CN111192481A - Method for determining boundary of unmanned aerial vehicle control area of approach and departure procedure based on collision risk - Google Patents

Method for determining boundary of unmanned aerial vehicle control area of approach and departure procedure based on collision risk Download PDF

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CN111192481A
CN111192481A CN201911307351.6A CN201911307351A CN111192481A CN 111192481 A CN111192481 A CN 111192481A CN 201911307351 A CN201911307351 A CN 201911307351A CN 111192481 A CN111192481 A CN 111192481A
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邹翔
张建平
谢方泉
吴卿刚
陈振玲
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Second Research Institute of CAAC
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Abstract

The invention provides a method for determining the boundary of an unmanned aerial vehicle control area in a runway area under an airport runway entering and leaving program based on collision risks, which comprises the following steps: s1 operating data and collision risk probability e according to the runway departure and arrival program, and flight section curve
Figure DDA0002322522930000011
s∈[0，s1]Establishing a boundary planning model of a control area; s2, setting an iteration termination threshold value according to a management and control area boundary planning model, and solving a flight curve through an iteration solving method
Figure DDA0002322522930000012
Arc length parameter s1The solution is approximated. The invention adopts the method to divide the unmanned plane control area of the runway area so as to ensure that under the premise of not influencing the running safety and efficiency of civil aircrafts,the realization is established to accurate drawing in civilian unmanned aerial vehicle management and control district, provides technical support for unmanned aerial vehicle's the operation management that becomes more meticulous.

Description

Method for determining boundary of unmanned aerial vehicle control area of approach and departure procedure based on collision risk
Technical Field
The invention relates to the technical field of air traffic control, in particular to air unmanned aerial vehicle control.
Background
In recent years, the market scale of domestic civil unmanned aerial vehicles is rapidly enlarged, and the unmanned aerial vehicle industry shows well-jet growth. The unmanned aerial vehicle has the characteristics of good maneuverability, high viability, small size, low cost, strong overload capacity and the like, and has wide application prospects in the fields of logistics transportation, electric power line patrol, agriculture and forestry plant protection, emergency rescue and relief, geographical mapping and the like. Because unmanned aerial vehicles are easy to manufacture, easy to acquire, the user is extensive, thereby resulting in a wide variety of risks hidden behind. Therefore, in order to prevent the unmanned aerial vehicle from interfering with the normal take-off and landing of civil aviation flights, relevant departments strictly control the operation of the unmanned aerial vehicle in the ultra-low altitude flight area around the airport.
At first, according to the peripheral obstacle limiting range of an airport specified in the first hundred sixty six civil airport operation safety management regulations (CCAR-140) issued by the civil aviation administration in most areas of China, the areas, which are 10 kilometers away from the two sides of the central line of the runway of the airport and contain the limiting surface of the obstacle of the airport and 20 kilometers away from the end of the runway, of the periphery of the airport are divided into unmanned aerial vehicle control areas.
In the 5 th month of 2017, the civil aviation administration successively announces the protection range of the obstacle limiting surface of the transportation airport in China according to the relevant regulations of the obstacle limiting surface in international civil aviation organization 'international civil aviation convention annex 14-airport', the range is formed by sequentially connecting 12 coordinate points as shown in fig. 1, wherein the radius of a circular arc part is 7070 meters, and then, the airspace above the range (the protection range of the obstacle limiting surface) is used as the management and control airspace of the civil light unmanned aerial vehicle for a plurality of times. This work has proposed the notion of unmanned aerial vehicle management and control regional tolerance buffer, and the tolerance buffer is the airport barrier and restricts the region that the outside certain distance that extends corresponds of face. Admittedly, an unmanned aerial vehicle control area is arranged in the peripheral ultra-low-altitude flight area of the airport, the operation of the unmanned aerial vehicle at the periphery of the airport is limited, and the unmanned aerial vehicle control area is a necessary measure for ensuring the safe operation of civil aviation flights. However, if the area of the airport periphery for unmanned aerial vehicle control is too large, the unmanned aerial vehicle flyable area is reduced, so that certain obstacles are caused to the development of the unmanned aerial vehicle industry. The lack scientificity of the existing unmanned aerial vehicle control region planning is mainly embodied as follows:
firstly, the limitation range of the obstacles around the airport, which is specified by civil airport operation safety management regulations, is defined by unmanned aerial vehicle control areas around the airport, and is the limitation to the static obstacles, and the limitation surface and the protection range (including a tolerance buffer zone) of the obstacles, such as an inner horizontal plane, a conical surface and the like, which are defined by international civil aviation organization international civil aviation convention annex 14-airport, which is currently referred to, are also the limitation to the static obstacles. Unmanned aerial vehicle is used as moving object, uses indiscriminately above-mentioned restriction range or the protection zone of ruling to static barrier to carry out the management and control to unmanned aerial vehicle flight activity, obviously is unreasonable.
Secondly, the two schemes are fixed schemes for all runways, and lack of adaptation to different runway running characteristics, and the theory is as follows: firstly, the corresponding approach and departure procedures of different runways are completely different, the fixed scheme is not necessarily scientific and reasonable to adapt to the different runways, and the planning of the unmanned aerial vehicle control airspace is suitable for the specific flight procedure. For example, in the case of the current scheme, the airport obstacle limiting surface is an area symmetrical to both sides of the runway, however, the takeoff and landing phases of the aircraft are not necessarily along the direction of the runway, and even may be obviously biased to one side of the runway, and the unmanned plane control area should be planned in combination with the actual running condition, and is not necessarily symmetrical; symmetrical unmanned aerial vehicle control area to above-mentioned runway, may lead to the scope in control area too big to restrict unmanned aerial vehicle flight area. Secondly, in terms of the current scheme, the arc radius of the tolerance buffer area corresponding to all runways is 7070 meters, and the fixed marking lacks relevant basis. In fact, according to the regulations of the international civil aviation convention annex 14-airport, the inner horizontal and conical surfaces of the different types of runways are of different sizes, resulting in different obstacle limiting surfaces of the different types of runways. Therefore, different types of runners draw different barrier limiting surfaces and the same tolerance buffer area arc radius at the same time, and scientific basis is lacked.
Because the existing laws and regulations specially aiming at the peripheral control area of the unmanned aerial vehicle at the airport are still in a missing state, a set of methods for planning the peripheral control area of the airport taking the unmanned aerial vehicle as an object is urgently needed, technical support is provided for the formulation of related laws and regulations, the range of the peripheral control area of the unmanned aerial vehicle at the airport is reduced as far as possible while the safe taking-off and landing of civil aviation flights are ensured, more flyable areas are provided for unmanned aerial vehicles running at the periphery of the airport, and the development of the unmanned aerial vehicle industry is further promoted.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects of the prior art, the method for determining the boundary of the unmanned aerial vehicle control area in the runway area based on the airport runway departure and departure procedure is provided for the first time in China, the boundary of the unmanned aerial vehicle control area in the runway area is planned by the method, the civil unmanned aerial vehicle control area is accurately planned on the premise of not influencing the operation safety and efficiency of civil aircrafts, and the technical support is provided for unmanned fine operation management.
The invention comprises the following steps:
a method for determining a boundary of an unmanned aerial vehicle control area of an approach and departure program based on collision risks comprises the following steps:
s1 according to the running data of the runway departure and departure procedure, the collision risk probability e and the flight section curve
Figure BDA0002322522910000031
s∈[0，s1]Establishing a boundary planning model of a control area;
s2, setting an iteration termination threshold value according to a management and control area boundary planning model, and solving a flight curve through an iteration solving method
Figure BDA0002322522910000032
Parameter s of1The solution is approximated.
Preferably, the management area boundary planning model in S1 includes:
s3(s1)＝min{s2(s1)+ρ3，s4(s1)+ρ2}
s1＝s3(s1)
wherein, flight curve
Figure BDA0002322522910000033
S is the arc length parameter of the horizontal projection curve L(s), s is the [0, s ]1]； s2、s3、s4The value of the arc length parameter, s, for the horizontal projection curve L(s)2(s1)，s3(s1)，s4(s1) Are all s1A function of (a);
s2＝inf CS(s1) (ii) a inf is an infimum function;
CS(s1) To satisfy the constraint condition
Figure BDA0002322522910000034
S of (a) into a set;
the airspace Ω is a three-dimensional airspace below the height h;
nplane(s2) Is a horizontal projection curve L(s) at a point s2A normal plane of (d);
ssf(s1) Is a curve with the flight segment
Figure BDA0002322522910000035
Parallel curved surfaces;
Figure BDA0002322522910000036
dzis the curve of the flight section and the bottom surface ssf(s)1) The distance between them;
dlis the distance between the flight curve and its corresponding left vertical surface
drIs the distance between the flight curve and its corresponding right vertical surface
dzIs the distance between the flight segment and the bottom surface;
Figure BDA0002322522910000037
a unit normal vector of curve L(s);
s4to satisfy the constraint condition
Figure BDA0002322522910000038
The maximum value of s of (a);
h2is the maximum altitude at which the drone flies during the contra-landing period;
Figure BDA0002322522910000039
is h2The equal height surface of (1);
ρ2the horizontal distance corresponding to the maximum height of the unmanned aerial vehicle; rho3The intent is to control the maximum horizontal distance that the drone can fly during the period in which the drone is countered to landing.
Preferably, the S2 includes the following steps:
s201, setting an iteration termination threshold β, and selecting a course curve
Figure BDA0002322522910000041
Intersection point with airspace omega
Figure BDA0002322522910000042
Corresponding to
Figure BDA0002322522910000043
As s1An initial value, and
Figure BDA0002322522910000044
s202, according to the management and control area boundary division model in S1, calculating a discriminant variable
Figure BDA0002322522910000045
S203 judges δiRelationship to β if
a. If deltai∈[0，β]Then go to S204;
b. if it is
Figure BDA0002322522910000046
Then get
Figure BDA0002322522910000047
And go to S202;
s204, outputting
Figure BDA0002322522910000048
As s1The approximate solution of (c).
Preferably, the maximum horizontal distance ρ that the unmanned aerial vehicle flies3The calculation formula of (2) is as follows:
Figure BDA0002322522910000049
wherein, TrThe time for the drone to be detected until the drone responds to the counter; t is the total time during which the drone is intended to be controlled until the drone is countered to land; (ii) a v. ofhIs the maximum horizontal velocity of the drone; v. ofzIs the maximum climbing speed of the unmanned aerial vehicle; rho3The intent is to control the maximum horizontal distance of the drone to fly during the period in which the drone is countered to landing.
Preferably, the unmanned aerial vehicle flies in the air for a horizontal distance ρ corresponding to a maximum height2The calculation formula of (2) is as follows: rho2＝vht2；
Wherein: rho2The horizontal distance corresponding to the maximum height of the unmanned aerial vehicle; t is t2Is the time for the drone to be counterproducted to the highest point.
The invention has the beneficial effects that:
the invention provides a scientific and complete unmanned aerial vehicle control area boundary planning method based on collision risk and entering and leaving procedures for the first time in China, overcomes the problem that the existing airport has too large unmanned aerial vehicle control area planning, provides technical support for scientifically and effectively realizing unmanned aerial vehicle fine management, and promotes the development of the unmanned aerial vehicle industry.
Drawings
The invention is further illustrated with reference to the following figures and examples.
FIG. 1 shows a protection range of an airport in China civil aviation;
FIG. 2 shows the risk of collision zone rzd(s1) A schematic diagram;
FIG. 3 is a diagram illustrating a core region structure of a management control region;
FIG. 4 is a diagram illustrating a structure of a buffer of a management area.
FIG. 5 is a schematic diagram of a regulated area buffer configuration.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not limit the invention.
The invention limits the airspace division problem to airspaces with 20 kilometers at the front end and the rear end of the runway and 10 kilometers at the left side and the right side
Figure BDA0002322522910000051
Focus on investigation
Figure BDA0002322522910000052
The three-dimensional space omega below the internal true height h.
A method for determining the boundary of an unmanned aerial vehicle control area of an entrance and exit program comprises the following steps:
s1, establishing a control region setting equation according to the runway departure and arrival program operation data and the collision risk probability e;
s3(s1)＝min{s2(s1)+ρ3，s4(s1)+ρ2}
s1＝s3(s1)
wherein s is1For space curves of approach and departure flight paths
Figure BDA0002322522910000053
Arc length parameter of (d), representing the point along the curve from which the particle follows
Figure BDA0002322522910000054
Move to a point
Figure BDA0002322522910000055
The distance traveled; s2(s1)，s4(s1)，s3(s1) Are all parameter s1A function of (a); rho2The horizontal distance corresponding to the maximum flying height of the unmanned aerial vehicle in the air; rho3The maximum horizontal distance for the unmanned aerial vehicle to fly;
s2 solving parameter S through an iterative solution method1The approximate solution comprises the following specific steps:
s201, setting an initial value, setting an iteration termination threshold value β, and selecting a route
Figure BDA0002322522910000056
And survey airspace
Figure BDA0002322522910000057
Old intersection
Figure BDA0002322522910000058
Corresponding to
Figure BDA0002322522910000059
As an initial value, and
Figure BDA00023225229100000510
s202 calculating according to the model
Figure BDA00023225229100000511
The value of (2), calculating the discriminative variable
Figure BDA00023225229100000512
S203 judges δiRelationship to β if
a. If deltai∈[0，β]Then go to S204;
b. if it is
Figure BDA00023225229100000513
Then get
Figure BDA00023225229100000514
And go to S202;
s204, outputting
Figure BDA00023225229100000515
As an approximate solution to the equation.
The detailed determination method is as follows:
s1, according to the running data of the runway departure and departure program, the collision risk probability e establishes a control region setting equation process as follows:
flight segment collision risk area
As shown in fig. 2, the flight
Figure BDA0002322522910000061
s∈[0，s1]Corresponding collision risk zone rz(s)1) Is a curve containing a flight segment
Figure BDA0002322522910000062
s∈ [0，s1]The boundary of the inner three-dimensional area is composed of the following parts:
rear vertical surface bsf(s)1): i.e. normal plane of the horizontal projection curve L(s) at the starting point
bsf(s1)＝nplane(0)
Left vertical face lsf(s)1): a vertical plane located at the left side of the curve L(s) and having an equal distance from each point on the curve L(s), i.e. a curve
Figure BDA0002322522910000063
Being vertical faces of the base
Figure BDA0002322522910000064
Right vertical side rsf(s)1): a vertical plane located to the right of the curve L(s) and having an equal distance to each point on L. I.e. by a curve
Figure BDA0002322522910000065
Is a bottom edgeVertical surface of
Figure BDA0002322522910000066
Front vertical plane fsf(s)1): comprising curve L(s) at point L(s)1) Plane of treatment
fsf(s1)＝nplane(0)
A bottom surface ssf(s)1): perpendicular to the vertical surfaces of the left and right side surfaces and the curve of the flight segment
Figure BDA0002322522910000067
Parallel curved surfaces
Figure BDA0002322522910000068
Collision risk zone boundary requirements
Assuming that the actual flight path has a lateral error ε at point L(s)y(s) has a distribution function of Fy(s，εy) Vertical error εz(s) has a distribution function of Fz(s，εz) If the acceptable collision probability is e, then the leg
Figure BDA0002322522910000069
The corresponding collision risk zone is the smallest zone that satisfies the following conditions:
the first condition is as follows: the maximum side width of the airplane of the flight section operation is assumed to be 2 lambdayThen the left and right vertical plane parameters dl、drThe following requirements are met:
Figure BDA0002322522910000071
Figure BDA0002322522910000072
Figure BDA0002322522910000073
p (x) is the probability of occurrence of event x
And a second condition: assuming that the maximum height of the airplane in the flight section is 2 lambdazThen the floor parameters should satisfy:
Figure BDA0002322522910000074
P(εz(s)＜-dz+λz)＝F(s，-dz+λz)≤e
p (x) is the probability of occurrence of event x
The invention calls the parameter d satisfying the above two conditionsl，dr，dzParameter d for avoiding collision risk probability el，dr，dzAre respectively represented as RAl(e)，RAr(e)，RAz(e) Then, the parameters corresponding to the collision risk zone boundary are respectively:
dl＝infRAl(e)
dr＝infRAr(e)
dz＝infRAz(e)
wherein: inf represents the infimum boundary of the real number set;
dlis the flight path curve and the left vertical plane lsf(s)1) The distance between them;
dzis the curve of the flight section and the bottom surface ssf(s)1) The distance between them;
dris the curve of the flight segment and the right vertical plane rsf(s)1) The distance between them.
Regulatory domain kernel region nfz(s)1)
Noting dep as a certain departure procedure corresponding to the runway in question, and noting a curve corresponding to the departure procedure
Figure BDA0002322522910000075
Then the off-site program management area kernel area nfz is accessed by the off-site program for a certain flight segment
Figure BDA0002322522910000076
s∈[0，s1]Zone rz of risk of collisiond(s1) Determining the starting point of the flight segment
Figure BDA0002322522910000077
The terminal point of the central line of the runway (simultaneously considered as the starting point of the flight departure course route), the flight segment
Figure BDA0002322522910000078
s∈[0，s1]Zone rz of risk of collisiond(s1) As shown in fig. 2. The invention records the navigation sections respectively
Figure BDA0002322522910000079
s∈[0，s1]Zone rz of risk of collisiond(s1) Corresponding front vertical surface fsf(s)1) Rear vertical surface bsf(s)1) Left vertical face 1 sf(s)1) Right vertical surface rsf(s)1) Then the corresponding regulatory domain kernel region nfz for that leg(s)1) Is a curve of voyage
Figure BDA00023225229100000710
s∈[0，s1]Corresponding rear vertical side bsf(s)1) Left vertical plane lsf(s)1) Right vertical surface rsf(s)i) Normal plane nplane(s)2) Enclosed curve containing flight segment
Figure BDA00023225229100000711
s∈[0，s2]The three-dimensional space domain of (2) as shown in fig. 3. The space structure of the kernel region in the control region is mainly composed of a parameter value s1，s2Determining, the value of the parameter s2Is selected as the management area kernel area nfz(s)1) Is a key factor of (1).
Regulatory domain kernel region nfz(s)1) Constraint conditions
Regulatory domain kernel region nfz(s)1) Mainly describing the collision risk zone rzd(s1) The part in the region omega and its upward and downward extension region, the parameter s2The intersection curve nplane(s) ∩ ssf(s) should be satisfied1) The true height is not less than h, namely:
Figure BDA0002322522910000081
let the set of all satisfied s satisfying the above constraint be CS(s)1) Then s2The following settings are set:
s2＝infCS(s1)
buffer setting model of control area
The runway departure program control area rfz is an airspace for ensuring safe operation of the civil aircraft when the civil aircraft is merged into the unmanned aircraft in the airspace, and is centered on the inner core area nfz, and extends outwards by a certain buffer distance to obtain a buffer area lfz. And guarantee that unmanned aerial vehicle in free flight area ffz can't be close to control district kernel area nfz under the condition of not having through the flight application in the airspace structure that keeps anti-system, to guarantee that non-cooperative type unmanned aerial vehicle and civil aviation passenger plane's operation are kept apart, stop the threat and produce.
As shown in FIG. 4, the pipe buffer lfz(s)1) The boundary consists of the following parts:
a top surface: an upper boundary of region Ω;
inner vertical surface: vertical surface of three-dimensional airspace surrounded by core area in control area
Outer rear vertical surface Bsf(s)1): with the rear-side vertical surface bsf(s)1) Parallel vertical planes
Figure BDA0002322522910000082
Outer left vertical plane Lsf(s)1): on the left vertical face lsf(s)1) Left side, and is spaced from lsf(s)1) Vertical surfaces with equal distance of each point, i.e. curved lines
Figure BDA0002322522910000083
Being vertical faces of the base
Lsf(s1)＝{(x，y，z)|(x，y，0)∈LL(s)，z≥0}
Outer right vertical surface Rsf(s)1): on the right vertical surface rsf(s)1) Right side, and distance rsf(s)1) Perpendicular to the plane of the upper point at equal distances, i.e. by a curve
Figure BDA0002322522910000084
Being vertical faces of the base
Rsf(s1)＝{(x，y，z)l(x，y，0)∈LR(s)，z≥0}
Outer front vertical face Fsf(s)1): horizontal projection curve L(s) at point L(s)3) Treatment plane nplane(s)3)
Wherein:
dlis the flight and left vertical plane lsf(s)1) The distance between them;
dzis the curve of the flight section and the bottom surface ssf(s)1) The distance between them;
dris the curve of the flight segment and the right vertical plane rsf(s)1) The distance between them;
Dbis the outer rear vertical surface Bsf(s)1) With rear vertical side bsf(s)1) The distance between them;
DLis the outer left vertical plane Lsf(s)1) With the left vertical face lsf(s)1) The distance between them;
DRis the outer right vertical surface Rsf(s)1) With right vertical surface rsf(s)1) The distance between them.
The spatial geometry of the buffer zone of the control zone is mainly defined by a parameter Db，DL，DR，s3Determine, buffer lfz(s)1) The key to the planning is to give the above parameters.
Buffer 1 fz(s)1) Limitation of conditions
Parameter Db，DL，DrIs mainly dependent on the extreme operating performance of the light unmanned plane, s3The selection of the unmanned aerial vehicle depends on the performance of the unmanned aerial vehicle and the operation data of the civil aircraft. As shown in fig. 5, the maximum horizontal flight speed of the light unmanned plane is assumed to be vhMaximum climbing speed vzThe time from the detection of the unauthorized unmanned aerial vehicle entering the unmanned aerial vehicle restricted area to the successful disturbance rejection is TrThen, if the drone rushes into the regulatory region at the free flight zone boundary with the maximum operation performance when t is 0, the case where the drone may fly farthest in the restricted region is as follows: t is an element of [0, T ∈r]In time, the drone is still at maximum performance (vertical and horizontal velocities v)z，vh) Flying; at TrConstantly, unmanned aerial vehicle loses driving system, will do the free fall motion of maximum performance initial velocity.
According to the physical knowledge, T is TrIn time, the unmanned aerial vehicle rises to a height Vz×TrHorizontal flight distance ρ1＝Vh×TrAt this time, the height of the unmanned plane is h1＝h+vz×Tr(ii) a At the time of passage
Figure BDA0002322522910000091
Afterwards, unmanned aerial vehicle reaches the system high point, and perpendicular speed all converts gravitational potential energy into this moment, so unmanned aerial vehicle place height at this moment
Figure BDA0002322522910000092
Unmanned plane at elapsed time t3After landing, the vertical speed of the drone is
Figure BDA0002322522910000093
Therefore, it is
Figure BDA0002322522910000094
To sum up, the maximum height that unmanned aerial vehicle rises at whole in-process is:
Figure BDA0002322522910000101
horizontal distance rho of unmanned aerial vehicle flight at the moment2＝vht2(ii) a The total flight time of the unmanned aerial vehicle in the air is as follows:
Figure BDA0002322522910000102
maximum horizontal distance rho of flight in the whole process3Comprises the following steps:
Figure BDA0002322522910000103
remember of s4＜s3To satisfy the conditions
Figure BDA0002322522910000104
S maximum, then the pipe buffer lfz(s)1) The minimum region satisfying the following conditions:
the first condition is as follows: outer rear vertical surface Bsf(s)1) Outer left vertical plane Lsf(s)1) Outer right vertical surface Rsf(s)1) Respectively with the rear vertical side bsf(s)1) Left vertical face lsf(s)1) Right vertical surface rsf(s)1) Are not less than rho3I.e. min { D }b，DL，DR}≥ρ3；
And a second condition: farplanar nplane(s)3) On the outer left vertical plane Lsf(s)1) Outer right vertical surface Rsf(s)1) Partial subset of (2) and normal plane nplane(s)2) On the left vertical face lsf(s)1) Right vertical surface rsf(s)1) Is not less than p3
And (3) carrying out a third condition: farplanar nplane(s)3) On the outer left vertical plane Lsf(s)1) Outer right vertical surface Rsf(s)1) Partial subset of (2) and normal plane nplane(s)4) On the left vertical face lsf(s)1) Right vertical surface rsf(s)1) Is not less than p2；
The spatial geometry of the buffer zone of the control zone is mainly defined by a parameter Db，DL，DR，s3Determine, buffer lfz(s)1) The key to the planning is to give the above parameters. Parameter Db，DL，DrIs mainly dependent on the extreme operating performance of the light unmanned plane, s3Is selected fromOperational data is taken that is dependent on both drone performance and airport flights.
Off-site program control area and certain flight segment
Figure BDA0002322522910000105
s∈[0，s1]That is to say that the spatial geometry of the control region rfz depends on the parameter s1The invention gives a parameter s1The constraint satisfied. When the distribution of flight errors and the limit flight performance of the unmanned aerial vehicle are known, the parameter s2，s4All can be determined by the parameter s1Fixed, i.e. can be regarded as parameter s2，s4Are all parameters s1Can be expressed as s2(s1)，s4(s1) Parameter s3Is a parameter s2，s4Is thus still the parameter s1As a function of (c). At this time, the parameter s1It should be given by the following system of equations:
s3(s1)＝min{s2(s1)+ρ3，s4(s1)+ρ2}
s1＝s3(s1)
ρ2the horizontal distance corresponding to the maximum flying height of the unmanned aerial vehicle in the air; rho3The maximum horizontal distance for the unmanned aerial vehicle to fly; the specific form of the equation depends on the distribution rule of the flight errors of the airplane and the limit flight performance of the unmanned aerial vehicle, and the equation is called a control area setting model equation.
S2 solving parameter S through an iterative solution method1Approximate solution
In general, the equation is determined by an implicit function, a specific expression cannot be given, the solution problem of an accurate solution cannot be realized, and the invention is to examine the solution method of an approximate solution of the equation in a specific project. First, according to the characteristics of the model, some properties are given:
for the same route
Figure BDA0002322522910000111
In other words, the flight
Figure BDA0002322522910000112
s∈[0，s1]Corresponding collision risk zone rz(s)1) With monotonic increase, i.e. arbitrary parameter s1，s′1If s is1＜s′1Then:
Figure BDA0002322522910000118
according to the zone rz(s) of risk of collision1) The composition of (a) is defined asl，dzAre respectively s1Monotonically increasing function of drIs s is1Is a monotonically decreasing function of (a).
Unmanned aerial vehicle management and control area kernel area nfz(s)1) Boundary nplane(s)2) Will follow s1Reduced forward movement, i.e. function s2(s1) Is a variable s1Is a monotonically increasing function of.
Due to the curved surface ssf(s)1) With s1Is smaller and is lifted upwards according to dzAnd s1Satisfied requirement-aware property holds for the same route
Figure BDA0002322522910000113
In other words, the flight
Figure BDA0002322522910000114
s∈[0，s1]Corresponding management region kernel region nfz(s)1) With monotonicity, i.e. arbitrary parameter s1，s′1If s is1＜s′1Then:
Figure BDA0002322522910000115
inner curved surface nplane(s) of unmanned aerial vehicle control area4) Will follow s1Reduced forward movement, i.e. function s4(s1) Is a variable s1Is monotonically decreasingAnd increasing the function.
For the same route
Figure BDA0002322522910000116
In other words, the flight
Figure BDA0002322522910000117
s∈[0，s1]Corresponding collision risk zone rz(s)1) With monotonic increase, i.e. arbitrary parameter s1，s′1If s is1＜s′1Then:
Figure BDA0002322522910000121
according to the airspace property of the control area, the parameter s can be realized1The iterative solution method comprises the following specific steps:
first, setting initial value, setting iteration termination threshold β, and selecting route
Figure BDA0002322522910000122
And survey airspace
Figure BDA0002322522910000123
Point of intersection
Figure BDA0002322522910000124
Corresponding to
Figure BDA0002322522910000125
As an initial value, and
Figure BDA0002322522910000126
second, calculating according to the model
Figure BDA0002322522910000127
The value of (2), calculating the discriminative variable
Figure BDA0002322522910000128
Third stepStep (d) to determineiRelationship to β if
a. If deltai∈[0，β]Then go to the fourth step
b. If it is
Figure BDA0002322522910000129
Then get
Figure BDA00023225229100001210
And turning to the second step
The fourth step, output
Figure BDA00023225229100001211
As an approximate solution to the equation.
Examples of the invention are as follows:
analyzing parameters of flight line collision risk area
Without loss of generality, the flight is in the final approach stage
Figure BDA00023225229100001212
The example shows an example of a meter approach procedure of RWY02R at north-Jiang airport of Chongqing, and the horizontal velocity v can be known according to the information of the meter approach diagramx93.05 m/s, vy0 m/s, vzSince 4.9 m/s, the descent gradient of the aircraft in the approach phase is known to be
Figure BDA00023225229100001213
Course section
Figure BDA00023225229100001214
s∈[0，10000]The conditions are satisfied:
x(s)＝s
y(s)＝0
z(s)＝k×s
for collision risk probability e 5 × 10-9In this example, the parameters corresponding to the collision risk zone may be taken:
dl＝dr＝167+0.0117×s1
dz＝72.3+0.00573×s1
analyzing unmanned aerial vehicle flight performance
Assuming that the operational performance of a free-flying unmanned aerial vehicle (UA) satisfies vz2 m/s, vh100 km/h 27.778 m/s, detection of the countering system and response time TrTaking the gravity acceleration g as 9.8 m/s as 0.5 s2Then from physical knowledge, T is knownrIn time, the unmanned aerial vehicle rises by a height h0Comprises the following steps:
h0＝vz×Tr2 × 0.5 ═ 1 m
Horizontal flight distance ρ1Comprises the following steps:
ρ1＝vh×Tr27.778 × 0.5 ═ 13.889 m
At the moment, the height h of the unmanned aerial vehicle1Comprises the following steps:
h1＝h0+ h-1 + 120-121 m
Because nobody is the even rectilinear motion that accelerates in the vertical direction, can know that when unmanned aerial vehicle reaches the peak and is zero for speed, by the even rectilinear motion formula that accelerates at this moment:
vend＝vinit+g×t
it can be known that the time that the unmanned aerial vehicle climbs to the highest point is:
Figure BDA0002322522910000131
at the moment, the vertical speed is converted into gravitational potential energy, and the energy conservation formula is as follows:
Figure BDA0002322522910000132
therefore, UA is located at the height h2Comprises the following steps:
Figure BDA0002322522910000133
when the unmanned aerial vehicle falls to the ground from a peak, the landing can be known by utilizing the energy conservation formula againTime vertical velocity vz3Comprises the following steps:
Figure BDA0002322522910000134
the time t for the unmanned plane to fall from the highest point to the ground3Comprises the following steps:
Figure BDA0002322522910000141
to sum up, the maximum height that unmanned aerial vehicle UA rises in the whole process is:
Figure BDA0002322522910000142
the horizontal distance rho of UA flight when UA reaches the high point2Comprises the following steps:
ρ2＝vh(Tr+t2) 19.558 m
The total flight time of the UAV UA in the air is as follows:
Figure BDA0002322522910000143
will Tr＝0.5，vzWhen the formula is substituted with 2, g is 9.8, h is 120, t is 5.678s, the maximum horizontal distance ρ is obtained in the whole flight process3Comprises the following steps:
Figure BDA0002322522910000144
establishing a design equation for a control region
Establishing a control area setting equation according to the runway entering and leaving program operation data and the collision risk probability e;
s3(s1)＝min{s2(s1)+ρ3，s4(s1)+ρ2}
s1＝s3(s1)
wherein s is1For space curves of approach and departure flight paths
Figure BDA0002322522910000145
Arc length parameter of (d), representing the point along the curve from which the particle follows
Figure BDA0002322522910000146
Move to a point
Figure BDA0002322522910000147
The distance traveled; s2(s1)，s4(s1)，s3(s1) Are all parameter s1A function of (a);
the unfolding iteration algorithm is based on the aforementioned assumptions, and the unfolding iteration:
initialization
Figure BDA0002322522910000148
β is 10, respectively
Figure BDA0002322522910000149
Now, it is known that:
Figure BDA0002322522910000151
Figure BDA0002322522910000152
Figure BDA0002322522910000153
at this moment, it can be known that:
δ0＝s1-s3(s1)＝10000-4902.96＝5097.04
due to the fact that
Figure BDA0002322522910000154
Updating
Figure BDA0002322522910000155
Respectively calculating according to the above steps
Figure BDA0002322522910000156
δ1The results obtained were:
Figure BDA0002322522910000157
Figure BDA0002322522910000158
Figure BDA0002322522910000159
δ1＝555.251
due to the fact that
Figure BDA00023225229100001510
Updating
Figure BDA00023225229100001511
Respectively calculating according to the above steps
Figure BDA00023225229100001512
δ2The results obtained were:
Figure BDA00023225229100001513
Figure BDA00023225229100001514
Figure BDA00023225229100001515
δ2＝60.4871
due to the fact that
Figure BDA00023225229100001516
Updating
Figure BDA00023225229100001517
Respectively calculating according to the above steps
Figure BDA00023225229100001518
δ3The results obtained were:
Figure BDA00023225229100001519
Figure BDA00023225229100001520
Figure BDA00023225229100001521
δ3＝6.5866
due to delta3∈[0，10]Terminating the iteration and outputting the result s1＝4287.22。
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict. Although the present invention has been described to a certain extent, it is apparent that appropriate changes in the respective conditions may be made without departing from the spirit and scope of the present invention. It is to be understood that the invention is not limited to the described embodiments, but is to be accorded the scope consistent with the claims, including equivalents of each element described.

Claims (5)

1. A method for determining the boundary of an unmanned aerial vehicle control area of an entrance and exit program based on collision risks is characterized by comprising the following steps:
s1 operating data and collision risk probability e according to the runway departure and arrival program, and flight section curve
Figure FDA0002322522900000018
s∈[0，s1]Establishing a boundary planning model of a control area;
s2, setting an iteration termination threshold value according to a management and control area boundary planning model, and solving a flight curve through an iteration solving method
Figure FDA0002322522900000016
Parameter s of1The solution is approximated.
2. The boundary determination method according to claim 1, wherein the management area boundary planning model in S1 includes:
s3(s1)＝min{s2(s1)+ρ3，s4(s1)+ρ2}
s1＝s3(s1)
wherein, flight curve
Figure FDA0002322522900000017
S is the arc length parameter of the horizontal projection curve L(s), s is the [0, s ]1]；s2、s3、s4The value of the arc length parameter, s, for the horizontal projection curve L(s)2(s1)，s3(s1)，s4(s1) Are all s1A function of (a);
s2＝inf CS(s1) (ii) a inf is an infimum function;
CS(s1) To satisfy the constraint condition
Figure FDA0002322522900000011
S of (a) into a set; Ω is a three-dimensional airspace below the true height h; nplane(s)2) Is a horizontal projection curve L(s) at a point s2A normal plane of (d);
ssf(s1) Is a curve with the flight segment
Figure FDA0002322522900000012
Parallel curved surfaces;
Figure FDA0002322522900000013
Figure FDA0002322522900000014
a unit normal vector of curve L(s);
dzthe distance between the flight section curve and the bottom surface parallel to the flight section curve is obtained;
dlis the distance between the flight curve and its corresponding left vertical surface
drThe distance between the flight section curve and the right vertical surface corresponding to the flight section curve is obtained;
s4to satisfy the constraint condition
Figure FDA0002322522900000015
The maximum value of s of (a);
h2is the maximum altitude at which the drone flies during the contra-landing period;
Figure FDA0002322522900000021
is h2The equal height surface of (1);
ρ2the horizontal distance corresponding to the maximum height of the unmanned aerial vehicle; rho3The intent is to control the maximum horizontal distance that the drone can fly during the period in which the drone is countered to landing.
3. The boundary determination method of claim 2, wherein the S2 includes the steps of:
s201, setting an iteration termination threshold β, and selecting a course curve
Figure FDA0002322522900000022
Intersection point with airspace omega
Figure FDA0002322522900000023
Corresponding to
Figure FDA0002322522900000024
As s1An initial value, and
Figure FDA0002322522900000025
s202, according to the management and control area boundary division model in S1, calculating a discriminant variable
Figure FDA0002322522900000026
S203 judges δiRelationship to β if
a. If deltai∈[0，β]Then go to S204;
b. if it is
Figure FDA0002322522900000027
Then get
Figure FDA0002322522900000028
And go to S202;
s204, outputting
Figure FDA0002322522900000029
As s1The approximate solution of (c).
4. The boundary determination method of claim 2, wherein the maximum horizontal distance ρ at which the drone flies3The calculation formula of (2) is as follows:
Figure FDA00023225229000000210
wherein, TrThe time for the drone to be detected until the drone responds to the counter; t is the total time from the unmanned aerial vehicle to be controlled to land in a reversed mode; (ii) a v. ofhIs the maximum horizontal velocity of the drone; v. ofzIs the maximum climbing speed of the unmanned aerial vehicle; rho3The intent is to control the maximum horizontal distance that the drone can fly during the period in which the drone is countered to landing.
5. The boundary determination method of claim 4, wherein the unmanned aerial vehicle flies in the air for a horizontal distance ρ corresponding to a maximum altitude2The calculation formula of (2) is as follows: rho2＝vht2；
Wherein: rho2The horizontal distance corresponding to the maximum height of the unmanned aerial vehicle; t is t2Is the time for the drone to be counterproducted to the highest point.
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