

[0017]

[0018] In the formula: Represents the vector addition operation in the Minkowski space; Represents the velocity vector of the unmanned aerial vehicle 2;

[0019] S3: Divide the absolute conflict area ACC into multiple triangular sections, and combine with the UAV power characteristic limitation conditions to detect UAV conflicts through the Möller - Trumbore algorithm;

[0020] S4: Solve the UAV escape velocity and escape heading.

[0021] Furthermore, in the step S1, the specific construction steps of the 3D ellipsoidal protection area model include:

[0022] Taking the counter - clockwise direction as the positive direction, the rotation matrix expression of the horizontal deflection angle rotating around the Z - axis is:

[0023]

[0024] In the formula: Represents the horizontal deflection angle of the UAV;

[0025] Taking the counter - clockwise direction as the positive direction, the rotation matrix expression of the vertical deflection angle rotating around the Y - axis is:

[0026]

[0027] In the formula: Represents the vertical deflection angle of the UAV;

[0028] The integrated rotation matrix expression of the rotating horizontal deflection angle and the vertical deflection angle is:

[0029]

[0030] The semi - axis length expression of the ellipsoid center along the U x axis is:

[0031]

[0032] Where: represents the safety time interval; represents the velocity vector of the UAV;

[0033] The expression of the three - dimensional ellipsoid protection area model after deflection and translation is:

[0034]

[0035] Where: represents the UAV position coordinates; respectively represent the semi - axis lengths of the ellipsoid center along U x 、U y and U z axis;

[0036]

[0037] Where: respectively represent the semi - axis lengths of the expanded ellipsoid of the ellipsoid center along U x 、U y and U z axis.

[0038] Furthermore, in the step S2, the specific establishment steps of the relative conflict area RCC include:

[0039] Assume to establish the relative conflict area RCC of UAV 1 and UAV 2. The conflict recognition can be achieved by judging whether there is an intersection between the ray where the relative velocity of UAV 1 is located and the three - dimensional ellipsoid protection area of UAV 2. And the ray where the relative velocity of UAV 1 is located can be represented in the vector parameterization form, and the expression is:

[0040]

[0041] Where: represents the center coordinates of UAV 1; s represents any real value; represents the of UAV 1 and the relative velocity vector of UAV 2;

[0042] Substitute it into the three - dimensional ellipsoid protection area model and let After simplification, we get:

[0043]

[0044] In the formula: represents the central coordinates of the UAV 1; R i represents the rotation matrix after the horizontal and vertical deflection angles of the UAV rotation; respectively represent the semi - axis lengths along the U x 、U y and U z axes;

[0045] Expand the quadratic form, and the expression is:

[0046]

[0047] Define:

[0048]

[0049] Get the quadratic equation:

[0050] As 2 + Bs + C = 0

[0051] Solve the quadratic equation to determine whether there is an intersection with the ellipsoid. If there is an intersection, there is a conflict; otherwise, there is no conflict. The relative conflict area RCC is represented as the velocity vector of the UAV 1 and the three - dimensional inflated ellipsoid protection area of the UAV 2 intersection area. The set expression for judging the conflict is:

[0052]

[0053] In the formula: represents the velocity vector of the UAV 1; represents the three - dimensional inflated ellipsoid protection area of the UAV 2.

[0054] Furthermore, the specific establishment steps of the absolute conflict area ACC include:

[0055] Translate the relative conflict area RCC along the velocity direction of the UAV 2 by a distance to obtain the absolute conflict area ACC. The expression is:

[0056]

[0057] In the formula: represents the position point obtained by translation according to the per unit time; represents the central coordinates of the UAV 1; Denoted as the translation distance along the velocity direction of the unmanned aerial vehicle 2 relative to the relative conflict area RCC ;

[0058] Repeating the above steps gives:

[0059]

[0060] In the formula: Denoted as The ellipsoid obtained by translation per unit time ; Denoted as the three-dimensional inflated ellipsoid protection area of the unmanned aerial vehicle 2;

[0061] Then the expression of the absolute conflict area ACC is:

[0062]

[0063] In the formula: Denoted as the vector addition operation in the Minkowski space.

[0064] Furthermore, the specific steps of the step S3 include:

[0065] Performing inverse translation and inverse rotation on any point on the ellipsoid surface of the unmanned aerial vehicle 1 to convert the point to the standard coordinate system;

[0066]

[0067] In the formula: Denoted as any point on the surface of the three-dimensional ellipsoid protection area of the unmanned aerial vehicle 1; Denoted as the position coordinate of the unmanned aerial vehicle 2; Denoted as the global coordinate According to The translated coordinate;

[0068]

[0069] In the formula: Denoted as the horizontal deflection angle of the unmanned aerial vehicle 2; Denoted as the vertical deflection angle of the unmanned aerial vehicle 2;

[0070]

[0071] In the formula: Denoted as The coordinate after inverse rotation, that is, the coordinate of the standard coordinate system;

[0072] Calculating the gradient of the standard equation of the inflated ellipsoid of the unmanned aerial vehicle 2 to obtain the gradient vector of this point;

[0073]

[0074] In the formula: respectively represent the semi - major axis lengths of the inflation ellipsoid along the U x , U y and U z axes;

[0075] Rotate the gradient vector of this point back to the original coordinate system to obtain the rotated gradient vector;

[0076]

[0077] For each point on the ellipsoid surface of the UAV 1, calculate the vector from the vertex of the relative conflict area RCC to this point;

[0078]

[0079] In the formula: direction vector of; is represented as the coordinate of the center point of the UAV 1;

[0080] Check whether this vector is orthogonal to the gradient vector of the ellipsoid at this point;

[0081]

[0082] In the formula: (x 1 , y 1 , z 1 ) is represented as the coordinate of the UAV 1;

[0083] If the dot product of these two vectors is close to zero, it indicates that they are perpendicular, and all points that satisfy the orthogonal condition are the tangent points;

[0084] Summarize all points that satisfy the orthogonal condition as tangent points, and connect these tangent points to form a tangent circle;

[0085]

[0086] In the formula: is the tangent point that satisfies orthogonality in the point ;

[0087]

[0088] In the formula: ATC is the circle obtained by translating TC according to the translation per unit time; is represented as the velocity vector of the UAV 2;

[0089] This point forms a cone with the tangent circle. Consider the lateral surface Ls of the cone as a set of multiple triangles. Traverse the tangent points on the translated tangent circle, and combine the adjacent tangent points and the translated cone vertex to form the translated triangles.

[0090] Define the triangle Two side vectors of the plane where it is located Determine the plane where it is located;

[0091]

[0092] In the formula: Is expressed as according to the Triangle formed by translation per unit time; Is expressed as According to unit time Translated position point; Is expressed as Adjacent tangent point of;

[0093]

[0094] In the formula: Is expressed as According to the Translated tangent point per unit time;

[0095]

[0096] Calculate Cross product of to obtain a vector perpendicular to this plane

[0097]

[0098] In the formula: Is the velocity vector of UAV 1; × represents the cross product operation;

[0099] Calculate Dot product of

[0100]

[0101] If Then the ray is parallel to the plane of the triangle and has no intersection point. Otherwise, the ray intersects the plane of the triangle;

[0102] Through the scale factor Calculate the position information of the intersection point;

[0103]

[0104] Calculate the parameter

[0105]

[0106] Where: is expressed as any real value; · represents the dot product operation;

[0107]

[0108] If then the intersection point is inside the boundary of the triangle, otherwise, the ray has no intersection with the triangle;

[0109] Calculate the cross product of

[0110]

[0111] Calculate the parameter

[0112]

[0113] Where: is expressed as any real value;

[0114] If then the ray has an intersection with the triangle, otherwise, the ray has no intersection with the triangle; Calculate the distance from

[0115]

[0116] Where: is expressed as any real value;

[0117] Determine whether the intersection point is on the positive direction of the ray. If the intersection point is the velocity release point κ, otherwise, it does not meet the definition of the positive ray;

[0118]

[0119] Where κ represents the velocity release point of UAV 1.

[0120] Furthermore, the specific steps of the step S4 include:

[0121] The heading release includes the horizontal deflection angle release and the vertical deflection angle release. During the release process of the horizontal deflection angle, the vertical deflection angle is kept unchanged. The step size of the horizontal deflection angle increases gradually by 1°. After each increase, calculate the intersection point of the new velocity vector and the velocity obstacle cone, and measure the distance from the intersection point to the starting point. If the distance is equal to the length of the original velocity vector, it indicates that the release point of the horizontal deflection angle has been found while keeping the velocity magnitude unchanged The release process of the vertical deflection angle is similar.

[0122] Furthermore, in the step S4, the adjustment amount of the horizontal deflection angle is limited to not exceed 30°, and the adjustment amount of the vertical deflection angle is limited within ±10°, that is, the adjustment times of the horizontal deflection angle do not exceed 30 times, and the adjustment times of the vertical deflection angle do not exceed 10 times. If the intersection point cannot be solved, this method is abandoned for release.

[0123] Compared with the prior art, the beneficial effects of the present invention are:

[0124] The present invention constructs a three-dimensional ellipsoidal protection area model based on the dynamic characteristics such as the position information, speed, and acceleration of the unmanned aerial vehicle (UAV) to accurately reflect the motion state and space occupation of the UAV during flight. Combining the improved speed obstacle method and the Möller-Trumbore algorithm to achieve a more accurate conflict detection and release strategy, which is especially suitable for complex flight environments in low-altitude airspace. BRIEF DESCRIPTION OF THE DRAWINGS

[0125] Figure 1 is the flowchart of the method of the present invention;

[0126] Figure 2 is the three-dimensional ellipsoidal protection area model diagram of the UAV of the present invention;

[0127] Figure 3 is the relative conflict area RCC diagram of the present invention;

[0128] Figure 4 is the absolute conflict area ACC diagram of the present invention;

[0129] Figure 5 is the release speed and release course diagram of the present invention;

[0130] Figure 6 is the VO three-dimensional conflict detection diagram of the present invention;

[0131] Figure 7 is the three-group experimental motion simulation result diagram of the present invention;

[0132] Figure 8 is the velocity vector translation diagram of VO along the inflated protection area of the present invention;

[0133] Figure 9 is the implementation diagram of the Möller-Trumbore algorithm of the present invention;

[0134] Figure 10 is of the present invention VO model release verification diagram. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0135] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0136] Referring to the attached Figure 1 , the present invention provides the following technical solution: A three-dimensional dynamic obstacle avoidance method for drones facing low-altitude cities, including the following steps:

[0137] S1: Collect and analyze the power characteristics, pose information, and position uncertainty of the drone, and construct a three-dimensional ellipsoidal protection area model variable based on the drone characteristics;

[0138] The expression of the three-dimensional ellipsoidal protection area model is:

[0139]

[0140] In the formula: represents the center coordinates of the drone; R i represents the rotation matrix after the horizontal deflection angle and vertical deflection angle of the drone rotation, respectively represent the semi-axis lengths along the U x , U y and U z axes;

[0141] The derivation process of the three-dimensional ellipsoidal protection area model is as follows:

[0142] Taking the counterclockwise direction as the positive direction, the expression of the rotation matrix of the horizontal deflection angle rotating around the Z axis is:

[0143]

[0144] In the formula: represents the horizontal deflection angle of the drone;

[0145] Taking the counterclockwise direction as the positive direction, the expression of the rotation matrix of the vertical deflection angle rotating around the Y axis is:

[0146]

[0147] In the formula: represents the vertical deflection angle of the drone;

[0148] The integrated rotation matrix expression of the horizontal deflection angle and vertical deflection angle rotation is:

[0149]

[0150] The semi - axis length expression of the ellipsoid center along the U x axis is:

[0151]

[0152] Where: represents the safety time interval; represents the velocity vector of the UAV;

[0153] The expression of the three - dimensional ellipsoid protection area model after deflection and translation is:

[0154]

[0155] Where: represents the UAV position coordinates; respectively represent the semi - axis lengths of the ellipsoid center along U x , U y and U z axis;

[0156]

[0157] Where: respectively represent the semi - axis lengths of the expanded ellipsoid of the ellipsoid center along U x , U y and U z axis, see Appendix Figure 2 ;

[0158] S2: Based on the improved velocity obstacle method of the three - dimensional ellipsoid protection area model built by the UAV, establish the relative conflict area RCC and the absolute conflict area ACC;

[0159] The expression of the relative conflict area RCC is:

[0160]

[0161] Where: represents the velocity vector of UAV 1; represents the three - dimensional expanded ellipsoid protection area of UAV 2;

[0162] The expression of the absolute conflict area ACC is:

[0163]

[0164] Where: represents the vector addition operation in the Minkowski space; represents the velocity vector of UAV 2;

[0165] The derivation process of the relative conflict area RCC is as follows:

[0166] Suppose the relative conflict area RCC of UAV 1 and UAV 2 is established. Conflict identification can be achieved by determining whether there is an intersection between the ray where the relative velocity of UAV 1 is located and the three-dimensional ellipsoidal protection area of UAV 2. The ray where the relative velocity of UAV 1 is located can be represented in vector parametric form, and the expression is:

[0167]

[0168] In the formula: represents the central coordinate of UAV 1; s represents an arbitrary real value; represents of UAV 1 and the relative velocity vector of UAV 2;

[0169] Substitute it into the three-dimensional ellipsoidal protection area model and let After simplification, we get:

[0170]

[0171] In the formula: represents the central coordinate of UAV 1; R i represents the rotation matrix after the UAV rotates by the horizontal deflection angle and the vertical deflection angle; respectively represent the semi-axis lengths along U x , U y and U z axes;

[0172] Expand the quadratic form, and the expression is:

[0173]

[0174] Define:

[0175]

[0176]

[0177] Get the quadratic equation:

[0178] As 2 +Bs + C = 0

[0179] Solve this quadratic equation to determine whether there is an intersection with the ellipsoid. If there is an intersection, there is a conflict; otherwise, there is no conflict. The relative conflict area RCC is represented as the intersection area between the velocity vector of UAV 1 and the three-dimensional inflated ellipsoidal protection area of UAV 2. The set expression for judging the conflict is:

[0180]

[0181] In the formula: is expressed as the velocity vector of UAV 1; is expressed as the three-dimensional inflated ellipsoidal protection area of UAV 2; refer to the appendix Figure 3 ;

[0182] The derivation process of the absolute conflict area ACC is as follows:

[0183] From the relative conflict area RCC along the velocity of UAV 2 direction to translate the distance to obtain the absolute conflict area ACC, and the expression is:

[0184]

[0185] In the formula: is expressed as According to the position point obtained by translation per unit time; is expressed as the central coordinate of UAV 1; is expressed as the relative conflict area RCC along UAV 2 the velocity direction of translation distance;

[0186] Repeat the above steps to obtain:

[0187]

[0188] In the formula: is expressed as According to the ellipsoid obtained by translation per unit time; is expressed as the three-dimensional inflated ellipsoidal protection area of UAV 2;

[0189] Then the expression of the absolute conflict area ACC is:

[0190]

[0191] In the formula: is expressed as the vector addition operation in the Minkowski space, refer to the appendix Figure 4 ;

[0192] S3: Divide the absolute conflict area ACC into multiple triangular sections, and combine the UAV power characteristic limitation conditions to perform conflict detection on the UAV through the Möller-Trumbore algorithm;

[0193] For any point on the ellipsoid surface of UAV 1, perform inverse translation and inverse rotation to convert the point to the standard coordinate system;

[0194]

[0195] In the formula: Any point on the surface of the three-dimensional ellipsoidal protection area represented by the UAV 1; Denoted as the position coordinates of the UAV 2; Denoted as the global coordinates According to The translated coordinates;

[0196]

[0197] In the formula: Denoted as the horizontal deflection angle of the UAV 2; Denoted as the vertical deflection angle of the UAV 2;

[0198]

[0199] In the formula: Denoted as The coordinates after inverse rotation, that is, the coordinates in the standard coordinate system;

[0200] Calculate the gradient of the standard equation of the inflated ellipsoid of the UAV 2 to obtain the gradient vector at this point;

[0201]

[0202] In the formula: Respectively denoted as the semi-axes lengths of the inflated ellipsoid along the U x 、U y and U z axes of the ellipsoid center;

[0203] Rotate the gradient vector at this point back to the original coordinate system to obtain the rotated gradient vector;

[0204]

[0205] For each point on the ellipsoid surface of the UAV 1, calculate the vector from the vertex of the relative conflict area RCC to this point;

[0206]

[0207] In the formula: The direction vector of; Denoted as the center point coordinates of the UAV 1;

[0208] Check whether this vector is orthogonal to the gradient vector of the ellipsoid at this point;

[0209]

[0210] In the formula: (x 1 ,y 1 ,z 1 ) Denoted as the coordinates of the UAV 1;

[0211] If the dot product of the two vectors is close to zero, it means that they are perpendicular, and all points that satisfy the orthogonal condition are tangent points;

[0212] All points that meet the orthogonal condition are summarized as tangent points, and these tangent points are connected to form a tangent circle;

[0213]

[0214] Where: For point Satisfied orthogonal tangent points;

[0215]

[0216] Where: ATC is TC according to unit time The circle obtained by translation; Represented as the velocity vector of UAV 2;

[0217] This point and the tangent circle form a cone. The side surface Ls of the cone is regarded as a collection of multiple triangles. The tangent points on the translated tangent circle are traversed, and the translated triangles are formed by combining the adjacent tangent points and the translated cone vertices.

[0218] Defining the triangle The two side vectors of the plane Determine the plane on which it lies;

[0219]

[0220] Where: Expressed as per unit time The triangle formed by translation; Expressed as According to unit time The position point after translation; Expressed as The adjacent tangent points of

[0221]

[0222] Where: Expressed as According to the unit time Tangent point after translation;

[0223]

[0224] calculate The cross product of

[0225]

[0226] Wherein: is the velocity vector of the drone 1; × represents the cross product operation;

[0227] Calculate the dot product of

[0228]

[0229] If then the ray is parallel to the plane of the triangle and there is no intersection point. Otherwise, the ray intersects the triangle plane;

[0230] Through the scale factor calculate the position information of the intersection point;

[0231]

[0232] Calculate the parameter

[0233]

[0234] Wherein: represents an arbitrary real value;! represents the dot product operation;

[0235]

[0236] If then the intersection point is located inside the boundary of the triangle. Otherwise, the ray has no intersection point with the triangle;

[0237] Calculate the cross product of

[0238]

[0239] Calculate the parameter

[0240]

[0241] Wherein: represents an arbitrary real value;

[0242] If then the ray has an intersection point with the triangle. Otherwise, the ray has no intersection point with the triangle; Calculate the distance from

[0243]

[0244] Wherein: t represents an arbitrary real value;

[0245] Determine whether the intersection point is on the positive direction of the ray. If the intersection point is the speed release point κ of the UAV, otherwise, it does not meet the definition of the positive ray;

[0246]

[0247] In the formula: κ represents the speed release point of UAV 1;

[0248] S4: Solve the release speed and release heading of the UAV;

[0249] The heading release includes the release of the horizontal deflection angle and the release of the vertical deflection angle. During the release process of the horizontal deflection angle, the vertical deflection angle remains unchanged. The step size of the horizontal deflection angle increases gradually by 1°. After each increase, calculate the intersection point of the new velocity vector and the velocity obstacle cone, and measure the distance from the intersection point to the starting point. If the distance is equal to the length of the original velocity vector, it indicates that the release point of the horizontal deflection angle has been found while keeping the speed magnitude unchanged The release process of the vertical deflection angle is similar, refer to Appendix Figure 5 and 6 ;

[0250] The adjustment amount limit of the horizontal deflection angle is not more than 30°, and the adjustment amount limit of the vertical deflection angle is within ±10°, that is, the adjustment times of the horizontal deflection angle do not exceed 30 times, and the adjustment times of the vertical deflection angle do not exceed 10 times. If the intersection point cannot be solved, this method is abandoned for release, refer to Appendix Figure 5 .

[0251] Experimental verification

[0252] Randomly set the pose information of 6 large UAVs and divide them into three experimental groups, as shown in Table 1:

[0253]

[0254] Table 1: Pose information of 6 large UAVs

[0255] The experimental results are as shown in Appendix Figure 6 where (a) represents 3D conflict detection, (b) represents 3D conflict detection, (c) represents 3D conflict detection;

[0256] It can be seen from Appendix Figure 6 that the UAVs are in the relative velocity direction The rays on it all produced two intersection points with the ellipsoid surface. The specific positions of the intersection points in experimental group 1 were: [14.84, 23.44, 35.20], [15.55, 23.90, 34.33]. The specific positions of the intersection points in experimental group 2 were: [11.34, 22.15, 24.05], [11.64, 21.97, 22.89]. The specific positions of the intersection points in experimental group 3 were: [43.35, 16.79, 34.17], [43.00, 16.50, 32.94];

[0257] The results showed that the relative velocity vectors were all located within the relative conflict region RCC;

[0258] Taking experimental group 1 as an example, the vertex of VO and the ellipsoid The calculated tangent point coordinates are shown in Table 2:

[0259]

[0260] Table 2: The tangent point information after establishing the VO model

[0261] Further analyzing the flight state of the UAV, a dynamic simulation of the UAV movement with a time of 600 s and a step size of 0.01 was carried out. The results of its movement trajectory are as shown in the appendix Figure 7 shown, where (a) represents the movement simulation, (b) represents the movement simulation, (c) represents the movement simulation. During the simulation process, the conflict region was marked in red to show the dynamic changes of the VO model;

[0262] At the same time, in the appendix Figure 6 not only was the VO model constructed, but also through a visualization method, the position state of the UAV at the 264th second during the simulation movement was depicted to intuitively show the changes in the attitudes of each UAV during the flight process;

[0263] To verify that the relative velocity ray is located within the RCC region, it can be considered that a conflict occurs. In the experiment, the UAV and the inflated obstacle were regarded as sphere models, and the Euclidean distance between the two during the simulation movement was calculated. When there was an overlap between the two (i.e., the distance was zero), it was determined as a conflict. The experimental results are as shown in the appendix Figure 7 shown, where (d) represents the shortest straight-line interval between, (e) represents the shortest straight-line interval between, (f) represents the shortest straight-line interval between;

[0264] From the appendix Figure 7As shown, the earliest occurrence time of conflicts in Experimental Group 1 was 267.01 seconds, in Experimental Group 2 was 157.60 seconds, and in Experimental Group 3 was 260.19 seconds. The end time of conflicts in Experimental Group 1 was 282.14 seconds, in Experimental Group 2 was 171.83 seconds, and in Experimental Group 3 was 271.68 seconds;

[0265] This data further verifies the effectiveness of the constructed three-dimensional improved VO model and its applicability in the collision avoidance path planning of unmanned aerial vehicles, providing an important guarantee for refined aviation operation management. Especially under complex environments and dynamically changing flight conditions, it can accurately identify UAV conflicts and reduce flight risks;

[0266] To visually judge potential conflicts through the speed of the unmanned aerial vehicle itself, a translation operation is performed on the VO model. For the translated VO model, by judging whether the speed of the unmanned aerial vehicle is within the ACC area, it is determined whether a conflict occurs. The experimental results are as shown in the appendix Figure 8 shown, where (a) represents the translation of VO along the unit time translation, (b) represents the translation of VO along the unit time translation, and (c) represents the translation of VO along the unit time translation;

[0267] As can be seen from the appendix Figure 8 : When the speeds of the unmanned aerial vehicles are all within the ACC area, conflicts occur between the unmanned aerial vehicles in the three groups of experiments and the corresponding obstacles. This strategy provides an intuitive and effective conflict warning mechanism for whether the unmanned aerial vehicle enters the conflict area of other objects at the current speed; After obtaining the ACC area through the translation operation, directly focus on the relationship between the velocity vector of the unmanned aerial vehicle and the ACC area. Among them, the tangent point and the tangent circle have both been translated. To avoid the non-uniform distribution of the tangent points, the equidistant point-taking method is used to discretize the tangent circle, so as to ensure the uniform distribution of the point set. Then, connect the adjacent discrete points with the vertices of the translated VO to form multiple small triangles, and apply the Möller-Trumbore algorithm to solve the intersection points between the velocity vector and the triangles;

[0268] To verify the accuracy of this method in determining the intersection points formed by the ray in the direction of the velocity vector and the interior of the triangle, a verification experiment was carried out, as shown in the appendix

[0269] shown. In the experiment, the three vertices of the triangle were [0,0,0], [1,0,0], and [0,1,0], and the starting point of the ray was [1,0.9,1], and the direction vector was [-1,-1,-2]; Figure 9

[0270] ​The experimental results show that the algorithm can accurately identify the intersection point of the ray and the triangle, and the intersection point is located inside the triangle. Specifically, compared with the point [0.5, 0.4, 0], the intersection point of the ray and the triangle is accurately located. This result verifies the effectiveness and accuracy of the method;

[0271] Based on this verification, by means of a loop, the intersection points between the ray and each triangle can be solved, and the final UAV release strategy can be deduced according to the obtained intersection point positions;

[0272] The same method is used to solve the release strategy for each of the three groups of experiments, specifically including two strategies: speed release and yaw angle release. Since the VO model is solved based on a geometric method, the obtained strategy can be regarded as a boundary release strategy, that is, the release strategy with the minimum change amount;

[0273] In other words, the obtained release strategy defines the minimum release point. Outside this point range, all corresponding change amounts can ensure the release of the UAV. The final solution results are shown in Tables 3 and 4, demonstrating the specific situations where the UAV can just achieve release under this strategy:

[0274]

[0275] Table 3: UAV conflict speed release strategy

[0276]

[0277] Table 4: UAV conflict yaw angle (horizontal, vertical) release strategy

[0278] To verify the effectiveness of the release strategy, a detailed analysis is carried out on the conflict experiment of experimental group 2 in the calculation results of the release strategy ;

[0279] The improved VO model is verified by selecting a release airspeed of 197 km / h, a release horizontal yaw angle of -3°, and a release vertical course angle of -103°. The experimental results are as shown in the appendix Figure 10 where (a) represents the VO model of the release speed, (b) represents the VO model of the release horizontal deflection angle, and (c) represents the VO model of the release vertical deflection angle. Under each release strategy, the velocity vector of the UAV does not enter the ACC area, indicating that no collision conflicts occur between the UAVs under this strategy;

[0280] To further verify this conclusion, a simulation experiment lasting 600 seconds with a step size of 0.01 second is carried out. During this process, the movement trajectory of the UAV is represented by the dark blue line, and the inflated protection area of the obstacle UAV The movement trajectory is presented by the sky-blue line. If at the same moment, the particle does not penetrate inside the ellipsoid, it is considered that a conflict collision occurs between the UAVs. In addition, the conflict area is marked in red. The simulation results are as attached Figure 10 as shown. Among them, (d) represents the simulation movement of the release speed, (e) represents the simulation movement of the release horizontal deflection angle, and (f) represents the simulation movement of the release vertical deflection angle. No red area appears during the entire simulation process, indicating that the UAV trajectories do not overlap in space, thus verifying that no actual conflict occurs between the UAVs during the simulation;

[0281] To further analyze the distance change between the UAVs in the simulation, calculate the shortest distance between the particle and the expanded protection area. The results are as attached Figure 10 as shown. Among them, (g) represents the shortest interval between the UAVs under the simulation movement of the release speed, (h) represents the shortest interval between the UAVs under the simulation movement of the release horizontal deflection angle, and (i) represents the shortest interval between the UAVs under the simulation movement of the release vertical deflection angle. The shortest distance between the UAVs first decreases and then increases with time. The minimum distance is close to zero but never reaches zero, indicating that the UAVs successfully avoid the obstacles; when the shortest distance is close to zero, it means that at a certain moment, the two UAVs almost pass by each other; this result further verifies the effectiveness of the improved VO model in conflict resolution;

[0282] Based on the above analysis, confirm the effectiveness of the UAV conflict recognition system.

[0283] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A three-dimensional dynamic obstacle avoidance method for UAVs at low altitudes in cities, characterized in that: The following steps are involved: S1: Collect and analyze the UAV’s dynamic characteristics, posture information, and position uncertainty, and construct a three-dimensional ellipsoid protection zone model based on the variable characteristics of the UAV; The three-dimensional ellipsoid protection zone model expression is: Where: Expressed as the center coordinate of the drone; R i It is represented as the rotation matrix after the drone rotates the horizontal deflection angle and the vertical deflection angle. and They are respectively represented as the ellipsoid center along U x , U y and U z The semi-axis length of the axis; S2: Based on the three-dimensional ellipsoid protection area model constructed by UAV, the speed barrier method is improved to establish the relative conflict area RCC and the absolute conflict area ACC; The relative conflict area RCC expression is: Where: It is represented as the velocity vector of UAV 1; It is represented as the three-dimensional expanded ellipsoid protection zone of UAV 2; The absolute conflict area ACC is expressed as: Where: ⊕ represents the vector addition operation in Minkowski space; Represented as the velocity vector of UAV 2; S3: Divide the absolute conflict area ACC into multiple triangular sections, and use the Moller-Trumboreck algorithm to detect conflicts between drones in combination with the constraints of the drone's dynamic characteristics; S4: Solve the UAV release speed and release heading.

2. The three-dimensional dynamic obstacle avoidance method for a UAV at low altitude in a city according to claim 1, characterized in that: In step S1, the specific steps of constructing the three-dimensional ellipsoid protection zone model include: The rotation matrix expression of the horizontal deflection angle rotating around the Z axis with the counterclockwise direction as the positive direction is: Where: It is expressed as the horizontal deflection angle of the UAV; The rotation matrix expression of the vertical deflection angle rotating around the Y axis with the counterclockwise direction as the positive direction is: Where: Expressed as the vertical deflection angle of the drone; The integrated rotation matrix expression of the horizontal deflection angle and the vertical deflection angle is: The center of the ellipsoid is along U x The semi-axis length expression of the axis is: Where: It is indicated as a safety time interval; Represented as the velocity vector of the drone; The expression of the three-dimensional ellipsoid protection zone model after deflection and translation is: Where: Represented as drone position coordinates; and They are respectively represented as the ellipsoid center along U x , U y and U z The semi-axis length of the axis; Where: and They are respectively represented as the ellipsoid center along U x , U y and U z The length of the semi-axis of the expanded ellipsoid about the axis.

3. The three-dimensional dynamic obstacle avoidance method for a UAV at low altitude in a city according to claim 1, characterized in that: In step S2, the specific steps of establishing the relative conflict area RCC include: Assuming that the relative conflict area RCC of UAV 1 and UAV 2 is established, conflict identification can be achieved by judging whether there is an intersection between the ray where the relative speed of UAV 1 is located and the three-dimensional ellipsoid protection area of ​​UAV 2. The ray where the relative speed of UAV 1 is located can be expressed in vector parameterized form, and the expression is: Where: It is represented by the center coordinates of UAV 1; s is represented by any real value; Represented as drone 1 and Drone 2 The relative velocity vector of Substitute into the three-dimensional ellipsoid protection zone model and let Simplified: Where: Represented as the center coordinate of UAV 1; R i It is represented as the rotation matrix after the drone rotates the horizontal deflection angle and the vertical deflection angle; and They are respectively represented as the ellipsoid center along U x , U y and U z The semi-axis length of the axis; Expanding the quadratic form, the expression is: definition: We get the quadratic equation: As 2 +Bs+C=0 Solve the quadratic equation to determine whether there is an intersection with the ellipsoid. If there is an intersection, there is a conflict. Otherwise, there is no intersection. The relative conflict area RCC is expressed as the intersection of drone 1 and drone 2. The velocity vector and the three-dimensional expanded ellipsoid protection area of ​​UAV 2 The intersection area of ​​, the set expression for judging the conflict is: Where: It is represented as the velocity vector of UAV 1; Represented as a three-dimensional inflated ellipsoid protection zone for UAV 2.

4. The three-dimensional dynamic obstacle avoidance method for a UAV at low altitude in a city according to claim 1, characterized in that: The specific steps of establishing the absolute conflict area ACC include: The speed of UAV 2 along the relative conflict area RCC Direction translation distance The absolute conflict area ACC is obtained, and the expression is: Where: Expressed as According to the unit time The position point obtained by translation; It is expressed as the center coordinates of UAV 1; Relative conflict area RCC along the UAV 2 The translation distance in the velocity direction; Repeat the above steps to get: Where: Expressed as According to the unit time The ellipsoid obtained by translation; It is represented as the three-dimensional expanded ellipsoid protection zone of UAV 2; Then the absolute conflict area ACC is expressed as: Where: ⊕ represents the vector addition operation in Minkowski space.

5. The three-dimensional dynamic obstacle avoidance method for a UAV at low altitude in a city according to claim 1, characterized in that: The specific steps of step S3 include: Perform inverse translation and inverse rotation on any point on the ellipsoid surface of the drone 1, and transform the point into a standard coordinate system; Where: It is represented as any point on the surface of the three-dimensional ellipsoid protection zone of UAV 1; Represented as the position coordinates of UAV 2; Expressed as global coordinates according to Coordinates after translation; Where: It is expressed as the horizontal deflection angle of UAV 2; It is represented as the vertical deflection angle of UAV 2; Where: Expressed as The coordinates after inverse rotation are the coordinates of the standard coordinate system; Calculate the gradient of the standard equation of the expanded ellipsoid of drone 2 and obtain the gradient vector of the point; Where: and They are respectively represented as the ellipsoid center along U x , U y and U z The length of the expanded ellipsoid semi-axis of the axis; Rotate the gradient vector of the point back to the original coordinate system to obtain the rotated gradient vector; ▽F rotated =▽F original ·R2; For each point on the ellipsoid surface of UAV 1, calculate the vector from the vertex of the relative conflict region RCC to the point; Where: for arrive The direction vector of It is represented by the coordinates of the center point of UAV 1; Check whether this vector is orthogonal to the gradient vector of the ellipsoid at this point; Where: (x1, y1, z1) represents the coordinates of UAV 1; If the dot product of the two vectors is close to zero, it means that they are perpendicular, and all points that satisfy the orthogonal condition are tangent points; All points that meet the orthogonal condition are summarized as tangent points, and these tangent points are connected to form a tangent circle; Where: For point Satisfied and orthogonal tangent points; Where: ATC is TC according to unit time The circle obtained by translation; Represented as the velocity vector of UAV 2; This point and the tangent circle form a cone. The side surface Ls of the cone is regarded as a collection of multiple triangles. The tangent points on the translated tangent circle are traversed, and the translated triangles are formed by combining the adjacent tangent points and the translated cone vertices. Defining the triangle The two side vectors of the plane and Determine the plane on which it lies; Where: Expressed as per unit time The triangle formed by translation; Expressed as According to unit time The position point after translation; Expressed as The adjacent tangent points of Where: Expressed as According to the unit time Tangent point after translation; calculate and The cross product of Where: is the velocity vector of UAV 1; × represents the cross product operation; calculate and The dot product of like Then the ray is parallel to the plane where the triangle is located and there is no intersection. Otherwise, the ray intersects with the plane of the triangle; By scaling factor Calculate the position information of the intersection point; Calculation parameters Where: Represented as any real value; Represented as a dot product operation; like Then the intersection point is within the boundary of the triangle, otherwise, the ray has no intersection with the triangle; calculate and The cross product of Calculation parameters Where: is represented as any real value; like and If the ray intersects the triangle, then the ray and the triangle have an intersection point, otherwise, the ray and the triangle have no intersection point; calculate Distance to κ Where: is represented as any real value; Determine whether the intersection point is in the positive direction of the ray. If The intersection point is the velocity release point κ, otherwise, the definition of the forward ray is not satisfied; Where: κ represents the speed release point of UAV 1.

6. The three-dimensional dynamic obstacle avoidance method for a UAV at low altitude in a city according to claim 1, characterized in that: The specific steps of step S4 include: Heading release includes horizontal deflection angle release and vertical deflection angle release. The release process of horizontal deflection angle keeps the vertical deflection angle unchanged. The step size of horizontal deflection angle increases gradually by 1°. After each increase, the intersection of the new velocity vector and the velocity obstacle cone is calculated, and the distance from the intersection to the starting point is measured. If the distance is equal to the length of the original velocity vector, it means that the release point of the horizontal deflection angle has been found while keeping the velocity unchanged. and The release process of the vertical deflection angle is similar.

7. A three-dimensional dynamic obstacle avoidance method for a UAV at low altitude in a city according to claim 6, characterized in that: In step S4, the adjustment amount of the horizontal deflection angle is limited to no more than 30°, and the adjustment amount of the vertical deflection angle is limited to ±10°, that is, the number of adjustments of the horizontal deflection angle does not exceed 30 times, and the number of adjustments of the vertical deflection angle does not exceed 10 times. If the intersection point cannot be solved, the method is abandoned and released.

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