CN116486655B - Urban low-altitude unmanned aerial vehicle airway configuration design method - Google Patents
Urban low-altitude unmanned aerial vehicle airway configuration design method Download PDFInfo
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Abstract
The invention relates to the technical field of low-altitude unmanned aerial vehicle airway configuration design, and discloses a city low-altitude unmanned aerial vehicle airway configuration design method, which comprises the following steps: step 1: designing unmanned aerial vehicle route operation modes and rules based on the urban airspace structure and unmanned aerial vehicle flight performance elements; step 2: combining the differential operation characteristics of the unmanned aerial vehicle, and carrying out configuration analysis and parameter design of the navigation section and the intersection; step 3: establishing an unmanned aerial vehicle body coordinate system and a global coordinate system, and constructing an unmanned aerial vehicle kinematics model based on a track error; step 4: and establishing unmanned aerial vehicle route operation evaluation indexes from the two aspects of efficiency and safety, simulating unmanned aerial vehicle movement behaviors through simulation experiments, and identifying various intersection operation situations. The method for designing the path configuration of the urban low-altitude unmanned aerial vehicle is beneficial to designing the efficient and safe path configuration, standardizes the operation flow of the unmanned aerial vehicle, and provides method support for accelerating the unmanned aerial vehicle to be integrated into the urban airspace.
Description
Technical Field
The invention relates to the technical field of low-altitude unmanned aerial vehicle airway configuration design, in particular to a city low-altitude unmanned aerial vehicle airway configuration design method.
Background
The city unmanned aerial vehicle way belongs to a special airspace and is an air channel for bearing the transportation function. At present, urban air traffic management is still in a primary stage, and no sound route operation mechanism exists. If the unmanned aerial vehicle is in a free airspace without a course, the flight order tends to be chaotic due to lack of course constraint and guidance along with the expansion of the operation scale of the unmanned aerial vehicle, collision and even collision accidents are extremely easy to occur among the unmanned aerial vehicles, and the life and property safety of ground people is seriously threatened. In order to standardize unmanned aerial vehicle operation management, unmanned aerial vehicle navigation configuration design is needed to ensure stable and orderly operation of various unmanned aerial vehicles.
In the prior art, conceptual design is carried out aiming at the microstructure of the air way, and the influence of the urban airspace structure and the unmanned aerial vehicle performance characteristics on the air way design is less considered for the defect of specific connotation research of operation modes, structural parameters and the like.
Disclosure of Invention
The invention aims to provide a method for designing the path configuration of an urban low-altitude unmanned aerial vehicle, which solves the problems in the background technology.
In order to achieve the above purpose, the invention provides a method for designing the path configuration of an urban low-altitude unmanned aerial vehicle, which comprises the following steps:
step 1: designing unmanned aerial vehicle route operation modes and rules based on the urban airspace structure and unmanned aerial vehicle flight performance elements;
step 2: combining the differential operation characteristics of the unmanned aerial vehicle, and carrying out configuration analysis and parameter design of the navigation section and the intersection;
step 3: establishing an unmanned aerial vehicle body coordinate system and a global coordinate system, and constructing an unmanned aerial vehicle kinematics model based on a track error;
step 4: and establishing unmanned aerial vehicle route operation evaluation indexes from the two aspects of efficiency and safety, simulating unmanned aerial vehicle movement behaviors through simulation experiments, and identifying various intersection operation situations.
Preferably, in the first step, a hierarchical airspace strategy is adopted to disperse the airspace into a plurality of horizontal height layers;
dividing the route into an east route and a west route according to the route angle by taking the north of the local warp as a reference, wherein each route height layer follows a unidirectional operation mode, and the operation directions of adjacent height layers are opposite;
and combining the vertical take-off and landing performance of the unmanned aerial vehicle, executing a take-off program at a take-off and landing field of a departure node by the unmanned aerial vehicle, entering a route after the unmanned aerial vehicle is vertically lifted to a designated height, and executing a landing program to vertically descend to the take-off and landing field when the unmanned aerial vehicle reaches an airspace near a destination node.
Preferably, in the second step, a spherical protection area is designed according to an unmanned aerial vehicle mechanism, and a cylindrical pipeline navigation section with a buffer area is designed by combining flight errors caused by attitude change and navigation positioning factors of the unmanned aerial vehicle;
designing a road-along type intersection and a roundabout type intersection, and setting the turning radius of the intersection according to the performance and the operation requirement of the unmanned aerial vehicle;
for the along-road type intersection, the unmanned aerial vehicle flies along the air path, and changes the course or keeps straight when arriving at the along-road type intersection, and the air path angles of the two air paths are respectively alpha 1 ,α 2 The included angle of the navigation path is tau= |alpha 1 -α 2 When the included angle of the air route is not more than the maximum turning angle tau of the unmanned aerial vehicle max When the unmanned aerial vehicle turns, unmanned aerial vehicle atress equilibrium equation is:
wherein F is rotor wing lift force, phi is unmanned plane roll angle, m is unmanned plane mass, v is unmanned plane speed, r is turning radius, g is gravitational acceleration;
deducing the minimum turning radius r of the unmanned aerial vehicle from the stress balance equation of the unmanned aerial vehicle min ：
Wherein phi is max The maximum roll angle of the unmanned aerial vehicle is set;
setting the unmanned aerial vehicle to execute turning operation in the road crossing area, wherein the unmanned aerial vehicle has a maximum turning radius r max The course turning radius satisfies:
r min ＜r＜r max
for a rotary island type intersection, an unmanned aerial vehicle flies anticlockwise along a central island after entering the rotary island, the minimum safety interval requirement is met between the channels connected with the rotary island, and the minimum intersection angle eta corresponding to the adjacent channels is met min The method comprises the following steps:
wherein S is min The minimum safety interval of the unmanned aerial vehicle is set, and R is the radius of the rotary island; the vertical navigation path is positioned at the center of the rotary island，R≥S lat The unmanned aerial vehicle is safe to operate;
according to the way intersection mode of the rotary island connection, the minimum rotary island radius has two calculation methods:
calculation method 1, wherein the routes connected with the rotary island are uniformly distributed along the circle center, the included angles between the adjacent routes are equal, the number of the maximum routes contained in the rotary island is n, and the corresponding minimum rotary island radius R is the same as the maximum number of the routes contained in the rotary island min The method comprises the following steps:
calculation method 2, wherein the rotary island is connected with n routes, extension lines of all routes are not intersected at the same point, and included angles between adjacent routes are respectively tau 1 ,τ 2 ,...,τ (n-1) Minimum roundabout radius R' min The method comprises the following steps:
based on the above analysis, the roundabout radius satisfies:
R≥max(r min ,R min ,R′ min )。
preferably, in the third step, the unmanned aerial vehicle positioning is performed by adopting a machine body coordinate system and a global coordinate system, and thenFor the position vector of the unmanned aerial vehicle in the global coordinate system,/->The position error vector of the unmanned aerial vehicle in the machine body coordinate system at the moment is represented as the position l of the unmanned aerial vehicle in the global coordinate system:
wherein R represents a rotation matrix;
assuming that the three directions of the unmanned aerial vehicle track error in the machine body coordinate system are mutually independent, thenRepresenting that the variable obeys normal distribution with expected 0 and variance Λ, taking the spherical center of the unmanned aerial vehicle protection area as a particle, and at the moment t, passing delta t time, the unmanned aerial vehicle position vector is expressed as:
wherein v is a velocity vector of the unmanned aerial vehicle in the global coordinate system.
Preferably, in the fourth step, three indexes of intersection passing rate, passing time and collision probability are adopted to evaluate the unmanned aerial vehicle route running situation from the two aspects of efficiency and safety:
the crossing passing rate is the ratio of the crossing traffic to the total departure unmanned aerial vehicle frame times, n unmanned aerial vehicles are planned to pass through the crossing in unit time, and the crossing passing rate C uav Expressed as:
wherein m is the number of routes connected at the intersection, f ijk Is a variable of 0-1, f ijk =1 denotes the flight of the kth unmanned aerial vehicle from the i-way to the j-way via the intersection, f ijk =0 means that the drone is not flying into the intersection or waiting at the intersection;
the traffic time of the intersection is the total traffic time of all unmanned aerial vehicles passing through the intersection, and the unmanned aerial vehicles passing through the intersection in unit time are gathered intoAll unmanned aerial vehicle intersection transit time W uav Expressed as:
wherein Δt is ijk Is thatThe unmanned plane passes through the intersection time of the i and j routes;
the collision probability is the possibility that two unmanned aerial vehicles collide on the route, and two unmanned aerial vehicles k f And (3) withThrough the same intersection successively, at the time t, the unmanned aerial vehicles have mutually independent track errors in the longitudinal direction, the lateral direction and the vertical direction, and the collision probability between two unmanned aerial vehicles is regarded as the product of three direction collision probabilities, which is:
wherein,d is the distance between the centers of the two unmanned aerial vehicle protection areas x ,D y ,D z The safety intervals along the x, y and z axes between the two unmanned aerial vehicles are respectively set;
for coordinate axis x, the probability of collision risk for two unmanned aerial vehicles is:
wherein sigma 1x ,σ 2x The standard deviation, mu, of the track errors of two unmanned aerial vehicles in a global coordinate system 1x ,μ 2x The method is a method for calculating collision probability of two unmanned aerial vehicles along y and z axes and a method along a coordinate axis x, wherein the collision probability is respectively the average value of flight path errors of the two unmanned aerial vehicles in a global coordinate system.
Therefore, the method for designing the urban low-altitude unmanned aerial vehicle route configuration has the following beneficial effects:
according to the method, the urban airspace structure and the unmanned aerial vehicle performance are comprehensively considered, configuration and parameter design is carried out from the microscopic angle of the urban low-altitude unmanned aerial vehicle airway, an unmanned aerial vehicle kinematic model based on a flight path error is established to describe unmanned aerial vehicle behaviors, and the unmanned aerial vehicle airway operation situation is evaluated from the two aspects of efficiency and safety through three indexes of intersection passing rate, passing time and collision probability. The method provided by the invention is used for analyzing and designing parameters of the unmanned aerial vehicle road configuration, is beneficial to improving the operation safety and efficiency of the unmanned aerial vehicle, and provides technical support for the unmanned aerial vehicle road configuration design. The method is beneficial to designing efficient and safe urban routes, standardizes the operation flow of the large-scale unmanned aerial vehicle, and has important significance for accelerating the integration of the unmanned aerial vehicle into the urban airspace.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a flow chart showing an implementation of a method for designing a path configuration of an urban low-altitude unmanned aerial vehicle;
FIG. 2 is a schematic view of a spherical protection zone of the unmanned aerial vehicle according to the present invention;
FIG. 3 is a schematic view of a low-altitude unmanned aerial vehicle in a city;
fig. 4 is a schematic diagram of the operation simulation of the unmanned aerial vehicle of the present invention.
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs. The terms "first," "second," and the like, as used herein, do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. The word "comprising" or "comprises", and the like, means that elements or items preceding the word are included in the element or item listed after the word and equivalents thereof, but does not exclude other elements or items. The terms "disposed," "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. "upper", "lower", "left", "right", etc. are used merely to indicate relative positional relationships, which may also be changed when the absolute position of the object to be described is changed.
Examples
As shown in fig. 1-4, the method for designing the path configuration of the low-altitude unmanned aerial vehicle in the city comprises the following steps:
step 1: based on factors such as urban airspace structure, unmanned aerial vehicle performance, etc., unmanned aerial vehicle airway operation modes and rules are designed.
The method comprises the following steps: adopting a layering airspace strategy to disperse the urban airspace into a plurality of horizontal altitude layers, wherein the distance between the altitude layers meets the minimum safety interval of the unmanned aerial vehicle in the vertical direction, and the unmanned aerial vehicle generally does not involve altitude change when in operation on a navigation path;
dividing the route into an eastern route and a western route according to the route angle by taking the north of the local warp as a reference, wherein the route is deviated to the eastern route by 0-180 degrees (excluding 180 degrees), the route is deviated to the eastern route by 180-360 degrees (excluding 360 degrees), the route is deviated to the eastern route, each height layer follows a unidirectional operation mode, and the operation directions of the adjacent height layers are opposite;
the unmanned aerial vehicle executes a take-off program at a departure node vertical take-off and landing field, enters a route after ascending to a specified height, starts to execute a transportation task according to a set flight plan, can execute vertical lifting operation at a crossing node to change a height layer of the route if special conditions occur when the unmanned aerial vehicle horizontally flies on the route, vertically descends to a take-off and landing field terminal area when reaching an airspace near a target node, and executes a landing program to reach the take-off and landing field to finish the task.
Step 2: and taking the differential operation characteristics of the unmanned aerial vehicle into consideration, and carrying out configuration analysis and parameter design of the navigation section and the intersection.
The method comprises the following steps: the unmanned aerial vehicle protection zone is the physical space that uses unmanned aerial vehicle as the center to contain certain region around, adopts unmanned aerial vehicle organism cylindrical minimum outer ball as unmanned aerial vehicle protection zone, can better hold unmanned aerial vehicle roll or every single move motion action, and protection zone size depends on unmanned aerial vehicle technical parameter, if unmanned aerial vehicle horizontal maximum size is D, and unmanned aerial vehicle height is h, then spherical protection zone diameter D is:
based on the spherical protection zone of the unmanned aerial vehicle, the cylindrical pipeline navigation section is designed, the flight error of the unmanned aerial vehicle caused by factors such as posture change and navigation positioning is considered, the navigation section is provided with a buffer zone on the basis of completely accommodating the unmanned aerial vehicle protection zone, the unmanned aerial vehicle flies along a central line in a single navigation section, and can still be positioned in the boundary of the navigation section when the unmanned aerial vehicle is slightly disturbed, and the section diameter is as follows:
D leg ＝D+2b
wherein b is the buffer distance;
designing a road-along type intersection and a roundabout type intersection, and setting the turning radius of the intersection according to the performance and the operation requirement of the unmanned aerial vehicle;
for the along-the-way intersection, the unmanned aerial vehicle flies along the air way, the course is changed or kept straight when the unmanned aerial vehicle arrives at the intersection, and if the air way angles of the two air ways are alpha respectively 1 ,α 2 Then the course included angle τ= |α 1 -α 2 When the included angle of the air way is not more than the maximum turning angle tau of the unmanned aerial vehicle due to the performance limitation of the unmanned aerial vehicle max When, unmanned aerial vehicle just can turn, unmanned aerial vehicle atress equilibrium equation is this moment:
wherein F is rotor wing lift force, phi is unmanned plane roll angle, m is unmanned plane mass, v is unmanned plane speed, r is turning radius, g is gravitational acceleration;
the minimum turning radius r of the unmanned aerial vehicle can be deduced by the stress balance equation of the unmanned aerial vehicle min ：
Wherein phi is max The maximum roll angle of the unmanned aerial vehicle is set;
setting that the unmanned aerial vehicle can only execute turning operation in the road crossing area, wherein the unmanned aerial vehicle has the maximum turning radius, and if the road width is w, the length d of the road crossing part is as follows:
maximum turning radius r of unmanned aerial vehicle max The method comprises the following steps:
the turning radius of the navigation path needs to satisfy:
r min ＜r＜r max
for a rotary island type intersection, an unmanned aerial vehicle flies anticlockwise along a central island after entering the rotary island, the minimum safety interval requirement needs to be met between the channels connected with the rotary island, and the minimum intersection angle eta corresponding to the adjacent channels is required to be met min The method comprises the following steps:
wherein S is min And R is the radius of the rotary island for the minimum safety interval of the unmanned aerial vehicle. The vertical navigation path is positioned at the center of the rotary island, and R is more than or equal to S in order to ensure the operation safety of the unmanned aerial vehicle lat ；
According to the way intersection mode of the rotary island connection, the minimum rotary island radius has two calculation methods:
case 1: the routes connected by the rotary island are uniformly distributed along the circle center, namely the included angles between the adjacent routes are equal, if the maximum number of routes contained by the rotary island is n, the corresponding minimum rotary island radius R min The method comprises the following steps:
case 2: the rotary island is connected with n routes, and all the route extension lines are not intersected at the same point, if the included angles between the adjacent routes are respectively tau 1 ,τ 2 ,...,τ (n-1) The minimum roundabout radius R' min The method comprises the following steps:
based on the above analysis, the roundabout radius needs to satisfy:
R≥max(r min ,R min ,R′ min )
step 3: and establishing an unmanned aerial vehicle body coordinate system and a global coordinate system, and constructing an unmanned aerial vehicle kinematics model based on the flight path error.
The method comprises the following steps: unmanned aerial vehicle positioning is carried out by adopting a machine body coordinate system and a global coordinate system, and is provided withFor the position vector of the unmanned aerial vehicle in the global coordinate system,/->For the position error vector of the unmanned aerial vehicle in the body coordinate system, the position l of the unmanned aerial vehicle in the global coordinate system at the moment can be expressed as:
wherein, R represents a rotation matrix used for transforming the machine body coordinate system into a global coordinate system;
according to the attitude parameters of the unmanned aerial vehicle, a rotation matrix from the body coordinate system to the global coordinate system can be obtained as follows:
wherein θ is the course angle of the unmanned aerial vehicle, the left bias of the machine body relative to the x-axis of the machine body coordinate system is positive, the right bias is negative,the pitch angle of the unmanned aerial vehicle is positive when the airframe is upward tilted relative to a y axis of the airframe coordinate system, and is negative when the airframe is downward tilted;
assuming that the three directions of the unmanned aerial vehicle track error in the machine body coordinate system are mutually independent, thenRepresenting a normal distribution of the variable obeying a variance Λ, where +.>The variances of the track errors on the x, y and z axes of the machine body coordinate system are respectively;
in order to describe the motion characteristics of the unmanned aerial vehicle relative to the ground, the spherical center of the unmanned aerial vehicle protection area is regarded as a mass point, and at the time t, the position vector of the unmanned aerial vehicle can be expressed as:
wherein v is a velocity vector of the unmanned aerial vehicle in the global coordinate system.
Step 4: and establishing an unmanned aerial vehicle body coordinate system and a global coordinate system, and constructing an unmanned aerial vehicle kinematics model based on the flight path error.
Three indexes of intersection passing rate, passing time and collision probability are adopted to evaluate the unmanned aerial vehicle route running situation from the two aspects of efficiency and safety:
(1) Crossing passing rate: the method is defined as the ratio of the traffic of the intersection to the total number of the unmanned aerial vehicle frames, and if n unmanned aerial vehicles are planned to pass through the intersection in unit time, the intersection passing rate C uav Can be expressed as:
wherein m is the number of routes connected at the intersection, f ijk Is a variable of 0-1, f ijk =1 denotes the flight of the kth unmanned aerial vehicle from the i-way to the j-way via the intersection, f ijk =0 means that the drone is not flying into the intersection or waiting at the intersection;
(2) Intersection transit time: defining the total passing time of all unmanned aerial vehicles passing through the intersection, if the unmanned aerial vehicle passing through the intersection in unit time is set asThen the transit time W of all unmanned aerial vehicle intersections uav Can be expressed as:
wherein Δt is ijk Is thatThe unmanned plane passes through the intersection time of the i and j routes;
(3) Probability of collision: defined as the possibility of collision of two unmanned aerial vehicles on the way, if two unmanned aerial vehicles k f And (3) withAt the time t, as the unmanned aerial vehicles have mutually independent track errors in the longitudinal direction, the lateral direction and the vertical direction, the collision probability between two unmanned aerial vehicles can be regarded as the product of three direction collision probabilities at the moment through the same intersection, namely:
wherein,d is the distance between the centers of the two unmanned aerial vehicle protection areas x ,D y ,D z The safety intervals along the x, y and z axes between the two unmanned aerial vehicles are respectively set;
for coordinate axis x, the probability of collision risk for two unmanned aerial vehicles is:
wherein sigma 1x ,σ 2x The standard deviation, mu, of the track errors of two unmanned aerial vehicles in a global coordinate system 1x ,μ 2x The method is the same as the calculation method of the collision probability of the unmanned aerial vehicles along the y and z axes respectively for the average value of the flight path errors of the two unmanned aerial vehicles in the global coordinate system.
Therefore, the method for designing the urban low-altitude unmanned aerial vehicle route configuration comprehensively considers the urban airspace structure and the unmanned aerial vehicle performance, designs the configuration and parameters from the microscopic angle of the urban low-altitude unmanned aerial vehicle route, establishes an unmanned aerial vehicle kinematic model based on the flight path error to describe unmanned aerial vehicle behaviors, evaluates the unmanned aerial vehicle route operation situation from the two aspects of efficiency and safety through three indexes of intersection passing rate, passing time and collision probability, and provides method support for accelerating the unmanned aerial vehicle to be integrated into the urban airspace.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (1)
1. A method for designing a city low-altitude unmanned aerial vehicle route configuration is characterized by comprising the following steps: the method comprises the following steps:
step 1: designing unmanned aerial vehicle route operation modes and rules based on the urban airspace structure and unmanned aerial vehicle flight performance elements;
step 2: combining the differential operation characteristics of the unmanned aerial vehicle, and carrying out configuration analysis and parameter design of the navigation section and the intersection;
step 3: establishing an unmanned aerial vehicle body coordinate system and a global coordinate system, and constructing an unmanned aerial vehicle kinematics model based on a track error;
step 4: establishing unmanned aerial vehicle route operation evaluation indexes from two aspects of efficiency and safety, simulating unmanned aerial vehicle movement behaviors through simulation experiments, and identifying various intersection operation situations;
step one, adopting a layering airspace strategy to disperse an airspace into a plurality of horizontal height layers;
dividing the route into an east route and a west route according to the route angle by taking the north of the local warp as a reference, wherein each route height layer follows a unidirectional operation mode, and the operation directions of adjacent height layers are opposite;
combining the vertical take-off and landing performance of the unmanned aerial vehicle, executing a take-off program at a take-off and landing field of a departure node by the unmanned aerial vehicle, entering a route after the unmanned aerial vehicle vertically rises to a designated height, and executing a landing program to vertically descend to the take-off and landing field when the unmanned aerial vehicle reaches an airspace near a destination node;
designing a spherical protection area according to an unmanned mechanism, and designing a cylindrical pipeline navigation section with a buffer area by combining flight errors of the unmanned aerial vehicle caused by posture change and navigation positioning factors;
designing a road-along type intersection and a roundabout type intersection, and setting the turning radius of the intersection according to the performance and the operation requirement of the unmanned aerial vehicle;
for the along-road type intersection, the unmanned aerial vehicle flies along the air path, and changes the course or keeps straight when arriving at the along-road type intersection, and the air path angles of the two air paths are respectively alpha 1 ,α 2 The included angle of the navigation path is tau= |alpha 1 -α 2 When the included angle of the air route is not more than the maximum turning angle tau of the unmanned aerial vehicle max When the unmanned aerial vehicle turns, unmanned aerial vehicle atress equilibrium equation is:
wherein F is rotor wing lift force, phi is unmanned plane roll angle, m is unmanned plane mass, v is unmanned plane speed, r is turning radius, g is gravitational acceleration;
deducing the minimum turning radius r of the unmanned aerial vehicle from the stress balance equation of the unmanned aerial vehicle min ：
Wherein phi is max The maximum roll angle of the unmanned aerial vehicle is set;
setting the unmanned aerial vehicle to execute turning operation in the road crossing area, wherein the unmanned aerial vehicle has a maximum turning radius r max The course turning radius satisfies:
r min ＜r＜r max
for a rotary island type intersection, an unmanned aerial vehicle flies anticlockwise along a central island after entering the rotary island, the minimum safety interval requirement is met between the channels connected with the rotary island, and the minimum intersection angle eta corresponding to the adjacent channels is met min The method comprises the following steps:
wherein S is min The minimum safety interval of the unmanned aerial vehicle is set, and R is the radius of the rotary island; the vertical navigation path is positioned at the center of the rotary island, R is more than or equal to S lat The unmanned aerial vehicle is safe to operate;
according to the way intersection mode of the rotary island connection, the minimum rotary island radius has two calculation methods:
calculation method 1, wherein the routes connected with the rotary island are uniformly distributed along the circle center, the included angles between the adjacent routes are equal, the number of the maximum routes contained in the rotary island is n, and the corresponding minimum rotary island radius R is the same as the maximum number of the routes contained in the rotary island min The method comprises the following steps:
computing method 2, rotary islandConnect n routes, and all route extension lines do not intersect at the same point, and the included angles between adjacent routes are τ 1 ,τ 2 ,…,τ (n-1) Minimum roundabout radius R' min The method comprises the following steps:
based on the above analysis, the roundabout radius satisfies:
R≥max(r min ,R min ,R′ min )
in the third step, the unmanned aerial vehicle is positioned by adopting a machine body coordinate system and a global coordinate system, and thenFor the position vector of the unmanned aerial vehicle in the global coordinate system,/->The position error vector of the unmanned aerial vehicle in the machine body coordinate system at the moment is represented as the position l of the unmanned aerial vehicle in the global coordinate system:
wherein R represents a rotation matrix;
assuming that the three directions of the unmanned aerial vehicle track error in the machine body coordinate system are mutually independent, thenRepresenting that the variable obeys normal distribution with expected 0 and variance Λ, taking the spherical center of the unmanned aerial vehicle protection area as a particle, and at the moment t, passing delta t time, the unmanned aerial vehicle position vector is expressed as:
wherein v is a velocity vector of the unmanned aerial vehicle in a global coordinate system;
in the fourth step, three indexes of intersection passing rate, passing time and collision probability are adopted to evaluate the unmanned aerial vehicle route running situation from the two aspects of efficiency and safety:
the crossing passing rate is the ratio of the crossing traffic to the total departure unmanned aerial vehicle frame times, n unmanned aerial vehicles are planned to pass through the crossing in unit time, and the crossing passing rate C uav Expressed as:
wherein m is the number of routes connected at the intersection, f ijk Is a variable of 0-1, f ijk =1 denotes the flight of the kth unmanned aerial vehicle from the i-way to the j-way via the intersection, f ijk =0 means that the drone is not flying into the intersection or waiting at the intersection;
the traffic time of the intersection is the total traffic time of all unmanned aerial vehicles passing through the intersection, and the unmanned aerial vehicles passing through the intersection in unit time are gathered intoAll unmanned aerial vehicle intersection transit time W uav Expressed as:
wherein Δt is ijk Is thatThe unmanned plane passes through the intersection time of the i and j routes;
the collision probability is the possibility that two unmanned aerial vehicles collide on the route, and two unmanned aerial vehicles k f And (3) withThrough the same intersection successively, at the time t, the unmanned aerial vehicles have mutually independent track errors in the longitudinal direction, the lateral direction and the vertical direction, and the collision probability between two unmanned aerial vehicles is regarded as the product of three direction collision probabilities, which is:
wherein,d is the distance between the centers of the two unmanned aerial vehicle protection areas x ,D y ,D z The safety intervals along the x, y and z axes between the two unmanned aerial vehicles are respectively set;
for coordinate axis x, the probability of collision risk for two unmanned aerial vehicles is:
wherein sigma 1x ,σ 2x The standard deviation, mu, of the track errors of two unmanned aerial vehicles in a global coordinate system 1x ,μ 2x The method is a method for calculating collision probability of two unmanned aerial vehicles along y and z axes and a method along a coordinate axis x, wherein the collision probability is respectively the average value of flight path errors of the two unmanned aerial vehicles in a global coordinate system.
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