Aircraft towing path planning method and device combining heuristic and optimal control

Abstract

The present application relates to a method and device for aircraft towing path planning combining heuristic and optimal control, the method comprising: using an A* algorithm for path planning to obtain an initial path; starting from the first node, re-searching each node in the initial path; when there is an obstacle within the preset range of the path between the first node and the second node, the second node is used as the key point, otherwise it is determined whether there is an obstacle within the preset range of the path between the first node and the third node, until it is determined whether there is an obstacle within the preset range of the path between the last node and the adjacent node, and a key point set is obtained; a kinematic model is established for the process of aircraft transportation on the platform, and constraints are met to obtain an optimal control model, and converted into a nonlinear programming model; key points are selected for geometric solution to obtain the corresponding key point posture; and the optimal path is output. The present method can be used to perform path planning and obtain the shortest path under the consideration of kinematic and terminal posture constraints.

Description

Technical Field

[0001] The present application relates to the technical field of path planning, and in particular to an aircraft towing path planning method and device combining heuristic and optimal control. Background Art

[0002] The efficiency of aircraft transportation is affected by many factors, such as equipment factors, human factors, environmental factors, etc. The narrow platform space is one of the important factors restricting the efficiency of sorting. Therefore, studying a path planning method suitable for the narrow platform space is the basis for ensuring the safe and efficient transportation of aircraft on the platform, which is of great significance to realize the automation of aircraft transportation and improve the efficiency of fleet transportation.

[0003] At present, the research on aircraft towing path planning is still in its infancy. For various path planning problems, research methods include geometric method, optimal control method, unit decomposition method, intelligent algorithm, artificial potential field method, reinforcement learning and combined algorithm.

[0004] The unit decomposition method performs path planning with the shortest path as the goal. Although it finds the shortest path, it cannot well display the motion state of the planned object. When the map is large and the number of units is large, the algorithm calculation amount increases dramatically. Moreover, it fails to consider the terminal posture constraints of the planning target.

[0005] The advantage of the artificial potential field method is its high computational efficiency. However, when the object is far away from the target point, the gravitational force will become particularly large, and the relatively small repulsive force can even be ignored, and the object may encounter obstacles on its path. When there are obstacles near the target point, the repulsive force will be very large and the gravitational force will be relatively small, making it difficult for the object to reach the target point. At a certain point, the gravitational force and the repulsive force are exactly equal in size and opposite in direction, and the object is likely to fall into a local optimal solution or oscillate.

[0006] Intelligent algorithms set objective functions and take large populations as the basis. Under certain constraints, they gradually search for the optimal solution that satisfies the constraints through continuous iterative screening. However, such algorithms are prone to fall into local optimal solutions, and with the increase of population and iteration times, the algorithm becomes computationally intensive and the solution is slow. It also fails to consider the terminal posture constraints of the planning target.

[0007] The optimal control method can perform path planning while considering kinematics, dynamics and terminal posture constraints. However, since this type of algorithm is sensitive to the initial state input, it is often difficult to converge when there are many obstacles in the initial and final positions and the space is small, or the initial and final positions are far apart (for a constant step size), or the obstacles in the path are complex and involve multiple turns. It is impossible to obtain a path or the obtained path does not conform to the actual situation. Summary of the invention

[0008] Based on this, it is necessary to provide an aircraft towing path planning method that combines heuristics and optimal control to address the above technical problems. It can perform path planning while considering kinematics and terminal posture constraints, quickly find the shortest path, and converge well to obtain the global optimum when the obstacle environment is complex.

[0009] The aircraft towing path planning method combining heuristics and optimal control includes:

[0010] Obtaining a path planning task for transporting an aircraft on a platform; the path planning task includes: an initial position of the aircraft, a target position of the aircraft, and obstacles;

[0011] Using the A* algorithm, a path is planned for the aircraft from an initial position to a target position to avoid obstacles, and an initial path is obtained, wherein the initial path includes a plurality of nodes;

[0012] Starting from the first node, each node in the initial path is re-searched; when there is an obstacle within the preset range of the path between the first node and the second node, the second node is used as the key point, otherwise, whether there is an obstacle within the preset range of the path between the first node and the third node is determined, until whether there is an obstacle within the preset range of the path between the last node and the adjacent node is determined, and a key point set is obtained;

[0013] A kinematic model is established for the process of aircraft transportation on the platform, and obstacle constraints, kinematic constraints and terminal posture constraints are satisfied to obtain an optimal control model; the optimal control model is transformed to obtain a nonlinear programming model;

[0014] One or more key points are selected from the key point set for geometric solution to obtain corresponding key point postures; and an optimal path is obtained according to the key point postures and the nonlinear programming model.

[0015] In one embodiment, the A* algorithm is used to plan a path from an initial position to a target position to avoid obstacles, and the initial path includes:

[0016] The A* algorithm is used to obtain the total cost of the current node based on the cost from the initial position to the current node, the estimated cost from the current node to the target position, and the dynamic measurement operator;

[0017] According to the minimum total cost of all nodes, obstacles are avoided and the initial path is obtained.

[0018] In one embodiment, the A* algorithm is used to plan a path from an initial position to a target position to avoid obstacles, and obtaining the initial path further includes:

[0019] When the obstacle is located on the horizontal axis of the current node, the path of the current node does not include the vertical adjacent nodes of the obstacle;

[0020] When the obstacle is located on the vertical axis of the current node, the path of the current node does not include the horizontally adjacent nodes of the obstacle.

[0021] In one embodiment, the dynamic metric is greater than or equal to one and gradually decreases from the initial stage to the final stage of the A* algorithm.

[0022] In one embodiment, the A* algorithm satisfies the obstacle convex hull expansion constraint;

[0023] The obstacle convex hull expansion constraint includes: connecting the maximum convex points of the aircraft contour into a convex polygon to obtain a convex hull model;

[0024] A polygon expansion algorithm is used to expand the convex hull model outward by a certain safety buffer distance to obtain a convex hull transition model;

[0025] Taking the vertex of the convex shell model as the center of the circle and the safety buffer distance as the radius, a plurality of circular models tangent to the convex shell transition model are obtained;

[0026] According to the convex hull transition model and the circle model, an obstacle convex hull expansion constraint is obtained.

[0027] In one embodiment, selecting one or more key points for geometric solution to obtain the corresponding key point postures includes:

[0028] Select one or more key points, obtain the angle bisector of two trajectories with the key point as the intersection point, take the normal line of the angle bisector as the speed direction of the aircraft at the key point, and take the maximum threshold speed as the speed magnitude of the aircraft at the key point;

[0029] According to the velocity direction and the velocity magnitude, one or more key point postures are obtained, and the key point postures correspond to the key points one by one.

[0030] In one embodiment, obtaining the optimal path according to the key point posture and the nonlinear programming model includes:

[0031] Inputting the key point posture into the nonlinear programming model, using a solver to solve the nonlinear programming model to obtain connection points; the connection points correspond to the key points one by one;

[0032] According to a key point and the connection points corresponding to the key point, a corresponding segmented path is obtained; according to all the segmented paths, an optimal path is obtained.

[0033] In one embodiment, the kinematic constraints and terminal posture constraints include:

[0034] The speed relationship constraints between the aircraft and the tractor, the steering angle and speed constraints of the aircraft, and the control variable constraints of the tractor.

[0035] In one embodiment, the optimal control model is transformed using a Radau pseudospectral algorithm.

[0036] An aircraft traction path planning device combining heuristic and optimal control includes:

[0037] An acquisition module is used to acquire a path planning task for the aircraft to be transported on the platform; the path planning task includes: an initial position of the aircraft, a target position of the aircraft, and obstacles;

[0038] An initial path establishment module is used to use the A* algorithm to plan a path from an initial position to a target position of the aircraft to avoid obstacles, and obtain an initial path, wherein the initial path includes a plurality of nodes;

[0039] A key point set establishment module is used to re-search each node in the initial path starting from the first node; when there is an obstacle within a preset range of the path between the first node and the second node, the second node is used as a key point; otherwise, it is determined whether there is an obstacle within a preset range of the path between the first node and the third node, until it is determined whether there is an obstacle within the preset range of the path between the last node and the adjacent node, thereby obtaining a key point set;

[0040] A model building module is used to establish a kinematic model for the process of aircraft transportation on the platform, and to satisfy obstacle constraints, kinematic constraints and terminal posture constraints to obtain an optimal control model; the optimal control model is transformed to obtain a nonlinear programming model;

[0041] The optimal path establishment module is used to select one or more key points in the key point set for geometric solution to obtain the corresponding key point posture; and obtain the optimal path according to the key point posture and the nonlinear programming model.

[0042] The above-mentioned aircraft towing path planning method combining heuristics and optimal control is designed in the A* algorithm to obtain a path that satisfies the kinematic and terminal posture constraints and has a short distance and short time, and avoids the initial value sensitivity problem of the optimal control method in a complex obstacle environment. The trajectory re-search algorithm is used to design a trajectory re-search algorithm in the A* algorithm, and the improved A* algorithm is used to perform preliminary path planning on the starting position and target position of the aircraft to obtain the shortest path to avoid obstacles. The key points of the shortest path are solved in the path, and an appropriate number of key points are selected to solve the motion state of the key points. The key points are used as the intermediate points of the final path planning. Combined with the optimal control algorithm, the starting position and target position of the aircraft are segmented and integrated. The road conditions are simplified through segmented planning, which effectively solves the initial value sensitivity problem of the optimal control algorithm and the problem that the optimal control algorithm falls into an iterative dead zone and cannot be solved due to complex obstacle conditions, and the shortest path that meets the kinematic and terminal posture constraints is obtained. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A schematic flow chart of an aircraft towing path planning method combining heuristics and optimal control in one embodiment;

[0044] Figure 2 A schematic diagram of the functional area division of the platform in one embodiment;

[0045] Figure 3 A schematic diagram of a path crossing a continuous oblique obstacle in one embodiment;

[0046] Figure 4 is a schematic diagram of an aircraft convex hull model in one embodiment;

[0047] Figure 5 is a schematic diagram of a polygon expansion algorithm in one embodiment;

[0048] Figure 6 Schematic diagram of the expansion process of a convex hull model in one embodiment; (a) is polygon expansion, (b) is vertex circle, and (c) is obstacle expansion model;

[0049] Figure 7 is a schematic diagram of the motion relationship of a rodless traction system in one embodiment;

[0050] Figure 8 A schematic diagram of kinematic solution of key points in one embodiment;

[0051] Fig. 9 A schematic diagram of a search range (a portion of retrieved nodes in the figure) before dynamic measurement optimization in one embodiment;

[0052] Fig.10 A schematic diagram of a search range after dynamic measurement optimization (the retrieved node portion in the figure) in one embodiment;

[0053] Fig.11 A schematic diagram of a trajectory before re-search optimization (the gray line in the figure) in one embodiment;

[0054] Fig.12 A schematic diagram of a trajectory (black line in the figure) after re-search optimization in one embodiment;

[0055] Fig.13 A schematic diagram of aircraft path planning based on an improved A* algorithm in one embodiment;

[0056] Fig.14 A schematic diagram of the optimal control algorithm path planning for scenario 1 in an embodiment;

[0057] Fig.15 A schematic diagram of a path planning combining heuristic and optimal control algorithms in scenario 1 in an embodiment;

[0058] Fig.16 Schematic diagram of the control amount of the optimal control algorithm and the aircraft speed change curve in scenario 1 in one embodiment; (a) is the tractor steering angle change curve, (b) is the tractor acceleration change curve, and (c) is the tractor speed change curve;

[0059] Fig.17 Schematic diagram of the control amount and aircraft speed change curve of scenario 1 combined with heuristic and optimal control algorithms in one embodiment; (a) is the tractor steering angle change curve, (b) is the tractor acceleration change curve, and (c) is the tractor speed change curve;

[0060] Fig.18 A schematic diagram of the optimal control algorithm path planning for scenario 2 in an embodiment;

[0061] Fig.19 A schematic diagram of path planning combining heuristic and optimal control algorithms for scenario 2 in an embodiment;

[0062] Fig. 20 Schematic diagram of the control amount of the optimal control algorithm and the aircraft speed change curve of scenario 2 in one embodiment; (a) is the tractor steering angle change curve, (b) is the tractor acceleration change curve, and (c) is the tractor speed change curve;

[0063] Fig.21 Schematic diagram of the control amount and aircraft speed change curve of scenario 2 combined with heuristic and optimal control algorithms in one embodiment; (a) is the tractor steering angle change curve, (b) is the tractor acceleration change curve, and (c) is the tractor speed change curve;

[0064] Fig. 22 A schematic diagram of a path planning combining heuristic and optimal control algorithms for scenario 3 in an embodiment;

[0065] Fig.23 Schematic diagram of the control amount and aircraft speed change curve of scenario 3 combined with heuristic and optimal control algorithms in one embodiment; (a) is the tractor steering angle change curve, (b) is the tractor acceleration change curve, and (c) is the tractor speed change curve;

[0066] Fig.24 FIG. 4 is a structural block diagram of a device in an embodiment. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0068] like Figure 1 As shown, the present application provides an aircraft towing path planning method combining heuristic and optimal control, in one embodiment, comprising the following steps:

[0069] Step 102, obtaining a path planning task for transporting an aircraft on a platform; the path planning task includes: an initial position of the aircraft, a target position of the aircraft, and obstacles.

[0070] Step 104, using the A* algorithm, a path planning is performed for the aircraft from the initial position to the target position to avoid obstacles, and an initial path is obtained, wherein the initial path includes a plurality of nodes.

[0071] Specifically, the A* algorithm is used to obtain the total cost of the current node according to the cost from the initial position to the current node, the estimated cost from the current node to the target position, and the dynamic weighting operator; and the initial path is obtained according to the minimum value of the total cost of all nodes. The initial path includes multiple nodes.

[0072] The dynamic weight operator is greater than or equal to one, and gradually decreases from the initial stage to the final stage of the A* algorithm.

[0073] When the obstacle is located on the horizontal axis of the current node, the path of the current node does not include the vertically adjacent nodes of the obstacle; when the obstacle is located on the vertical axis of the current node, the path of the current node does not include the horizontally adjacent nodes of the obstacle.

[0074] The A* algorithm satisfies the obstacle convex hull expansion constraint; the obstacle convex hull expansion constraint includes: connecting the maximum convex points of the aircraft contour into convex polygons to obtain a convex hull model; using a polygon expansion algorithm to expand the convex hull model outward by a certain safety buffer distance to obtain a convex hull transition model; using the vertex of the convex hull model as the center of the circle and the safety buffer distance as the radius to obtain multiple circle models tangent to the convex hull transition model; according to the convex hull transition model and the circle model, the obstacle convex hull expansion constraint is obtained.

[0075] Step 106, starting from the first node, re-search each node in the initial path; when there is an obstacle within the preset range of the path between the first node and the second node, the second node is used as the key point, otherwise it is determined whether there is an obstacle within the preset range of the path between the first node and the third node, until it is determined whether there is an obstacle within the preset range of the path between the last node and the adjacent node, and a key point set is obtained.

[0076] Step 108, establishing a kinematic model for the process of maneuvering the aircraft on the platform, and satisfying obstacle constraints, kinematic constraints and terminal posture constraints to obtain an optimal control model; transforming the optimal control model to obtain a nonlinear programming model.

[0077] The kinematic constraints and terminal posture constraints include: speed relationship constraints between the aircraft and the tractor, steering angle and speed constraints of the aircraft, and control variable constraints of the tractor.

[0078] The optimal control model is transformed by using a Radau pseudo-spectral algorithm, or other algorithms in the prior art.

[0079] Step 110, selecting one or more key points in the key point set to perform geometric calculations to obtain corresponding key point postures; and obtaining an optimal path based on the key point postures and the nonlinear programming model.

[0080] Specifically, one or more key points are selected to obtain the angular bisector of two trajectories with the key point as the intersection point, the normal line of the angular bisector is the speed direction of the aircraft at the key point, and the maximum threshold speed is the speed magnitude of the aircraft at the key point; according to the speed direction and the speed magnitude, one or more key point postures are obtained, and the key point postures correspond to the key points one by one.

[0081] The key point posture is input into the nonlinear programming model, and the nonlinear programming model is solved by a solver to obtain connection points; the connection points correspond to the key points one by one; according to a key point and the connection points corresponding to the key point, a corresponding segmented path is obtained; according to all the segmented paths, an optimal path is obtained.

[0082] It should be noted that the maximum threshold speed can be preset according to safety requirements, and can be specifically set through experience or existing technology.

[0083] The above-mentioned aircraft towing path planning method combining heuristics and optimal control, firstly, establishes a convex hull obstacle expansion model for the complex platform layout environment; secondly, introduces a dynamic measurement factor into the A* algorithm and designs a trajectory re-search algorithm, uses the improved A* algorithm to perform preliminary path planning for the starting position and target position of the aircraft, obtains the shortest path to avoid obstacles, solves the key points of the shortest path in the path, selects an appropriate number of key points to solve the motion state of the key points, uses the key points as the middle points of the pseudo-spectral path planning, combines the optimal control algorithm, performs segmented planning and integration for the starting position and target position of the aircraft, simplifies the road conditions through segmented planning, effectively solves the initial value sensitivity problem of the optimal control algorithm in a complex obstacle environment, and the problem that the optimal control algorithm falls into an iterative dead zone and cannot be solved due to complex obstacle conditions, and obtains the shortest path that meets the kinematic and terminal posture constraints and has a short distance and short time.

[0084] It should be understood that although Figure 1 The steps in the flowchart are shown in sequence as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least part of the sub-steps or stages of other steps.

[0085] Aircraft towing and transportation is a key link in the full-cycle recovery operation of a fleet. In order to improve the efficiency of aircraft transportation and to obtain the optimal path that meets the kinematic and terminal posture constraints, in a specific embodiment, the heuristic and optimal control methods are combined to study the aircraft towing path planning.

[0086] Aircraft take-off and landing support operations are usually carried out in a wave-based cyclic operation mode, which can be specifically divided into wave-based operation mode and continuous operation mode. In the wave-based operation mode, each wave is organized into a fleet according to the maximum dispatchable capacity to perform cyclic dispatch and recovery operations, while the continuous operation mode will divide different fleets to perform cyclic dispatch and recovery operations respectively, and their respective flight cycles are staggered and overlapped, but the platform can only accommodate the support operations of one fleet at the same time.

[0087] Platform support operations mainly include two types of processes: the direct dispatch process for the first wave of aircraft and the re-dispatch process when the aircraft is dispatched again to perform the mission after recovery. However, no matter which support process is used, maintenance service supports such as aircraft filling and adding attachments and operational processes such as warm-up self-inspection before takeoff are indispensable.

[0088] like Figure 2 As shown in the figure, since the narrow space platform is divided into different functional areas to perform corresponding support tasks, it is necessary to go to different areas to perform corresponding work during the aircraft dispatch support process, which requires the aircraft to be transferred. For example, in the direct dispatch process, the mission aircraft parked in the hangar must first be transferred to the platform support parking position by a tractor and an aircraft elevator to perform maintenance services such as filling and adding. Afterwards, during the dispatch and departure phase, each aircraft will warm up and self-check, taxi into position, prepare for takeoff, and eject / ski-jump takeoff in turn; after the fleet is recovered to the platform, some faulty or scheduled inspection aircraft will be transferred to the hangar for maintenance, and aircraft that need to perform another dispatch mission will be dispatched again for support. During the entire process, the aircraft was transferred multiple times between different work areas of the platform.

[0089] Therefore, in the narrow platform space, finding a path from the initial parking position to the target parking position that is safe, efficient and in line with work reality is of great significance to ensuring aircraft transportation, executing various types of dispatch and recovery support operations, and improving the efficiency of fleet transportation.

[0090] Step 102 obtains a path planning task for transporting the aircraft on the platform; the path planning task includes: an initial position of the aircraft, a target position of the aircraft, and obstacles.

[0091] The A* algorithm is a classic heuristic algorithm that is the most effective in solving the shortest path in a static road network. By setting a specific heuristic function as a heuristic factor, the algorithm's calculation direction is induced to find the shortest path. This algorithm is applied to aircraft towing path planning. In order to simplify the problem model and obtain the shortest path, the following assumptions are made: (1) The aircraft is regarded as a particle during transportation; (2) Kinematic and dynamic constraints such as steering angles are not considered during aircraft transportation; (3) The posture constraints of the aircraft during transportation and at the terminal are not considered.

[0092] Step 104 uses the A* algorithm to obtain the total cost of the current node based on the cost from the initial position to the current node, the estimated cost from the current node to the target position, and a dynamic weighting operator; and obtains the initial path based on the minimum total cost of all nodes. The initial path includes multiple nodes.

[0093] The A* algorithm compares the current node information:

[0094] F(x i ,y i )=G(x i,y i )+H(x i ,y i ) (1)

[0095] Where: F is the total cost of the current node; G is the cost from the starting point to the current node; H is the estimated cost from the current node to the target point, that is, the heuristic function value; (x i ,y i ) are the current node coordinates.

[0096] By continuously selecting nodes with the smallest total cost value to form the shortest path, since the aircraft can travel in any direction, not just along the vertical, horizontal or diagonal direction of the grid, the heuristic function selects the Euclidean distance, also known as the straight-line distance. The heuristic function is:

[0097]

[0098] Where: H is the estimated cost from the current node to the target point, that is, the heuristic function value; (x i ,y i ) is the current node coordinate; D is the unit node distance cost; (x goal ,y goal ) are the target node coordinates.

[0099] Due to the limitations of the A* algorithm, when searching for path planning, it is necessary to start from the starting point and continue to diffuse the search around under the guidance of the heuristic function, but this still leads to searching a large number of useless nodes (such as nodes in the opposite direction of the target node). In order to optimize the search efficiency of the A* algorithm and reduce redundant searches, this paper uses a dynamic measurement method to improve the A* algorithm. The improved node information algorithm is as follows:

[0100]

[0101] Where: F is the total cost of the current node; G is the cost from the starting point to the current node; ω is the dynamic measurement operator of the current node; H is the estimated cost from the current node to the target point, that is, the heuristic function value; (x i ,y i ) are the current node coordinates.

[0102] According to the characteristics of different search stages of the algorithm, the dynamic measurement operator is adjusted. When the algorithm is in the initial stage, its main purpose is to quickly approach the goal, that is, the heuristic function value is relatively important; and in the final stage of the algorithm, its main purpose is to accurately find the shortest path, that is, the true cost of the path is relatively important. As the A* algorithm search proceeds, the dynamic measurement operator is constantly adjusted to improve the algorithm's search efficiency and increase the algorithm's search depth, which can effectively prevent the algorithm from blindly searching and increasing the search volume, and ensure the quality of the optimal solution.

[0103] The dynamic weight operator is greater than or equal to one, and gradually decreases from the initial stage to the final stage of the A* algorithm.

[0104] The traditional A* algorithm usually does not consider oblique angle avoidance when planning a path. That is, when the obstacle is located on the horizontal or vertical axis of the current node, the path can cross the oblique angle of the obstacle and directly reach the node adjacent to the obstacle. This results in the algorithm being unable to correctly identify the obstacle node when the obstacle is a continuous oblique obstacle node, resulting in path planning errors, such as Figure 3 shown.

[0105] This paper improves the algorithm to solve the above problems. The improved algorithm flow is shown in Table 1. When the obstacle node is located on the horizontal axis of the current node, the path of the current node does not include the vertical adjacent nodes of the obstacle; when the obstacle node is located on the vertical axis of the current node, the path of the current node does not include the horizontal adjacent nodes of the obstacle (i.e., row 18 in Table 1, where 1 to 8 are the eight adjacent nodes of the current node, numbered from left to right and from top to bottom).

[0106] When the obstacle is located on the horizontal axis of the current node, the path of the current node does not include the vertically adjacent nodes of the obstacle; when the obstacle is located on the vertical axis of the current node, the path of the current node does not include the horizontally adjacent nodes of the obstacle.

[0107] Table 1 Improved A* algorithm process

[0108]

[0109]

[0110] The A* algorithm satisfies the barrier convex hull expansion constraint.

[0111] The obstacles in the process of platform transportation are mainly other aircraft parked on the platform. The traditional aircraft entity model is a circumscribed circle model. However, this model greatly expands the space occupied by the aircraft, which may lead to no path in densely populated environments such as hangar platforms. In this regard, the approximation and safety of the model are weighed, and a convex hull model is established based on the characteristics of the aircraft shape. The maximum convex points of the aircraft outline are connected into convex polygons. When the aircraft is parked as an obstacle, the wings are always retracted. The convex hull model is as follows: Figure 4 .

[0112] The transported aircraft is regarded as a particle, ignoring the influence of the aircraft's shape and attitude. Therefore, when performing path planning and obstacle avoidance, it is necessary to add a safety buffer distance to the obstacles to ensure the safe transportation of the actual aircraft on the path. To address this problem, a polygon expansion algorithm is used to expand the convex hull model outward by a certain safety buffer distance, such as Figure 5 .

[0113] The calculation formula of vertex coordinates after expansion is as follows:

[0114]

[0115] Where: (x Q ,y Q ) is the coordinate of point Q; (x P ,y P ) are the coordinates of point P; d is the expansion distance; v1 is the direction vector of line l1; v2 is the direction vector of line l2; Normalize(v1) and Normalize(v2) are the unit vectors of v1 and v2.

[0116] The convex hull model after expansion, that is, the convex hull transition model is as follows Figure 6 As shown in (a), it can be seen from the figure that at the sharp corner of the convex hull model, after the polygon expansion, there is a more serious stretching, and the stretching distance far exceeds the required safety buffer distance, resulting in excessive expansion of the obstacle at the sharp corner. In this regard, the original convex hull model vertex is taken as the center and the expansion distance is taken as the radius. Figure 6 The circle shown in (b) is used to obtain multiple circle models tangent to the convex hull transition model. An appropriate number of key points are selected on the circle to improve the original obstacle expansion model (convex hull transition model) to obtain the improved obstacle expansion model, that is, the obstacle convex hull expansion model is as follows: Figure 6 As shown in (c).

[0117] Satisfying the obstacle convex hull expansion model means satisfying the obstacle convex hull expansion constraint.

[0118] Starting from the first node, each node in the initial path is re-searched; when there is an obstacle within the preset range of the path between the first node and the second node, the second node is taken as the key point, otherwise it is determined whether there is an obstacle within the preset range of the path between the first node and the third node, until it is determined whether there is an obstacle within the preset range of the path between the last node and the adjacent node, and a key point set is obtained.

[0119] The improved A* algorithm can quickly and accurately search for the shortest path to transport the aircraft from the starting position to the target position under the assumptions of this article. However, since the A* algorithm belongs to the unit decomposition method, its path is composed of adjacent nodes that are continuously connected, resulting in a large number of turns in its trajectory, and is limited by the unit length. When the target node is far away and the slope of the line connecting the two nodes and the target node changes little, it is not enough to identify the angle change perpendicular to the direction of the line, and a suboptimal path will be generated.

[0120] In this regard, a re-search trajectory optimization algorithm is designed. By re-searching the trajectory nodes, the above two problems are optimized. The algorithm flow is shown in Table 2. The initial node is taken as the first node, and the second node is selected along the path in sequence to determine whether there is an obstacle node within a certain distance between the two nodes. If not, the next node is selected along the path as the second node for re-judgment. If so, the current second node is marked as a key point, and the current second node is taken as the first node. The second node is selected along the path in sequence to continue searching until the search is completed.

[0121] Table 2 Re-search trajectory optimization algorithm flow

[0122]

[0123] The Walkable function connects two nodes and determines whether there are any obstacle nodes within a certain distance of the connection. By re-searching the trajectory, the key points of the original trajectory are obtained and the optimal path is generated.

[0124] Since the path generated by the A* algorithm does not take into account kinematic and dynamic constraints such as steering angles during transportation and aircraft terminal posture constraints during transportation, these factors have an important impact on obstacle avoidance, outbound and inbound operations during multi-aircraft transportation when conducting research on practical problems, such as aircraft scheduling. In order to obtain an aircraft transportation path that meets kinematic, dynamic and aircraft terminal posture constraints, this paper solves the motion state of the key points based on the key points of the path obtained by the above A* algorithm, and plans the path in segments with the key points as nodes combined with the optimal control model, and connects each segment of the path to obtain a complete path.

[0125] The aircraft transportation system without a pole but with a tractor is taken as an example for modeling and analysis.

[0126] A kinematic model is established for the process of transporting the aircraft on the platform. The rodless traction system for aircraft transport is similar to the trailer system, so it can also be regarded as a type of trailer system. Since the aircraft moves slowly during transport and the surface of the narrow space platform is flat, it is assumed that the tires do not slide during the movement. Due to the slow movement, the inertia force and lateral force can be ignored. The simplified system model is as follows: Figure 7 shown.

[0127] Figure 7 In the equation, θ1 and θ2 represent the angles between the axes of the aircraft and the tractor and the x-axis, L1 and L2 represent the front and rear wheel tracks of the aircraft and the tractor, (x1, y1), (x2, y2), (x3, y3) represent the coordinate positions of the aircraft, the hinge point between the aircraft and the tractor, and the tractor, β1 and β2 represent the steering angles of the aircraft and the tractor, and M0 is the distance between the hinge point of the tractor and the rear wheel of the tractor.

[0128] According to the system structure and motion relationship, its kinematic equation is:

[0129]

[0130] Where X = [x1, y1, θ1, θ2, v2] T , U=[u1,u2] T , u1=tanβ2, u2=a2, i.e. the acceleration of the tractor, and v2 is the translational speed of the tractor.

[0131] The kinematic model satisfies obstacle constraints.

[0132] Different from the obstacle model of the A* algorithm, the optimal control algorithm requires an analytical expression of the obstacle to perform path calculation. To facilitate the calculation, the aircraft model uses the traditional characteristic circle model, and uses the Euclidean distance between the center of the circle and the obstacle and the safety distance to perform collision judgment. The judgment formula is as follows:

[0133]

[0134] Where: n is the total number of obstacles, x oi and oi are the center coordinates of the ith obstacle, a i and b i is the length of the obstacle along the horizontal axis and half of its length along the vertical axis; d represents the safety buffer distance; p is the shape parameter. When 2p = 1, the figure described by the formula is a rhombus; when 2p = 2, the figure described is a circle or an ellipse; when p → ∞, the figure described is a rectangle.

[0135] The kinematic model also satisfies kinematic constraints and terminal posture constraints, which include: speed relationship constraints between the aircraft and the tractor, aircraft steering angle and speed constraints, and tractor control variable constraints.

[0136] According to the structural characteristics of the traction system used on the platform, the speed relationship between the aircraft's translation speed and the tractor's speed can be expressed as:

[0137]

[0138] Among them, the turning angle and speed of the aircraft should meet:

[0139]

[0140] In addition, the control variables of the tractor should also satisfy the corresponding constraints, namely:

[0141]

[0142] Among them, the upper and lower limits of translation speed and translation acceleration should be given according to the specific models of the aircraft and barless towing equipment involved and the relevant safety regulations. The steering angle is generally calculated based on the turning radius of the aircraft and towing vehicle. The specific calculation method is as follows:

[0143]

[0144] Since obstacle constraints, translation speed, control variables and other constraints are all inequality constraints, these two parts can be considered together to form a unified form of inequality constraint relationship, and all inequality constraints can be uniformly expressed as:

[0145] h≤0 (11)

[0146] Among them, formula (11) can be composed of formula (6), formula (8) and formula (9).

[0147] Then the optimal control model of the path planning of the towbarless traction system can be described as equation (12).

[0148]

[0149] Where: For the system described by equation (5), t f is the time of reaching the destination, t0 is the time of departure, wk is the weight adjustment factor, J is the objective function, and R is the weight matrix.

[0150] After the kinematic model satisfies the constraints, an optimal control model is obtained; the optimal control model is transformed to obtain a nonlinear programming model.

[0151] The optimal control model may be transformed using a variety of algorithms in the prior art, such as the Radau pseudo-spectral algorithm, and the solution steps are as follows.

[0152] (1) Parameter initialization

[0153] Firstly, each parameter in the optimal control model is assigned and initialized.

[0154] (2) Time interval discretization

[0155] To solve the problem using the Radau pseudospectral method, we first need to set the time interval [t0,t f ] is divided into K subintervals [t k-1 ,t k ], t0<t1<…<t k <…<t K =t f , k = 1, 2, ..., K, for convenience, (·) is used in the following (k)Represents the relevant parameters in the kth interval, which is Transform to the interval [-1,1] using the following transformation:

[0156]

[0157] In order to perform discretization solution, the state variables, control variables, constraint functions, and optimization objective functions need to be interpolated and transformed. The matching points of Radau pseudospectral method are Legendre Gauss Radau (LGR) points. The Nth-order LGR points are polynomial equations P N (T)+P N-1 (T) = 0, where P N (T) represents the Legendre polynomial of order N:

[0158]

[0159] (3) Subinterval variable approximation

[0160] ①For state variables, for the first N (k) The LGR points are T i (k) ,i=1,2,…,N (k) ,for Using N (k) Lagrange interpolation polynomial As the basis function, the state variables can be interpolated and approximated to obtain:

[0161]

[0162] where k = 1, 2, ..., K, X (k) (T i (k) ) is X (k) At node T i (k) Take the value at is the Lagrange interpolation basis function, which satisfies:

[0163]

[0164] ②For the control variables, similar to the state variables, for the first K-1 intervals:

[0165]

[0166] Where k = 1, 2, ..., K-1;

[0167] For the Kth interval, use N (k) -1st order Lagrange interpolation polynomial As the basis function, the control variable can be interpolated and approximated to obtain:

[0168]

[0169] in:

[0170]

[0171] ③For the constraint function. First, take the derivative of the state variable:

[0172]

[0173] For formula (20), Discretize at, and get:

[0174]

[0175] In the formula, Among them, is the Radau pseudo-spectral differential matrix, the order is N (k) ×(N (k) +1).

[0176] Substituting equation (21) into equation (12) can transform the differential constraint equation into:

[0177]

[0178] Path constraint discretization:

[0179]

[0180] Where i=1,2,…,N (k)

[0181] Performance indicators:

[0182]

[0183] The state variables of the endpoints of adjacent subintervals are equal, satisfying:

[0184]

[0185] One or more key points are selected from the key point set for geometric solution to obtain corresponding key point postures; and an optimal path is obtained according to the key point postures and the nonlinear programming model.

[0186] It is advisable to select key points in the flat section of the trajectory, and it is not advisable to select key points where the aircraft heading angle changes greatly, otherwise a large turning trajectory will be generated, causing the planned path to deviate from the shortest path.

[0187] Geometric solution means: selecting one or more key points, obtaining the angular bisector of two trajectories with the key point as the intersection point, taking the normal line of the angular bisector as the speed direction of the aircraft at the key point, and taking the maximum threshold speed as the speed magnitude of the aircraft at the key point; according to the speed direction and the speed magnitude, obtaining one or more key point postures, and the key point postures correspond to the key points one by one.

[0188] Specifically: Establish a kinematic solution model for the key points of the A* trajectory, assuming that the speed of the aircraft remains constant during the movement, that is, the tangential acceleration is 0; the movement direction of the tractor is consistent with the movement direction of the aircraft, that is, θ1 = θ2. The normal line of the bisector of the two intersecting trajectory angles is taken as the aircraft speed direction, such as Figure 8 As shown:

[0189] Figure 8 The midline ABC is the path planned by the A* algorithm, where B is the key point, n is the angle bisector of ∠ABC, and l is the normal line of n. If the aircraft moves along ABC in sequence, its velocity direction is as follows Figure 8 As shown in v.

[0190] The key point is used as the intermediate point, and its state parameter, i.e., the key point attitude, is input into the nonlinear programming model. The path of the aircraft is segmented by using the optimal control algorithm. The nonlinear programming model is solved by using a solver (e.g., SNOPT software package, etc.) to obtain connection points; the connection points correspond to the key points one by one; the corresponding segmented path is obtained according to a key point and the connection point corresponding to the key point; all segmented paths are merged to obtain the optimal path. The optimal path is the shortest path that meets the constraint conditions.

[0191] In order to intuitively demonstrate the path planning effect of the improved A* algorithm in this paper, the layout of a narrow space platform is taken as an example, and a parking position in a parking area with a high aircraft density and a temporary parking position at a farther distance are taken as examples. The algorithms before and after the improved dynamic measurement and before and after the trajectory re-search optimization are used to plan the aircraft transfer path between the two parking positions under full staffing. The superiority of the improved A* algorithm is demonstrated through horizontal comparison.

[0192] Fig. 9 and Fig.10 The figure shows the search range of the algorithm before and after dynamic measurement optimization. The searched node area in the figure is the CLOSELIST set in the algorithm. The smaller the set, the higher the algorithm search efficiency. Before dynamic measurement optimization, the algorithm needs to search a large number of areas for path planning, which is inefficient. After adding dynamic measurement optimization, no redundant search nodes are generated except for necessary paths and obstacle detection needs. The optimization effect is significant, which greatly improves the efficiency of the algorithm.

[0193] Fig.11 and Fig.12 The figure shows the path planning diagram before and after re-search optimization. Fig.11 The area A in the middle is the problem of too many trajectory turns mentioned above. Fig.11 The middle circle B area is the previously mentioned limited unit length. When the distance to the target node is far away, the slope change of the line connecting the two nodes and the target node is small, which is not enough to identify the angle change perpendicular to the direction of the line. After optimization by the re-search algorithm, its trajectory is as follows Fig.12 As shown by the black path in the middle, the broken line part in area A and the suboptimal path in area B are both optimized, and the algorithm successfully generates the shortest path.

[0194] The final full-segment path planning effect is as follows Fig.13 shown.

[0195] Taking a certain type of aircraft as an example, a kinematic model of the aircraft is established, and the optimal control method and multi-scenario path planning simulation experiments combining heuristic and optimal control algorithms are carried out, and the experimental results are analyzed.

[0196] In the simulation experiments, a single key point is selected. The narrow space platform is in full deployment state. The aircraft is a large fixed-wing aircraft. In each scenario simulation experiment, only the initial parking position, target parking position and obstacle aircraft deployment are changed. The various parameters and constraints of the aircraft and tractor remain unchanged. The values ​​of each parameter are p = 3, L1 = 5.88m, L2 = 2.4m, β 1max =π / 4, -1m / s≤v2≤1m / s, -1m / s 2 ≤u2≤1m / s 2 , -π≤θ1≤π, -π≤θ2≤π. Since the distance between the tractor articulation point and the center of the rear wheel of the tractor is extremely small in an actual tractor, M0=0, -1≤u1≤1, that is, -π / 4≤β2≤π / 4.

[0197] Table 3 Comparison of simulation results of scenario 1

[0198]

[0199] Fig.14 The trajectory diagram for aircraft scheduling path planning for the optimal control algorithm, Fig.15 This is the trajectory diagram of the path planning of this paper combining heuristic and optimal control algorithms. By comparing the two, it can be found that both algorithms can effectively achieve obstacle avoidance, but the trajectory diagram obtained by the algorithm in this paper is smoother than the trajectory obtained by the simple optimal control algorithm. For further analysis, the control quantity U = [u1, u2] T Analyze the curve of aircraft speed changing with time, such as Fig.16 and Fig.17 .

[0200] (a) in both figures shows the change curve of the control quantity u1, i.e., the steering angle of the tractor. It can be seen from the figure that the algorithm in this paper significantly reduces the fluctuation amplitude and frequency of the control quantity u1, where the reduction value in the fluctuation amplitude can reach 45%, indicating that the improved algorithm makes the target search process more stable and the search efficiency is higher. The change trend of the control quantity is also consistent with the turning situation of the aircraft, that is, u1>0 when the aircraft turns left, and u1<0 when the aircraft turns right, and the control effect is good.

[0201] (b) in both figures shows the change curve of the control quantity u2, that is, the acceleration of the tractor. It can be seen from the figure that the stability of the results obtained by the algorithm in this paper is obviously better than that of simply using the optimal control algorithm. The aircraft only accelerates in the initial stage and decelerates in the final stage. The speed is kept unchanged in the intermediate process of its movement, and it travels smoothly. Combined with (c) in the two figures, it can be seen that it is better than the simple optimal control algorithm. Due to the fluctuation of acceleration, the aircraft reverses during the movement. This is because the planned path is too long or the obstacle situation is complicated, making it difficult for the algorithm to converge. The effect achieved by the algorithm in this regard is also very significant, effectively avoiding the problem of incorrect planning caused by complex target distance or obstacle situation.

[0202] Table 4 Comparison of simulation results of scenario 2

[0203]

[0204] like Figures 18 to 21 As shown in the figure, the simulation results of the two algorithms in scenario 2 are compared. The difference between the four types of data in Table 4 is not large, but the comparison Fig.18 and Fig.19 It can be found that the path trajectory planned by the algorithm in this paper occupies much less space than the optimal control algorithm, and is more in line with the shortest path. The transportation process is concentrated in the lower half of the platform, and the upper half is basically unoccupied. In such a small space, improving space utilization is of great significance to the transportation of aircraft fleets. This algorithm guarantees the platform space utilization to the greatest extent, leaving enough safe passages for the transportation of other aircraft, which is more practical.

[0205] For complex obstacles, such as Fig. 22 As shown in the obstacle situation in scenario 3, the optimal control algorithm cannot converge to the optimal path and find the optimal solution because the target distance is too far and the obstacles are complex. However, the proposed algorithm can still avoid complex obstacles to reach the target position and plan the optimal path. Fig.23 From the transformation curves (a), (b), and (c), we can see that the aircraft's motion is smooth and stable, and the change trend of the control quantity is consistent with the aircraft's turning situation, indicating a good control effect.

[0206] Through simulation experiments of three types of scenarios, the following advantages of the algorithm in this paper are verified compared with the traditional optimal control algorithm: ① It effectively solves the problem of initial value sensitivity of the optimal control algorithm in a complex obstacle environment; ② It makes the path more in line with the shortest path, effectively shortens the time required for aircraft transportation and takes into account the space limitations of the platform, leaving enough safe channels for the platform; ③ It reduces the fluctuation of the aircraft transportation trajectory, makes the trajectory smoother, and enhances the stability of aircraft transportation.

[0207] This method establishes a convex hull obstacle expansion model for complex layout environments, introduces dynamic measurement factors into the A* algorithm, designs a trajectory re-search algorithm, solves the key points of the shortest path, and then solves the motion state of the key points. Combined with the optimal control algorithm, the segmented paths between the key points are planned and integrated. In addition, a path planning simulation experiment under a typical platform environment is carried out, and the superiority of this method is verified by comparing it with the simulation experiment results of the optimal control algorithm. This method improves the A* algorithm and combines it with the optimal control algorithm. By improving the A* algorithm, the shortest path is established and key points are selected, and the long path is segmented for key point processing. The optimal control algorithm is used for path planning in each segment, which not only ensures that the path is the shortest path, but also fully considers the kinematics and terminal posture constraints in the aircraft transportation process, and avoids the initial value sensitivity problem in a complex obstacle environment, effectively improving the optimization performance of aircraft transportation.

[0208] In one embodiment, Fig.24 As shown, an aircraft towing path planning device combining heuristic and optimal control is provided, including: an acquisition module 2402, an initial path establishment module 2404, a key point set establishment module 2406, a model establishment module 2408 and an optimal path establishment module 2410, wherein:

[0209] The acquisition module 2402 is used to acquire the path planning task for the aircraft to be transported on the platform; the path planning task includes: the initial position of the aircraft, the target position of the aircraft and obstacles;

[0210] An initial path establishment module 2404 is used to use an A* algorithm to plan a path from an initial position to a target position of the aircraft to avoid obstacles, and obtain an initial path, wherein the initial path includes a plurality of nodes;

[0211] The key point set establishing module 2406 is used to re-search each node in the initial path starting from the first node; when there is an obstacle within the preset range of the path between the first node and the second node, the second node is used as the key point; otherwise, it is determined whether there is an obstacle within the preset range of the path between the first node and the third node, until it is determined whether there is an obstacle within the preset range of the path between the last node and the adjacent node, thereby obtaining a key point set;

[0212] The model building module 2408 is used to build a kinematic model for the process of aircraft transportation on the platform, and satisfy the obstacle constraints, kinematic constraints and terminal posture constraints to obtain an optimal control model; transform the optimal control model to obtain a nonlinear programming model;

[0213] The optimal path establishment module 2410 is used to select one or more key points in the key point set to perform geometric calculations to obtain the corresponding key point postures; and obtain the optimal path based on the key point postures and the nonlinear programming model.

[0214] The specific definition of the aircraft towing path planning device combining heuristics and optimal control can be found in the above definition of the aircraft towing path planning method combining heuristics and optimal control, which will not be repeated here. Each module in the above device can be implemented in whole or in part by software, hardware and a combination thereof. Each of the above modules can be embedded in or independent of the processor in the computer device in the form of hardware, or can be stored in the memory of the computer device in the form of software, so that the processor can call and execute the operations corresponding to each of the above modules.

[0215] The technical features of the above embodiments may be arbitrarily combined. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0216] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. An aircraft towing path planning method combining heuristics and optimal control, characterized in that: include: Obtain the path planning task for aircraft transportation on the platform; The path planning task includes: the initial position of the aircraft, the target position of the aircraft and obstacles; Using the A* algorithm, a path is planned for the aircraft from an initial position to a target position to avoid obstacles, and an initial path is obtained, wherein the initial path includes a plurality of nodes; Starting from the first node, each node in the initial path is re-searched; when there is an obstacle within the preset range of the path between the first node and the second node, the second node is used as the key point, otherwise, whether there is an obstacle within the preset range of the path between the first node and the third node is determined, until whether there is an obstacle within the preset range of the path between the last node and the adjacent node is determined, and a key point set is obtained; A kinematic model is established for the process of aircraft transportation on the platform, and obstacle constraints, kinematic constraints and terminal posture constraints are satisfied to obtain an optimal control model; the optimal control model is transformed to obtain a nonlinear programming model; Select one or more key points in the key point set to perform geometric calculations to obtain corresponding key point postures; obtain an optimal path based on the key point postures and the nonlinear programming model; The optimal control model for the path planning of the towbarless traction system can be described as: ； Where: To reach the end moment, It's time to depart. is the weight adjustment factor, is the objective function, is the weight matrix, , , , represents the steering angle of the tractor, is the tractor acceleration; Convert the differential constraint equation to: ； Path constraint discretization: ； In the formula, Indicates obstacles, ; Performance indicators: ； The state variables of the endpoints of adjacent subintervals are equal, satisfying: 。 2. The method according to claim 1, characterized in that: The A* algorithm is used to plan the path of the aircraft from the initial position to the target position to avoid obstacles. The initial path includes: The A* algorithm is used to obtain the total cost of the current node based on the cost from the initial position to the current node, the estimated cost from the current node to the target position, and the dynamic measurement operator; According to the minimum total cost of all nodes, obstacles are avoided and the initial path is obtained.

3. The method according to claim 2, characterized in that The A* algorithm is used to plan the path of the aircraft from the initial position to the target position to avoid obstacles. The initial path also includes: When the obstacle is located on the horizontal axis of the current node, the path of the current node does not include the vertical adjacent nodes of the obstacle; When the obstacle is located on the vertical axis of the current node, the path of the current node does not include the horizontally adjacent nodes of the obstacle.

4. The method according to claim 3, characterized in that The dynamic weight operator is greater than or equal to one, and gradually decreases from the initial stage to the final stage of the A* algorithm.

5. The method according to any one of claims 1 to 4, characterized in that: The A* algorithm satisfies the obstacle convex hull expansion constraint; The obstacle convex hull expansion constraint includes: connecting the maximum convex points of the aircraft contour into a convex polygon to obtain a convex hull model; A polygon expansion algorithm is used to expand the convex hull model outward by a certain safety buffer distance to obtain a convex hull transition model; Taking the vertex of the convex shell model as the center of the circle and the safety buffer distance as the radius, a plurality of circular models tangent to the convex shell transition model are obtained; According to the convex hull transition model and the circle model, an obstacle convex hull expansion constraint is obtained.

6. The method according to any one of claims 1 to 4, characterized in that: Select one or more key points for geometric solution, and get the corresponding key point postures including: Select one or more key points, obtain the angle bisector of two trajectories with the key point as the intersection point, take the normal line of the angle bisector as the speed direction of the aircraft at the key point, and take the maximum threshold speed as the speed magnitude of the aircraft at the key point; According to the velocity direction and the velocity magnitude, one or more key point postures are obtained, and the key point postures correspond to the key points one by one.

7. The method according to any one of claims 1 to 4, characterized in that: According to the key point posture and the nonlinear programming model, obtaining the optimal path includes: Inputting the key point posture into the nonlinear programming model, using a solver to solve the nonlinear programming model to obtain connection points; the connection points correspond to the key points one by one; According to a key point and the connection points corresponding to the key point, a corresponding segmented path is obtained; according to all the segmented paths, an optimal path is obtained.

8. The method according to any one of claims 1 to 4, characterized in that: The kinematic constraints and terminal posture constraints include: The speed relationship constraints between the aircraft and the tractor, the steering angle and speed constraints of the aircraft, and the control variable constraints of the tractor.

9. The method according to any one of claims 1 to 4, characterized in that: The Radau pseudospectral algorithm is used to transform the optimal control model.

10. An aircraft towing path planning device combining heuristic and optimal control, characterized in that: include: An acquisition module is used to obtain the path planning task for the aircraft to be transported on the platform; The path planning task includes: the initial position of the aircraft, the target position of the aircraft and obstacles; An initial path establishment module is used to use the A* algorithm to plan a path from an initial position to a target position of the aircraft to avoid obstacles, and obtain an initial path, wherein the initial path includes a plurality of nodes; A key point set establishment module is used to re-search each node in the initial path starting from the first node; when there is an obstacle within a preset range of the path between the first node and the second node, the second node is used as a key point; otherwise, it is determined whether there is an obstacle within a preset range of the path between the first node and the third node, until it is determined whether there is an obstacle within the preset range of the path between the last node and the adjacent node, thereby obtaining a key point set; A model building module is used to establish a kinematic model for the process of aircraft transportation on the platform, and to satisfy obstacle constraints, kinematic constraints and terminal posture constraints to obtain an optimal control model; the optimal control model is transformed to obtain a nonlinear programming model; An optimal path establishment module is used to select one or more key points in the key point set to perform geometric calculations to obtain corresponding key point postures; and obtain an optimal path based on the key point postures and the nonlinear programming model; The optimal control model for the path planning of the towbarless traction system can be described as: ； Where: To reach the end moment, It's time to depart. is the weight adjustment factor, is the objective function, is the weight matrix, , , , represents the steering angle of the tractor, is the tractor acceleration; Convert the differential constraint equation to: ； Path constraint discretization: ； In the formula, Indicates obstacles, ; Performance indicators: ； The state variables of the endpoints of adjacent subintervals are equal, satisfying: 。

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