JP2021110744A - Method to speedily plan flight track of smart aircraft under multiple constraints - Google Patents

Abstract

To provide a method to speedily plan a flight track of a smart aircraft under multiple constraints in order to solve various situations an aircraft encounters during an actual flight.SOLUTION: A method includes: a step to establish a mathematical optimization model of multiple purpose and multiple constraint conditions; a step to acquire instance information; and a step to characterize by acquiring various executable path schemes by acquiring an instance by operating a heuristic vicinity search algorithm. A minimizing path and minimizing compensation number of times are made target functions, a mathematical optimization model of multiple purpose multiple constraints such as path balance constraint, path uniqueness constraint, and traverse path circuit constraint is established; a local optimizing node is searched as the next traversal node by combining annealing ideas; and convergent performance of the algorithm is improved by stipulating a corresponding search step size.SELECTED DRAWING: None

Description

The present invention belongs to the field of aircraft wake planning and control, and specifically relates to a method of rapidly planning the wake of a smart aircraft under multiple constraints.

Since the British invented the world's first Air Vehicle in 1917, aircraft technology has already become a very important development in the military and civilian fields. In the military arena, aircraft can perfectly complete many military tasks, including reconnaissance and ground attacks on terrain and enemies. In the civilian field, aircraft also play a huge role in areas such as mapping, resource exploration and aerial photography. With the rapid development of computers, information and science and technology, the performance, results and operations of aircraft will become more and more complex. Aircraft wake planning is an important technology for realizing autonomous navigation of aircraft, and has important meaning both theoretically and in practical applications. Based on the various causes described above, aircraft There is a growing demand for effective wake planning methods that not only provide the shortest flight distance to the aircraft, but also accurately position and complete the task, which is also an urgent need today. ing.

A wake plan is a type of route plan, but the wake plan may be more complicated than a general route plan due to the complexity of the flight process of an aircraft and the complexity of the environment when performing tasks. A typical aircraft route planning is to plan a flight trajectory for an aircraft that meets one or more requirements. Conventional patents (patent number CN201910556400.3 unmanned aerial vehicle track planning device and method, patent number CN2018105196664.7 unmanned aerial vehicle track planning, and patent number CN20181051945.4. However, traditional patented track planning methods are less constrained by the various real-world environments that aircraft encounter during flight.

However, in actual applications, there are many restrictions on the system configuration of the aircraft and complicated environmental impacts and constraints, so rapid planning of wakes in a complicated environment has become one of the important issues for aircraft control. Horizontal error constraints, vertical error constraints, effective route constraints and turning radius of the aircraft, taking into account environmental factors during flight, to ensure that the aircraft flies exactly on a given route and avoids flight task failures due to positioning errors. In order to select good spatial nodes that meet the constraints and allow these spatial nodes to form one viable route as an effective aircraft track plan, the present invention presents an aircraft track due to restrictions on the positioning accuracy of the system. Provide a rapid planning method.

In order to solve various situations that an aircraft encounters during actual flight to the problems existing in the background technology, the present invention provides a method for rapidly planning the wake of a smart aircraft under multiple constraints. That is the purpose.

を通り、
式中、Ｎは、飛行領域内の補正点のノード集合であり、ｉ、ｊは、ノード集合Ｎにおけるｉ、ｊ番目のノードの略号であり、ｄ_ijは、ノードｉからノードｊまでの航空機の距離であり、ｘ_ijは、航空機がノードｉからノードｊまで飛行しているか否かを示すバイナリ変数であり、航空機がノードｉからノードｊまで飛行すれば、ｘ_ij＝１であり、そうでなければｘ_ij＝０であり、
該目的関数は、以下の１）〜３）の制約条件を満たし、
１）経路バランス制約であり、航空機が一回の飛び込みと飛び出しのみを行い、すなわち、航空機が該ノードをトラバースした後に該ノードをトラバースすることがないとする制限であり、経路バランス制約式は以下のとおりであり、

式中、ｋは、ノード集合Ｎにおけるｋ番目のノードの略号であり、ｎは、ノード集合Ｎにおけるノード総数であり、ｘ_ikは、航空機がノードｉからノードｋまで飛行しているか否かを示すバイナリ変数であり、航空機がノードｉからノードｋまで飛行すれば、ｘ_ik＝１であり、そうでなければ、ｘ_ik＝０であり、ｘ_kjは、航空機がノードｋからノードｊまで飛行しているか否かを示すバイナリ変数であり、航空機がノードｋからノードｊまで飛行すれば、ｘ_kj＝１であり、そうでなければ、ｘ_kj＝０であり、
２）経路唯一性制約であり、航空機が各ノードを順次トラバースし、１つの有効経路のみを形成するという制限であり、経路唯一性制約式は以下のとおりであり、

式中、ｙ_i は、ノードｉが航空機によりトラバースされているか否かを示すバイナリ変数であり、航空機が該ノードｉから飛び出したり、飛び込んだりすれば、すなわち、ノードｉが航空機によりトラバースされたことを表せば、ｙ_i ＝１であり、そうでなければ、ｙ_i ＝０であり、
３）トラバース経路回路制約であり、航空機が飛行中にいかなるサブループ解も発生しないとする制限であり、トラバース経路回路制約式は以下のとおりであり、

ステップＳ２では、航空機の始点座標と、終点座標と、飛行領域内の全ての補正点の空間位置座標と、水平誤差補正タイプ及び垂直誤差補正タイプを含むその誤差補正タイプを含むインスタンス情報を取得し、
ステップＳ３では、ヒューリスティックな近傍探索アルゴリズムを運用してインスタンスを求めることにより、複数の選択可能なスキームを取得して選択する。 Specifically, the method of the present invention is as follows.
The method of rapidly planning the track of a smart aircraft under the multi-constrained conditions of the present invention specifically includes the following steps S1 to S3.
In step S1, the characteristics of the aircraft track plan are analyzed, a mathematical optimization model of multi-constraints is established with a multi-objective function, and the model is established.
Based on the characteristics of the aircraft's wake plan, the aircraft is simplified to mass points, ignoring the size of the aircraft, and the flight path between the nodes of the aircraft is the Euclidean distance, and the objective function F ₁ of the following mathematical optimization model, Establish F ₂ and

Through
In the equation, N is the node set of correction points in the flight area, i and j are the abbreviations for the i and jth nodes in the node set N, and _di j is the aircraft from node i to node j. X _ij is a binary variable indicating whether or not the aircraft is flying from node i to node j, and if the aircraft flies from node i to node j, x _ij = 1, so Otherwise, x _ij = 0,
The objective function satisfies the following constraints 1) to 3).
1) It is a route balance constraint, which is a restriction that the aircraft makes only one dive and jump, that is, the aircraft does not traverse the node after traversing the node, and the route balance constraint formula is as follows. Is as

In the equation, k is the abbreviation for the kth node in the node set N, n is the total number of nodes in the node set N, and x _ik is whether or not the aircraft is flying from node i to node k. It is a binary variable shown, and if the aircraft flies from node i to node k, then x _ik = 1, otherwise x _ik = 0, and x _kj is that the aircraft flies from node k to node j. It is a binary variable indicating whether or not the aircraft is flying, and if the aircraft flies from node k to node j, x _kj = 1, otherwise x _kj = 0.
2) The route uniqueness constraint is a restriction that the aircraft traverses each node in sequence to form only one effective route. The route uniqueness constraint formula is as follows.

In the equation, y _i is a binary variable indicating whether or not the node i is traversed by the aircraft, and if the aircraft jumps out or jumps out of the node i, that is, the node i is traversed by the aircraft. If, y _i = 1, otherwise y _i = 0,
3) It is a traverse route circuit constraint, which is a restriction that no subloop solution occurs during flight. The traverse route circuit constraint formula is as follows.

In step S2, the start point coordinates of the aircraft, the end point coordinates, the spatial position coordinates of all the correction points in the flight area, and the instance information including the error correction type including the horizontal error correction type and the vertical error correction type are acquired. ,
In step S3, a plurality of selectable schemes are acquired and selected by operating a heuristic neighborhood search algorithm to obtain an instance.

式中、θは、累積誤差閾値であり、ｈ_j は、航空機がノードｊの位置に到達したときの総水平ずれ量であり、ｖ_j は、航空機がノードj の位置に到達したときの総垂直ずれ量であり、Ｈは、水平補正点集合であり、

は、ノードｉが集合Ｈに属するか否かを示すバイナリ変数であり、ノードがｉ∈Ｈであれば、

であり、そうでなければ、

であり、
Ｖは、垂直補正点集合であり、

は、ノードｉが集合Ｖに属するか否かを示すバイナリ変数であり、ノードがｉ∈Ｖであれば、

であり、そうでなければ、

であり、δは、航空機が１ｍ飛行する毎に水平誤差と垂直誤差の増加量であり、
状況２では、航空機がノードｉからノードｊまで飛行し、理想的な誤差補正を行うことができない場合には、次のノードｋを選択して誤差補正を行い、このときに累積水平誤差及び累積垂直誤差の制約式が以下のとおりであり、

式中、Ｐ_ijk は、航空機がノードｉ、ｊ、ｋを順次トラバースしているか否かを示すバイナリ変数であり、航空機がノードｉ、ｊ、ｋを順次トラバースすれば、Ｐ_ijk ＝１であり、そうでなければ、Ｐ_ijk ＝０であり、ｄ_jkは、ノードｊからノードｋまでの航空機の距離であり、

は、ノードｋが集合Ｈに属するか否かを示すバイナリ変数であり、ノードｋ∈Ｈであれば、

であり、そうでなければ、

であり、ηは、補正マージンであり、単位がｍであり、η∈[2,8] であり、Ｄは、補正に失敗したノード集合であり、Ｓは、誤差補正が０である確率がξであるノード集合である。 The constraints further include cumulative horizontal error and cumulative vertical error constraints, and can be divided into the following two situations regarding whether or not to perform ideal error correction when the aircraft reaches node j from node i.
In Situation 1, if the aircraft reaches node j from node i and can perform ideal error correction, the constraint equations are as follows: Cumulative horizontal error and cumulative vertical error are within the maximum positioning error range. Guarantee the effectiveness of the flight path by limiting that

In the equation, θ is the cumulative error threshold, h _j is the total horizontal displacement when the _{aircraft reaches the position of node j, and v j} is the total when the aircraft reaches the position of node j. It is the amount of vertical deviation, and H is a set of horizontal correction points.

Is a binary variable indicating whether or not the node i belongs to the set H, and if the node is i ∈ H,

And otherwise

And
V is a set of vertical correction points,

Is a binary variable indicating whether or not the node i belongs to the set V, and if the node is i ∈ V,

And otherwise

And δ is the amount of increase in horizontal error and vertical error for each 1 m flight of the aircraft.
In situation 2, if the aircraft flies from node i to node j and the ideal error correction cannot be performed, the next node k is selected and error correction is performed, and at this time, the cumulative horizontal error and the cumulative error are accumulated. The constraint formula for vertical error is as follows,

In the equation, _Pijk is a binary variable indicating whether or not the aircraft is traversing the nodes i, j, k in sequence, and if the aircraft traverses the nodes i, j, k in sequence, _Pijk = 1. Otherwise, _Pijk = 0 and d _jk is the distance of the aircraft from node j to node k.

Is a binary variable indicating whether or not the node k belongs to the set H, and if the node k ∈ H,

And otherwise

, Η is the correction margin, the unit is m, η ∈ [2,8], D is the set of nodes that failed to correct, and S is the probability that the error correction is 0. It is a set of nodes that is ξ.

Further, operating the heuristic neighborhood search algorithm to obtain an instance includes the following steps A to D.
In step A, the maximum number of cycles, the cumulative error threshold θ, the vertical error correction conditions that are the first vertical error threshold and the first horizontal error threshold, and the horizontal error correction that is the second vertical error threshold and the second horizontal error threshold. Enter the initial parameters including the conditions, the minimum turning radius, the error increment for each 1 m flight of the aircraft, and the instance information.
In step B, the related candidate point set P ₄ is determined as shown in (1) to (3) below.
(1) In the node set N, the node that the aircraft has not traversed is selected as the next candidate node, and when the aircraft reaches from the current node to the next candidate node, both the cumulative horizontal error and the cumulative vertical error are cumulative errors. Select nodes smaller than the threshold θ _{, store them in the set P 1,} and store them.
(2) In P ₁ , a node having an X-axis coordinate value larger than the X-axis coordinate value of the current node of the aircraft is selected, stored in the _{candidate point set P 2, and stored.}
(3) Error value type that needs to be calibrated when reaching the next point based on the current cumulative horizontal and cumulative vertical error values of the aircraft to avoid large cumulative error values of the aircraft. And determine the candidate point set P _{4 by the following two methods,}
In method 1,
a, in the set P _2, constitute a set P ₃ to select the vertical correction satisfying node called vertical error horizontal error below the first vertical error threshold is less than or equal to the first horizontal error threshold, vertically in P ₂ If there is no node that satisfies the correction condition, in P ₂ , a node that satisfies the horizontal correction condition that the vertical error is equal to or less than the second vertical error threshold and the horizontal error is equal to or less than the second horizontal error threshold is selected and set P ₃ Configure and
b, determining the position coordinates of the current node and the previous node of the aircraft, the any point in the P ₃ randomly selected as the next node, this three nodes constitute a space triangular, following the current node If the turning radius obtained by obtaining the turning radius when reaching the node of is larger than the _{minimum turning radius R min, the node selected from the set P 3} satisfies the turning radius constraint, and the node is selected. stored in the candidate point set P _4, constitute the candidate point set P ₄ by selecting all the nodes that satisfy the turning radius constraints from P _3,
In method 2,
A vertical correction point that can achieve perfect calibration in set P ₂ or satisfies the correction margin η is selected as the _{candidate point set P 4} , otherwise horizontal that can be completely calibrated in _{set P 2 or satisfies the correction margin η.} selects the correction point as the candidate point set P _4,
In step C, the current and node a step forward by selecting one of the nodes from the candidate point set P _4, and determining the candidate point set P ₄ of the next node, the specific method is as follows ..
Select one of the candidates from the candidate point set P ₄ obtained in step B, take a step forward to make it the current node, return to step B, _{select the candidate point set P 4} of the next node, and then If the candidate point set P ₄ of the node is an empty set, return to the candidate point set P ₄ obtained in step B, select another node as the current node, continue the calculation, and all in the _{candidate point set P 4 If the candidate point set P 4} of the next node acquired by returning to step B is an empty set, _{the current node of the original candidate point set P 4} is acquired as a dead point. Return to the node before the current node, recalculate the previous node as the current node, and
Step B, In C, it is determined whether contains the end point coordinates for each candidate point set P ₄ is not empty, if it contains, the process proceeds to step D to save the track, otherwise , step B, and back to the C continues to determine the candidate point set P ₄ of the next node,
In step D, the number of cycles increases by 1 each time one track is obtained, and it is determined whether or not the cumulative number of cycles reaches the maximum number of cycles. If not, the process returns to step A and a new track is searched for. Continue to, otherwise output all wakes.

したがって、得られた旋回半径の計算方法は、以下のとおりである。

式中、Ｒ_ijk は、旋回半径であり、ｓは、ノードｉ、ｊ、ｋで囲まれた三角形の面積であり、ｐは、ノードｉ、ｊ、ｋで囲まれた三角形の半周長である。 Furthermore, the calculation method of the turning radius of the aircraft is obtained based on Heron's formula, and specifically, it is as follows.
As shown in FIG. 1, when the aircraft traverses the nodes i, j, and k in sequence, the nodes i, j, and k form one space triangle, and the radius of the inscribed circle thereof is R. Assuming, the triangles are divided into three triangles with the _{bases d ij} , d _jk , and _di k, respectively, and the areas s ₁ , s ₂ , and s ₃ , respectively. Based on Heron's formula,

Therefore, the calculation method of the obtained turning radius is as follows.

In the equation, R _ijk is the turning radius, s is the area of the triangle surrounded by nodes i, j, k, and p is the semiperimeter of the triangle surrounded by nodes i, j, k. ..

The present invention uses the minimization path and the number of minimization corrections as objective functions for the problem of rapid planning of effective tracks in different actual flight environments of aircraft, and has a route balance constraint, a route uniqueness constraint, and a traverse route circuit constraint. At the same time as establishing a mathematical optimization model of multi-objective and multi-constraints such as, the convergence performance of the algorithm is determined by searching for the local optimization node as the next traversal node of the aircraft by combining the tanning ideas and specifying the corresponding search step size. A heuristic neighborhood search algorithm for improving the above is provided, and an excellent track route can be quickly obtained by the present invention.

It is the official principle diagram of Heron. It is a track map by schemes 1 and 2. It is a track map by schemes 3 and 4.

In order to better understand the technical features, purpose and beneficial effects of the present invention, examples of the present invention will be further described with reference to the drawings. It should not be understood that the examples are merely for further explaining the present invention and limiting the scope of protection of the present invention, and those skilled in the art have made it based on the contents of the present invention. Some non-essential improvements and adjustments also fall within the scope of the invention.
Specifically, the method of rapidly planning the track of a smart aircraft under the multi-constrained conditions of the present invention includes the following steps 1-5.
In step 1, the characteristics of the aircraft track plan are comprehensively analyzed, and the following assumptions (1) and (2) are made.
(1) Ignore the size of the aircraft, simplify the aircraft to mass points, and ignore the effects of terrain and obstacles on the aircraft during flight.
(2) The flight path between the nodes of the aircraft is the Euclidean distance.

In step 2, a mathematical model and constraints are established.
For the problem of planning the optimal wake route for an aircraft, based on the correction points in the flight area, it is converted into searching for multiple sets of routes, as the aircraft meets the maximum margin of error and passes through the minimum correction points. It guarantees timely vertical and horizontal error correction during the flight of the aircraft and can minimize the wake path from point A to point B of the aircraft. Create the following objective function.

The constraints are as follows.

Regarding the objective function, F ₁ of the objective function is the shortest path, and F ₂ is the minimum correction point.
Regarding the constraints, the constraints (1) and (2) are route balance constraints, in which the aircraft makes only one dive and jump for any node k, i.e., after the aircraft traverses the node. The constraint (3) is a linear expression of the number of nodes and the number of flight paths that the aircraft traverses, guaranteeing the uniqueness of the flight path, and the constraint (4). ) And (5) are traverse path circuit constraints, ensuring that no empty subloop solution occurs during flight, and constraints (6) and (7) are correction error constraints, respectively. The validity of the flight path is guaranteed by limiting the cumulative horizontal error and the cumulative vertical error to be less than or equal to the maximum allowable positioning error, and the constraint (8) is that the distance between the two nodes is acceptable for the maximum positioning error. Equation (9) constrains the aircraft to traverse nodes i, j, k in sequence, and equations (11) and (12) are constraints. The guidance constraints of (6) and (7), that is, considering whether or not the aircraft can be successfully corrected due to environmental factors, and if it can be successfully corrected, select equations (11) and (12). , Otherwise, select (6) and (7), and equation (10) is the turning radius constraint of the aircraft.

The symbols will be described.
N is a set of nodes of correction points in the flight area.
i, j, and k are abbreviations for the i, j, and kth nodes in the node set N.
n is the total number of nodes in the node set N.
di _ij is the distance of the aircraft from node i to node j.
x _ij is a binary variable indicating whether or not the aircraft is flying from node i to node j. If the aircraft flies from node i to node j, x _ij = 1, otherwise x _ij. = 0.
x _ik is a binary variable indicating whether or not the aircraft is flying from node i to node k. If the aircraft flies from node i to node k, x _ik = 1, otherwise x _ik. = 0.
x _kj is a binary variable indicating whether or not the aircraft is flying from node k to node j. If the aircraft flies from node k to node j, x _kj = 1, otherwise x _kj. = 0.
y _i is a binary variable indicating whether or not the node i is traversed by the aircraft, and if the aircraft jumps out or jumps out of the node i, that is, if the node i is traversed by the aircraft. , Y _i = 1, otherwise y _i = 0.

は、ノードｉが集合Ｈに属するか否かを示すバイナリ変数であり、ノードがｉ∈Ｈであれば、

であり、そうでなければ、

である。
Ｖは、垂直補正点集合であり、

は、ノードｉが集合Ｖに属するか否かを示すバイナリ変数であり、ノードがｉ∈Ｖであれば、

であり、そうでなければ、

である。 δ is the amount of increase in horizontal error and vertical error for each 1 m flight of the aircraft.
θ is the cumulative error threshold.
h _j is the total amount of horizontal deviation when the aircraft reaches the position of node j. h _k is the total amount of horizontal deviation when the aircraft reaches the position of node k.
v _j is the total amount of vertical deviation when the aircraft reaches the position of node j. v _k is the total amount of horizontal deviation when the aircraft reaches the position of node k.
H is a set of horizontal correction points,

Is a binary variable indicating whether or not the node i belongs to the set H, and if the node is i ∈ H,

And otherwise

Is.
V is a set of vertical correction points,

Is a binary variable indicating whether or not the node i belongs to the set V, and if the node is i ∈ V,

And otherwise

Is.

は、ノードｋが集合Ｈに属するか否かを示すバイナリ変数であり、ノードｋ∈Ｈであれば、

であり、そうでなければ、

である。
ηは、補正マージンであり、単位がｍであり、η∈[2,8] である。 δ is the amount of increase in horizontal error and vertical error for each 1 m flight of the aircraft.
P _ijk is a binary variable that indicates whether the aircraft is traversing nodes i, j, k in sequence, and if the aircraft traverses nodes i, j, k in sequence, P _ijk = 1, otherwise. For example, _Pijk = 0.
d _jk is the distance of the aircraft from node j to node k.

Is a binary variable indicating whether or not the node k belongs to the set H, and if the node k ∈ H,

And otherwise

Is.
η is the correction margin, the unit is m, and η ∈ [2,8].

D is a set of nodes that failed to be corrected. S is a set of nodes whose probability that the error correction is 0 is ξ.
R _ijk is the turning radius. R _min is the minimum turning radius.
S _ijk is the area of a triangle surrounded by nodes i, j, k.
d _jk is the distance from node j to node k. _{di ik} is the distance from node i to node k.
p is the semiperimeter of the triangle surrounded by the nodes i, j, k.

In step 3, an instance of the method of rapidly planning the wake of a smart aircraft under multi-constraint conditions is calculated, and the original instance information is shown in Table 1. Node A is the start position coordinate, B node is the end position coordinate, and the correction point attribute types are classified into I and II. In class I, 0 is the horizontal error correction point (the aircraft corrects it). When passing through a point, the horizontal error is automatically reset to 0), and 1 represents a vertical error correction point (when the aircraft passes the correction point, the vertical error is automatically reset to 0). In class II, 1 indicates that the probability ξ that can successfully correct an error to 0 is 0.8, and 0 indicates that an error can be successfully corrected to 0.

In step 4, the starting point is point A (0.50000, 5000), the destination is point B (100,000, 59652.34, 5022), and the track length is as small as possible among the 99 spatial nodes. Find the track plan that has been corrected through the correction area and has the least number of times, and linearize the specific values of the constraints.

The following are specific steps to be obtained by operating a heuristic neighborhood search algorithm.
In step A, the initial parameters and instance information are input. The instance information is shown in Table 1. The initial parameters are as follows.
(1) The maximum number of cycles is 100.
(2) The cumulative error threshold value θ = 30, and the error increases by δ each time the aircraft flies 1 m. The value is δ = 0.001.
(3) Regarding the vertical error correction conditions, the vertical error of the aircraft is α ₁ = 25 m or less, and the horizontal error is α ₂ = 15 m or less.
(4) Regarding the horizontal error correction conditions, the vertical error of the aircraft is β ₁ = 20 m or less, and the horizontal error is β ₂ = 25 m or less.
(5) The aircraft is restricted by the structure and control system when turning, and its minimum turning radius is R _min = 200 m.
(6) The correction margin η is 5.
At the same time, the following error correction rules are created.
At the departure point A, the vertical and horizontal errors of the aircraft are both 0, and after correcting the vertical error for the aircraft at the vertical error correction point, the vertical error becomes 0, the horizontal error remains as it is, and it is horizontal. After correcting the horizontal error for the aircraft at the error correction point, it is set that the horizontal error becomes 0 and the vertical error remains as it is.

In step B, the related candidate point set P ₄ is determined as shown in (1) to (3) below.
(1) In the node set N, the node that the aircraft has not traversed is selected as the next candidate node, and when the aircraft reaches from the current node to the next candidate node, both the cumulative horizontal error and the cumulative vertical error are cumulative errors. selects a smaller nodes than the threshold theta, and stores the set P _1.
(2) In P ₁ , a node having an X-axis coordinate value larger than the X-axis coordinate value of the current node of the aircraft is selected and stored _{in the candidate point set P 2.}
(3) Error value type that needs to be calibrated when reaching the next point based on the current cumulative horizontal and cumulative vertical error values of the aircraft to avoid large cumulative error values of the aircraft. Is selected, and the candidate point set P ₄ is determined by the following two methods.

In method 1,
a, configured in the set P _2, the set P ₃ to select the vertical correction satisfying node called vertical error horizontal error in the first vertical error threshold alpha ₁ or less is first horizontal error threshold alpha ₂ or less, If there is no node that satisfies the vertical correction condition in P ₂ , the horizontal correction condition that the vertical error is the second vertical error threshold β ₁ or less and the horizontal error is the second horizontal error threshold β ₂ or less is satisfied _{in P 2.} Select the nodes to form the set P ₃ and
b, determines the current node and the position coordinates of the previous node of the aircraft, randomly selects any point in the P ₃ as the next node, this three nodes constitute a space triangular, following the current node If the turning radius obtained by obtaining the turning radius when reaching the node of is larger than the _{minimum turning radius R min, the node selected from the set P 3} satisfies the turning radius constraint, and therefore the node a is stored in the candidate point set P _4. Select all the nodes satisfying the turning radius constraint from P _{3 to form the candidate point set P 4} .

In method 2,
A vertical correction point that can achieve perfect calibration in set P ₂ or satisfies the correction margin η is selected as the _{candidate point set P 4} , otherwise horizontal that can be completely calibrated in _{set P 2 or satisfies the correction margin η.} selecting a correction point as candidate point set P _4.
In step C, the current and node a step forward by selecting one of the nodes from the candidate point set P _4, determines the candidate point set P ₄ of the next node. The specific method is as follows.

_{Select one of the nodes from the candidate point set P 4} obtained in step B, take a step forward to make it the current node, return to step B, _{select the candidate point set P 4} of the next node, and then If the candidate point set P ₄ of the node of is an empty set, the process _{returns to the candidate point set P 4} obtained in step B, another node is selected as the current node, and the calculation is continued. If all the nodes in the candidate point set P ₄ are the current nodes, and if the candidate point set P ₄ of the next node acquired by returning to step B is an empty set, the current node of the _{original candidate point set P 4} Is acquired as a dead point, returned to the node before the current node, and the previous node is recalculated as the current node.
Step B, In C, it is determined whether contains the end point coordinates for each candidate point set P ₄ is not empty, if it contains, the process proceeds to step D to save the track, otherwise , Steps B and C, and continue to determine _{the candidate point set P 4 of the next node.}
In step D, the number of cycles increases by 1 each time one track is obtained, and it is determined whether or not the cumulative number of cycles reaches the maximum number of cycles. If not, the process returns to step A and a new track is searched for. Continue to, otherwise output all wakes.

In step 5, the calculation result is analyzed.
(1) of the method described in Step 4 to obtain the candidate point set P ₄ Select method 1 to obtain a plurality of sets of not mutually dominant scheme calculated demanded. Two of these schemes are selected and shown in Table 2 and FIG.

As can be seen from the above, with respect to Scheme 1, the aircraft can reach the end position B from the start position A through nine nodes excluding the start and end positions, the sum of the minimum traverse routes is 120787.00 m, and each The cumulative error reaching the node is both smaller than the associated horizontal and vertical error constraints and satisfies the set minimum radius constraint. Regarding scheme 2, the number of nodes traversed by the aircraft is 10, but the sum of the minimum routes found is 119754.84m, and when comparing the two schemes, there are solutions that are not dominant in the multipurpose process. It has been put on hold, and it can be seen that each has its own advantages.

(2) of the method described in Step 4 to obtain the candidate point set P ₄ Select method 2 to obtain a plurality of sets of not mutually dominant scheme calculated demanded. Two of these schemes are selected and shown in Table 3 and FIG.

As can be seen from Table 3, assuming that the number of spatial nodes is 99, considering the correction uncertainty constraint, in Scheme 3, the aircraft passes through eight nodes excluding the start and end positions, and the minimum traverse route. The sum of is 118132.68m, and in scheme 4, the aircraft passes through nine nodes excluding the start and end positions, but the sum of the obtained minimum traverse routes is 117006.88m, which contrasts the two schemes. Then, in the process of seeking for multiple purposes, solutions that are not dominant to each other are reserved, and it can be seen that each has its own advantages.

Although the contents relating to the present invention have been described above, those skilled in the art can realize the present invention based on these explanations. Based on the above contents of the present invention, all other examples obtained by those skilled in the art without the need for creative acts should be included in the scope of protection of the present invention.

Claims (4)

Including the following steps S1 to S3
In step S1, the characteristics of the aircraft track plan are analyzed, a mathematical optimization model of multi-constraints is established with a multi-objective function, and the model is established.
Based on the characteristics of the aircraft's track plan, the aircraft is simplified to mass points, ignoring the size of the aircraft, and the flight path between the nodes of the aircraft is the Euclidean distance, and the objective function of the following mathematical optimization model is established. ..

Through
In the equation, N is the node set of correction points in the flight area, i and j are the abbreviations for the i and jth nodes in the node set N, and _di j is the aircraft from node i to node j. X _ij is a binary variable indicating whether or not the aircraft is flying from node i to node j, and if the aircraft flies from node i to node j, x _ij = 1, so Otherwise, x _ij = 0,
The objective function satisfies the following constraints 1) to 3).
1) Route balance constraint: The restriction is that the aircraft makes only one dive and jump, that is, the aircraft does not traverse the node after traversing the node, and the route balance constraint formula is as follows. can be,

In the equation, k is the abbreviation for the kth node in the node set N, n is the total number of nodes in the node set N, and x _ij is whether or not the aircraft is flying from node i to node k. It is a binary variable shown, and if the aircraft flies from node i to node k, then x _ij = 1, otherwise x _ij = 0, and x _kj is that the aircraft flies from node k to node j. It is a binary variable indicating whether or not the aircraft is flying, and if the aircraft flies from node k to node j, x _kj = 1, otherwise x _kj = 0.
2) Route uniqueness constraint: The restriction is that the aircraft traverses each node in sequence to form only one effective route, and the route uniqueness constraint formula is as follows.

In the equation, y _i is a binary variable indicating whether or not the node i is traversed by the aircraft, and if the aircraft jumps out or jumps out of the node i, that is, the node i is traversed by the aircraft. If, y _i = 1, otherwise y _i = 0,
3) Traverse route circuit constraint: It is a restriction that no subloop solution occurs during flight of the aircraft, and the traverse route circuit constraint formula is as follows.

In step S2, the start point coordinates of the aircraft, the end point coordinates, the spatial position coordinates of all the correction points in the flight area, and the instance information including the error correction type including the horizontal error correction type and the vertical error correction type are acquired. ,
In step S3, a heuristic neighborhood search algorithm is operated to obtain an instance to acquire and select a plurality of selectable schemes.
A method of rapidly planning the wake of a smart aircraft under multiple constraints. The constraints further include cumulative horizontal error and cumulative vertical error constraints, and can be divided into the following two situations regarding whether or not to perform ideal error correction when the aircraft reaches node j from node i.
In Situation 1, when the aircraft reaches node j from node i and can perform ideal error correction, the cumulative horizontal error and cumulative vertical error whose constraint equations are as follows are within the maximum positioning error range. Guarantee the effectiveness of the flight path by limiting that

In the equation, θ is the cumulative error threshold, h _j is the total horizontal displacement when the _{aircraft reaches the position of node j, and v j} is the total when the aircraft reaches the position of node j. It is the amount of vertical deviation, and H is a set of horizontal correction points.

Is a binary variable indicating whether or not the node i belongs to the set H, and if the node is i ∈ H,

And otherwise

And V is a set of vertical correction points,

Is a binary variable indicating whether or not the node i belongs to the set V, and if the node is i ∈ V,

And otherwise

And δ is the amount of increase in horizontal error and vertical error for each 1 m flight of the aircraft.
In situation 2, if the aircraft flies from node i to node j and the ideal error correction cannot be performed, the next node k is selected and error correction is performed, and at this time, the cumulative horizontal error and the cumulative error are accumulated. The constraint formula for vertical error is as follows:

In the equation, _Pijk is a binary variable indicating whether or not the aircraft is traversing the nodes i, j, k in sequence, and if the aircraft traverses the nodes i, j, k in sequence, _Pijk = 1. Otherwise, _Pijk = 0 and d _jk is the distance of the aircraft from node j to node k.

Is a binary variable indicating whether or not the node k belongs to the set H, and if the node k ∈ H,

And otherwise

, Η is the correction margin, the unit is m, η ∈ [2,8], D is the set of nodes that failed to correct, and S is the probability that the error correction is 0. The method for rapidly planning the track of a smart aircraft under the multi-constraint condition according to claim 1, wherein the node set is ξ. Obtaining an instance by operating the heuristic neighborhood search algorithm includes the following steps A to D.
In step A, the maximum number of cycles, the cumulative error threshold θ, the vertical error correction conditions that are the first vertical error threshold and the first horizontal error threshold, and the horizontal error correction that is the second vertical error threshold and the second horizontal error threshold. Enter the initial parameters including the conditions, the minimum turning radius, the error increment for each 1 m flight of the aircraft, and the instance information.
In step B, the related candidate point set P ₄ is determined as shown in (1) to (3) below.
(1) In the node set N, the node that the aircraft has not traversed is selected as the next candidate node, and when the aircraft reaches from the current node to the next candidate node, both the cumulative horizontal error and the cumulative vertical error are cumulative errors. Select nodes smaller than the threshold θ _{, store them in the set P 1,} and store them.
(2) In P ₁ , a node having an X-axis coordinate value larger than the X-axis coordinate value of the current node of the aircraft is selected, stored in the _{candidate point set P 2, and stored.}
(3) Error value type that needs to be calibrated when reaching the next point based on the current cumulative horizontal and cumulative vertical error values of the aircraft to avoid large cumulative error values of the aircraft. And determine the candidate point set P _{4 by the following two methods,}
In method 1,
a, in the set P _2, constitute a set P ₃ to select the vertical correction satisfying node called vertical error horizontal error below the first vertical error threshold is less than or equal to the first horizontal error threshold, vertically in P ₂ If there is no node that satisfies the correction condition, in P ₂ , a node that satisfies the horizontal correction condition that the vertical error is equal to or less than the second vertical error threshold and the horizontal error is equal to or less than the second horizontal error threshold is selected and set P ₃ Configure and
b, determining the position coordinates of the current node and the previous node of the aircraft, the any point in the P ₃ randomly selected as the next node, this three nodes constitute a space triangular, following the current node If the turning radius obtained by obtaining the turning radius when reaching the node of is larger than the _{minimum turning radius R min, the node selected from the set P 3} satisfies the turning radius constraint, and the node is selected. stored in the candidate point set P _4, constitute the candidate point set P ₄ by selecting all the nodes that satisfy the turning radius constraints from P _3,
In method 2,
A vertical correction point that can achieve perfect calibration in the set P ₂ or satisfies the correction margin is selected as the _{candidate point set P 4} , otherwise a horizontal correction point that can be completely calibrated in _{the set P 2 or satisfies the correction margin.} selected as the candidate point set P _4,
In step C, the current and node a step forward by selecting one of the nodes from the candidate point set P _4, and determining the candidate point set P ₄ of the next node, specific methods are as follows ,
Select one of the candidates from the candidate point set P ₄ obtained in step B, take a step forward to make it the current node, return to step B, _{select the candidate point set P 4} of the next node, and then If the candidate point set P ₄ of the node is an empty set, return to the candidate point set P ₄ obtained in step B, select another node as the current node, continue the calculation, and all in the _{candidate point set P 4 If the candidate point set P 4} of the next node acquired by returning to step B is an empty set, _{the current node of the original candidate point set P 4} is acquired as a dead point. Return to the node before the current node, recalculate the previous node as the current node, and
Step B, In C, it is determined whether contains the end point coordinates for each candidate point set P ₄ is not empty, if it contains, the process proceeds to step D to save the track, otherwise , step B, and back to the C continues to determine the candidate point set P ₄ of the next node,
In step D, the number of cycles increases by 1 each time one track is obtained, and it is determined whether or not the cumulative number of cycles reaches the maximum number of cycles. If not, the process returns to step A and a new track is searched for. Continue to, otherwise output all wakes,
A method for rapidly planning the track of a smart aircraft under the multi-constraint condition according to claim 2. The calculation method of the turning radius is as follows.

In the equation, is the turning radius, s is the area of the triangle surrounded by nodes i, j, k, and p is the semiperimeter of the triangle surrounded by nodes i, j, k.
A method for rapidly planning the track of a smart aircraft under the multi-constraint condition according to claim 3.

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