An Optimal Feasible Path Planning Method for Aircraft Based on Graph Theory

Abstract

This application belongs to the technical field of path planning, and specifically relates to an optimal feasible path planning method for aircraft based on graph theory. First, digital modeling is performed on the airport, and useful information in the useful airport model is extracted. Then, the Dijkstra algorithm is used for path search, and combined with the Dubins path optimization algorithm for the airport environment, the performance constraints of the aircraft itself during taxiing are introduced to generate the optimal feasible taxiing path for the aircraft. The present invention combines the graph theory method with the smoothing algorithm to solve the problem of automatic arrival and departure path planning at real airports. After the planning is completed in the ground command and control system, the planning result is uploaded to the aircraft to enable the aircraft to taxi to the target position from any initial position along the shortest path.

Description

Technical Field

[0001] This application belongs to the technical field of path planning, and particularly relates to an optimal feasible path planning method for aircraft based on graph theory. Background Art

[0002] With the rapid development of China's civil aviation industry, the flight pressure borne by airports has been increasing day by day, and the previous flight delays from the air have gradually shifted to the ground. At the same time, due to the complexity of airport layouts and the increasingly frequent low visibility operations, the chaos of airport ground traffic has been exacerbated. The operation of the airport surface mainly refers to the process of aircraft arrival and departure. After an arriving aircraft completes the approach and landing, it leaves the runway and enters the taxiway system, and then taxis to the designated apron or stand according to the instructions of the airport tower control, and represents the end of the entire arrival process after receiving ground services or connecting to the jet bridge. After receiving the release instructions from the control, a departing aircraft starts up and taxis out of the stand by its own power or is towed out by a tractor and enters the taxiway system, and taxis to the waiting point of the takeoff runway according to the instructions of the controller and joins the departure queue.

[0003] The airport surface taxiing planning problem can fundamentally be regarded as a shortest path planning problem. Traditional path planning methods such as the A* algorithm and genetic algorithm only generate discrete points for path planning, which is equivalent to path searching, but do not consider the dynamic constraints during the aircraft surface taxiing process. And polynomial interpolation and circular arc straight line planning algorithms only smooth the existing path points and do not have the ability of path searching. Therefore, in order to generate the optimal feasible taxiing path for an aircraft, a path planning method that combines path searching and smoothing is needed to be invented. Summary of the Invention

[0004] In order to solve the above problems, this application provides an optimal feasible path planning method for aircraft based on graph theory, which mainly includes:

[0005] Step S1, construct a digital airport model, and abstract the digital airport model into a point-line model with turning constraints and connection relationships;

[0006] Step S2, for the digital airport model, use the Dijkstra algorithm to perform optimal path search;

[0007] Step S3, use the Dubins algorithm to smooth the search result of the Dijkstra algorithm.

[0008] Preferably, in step S1, it further includes:

[0009] Take the center point of the stand, the intersection point of the taxiway center line and the connecting taxiway center line, and the intersection point of the runway center line and the connecting taxiway center line as key path points;

[0010] Extract the position coordinates of the key path points, the connectivity relationship of all key path points, and the maximum allowable radius of the airport turning terrain.

[0011] Preferably, step S2 further includes:

[0012] Step S21: Let r be 0, and the initial taxiing node v1 of the aircraft obtains a label: P0 = {v1}, T0 = V - {v1}, v j (j ≠ 1) t-label:

[0013] Step S22: Assume r ≥ 1, and Mark it at the corresponding node v i to indicate that v i obtains a p-label, and modify the passed set and the unpassed set: P r = P r-1 ∪{v i}, T r = T r-1 - {v i}. If T r is an empty set, the algorithm ends and outputs the shortest taxiing path; otherwise, continue;

[0014] Step S23: Let be the p-label of the node that has just obtained the p-label; let r be r + 1, and transfer to step S21;

[0015] Among them, if is the weight of the shortest taxiing path from the initial taxiing node v1 of the aircraft to the node v i , if the node v i obtains the label then it is said that v i obtains the p-label at the r-th step If is the upper bound of the shortest path weight from the initial taxiing node v1 of the aircraft to the node v j , if v j obtains it is said that v j obtains the t-label at the r-th step P r = {v|v has obtained the p-label} is the passed set at the r-th step, T r = V - P r is the unpassed set at the r-th step, r ≥ 0.

[0016] Preferably, step S3 further includes:

[0017] Solve the shortest trajectory between two points with specific direction vectors when the turning radius of the aircraft is used as the curvature through the Dubins algorithm.

[0018] Preferably, the trajectory is composed of a curved part and a straight part. The straight part is one of two tangents tangent to two circles, where the starting and ending positions are respectively located on the arcs of one of the circles. The radius of the arc is the radius of curvature, which is determined by the turning radius of the aircraft, and the center of the arc is the center of curvature.

[0019] Preferably, the tangents include inner tangents and outer tangents.

[0020] The present invention proposes an optimal feasible taxiing path planning method for aircraft based on graph theory to solve the problem of planning the optimal feasible taxiing path for automatic entry and exit at airports. This method first digitally models the airport, extracts useful information from the useful airport model, then uses the Dijkstra algorithm for path search, and then combines with the Dubins path optimization algorithm for the airport environment, introducing the performance constraints of the aircraft itself during taxiing to generate the optimal feasible taxiing path for the aircraft.

[0021] The present invention combines the graph theory method with the smoothing algorithm to solve the problem of automatic airport approach and departure path planning in reality. After the planning is completed in the ground command and control system, the planning result is uploaded to the aircraft to enable the aircraft to taxi from any initial position to the target position along the shortest path. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flowchart of a preferred embodiment of the present invention.

[0023] Figure 2 Shown is a schematic diagram of key information extraction of the airport model of the present invention.

[0024] Figure 3 Shown is a schematic diagram of the path calculation parameters of Dubins with an outer common tangent of the present invention.

[0025] Figure 4 Shown is a schematic diagram of the path calculation parameters of Dubins with an inner common tangent of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0026] To make the purpose, technical solution and advantages of the present application clearer, the technical solution in the embodiments of the present application will be described in more detail below with reference to the accompanying drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements with the same or similar functions throughout. The described embodiments are part of the embodiments of the present application, not all of the embodiments. The embodiments described below by referring to the drawings are exemplary and are intended to explain the present application, and should not be construed as a limitation to the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts fall within the scope of protection of the present application. The embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0027] The present invention is used to solve the problem of automatic planning of the taxiing path for an aircraft to drive from the apron to the runway take-off point and to drive out of the runway from the landing point and reach the designated parking position.

[0028] To achieve the above purpose, the present application provides an optimal feasible path planning method for an aircraft based on graph theory, as Figure 1 shown, mainly including:

[0029] Step S1: Construct an airport digital model, and abstract the airport digital model into a point-line model with turning constraints and connection relationships;

[0030] Step S2: For the airport digital model, use the Dijkstra algorithm to perform an optimal path search;

[0031] Step S3: Use the Dubins algorithm to smooth the path obtained by the Dijkstra algorithm.

[0032] The following is a detailed description.

[0033] First, in step S1, the airport is digitally modeled to extract the key information for path planning.

[0034] The airport system is mainly divided into two parts: landside and airside. The landside part includes the terminal building and the ground arrival system, which is the place where passengers transfer their transportation modes. The airside part includes the runway, taxiway and apron, which is the place where aircraft operate. The runway, taxiway and apron are also called the airfield, and sometimes the terminal area or even the approach area is classified as the basic airside part.

[0035] The runway is a rectangular area within the airport that provides take-off, landing and taxiing for aircraft. The attributes of the runway include: direction, length, width, number, configuration, operating category and operating mode, etc. The runway is one of the important components of the airport, and the attributes of the runway can determine the grade and standard of the airport.

[0036] The taxiway is one of the important ground facilities of an airport. It is the designated passage for aircraft to taxi on a land airport, connecting various functional areas of different natures. The taxiway system mainly includes: main taxiways (parallel taxiways), connecting taxiways, aircraft stand taxiways, apron taxiways, rapid exit taxiways, auxiliary taxiways, taxiway shoulders, and taxiway strips.

[0037] The apron, also called the aircraft parking area, is a place where aircraft park, passengers board and alight, cargo is loaded and unloaded, and various ground services are provided for the aircraft (such as aircraft maintenance, water supply, catering, power supply, cleaning, etc.). The apron needs to have a sufficient area to ensure passage for vehicles and personnel for the above activities. Operating lines are marked on the apron with paint to enable aircraft to enter and exit the taxiway along a certain route. The apron is divided into a parking apron and a boarding apron. Aircraft load and unload cargo and refuel on the boarding apron, and stay overnight, are repaired, and parked for a long time on the parking apron. According to the distance between the aircraft stand and the terminal building, aircraft stands are generally divided into near stands and far stands.

[0038] For the airport information required by the Dijkstra path search algorithm, a plane coordinate system with O as the origin is established, as Figure 2 shown. Taking the center points of aircraft stands, the intersections of the centerlines of taxiways and connecting taxiways, and the intersections of the centerlines of runways and connecting taxiways as the typical features of the digital airport, which are called key path points in this paper. By extracting the position coordinates of key path points, the connection relationships of all key path points, and the maximum allowable radius of the airport turning terrain, the airport model can be abstracted into a point-line model with turning constraints and connection relationships. Taking the aircraft approach as an example, there are two ways to drive out from the apron: aircraft on the stands on both sides of the apron drive into the taxiway through the center line of the apron; aircraft on the stands at the bottom of the apron drive directly into the corresponding connecting taxiway entrance.

[0039] After that, in step S2, for the digital airport model, the Dijkstra algorithm is used to search for the optimal path.

[0040] The Dijkstra algorithm is a typical single-source shortest path algorithm in graph theory. Compared with algorithms such as the A* algorithm and genetic algorithm, it not only has better breadth-first search characteristics, but also has a fast algorithm running speed and is more suitable for application in path planning. In this paper, an optimized algorithm based on the Dijkstra algorithm is used to optimize the taxiing path. The Dijkstra algorithm is widely applied, such as in multi-point routing, in surveying and mapping science, and in the shortest path of logistics transportation, etc. The Dijkstra algorithm expands layer by layer outward with the starting point as the center until it reaches the end point, that is, the shortest path is obtained through the forward traversal and comparison of all nodes. Because it obtains the shortest path after traversing all nodes, the success rate of the obtained shortest path is very high and the robustness is also very good.

[0041] The Dijkstra algorithm is also known as the double - labeling algorithm. The meaning of double - labeling is as follows: For a point v1 in the graph, two labels (P(v i ), x i ) are assigned, where the label P(v i ) represents the distance of the shortest path from the starting point v1 to v i , and the label x i represents the subscript of the adjacent point before v i on the shortest path from v1 to v i , that is, it is used to represent the path, so that the reverse tracing can be carried out from the end point to the starting point to find the shortest path from v1 to v n . The Dijkstra algorithm is applicable to the case where the weight of each edge in the network graph is greater than or equal to zero. The following is the specific content of the Dijkstra algorithm:

[0042] Let G = <V, E, w> be the network graph of the airport taxiing path, where w ij is the weight of the taxiway, and w ij ≥0. If the nodes v i and v j are not adjacent, then w ij = ∞. To find the shortest path from the starting node (taxi - stand or air - ground connection point) v1 to the terminating node (runway end or taxi - stand) in G (in fact, the shortest taxiing path between any two nodes can be calculated), for this purpose, the following definitions are given first:

[0043] Let be the weight of the shortest taxiing path from the initial taxiing node v1 of the aircraft to the node v i . If the node v i obtains the label , then v i is said to obtain the p - label (permanent label) at the r - th step, where r≥0.

[0044] Let be the upper bound of the weight of the shortest path from the initial taxiing node v1 of the aircraft to the node v j . If v j obtains , then v j is said to obtain the t - label (temporary label) at the r - th step.

[0045] Let P r = {v|v has obtained the p - label} be the passed - set at the r - th step, and let T r = V - P r be the un - passed - set at the r - th step, r≥0.

[0046] The Dijkstra algorithm starts:

[0047] Step S21: r ← 0, the initial taxiing node v1 of the aircraft obtains a label: P0 = {v1}, T0 = V - {v1}, v j The t label of (j ≠ 1):

[0048] Step S22: Let r ≥ 1. Place on the corresponding node v i to indicate that v i obtains a p label, and modify the passed set and the unpassed set: P r = P r-1 ∪ {v i}, T r = T r-1 - {v i}. Check T r : If T r is an empty set, the algorithm ends and outputs the shortest taxiing path; otherwise, continue.

[0049] Step S23: is the p label of the node that just obtained the p label. Let r ← r + 1, and go to Step S21.

[0050] Finally, in this application, the Dubins algorithm is used in Step S3 to perform path smoothing on the search results of the Dijkstra algorithm.

[0051] The core of the Dubins curve theory is that under certain curvature conditions, the shortest trajectory connecting any two points with specific direction vectors in the same plane is a curve. In the absence of other constraint factors, the shortest path between any two points on the same plane is a straight line, but under certain curvature constraints, the shortest path is an arc. The Dubins curve theory is mainly used to solve the shortest path with curvature constraints. By choosing one of the two tangents tangent to two circles, the Dubins path can be obtained, where the starting and ending positions are both on the arc, the radius of the arc is the curvature radius, which is determined by the turning radius of the aircraft, and the center of the arc is the curvature center. Thus, the problem is simplified to finding the common tangent of two arcs. There are two types of common tangents between two circles: internal tangent and external tangent.

[0052] The solution process of the external tangent is to find the center o s of the starting circle C s (x cs , y cs ), and the center o f of the ending circle C f (x cf , y cf ):

[0053] xcs = x s - r s cos(φ s ±π / 2)

[0054] y cs = y s - r s sin(φ s ±π / 2)

[0055] x cf = x f - r f cos(φ f ±π / 2)

[0056] y cf = y f - r f sin(φ f ±π / 2)

[0057] In the formula, C s and C f are also called the base circles. When the circle is on the right side of the tangent line, the sign is positive; when the circle is on the left side of the tangent line, the sign is negative; there are two cases where the directed curve is tangent to the circle, one is that the circle is on the right side of the tangent line and the other is that the circle is on the left side of the tangent line. When determining whether the circle is on the left or right side, the present application is based on looking along the direction of the tangent line.

[0058] Reference Figure 3 , (1) When r f ≥ r s , draw a circle C f with a radius of |r f - r s | at o sec ;

[0059] (2) Connect o s and o f with the center line c, and its length

[0060] (3) Draw a right triangle with c as the hypotenuse. One right side of this right triangle intersects C sec at T' and C f at P N , where P N is called the entry point;

[0061] (4) Connect o s and T';

[0062] (5) Starting from o s , draw a line that is parallel to o f P NParallel lines, intersecting with C s at point P X , called the cut-off point;

[0063] (6) Connect point P X and point P N , to obtain a line P s parallel to o X , P N , called the external tangent;

[0064] (7) Draw an arc with radius r s to connect point P s and point P X , and a line segment connecting point P X and P N , and another arc with radius r f to connect point P N and point P f . The interconnected arcs and lines form a Dubins path containing the external tangent.

[0065] Finally, the Dubins path can be obtained from the figure. In the above figure, Δo s o f T′ is a right triangle, o f T′ and o s T′ are its two right sides, o s o f is its hypotenuse. The angle between o s o f and o s T′ can be calculated:

[0066]

[0067] The slope of the center line is:

[0068]

[0069] Therefore, the position of the cut-off point s on C and the entry point f on C can be calculated by the following formula:

[0070]

[0071]

[0072]

[0073]

[0074] The angles corresponding to the arcs from the starting point to the tangent point and from the tangent point to the ending point can be calculated through the following steps:

[0075] (1) The angle from the starting point to the cut-off point P X is

[0076] (2) The rotation from point P X to point P N is a zero-degree rotation. The angle from the entry point P N to the ending point is:

[0077]

[0078] (3) The length of the straight line between the entry point and the cut-off point is:

[0079]

[0080] The design of the Dubins path based on the inner tangent is basically the same as that based on the outer tangent. The only difference is the rotation angle. As Figure 4 shown, the solution steps are as follows:

[0081] (1) Locate the center o s of the starting circle C s (x cs , y cs ), and the center o f of the ending circle C f (x cf , y cf );

[0082] (2) When r f ≤ r s , draw a circle C f with a radius of |r f + r s | at o sec ;

[0083] (3) Connect o s and o f with the center line c, and its length

[0084] (4) Draw a right triangle with c as the hypotenuse. One right side of this right triangle intersects C sec at T′ and C f at P N , where P N is called the entry point;

[0085] (5) Connect o s and T′;

[0086] (6) Starting from o s , draw a straight line parallel to o f P N , which intersects C s at point P X , which is called the cut-off point;

[0087] (7) Connect point P X and point P N , to obtain a straight line parallel to o s T′, P X P N , which is called the internal tangent.

[0088] In Figure 4 , Δo s o f T′ is a right triangle, o f T′ and o s T′ are its two right sides, o s o f is its hypotenuse. The included angle between o s o f and o f T′ can be calculated:

[0089]

[0090] The rotation angle required to design the Dubins path can be calculated by the following formula:

[0091] (1) The angle of rotation from the starting point to the cut-off point P X is

[0092] (2) The rotation from point P X to point P N is a zero-degree rotation;

[0093] (3) The angle of rotation from the cut-in point P N to the end point is

[0094] Although the present application has been described in detail above with general descriptions and specific implementation manners, based on the present application, some modifications or improvements can be made, which are obvious to those skilled in the art. Therefore, these modifications or improvements made without departing from the spirit of the present application fall within the scope of protection required by the present application.

Claims

1. An optimal feasible path planning method for an aircraft based on graph theory, characterized in that, Including: Step S1: Construct an airport digital model, which is abstracted as a point-line model with turning constraints and connection relationships; Step S2: For the airport digital model, use the Dijkstra algorithm to search for the optimal path; Step S3: Use the Dubins algorithm to smooth the path of the search result of the Dijkstra algorithm; Among them, in step S1, it further includes: Taking the center points of the parking bays, the intersections of the taxiway centerlines and the connecting taxiway centerlines, and the intersections of the runway centerlines and the connecting taxiway centerlines as key path points; Extracting the position coordinates of the key path points, the connection relationships of all key path points, and the maximum allowable radius of the airport turning terrain; Step S3 further includes: Solving the shortest trajectory between two points with specific direction vectors when the curvature is the turning radius of the aircraft through the Dubins algorithm; The trajectory consists of a curved part and a straight part. The straight part is one of the two tangents tangent to two circles, where the starting and ending positions are respectively located on the arcs of one of the circles. The radius of the arc is the curvature radius, which is determined by the turning radius of the aircraft, and the center of the arc is the curvature center; The tangents include inner tangents and outer tangents.

2. The optimal feasible path planning method for an aircraft based on graph theory according to claim 1, characterized in that, Step S2 further includes: Step S21: Let r be 0, and the initial taxiing node v1 of the aircraft obtains a label: P0 = {v1}, T0 = V - {v1}, v j t label for (j ≠ 1): Step S22, set Label at the corresponding node v i to indicate that v i obtains a p-label, and modifies the passed set and the non-passed set: P r = P r-1 ∪ {v i}, T r = T r-1 - {v i}; if T r is an empty set, the algorithm ends and outputs the shortest taxiing path, otherwise continue; Step S23. Let be the p label of the node that has just obtained the p label. Let r be r + 1, and go to Step S21. Among them, if is the weight of the shortest taxiing path from the initial taxiing node v1 of the aircraft to node v i and if node v i obtains the label then it is said that v i obtains the p label at the r-th step If is the upper bound of the weight of the shortest path from the initial taxiing node v1 of the aircraft to node v j and if v j obtains then it is said that v j obtains the t label at the r-th step P r ={v|v has obtained the p label} is the passing set at the r-th step, and T r =V - P r is the non-passing set at the r-th step, r≥0.

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