CN114740891A

CN114740891A - Aircraft traction path planning method and device combining heuristic and optimal control

Info

Publication number: CN114740891A
Application number: CN202210394479.6A
Authority: CN
Inventors: 苏析超; 韩维; 刘子玄; 张凯伦; 赵凌业; 王鑫; 万兵; 郭放
Original assignee: Naval Aeronautical University
Current assignee: Naval Aeronautical University
Priority date: 2022-04-12
Filing date: 2022-04-12
Publication date: 2022-07-12

Abstract

The application relates to an aircraft traction path planning method and device combining heuristic and optimal control, wherein the method comprises the following steps: planning a path by adopting an A-algorithm to obtain an initial path; searching each node in the initial path again from the first node; when an obstacle exists in a preset range of a path between a first node and a second node, the second node is taken as a key point, otherwise, whether the obstacle exists in the preset range of the path between the first node and a third node is judged, until whether the obstacle exists in the preset range of the path between the last node and an adjacent node is judged, and a key point set is obtained; establishing a kinematic model for the process of debugging and transporting the airplane on the platform, meeting constraint conditions, obtaining an optimal control model, and converting the optimal control model into a nonlinear programming model; selecting key points to carry out geometric solution to obtain corresponding key point postures; and outputting the optimal path. By adopting the method, the shortest path can be obtained by planning the path under the condition of considering kinematics and terminal pose constraint.

Description

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

Technical Field

The application relates to the technical field of path planning, in particular to an aircraft traction path planning method and device combining heuristic and optimal control.

Background

The airplane dispatching efficiency is influenced by a plurality of factors such as equipment factors, human factors, environmental factors and the like, and the narrow platform space is one of the important factors for limiting the movement efficiency, so that the research on a path planning method suitable for the narrow platform space is a basis for ensuring safe and efficient dispatching operation of the airplane on the platform, and has important significance for realizing airplane dispatching automation and improving the airplane group dispatching efficiency.

At present, the research aiming at the planning of the aircraft traction path is in a starting stage, and aiming at various path planning problems, the research method comprises a geometric method, an optimal control method, a unit decomposition method, an intelligent algorithm, an artificial potential field method, reinforcement learning, a combination algorithm and the like.

The unit decomposition method carries out path planning by taking the shortest path as a target, and although the shortest path is found, the motion state of a planning object cannot be well shown; when the map is large and the number of units is large, the arithmetic operation amount is increased sharply; and terminal pose constraints of the planning target cannot be considered.

The artificial potential field method has the advantages that the calculation efficiency is high, but when an object is far away from a target point, the attraction force becomes extremely large, and the relatively small repulsion force can even be ignored, so that the object path can touch an obstacle; when an obstacle exists near the target point, the repulsive force is very large, the attractive force is relatively small, and an object can hardly reach the target point; at a certain point, the attraction force and the repulsion force are just equal in size and opposite in direction, and the object is easy to fall into local optimal solution or vibrate.

The intelligent algorithm is characterized in that an objective function is set, based on a large population, under a certain constraint condition, through continuous iterative screening, an optimal solution meeting the constraint is gradually searched, but the algorithm is easy to fall into a local optimal solution, along with the increase of the population and the iteration times, the calculation amount of the algorithm is large, the solution is slow, and the terminal pose constraint of a planning target cannot be considered.

The optimal control method can plan a path under the condition of considering kinematics, dynamics and terminal pose constraints, but because the algorithm is sensitive to initial state input, when the initial and final positions have more obstacles and the space is narrow, or the initial and final positions are far away (for a constant step length) or the obstacle condition in the path is complex, the convergence is difficult when the steering is performed for multiple times, and the path cannot be obtained or the path which does not conform to the actual condition cannot be obtained.

Disclosure of Invention

Therefore, it is necessary to provide an aircraft traction path planning method combining heuristic and optimal control for solving the above technical problems, which can perform path planning under the condition of considering kinematics and terminal pose constraints, find the shortest path quickly, and converge well to obtain global optimization when the obstacle environment is complex.

The aircraft traction path planning method combining heuristic and optimal control comprises the following steps:

acquiring a path planning task for the airplane to be dispatched on the platform; the path planning task comprises the following steps: an initial position of the aircraft, a target position of the aircraft, and an obstacle;

planning a path for avoiding obstacles from an initial position to a target position of the airplane by adopting an A-x algorithm to obtain an initial path, wherein the initial path comprises a plurality of nodes;

searching each node in the initial path again from the first node; when an obstacle exists in a preset range of a path between a first node and a second node, the second node is taken as a key point, otherwise, whether the obstacle exists in the preset range of the path between the first node and a third node is judged, and until whether the obstacle exists in the preset range of the path between the last node and an adjacent node is judged, a key point set is obtained;

establishing a kinematics model for the process of the airplane to be dispatched on the platform, and satisfying obstacle constraint, kinematics constraint and terminal pose constraint to obtain an optimal control model; converting the optimal control model to obtain a nonlinear programming model;

selecting more than one key point in the key point set for geometric calculation to obtain corresponding key point postures; and obtaining an optimal path according to the key point posture and the nonlinear programming model.

In one embodiment, the method for planning a path avoiding an obstacle from an initial position to a target position of an aircraft by using an a-x algorithm includes:

obtaining the total cost of the current node by adopting an A-algorithm 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 weighing operator;

and avoiding the obstacles according to the minimum value of the total cost of all the nodes to obtain an initial path.

In one embodiment, the method for planning a path avoiding the obstacle from the initial position to the target position of the aircraft by using an a-star algorithm, and obtaining the initial path further comprises:

when the obstacle is located in the horizontal axis of the current node, the path of the current node does not include vertically adjacent nodes of the obstacle;

when the obstacle is located in a vertical axis of the current node, the path of the current node does not include horizontally adjacent nodes of the obstacle.

In one embodiment, the dynamic scaling operator is greater than or equal to one, and gradually decreases from the initial stage to the final stage of the a-algorithm.

In one embodiment, the a-algorithm satisfies the barrier convex hull expansion constraint;

the barrier dome expansion constraint comprises: connecting the maximum salient points of the airplane outline into a convex polygon to obtain a convex shell model;

expanding the convex shell model outwards by a certain safe buffer distance by adopting a polygon expansion algorithm to obtain a convex shell transition model;

obtaining a plurality of circular models tangent to the convex shell transition model by taking the vertex of the convex shell model as the circle center and the safe buffer distance as the radius;

and obtaining obstacle convex hull expansion constraint according to the convex hull transition model and the circular model.

In one embodiment, selecting more than one keypoint for geometric solution to obtain the corresponding pose of the keypoint comprises:

selecting more than one key point to obtain an angular bisector of two tracks taking the key point as an intersection point, taking a normal line of the angular bisector as the speed direction of the airplane at the key point, and taking the maximum threshold speed as the speed of the airplane at the key point;

and obtaining more than one key point gestures according to the speed direction and the speed, wherein the key point gestures correspond to the key points one to one.

In one embodiment, obtaining the optimal path according to the pose of the keypoint and the nonlinear programming model includes:

inputting the key point posture into the nonlinear programming model, and solving the nonlinear programming model by adopting a solver to obtain a connection point; the connecting points correspond to the key points one by one;

obtaining a corresponding segmented path according to a key point and a connecting point corresponding to the key point; and obtaining an optimal path according to all the segmented paths.

In one embodiment, the kinematic constraints and the terminal pose constraints include:

a speed relationship constraint between the aircraft and the tow vehicle, a steering angle and speed constraint of the aircraft, and a control variable constraint of the tow vehicle.

In one embodiment, the optimal control model is transformed by using a Radau pseudo-spectral algorithm.

The plane traction path planning device combining heuristic and optimal control comprises:

the acquisition module is used for acquiring a path planning task for the debugging and transportation of the airplane on the platform; the path planning task comprises the following steps: an initial position of the aircraft, a target position of the aircraft, and an obstacle;

the system comprises an initial path establishing module, a route planning module and a route planning module, wherein the initial path establishing module is used for planning a path which avoids obstacles from an initial position to a target position of an airplane by adopting an A-x algorithm to obtain an initial path, and the initial path comprises a plurality of nodes;

a key point set establishing module, configured to re-search each node in the initial path, starting from a first node; when an obstacle exists in a preset range of a path between a first node and a second node, the second node is taken as a key point, otherwise, whether the obstacle exists in the preset range of the path between the first node and a third node is judged, and until whether the obstacle exists in the preset range of the path between the last node and an adjacent node is judged, a key point set is obtained;

the model building module is used for building a kinematic model for the process of debugging and transporting the airplane on the platform, and meeting obstacle constraint, kinematic constraint and terminal pose constraint to obtain an optimal control model; converting the optimal control model to obtain a nonlinear programming model;

the optimal path establishing module is used for selecting more than one key point in the key point set to carry out geometric solution so as to obtain the corresponding key point postures; and obtaining an optimal path according to the key point posture and the nonlinear programming model.

The aircraft traction path planning method combining heuristic and optimal control is characterized in that in order to obtain a path which meets kinematics and terminal pose constraints and has short distance and short time, and avoid an optimal control method aiming at an initial value sensitivity problem under a complex obstacle environment, a track re-search algorithm is designed in an A algorithm, an initial position and a target position of the aircraft are preliminarily planned by using an improved A algorithm to obtain a shortest path of an obstacle, a shortest path key point is solved in the path, a proper amount of key points are selected to solve a key point motion state, the key points are used as intermediate points of final path planning, the optimal control algorithm is combined to perform sectional planning and integration on the initial position and the target position of the aircraft, the road condition is simplified through sectional planning, the initial value sensitivity problem of the optimal control algorithm is effectively solved, and the problem that the optimal control algorithm cannot be solved due to complex obstacle conditions because of iterative dead zones is solved, and obtaining the shortest path meeting the constraints of kinematics and terminal pose.

Drawings

FIG. 1 is a schematic flow diagram of a method for aircraft traction path planning incorporating heuristic and optimal control in one embodiment;

FIG. 2 is a diagram illustrating the partitioning of functional regions of a platform according to one embodiment;

FIG. 3 is a schematic diagram of a path traversing a continuous diagonal barrier in one embodiment;

FIG. 4 is a schematic illustration of a convex hull model of an aircraft in one embodiment;

FIG. 5 is a schematic diagram of a polygon dilation algorithm in one embodiment;

FIG. 6 is a schematic illustration of the convex hull form expansion process in one embodiment; (a) is a polygonal expansion, (b) is a vertex circle, and (c) is an obstacle expansion model;

FIG. 7 is a schematic illustration of the kinematic relationships of a rodless traction system in one embodiment;

FIG. 8 is a diagram of a keypoint kinematics solution in one embodiment;

FIG. 9 is a diagram illustrating dynamic scaling of search ranges (portions of retrieved nodes in the graph) prior to optimization, in accordance with an embodiment;

FIG. 10 is a diagram illustrating dynamic scaling of the optimized search range (portion of the retrieved nodes in the graph) in one embodiment;

FIG. 11 is a diagram of a pre-re-search optimization trajectory (gray lines in the figure) in one embodiment;

FIG. 12 is a diagram of a re-search optimized trajectory (black lines in the figure) in one embodiment;

FIG. 13 is a schematic representation of an aircraft path plan based on the modified A-algorithm in one embodiment;

FIG. 14 is a schematic diagram of an optimal control algorithm path planning for scenario 1 in one embodiment;

FIG. 15 is a schematic diagram of scenario 1 in combination with heuristic and optimal control algorithm path planning in one embodiment;

FIG. 16 is a diagram illustrating the control variables and the aircraft speed profile of the optimal control algorithm for scenario 1 in one embodiment; (a) a tractor steering angle change curve, (b) a tractor acceleration change curve, and (c) a tractor speed change curve;

FIG. 17 is a graphical illustration of scenario 1 in combination with heuristic and optimal control algorithm control quantities and aircraft speed variation curves, under an embodiment; (a) a tractor steering angle change curve, (b) a tractor acceleration change curve, and (c) a tractor speed change curve;

FIG. 18 is a schematic diagram of a scenario 2 optimal control algorithm path planning in one embodiment;

FIG. 19 is a schematic diagram of a path plan incorporating heuristic and optimal control algorithms for scenario 2 in one embodiment;

FIG. 20 is a graphical illustration of the control variables and aircraft speed profiles for the optimal control algorithm for scene 2 in one embodiment; (a) a tractor steering angle change curve, (b) a tractor acceleration change curve, and (c) a tractor speed change curve;

FIG. 21 is a graphical illustration of scenario 2 in combination with heuristic and optimal control algorithm control quantities and aircraft speed variation curves, under an embodiment; (a) a tractor steering angle change curve, (b) a tractor acceleration change curve, and (c) a tractor speed change curve;

FIG. 22 is a schematic diagram of scenario 3 in combination with heuristic and optimal control algorithm path planning in one embodiment;

FIG. 23 is a graphical illustration of scenario 3 in combination with heuristic and optimal control algorithm control quantities and aircraft speed variation curves, under an embodiment; (a) a tractor steering angle change curve, (b) a tractor acceleration change curve, and (c) a tractor degree change curve;

FIG. 24 is a block diagram of an apparatus according to an embodiment.

Detailed Description

In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application.

As shown in fig. 1, the present application provides an aircraft traction path planning method combining heuristic and optimal control, which in one embodiment includes the following steps:

102, acquiring a path planning task for the airplane to be dispatched on a platform; the path planning task comprises the following steps: an initial position of the aircraft, a target position of the aircraft, and an obstacle.

And 104, planning a path for avoiding the obstacle from the initial position to the target position of the airplane by adopting an A-algorithm to obtain an initial path, wherein the initial path comprises a plurality of nodes.

Specifically, an A-x algorithm is adopted, and the total cost of the current node is obtained 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 weighing operator; and obtaining an initial path according to the minimum value of the total cost of all the nodes. The initial path includes a plurality of nodes.

The dynamic weighing operator is greater than or equal to one and gradually decreases from the initial stage to the final stage of the A-star algorithm.

When the obstacle is located in the horizontal axial direction of the current node, the path of the current node does not include a vertically adjacent node of the obstacle; when the obstacle is located in a vertical axis of the current node, the path of the current node does not include horizontally adjacent nodes of the obstacle.

The A algorithm satisfies barrier convex hull expansion constraints; the barrier dome expansion constraint comprises: connecting the maximum salient points of the airplane outline into a convex polygon to obtain a convex shell model; expanding the convex shell model outwards by a certain safe buffer distance by adopting a polygon expansion algorithm to obtain a convex shell transition model; obtaining a plurality of circular models tangent to the convex shell transition model by taking the vertex of the convex shell model as the circle center and the safe buffer distance as the radius; and obtaining obstacle convex hull expansion constraint according to the convex hull transition model and the circular model.

106, searching each node in the initial path again from the first node; and when an obstacle exists in the preset range of the path between the first node and the second node, taking the second node as a key point, otherwise, judging whether the obstacle exists in the preset range of the path between the first node and the third node, and obtaining a key point set until judging whether the obstacle exists in the preset range of the path between the last node and the adjacent node.

108, establishing a kinematic model for the process of debugging and transporting the airplane on the platform, and meeting obstacle constraint, kinematic constraint and terminal pose constraint to obtain an optimal control model; and converting the optimal control model to obtain a nonlinear programming model.

The kinematic constraints and terminal pose constraints include: a speed relationship constraint between the aircraft and the tow vehicle, a steering angle and speed constraint of the aircraft, and a control variable constraint of the tow vehicle.

And the optimal control model is converted by adopting a Radau pseudo-spectrum algorithm, and other algorithms in the prior art can also be adopted.

110, selecting more than one key point in the key point set to carry out geometric solution to obtain corresponding key point postures; and obtaining an optimal path according to the key point posture and the nonlinear programming model.

Specifically, more than one key point is selected to obtain an angular bisector of two tracks taking the key point as an intersection point, a normal line of the angular bisector is taken as the speed direction of the aircraft at the key point, and the maximum threshold speed is taken as the speed of the aircraft at the key point; and obtaining more than one key point gestures according to the speed direction and the speed, wherein the key point gestures correspond to the key points one to one.

Inputting the key point posture into the nonlinear programming model, and solving the nonlinear programming model by adopting a solver to obtain a connection point; the connecting points correspond to the key points one by one; obtaining a corresponding segmented path according to a key point and a connecting point corresponding to the key point; and obtaining an optimal path according to all the segmented paths.

It should be noted that the maximum threshold speed may be preset according to safety requirements, and may be set through experience or the prior art.

Firstly, establishing a convex hull obstacle expansion model aiming at a complex arrangement environment of a platform; secondly, dynamic weighing factors are introduced into the A algorithm, a track re-searching algorithm is designed, the initial position and the target position of the airplane are subjected to primary path planning by using the improved A algorithm, the shortest path for avoiding obstacles is obtained, the key points of the shortest path are solved in the path, a proper amount of key points are selected to solve the motion state of the key points, the key points are used as intermediate points for pseudo-spectrum path planning, the optimal control algorithm is combined to perform segmented planning and integration on the initial position and the target position of the airplane, the road condition is simplified through segmented planning, the problem that the optimal control algorithm aims at the initial value sensitivity under the complex obstacle environment and the problem that the optimal control algorithm cannot be solved due to the fact that the obstacle situation is complex and falls into the iteration dead zone is effectively solved, and the shortest path which meets the kinematic and terminal pose constraints and is short in distance and use is obtained.

It should be understood that, although the steps in the flowchart of fig. 1 are shown in order as indicated by the arrows, the steps are not necessarily performed in order as indicated by the arrows. The steps are not performed in the exact order shown and described, and may be performed in other orders, unless explicitly stated otherwise. Moreover, at least a portion of the steps in fig. 1 may include multiple sub-steps or multiple stages that are not necessarily performed at the same time, but may be performed at different times, and the order of performance of the sub-steps or stages is not necessarily sequential, but may be performed in turn or alternately with other steps or at least a portion of the sub-steps or stages of other steps.

The aircraft traction and allocation is a key link of the complete cycle of the operation and recovery operation of the aircraft fleet, and in order to improve the efficiency of the aircraft allocation and to aim at obtaining the optimal path meeting the kinematics and the terminal pose constraint, in a specific embodiment, the heuristic and optimal control method is combined to carry out the planning research of the aircraft traction path.

The take-off and landing guarantee operation of the airplane is generally carried out according to a mode of wave-division repeated cycle operation, and specifically can be divided into a wave-division operation mode and a continuous operation mode. The continuous operation mode divides different fleets into different fleets, and the fleets respectively execute the circulating movement recovery operation, and the respective flight periods are staggered and overlapped end to end, but the platform can only accommodate the guarantee operation of one fleet in the same period.

The platform support operation mainly comprises two types of flows, namely a direct movement flow of the first-wave airplane movement and a movement flow of the recovered airplane when the recovered airplane moves again to execute a task, but no matter which type of support flow is adopted, the operation flows of filling, hanging and other machine service support of the airplane and warming self-checking and the like before taking off are necessary.

As shown in fig. 2, since the narrow space platform divides different functional areas to execute corresponding support tasks, different areas are required to perform corresponding work in the support process of the aircraft takeoff, which requires the aircraft to be dispatched. For example, in the direct departure process, a mission aircraft parked in a hangar needs to be transported to a platform guarantee parking position through a tractor and an aircraft elevator to perform the maintenance service guarantees such as filling and hanging. Then, in the stage of moving out of the field, each machine is sequentially warmed up, self-checked, slided in and out of the field, prepared in a take-off position and ejected/slided for take-off; after the aircraft fleet is recovered to the platform, part of the faulty or scheduled maintenance aircraft is transferred to the hangar for maintenance, the aircraft needing to execute the second-time moving task is subjected to the second-time moving guarantee, and the aircraft is dispatched and transported for many times among different working areas of the platform in the whole process.

Therefore, a path which has safety and high efficiency and accords with the actual work from the initial machine position to the target machine position is searched in a narrow platform space, and the method has important significance for guaranteeing the dispatching of the airplane, executing various movement recovery guarantee operations and improving the dispatching efficiency of the airplane group.

102, acquiring a path planning task for dispatching and transporting an airplane on a platform; the path planning task comprises the following steps: an initial position of the aircraft, a target position of the aircraft, and an obstacle.

The A-algorithm is a classic heuristic algorithm which is most effective in solving the shortest path in a static road network, and the shortest path is found by setting a specific heuristic function as a heuristic factor and inducing the calculation direction of the algorithm. In the aircraft traction path planning applying the algorithm, in order to simplify the problem model and obtain the shortest path, the following assumptions are made: (1) the mass point is regarded as in the process of airplane allocation and transportation; (2) kinematic and dynamic constraints such as steering angles and the like in the process of airplane transfer are not considered; (3) and (4) the pose constraints of the airplane during the dispatching and transportation process and the terminal are not considered.

104, obtaining the total cost of the current node by adopting an A-algorithm 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 weighing operator; and obtaining an initial path according to the minimum total cost of all the nodes. The initial path includes a plurality of nodes.

Algorithm a compares the current node information:

F(x_i,y_i)＝G(x_i,y_i)+H(x_i,y_i) (1)

in the formula: 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, namely a heuristic function value; (x)_i,y_i) Is the current node coordinate.

The shortest path is formed by continuously selecting the nodes with the minimum total cost value, and the airplane can run along any direction instead of the longitudinal direction, the transverse direction or the diagonal direction of the grid, so that the heuristic function selects the European geometric distance, which is also called the linear distance. The heuristic function is then:

in the formula: h is the estimated cost from the current node to the target point, namely a heuristic function value; (x)_i,y_i) Is the current node coordinate; d is unit node distance cost value; (x)_goal,y_goal) Is the target node coordinates.

Due to the limitation of the a-algorithm, when a search for path planning is performed, the search needs to be spread from the starting point to the periphery under the guidance of the heuristic function, but this still results in a large number of useless nodes (e.g., nodes in the opposite direction from the target node) being searched. In order to optimize the search efficiency of the a-algorithm and reduce redundant search, the a-algorithm is improved by adopting a dynamic weighing method, and the improved node information algorithm is as follows:

in the formula: f is the total cost of the current node; g is the cost from the starting point to the current node; omega is a dynamic measurement operator of the current node; h is the estimated cost from the current node to the target point, namely a heuristic function value; (x)_i,y_i) Is the current node coordinates.

The dynamic weighing operator is adjusted according to the characteristics of different search stages of the algorithm, and when the algorithm is in an initial stage, the algorithm is mainly used for rapidly approaching a target, namely, a function value is relatively important to be inspired; and in the final stage of the algorithm, the main purpose is to find the shortest path accurately, i.e. the true cost of the path is relatively important. With the search of the A-star algorithm, the dynamic weighing operator is continuously adjusted, so that the search efficiency of the algorithm is improved, the search depth of the algorithm is increased, the blind search of the algorithm can be effectively prevented from increasing the search quantity, and the quality of the optimal solution is ensured.

The traditional a-algorithm does not usually consider oblique angle evasion when planning a path, that is, when an obstacle is located in the horizontal or vertical axial direction of a current node, the path may directly reach an obstacle adjacent node across an obstacle oblique angle, which causes that when the obstacle is a continuous oblique obstacle node, the algorithm cannot correctly identify the obstacle node, resulting in a path planning error, as shown in fig. 3.

The algorithm is improved aiming at the problems, the improved algorithm flow is shown in table 1, and when the barrier node is located in the horizontal axial direction of the current node, the path of the current node does not include the vertically adjacent node of the barrier; when the barrier node is located in the vertical axial direction of the current node, the path of the current node does not include the horizontally adjacent nodes of the barrier (i.e., 18 rows in table 1, where 1-8 are eight adjacent nodes of the current node, and the nodes are numbered sequentially from left to right and from top to bottom).

When the obstacle is located in the horizontal axis of the current node, the path of the current node does not include vertically adjacent nodes of the obstacle; when the obstacle is located in a vertical axis of the current node, the path of the current node does not include horizontally adjacent nodes of the obstacle.

Table 1 modified a algorithm flow

The a-algorithm satisfies the barrier convex hull expansion constraint.

Obstacles of the airplane in the process of dispatching the platform are mainly other airplanes parked on the platform, the traditional airplane entity model is a circumscribed circle model, however, the space occupied by the airplane is greatly expanded by the model, and no path can be caused in the high-density environment such as an airplane warehouse platform. And meanwhile, weighing the approximation degree and the safety of the model, establishing a convex shell model by combining the body characteristics of the airplane, and connecting the maximum convex points of the outline of the airplane into a convex polygon. The airplane is in a wing-retracting state when being parked as an obstacle, and the convex hull model is shown in figure 4.

Regarding the dispatched airplane as a particle, neglecting the shape and posture influence of the airplane, therefore, when planning a path and avoiding an obstacle, a safe buffer distance needs to be added to the obstacle, and the safe dispatch of the actual airplane on the path is ensured, and for this problem, a certain safe buffer distance is expanded outwards by the convex hull model by adopting a polygon expansion algorithm, as shown in fig. 5.

The post-dilation vertex coordinate calculation formula is as follows:

in the formula: (x)_Q,y_Q) Is a coordinate of the point Q; (x)_P,y_P) Is a P point coordinate; d is the expansion distance; v. of₁Is a straight line l₁The direction vector of (a); v. of₂Is a straight line l₂The direction vector of (a); normaize (v)₁) With normaize (v)₂) Is v is₁And v₂The unit vector of (2).

The expanded convex hull model, i.e. the convex hull transition model, is as shown in fig. 6 (a), the sharp corner of the convex hull model can be obtained from the figure, the convex hull model is subjected to more severe stretching after polygonal expansion, and the stretching distance is far beyond the required safety buffer distance, so that the barrier at the sharp corner is excessively expanded, for this, the vertex of the original convex hull model is taken as the center of a circle, the expanding distance is taken as the radius to form a circle as shown in fig. 6 (b), a plurality of circular models tangent to the convex hull transition model are obtained, a proper amount of key points are selected on the circle to improve the original barrier expansion model (the convex hull transition model), and the improved barrier expansion model, i.e. the barrier convex hull expansion model, is as shown in fig. 6 (c).

And the obstacle convex hull expansion model is satisfied, namely the obstacle convex hull expansion constraint is satisfied.

Searching each node in the initial path again from the first node; and when an obstacle exists in the preset range of the path between the first node and the second node, taking the second node as a key point, otherwise, judging whether the obstacle exists in the preset range of the path between the first node and the third node, and obtaining a key point set until judging whether the obstacle exists in the preset range of the path between the last node and the adjacent node.

The improved A-algorithm can quickly and accurately search the shortest path from the starting position to the target position of the airplane when the assumed condition is met, but the A-algorithm belongs to a unit decomposition method, the path is formed by continuously connecting adjacent nodes, so that the track has a large amount of turns and is limited by the length of a unit, and when the distance of a target node is longer, the slope change of a connecting line between the two nodes and the target node is small, and the angle change of the connecting line perpendicular to the connecting line is not enough to be identified, a suboptimal path can be generated.

And designing a re-searching track optimization algorithm, optimizing the two problems by re-searching track nodes, wherein the algorithm flow is shown in table 2, taking an initial node as a first node, sequentially selecting a second node along a path, judging whether an obstacle node exists within a certain distance of a connecting line of the two nodes, if not, continuously selecting a next node along the path as the second node for re-judgment, if so, marking the current second node as a key point, taking the current second node as the first node, and sequentially selecting the second node along the path to continuously search until the search is finished.

TABLE 2 Re-search trajectory optimization algorithm flow

The Walkable function is used for connecting two nodes and judging whether barrier nodes exist in a certain distance of a connecting line. And (4) obtaining key points of the original track by re-searching the track and generating an optimal path.

Because the path generated by the A-star algorithm does not consider kinematics such as steering angle in the dispatching process, dynamics constraint, airplane dispatching process and terminal pose constraint, when practical problem research is carried out, such as the research of problems such as airplane dispatching, the factors have important influence on the operations of obstacle avoidance, warehouse exit, warehouse entry and the like in the multi-airplane dispatching process. In order to obtain an airplane dispatching path meeting kinematics, dynamics and airplane terminal pose constraints, the motion state of key points is calculated on the basis that the A-x algorithm obtains the key points of the path, the key points are taken as nodes, the optimal control model is combined to plan the path in a segmented mode, and all the segments of the path are connected to obtain a complete path.

Modeling analysis is performed by taking an airplane dispatching system without a rod and with a tractor as an example.

And establishing a kinematic model for the process of dispatching the airplane on the platform. The rodless airplane haulage system is similar to the trailer system and thus may also be considered one type of trailer system. Because the movement speed is slow in the airplane transfer process, the surface of the platform is flat in a narrow space, and if the tire does not slide in the movement process, the inertia force and the lateral force can be ignored due to the slow movement, and a simplified system model is shown in fig. 7.

In FIG. 7, θ₁And theta₂Respectively, the angle between the axial direction and the x-axis of the aircraft and of the towing vehicle, L₁And L₂The wheelbase of the airplane and the wheelbase of the tractor, (x)₁,y₁)、(x₂,y₂)、(x₃,y₃) Respectively representing the aircraft, the hinge point of the aircraft and the towing vehicle and the coordinate position of the towing vehicle, beta₁And beta₂Respectively representing steering angles, M, of aircraft and towing vehicle₀The distance between the hinged point of the tractor and the rear wheel of the tractor is measured for traction.

According to the system structure and the motion relation, the kinematic equation is as follows:

wherein X ═ X₁,y₁,θ₁,θ₂,v₂]^T，U＝[u₁,u₂]^T，u₁＝tanβ₂，u₂＝a₂I.e. tractor acceleration, v₂Is the tractor translation speed.

The kinematic model satisfies the obstacle constraints.

Different from an A-algorithm obstacle model, the obstacle avoidance in the optimal control algorithm can be realized by the analysis expression form of the obstacle, the path calculation is carried out, in order to facilitate the calculation, the airplane model adopts a traditional characteristic circle model, the collision judgment is carried out by the concern of the Euclidean distance between the circle center and the obstacle and the safety distance, and the judgment formula is as follows (6):

in the formula: n is the total number of obstacles, x_oiAnd y_oiRespectively, the center position coordinates of the i-th obstacle, a_iAnd b_iIs half of the length of the barrier along the transverse axis direction and half of the length of the barrier along the longitudinal axis direction; d represents a safe buffer distance; p is a shape parameter. When 2p is 1, the graph described by the formula is a diamond; when 2p is 2, the depicted graph is a circle or an ellipse; when p → ∞, the depicted graph is rectangular.

The kinematic model also satisfies kinematic constraints and terminal pose constraints. Kinematic constraints and terminal pose constraints include: a speed relationship constraint between the aircraft and the tow vehicle, a steering angle and speed constraint of the aircraft, and a control variable constraint of the tow vehicle.

Depending on the structural characteristics of the towing system used on the platform, the relationship between the translational speed of the aircraft and the speed of the towing vehicle can be expressed as:

wherein, the steering angle and the speed of the airplane should satisfy:

furthermore, the control variables of the tractor should also satisfy the corresponding constraint relationships, namely:

the upper and lower limits of the translational velocity and the translational acceleration are given according to the specific models of the airplane and the rodless traction equipment and related safety specification requirements, and the steering angle is generally calculated according to the turning radius of the airplane and the tractor in the following specific calculation mode:

since the constraints of the obstacle, the translation speed, the control variables and the like are inequality constraints, the two parts can be considered together to form an inequality constraint relation in a uniform form, and all inequality constraints can be uniformly expressed as:

h≤0 (11)

wherein, the formula (11) can be composed of the formula (6), the formula (8) and the formula (9).

The optimal control model for the path planning for the rodless traction system can be described as equation (12).

In the formula:

the system described for formula (5), t_fTo the time of arrival at the end point, t₀At the departure time, wk is a weight adjustment factor, J is an objective function, and R is a weight matrix.

Obtaining an optimal control model after the kinematics model meets the constraint; and converting the optimal control model to obtain a nonlinear programming model.

The optimal control model can be converted by using various algorithms in the prior art, for example, using a Radau pseudo-spectrum algorithm, and the solving steps are as follows.

(1) Parameter initialization

Firstly, assigning and initializing each parameter in the optimal control model.

(2) Time interval discretization

The solution is carried out by using Radau pseudo-spectrum method, and firstly, the time interval [ t ] of the solution is required₀,t_f]Divided into K sub-intervals t_k-1,t_k]，t₀＜t₁＜…＜t_k＜…＜t_K＝t_fK is 1,2, …, K, for convenience, and is used subsequently(·)^(k)The correlation parameter in the k-th interval is expressed as

Conversion to the interval [ -1,1]Above, the following transformation is employed:

for the discretization solution, the state variable, the control variable, the constraint function and the optimization objective function need to be subjected to interpolation transformation, the matching point of the Radau pseudo-spectrum method is a Legendre Gauss Radau (LGR) point, and the LGR point of the N-order is a polynomial equation P_N(T)+P_N-1(T) 0, where P_N(T) Legendre polynomial in order N:

(3) subinterval variable approximation

For state variables, for the first N^(k)Each LGR distribution point is T_i ^(k)，i＝1,2,…,N^(k)To a

By the use of N^(k)Order Lagrange interpolation polynomial

As a basis function, interpolating the state variables to approximate:

wherein K is 1,2, …, K, X^(k)(T_i ^(k)) Is X^(k)At node T_i ^(k)The value of the position is selected,

is a Lagrange interpolation basis function which satisfies:

for the control variables, similar to the state variables, for the first K-1 intervals:

wherein K is 1,2, …, K-1;

for the Kth interval, use N^(k)Lagrange interpolation polynomial of order-1

As a basis function, interpolating the control variables to approximate:

wherein:

and thirdly, for a constraint function. First, the state variables are derived:

to formula (20) at

Discretizing to obtain:

in the formula (I), the compound is shown in the specification,

wherein, the order is N, the Rafau pseudo-spectrum differential matrix is^(k)×(N^(k)+1)。

Substituting equation (21) for equation (12) may transform the differential constraint equation into:

path constraint discretization:

where i is 1,2, …, N^(k)

Performance indexes are as follows:

the state variables of the connection end points of the adjacent subintervals are equal, and the following conditions are met:

The selection of the key points is preferably performed on the gentle track section, the key points with large change of the aircraft course angle are not preferably selected, otherwise, a large turning track is generated, and the planned path deviates from the shortest path.

The geometric solution means: selecting more than one key point to obtain an angular bisector of two tracks taking the key point as an intersection point, taking a normal line of the angular bisector as the speed direction of the airplane at the key point, and taking the maximum threshold speed as the speed of the airplane at the key point; and obtaining more than one key point gestures according to the speed direction and the speed, wherein the key point gestures correspond to the key points one to one.

Specifically, the method comprises the following steps: establishing a trajectory key point kinematics calculation model, and assuming that the speed is moderate and remains unchanged in the movement process of the airplane, namely the tangential acceleration is 0; the direction of movement of the towing vehicle being coincident with the direction of movement of the aircraft, i.e. theta₁＝θ₂. Taking the normal line of the intersecting two trajectory angle bisectors as the aircraft speed direction, as shown in fig. 8:

broken line ABC in FIG. 8 is an A-algorithm planning path, wherein B is a key point, n is an angle bisection line of ^ ABC, and l is a normal line of n, and if the aircraft moves along ABC in sequence, the speed direction is shown as v in FIG. 8.

Taking the key point as a middle point, inputting the state parameter, namely the attitude of the key point, into the nonlinear programming model, performing sectional programming on the path of the airplane by using an optimal control algorithm, and solving the nonlinear programming model by using a solver (such as an SNOPT software package) to obtain a connection point; the connecting points correspond to the key points one by one; obtaining a corresponding segmented path according to a key point and a connecting point corresponding to the key point; and merging all the segmented paths to obtain the optimal path. The optimal path is the shortest path that satisfies the constraint.

In order to visually display the improved algorithm A path planning effect, narrow space platform layout is selected as an example, a certain parking place in a parking area with high airplane density and a temporary parking place far away are selected as examples, the airplane dispatching path between two parking places in a full-editing state is planned by algorithms before and after improved dynamic measurement and before and after track re-searching optimization respectively, and the superiority of the improved algorithm A is displayed through transverse comparison.

Fig. 9 and fig. 10 are schematic diagrams illustrating the algorithm search range before and after dynamic scaling optimization, where the searched node area in the diagrams is a close list set in the algorithm, and the smaller the set is, the higher the algorithm search efficiency is. Before dynamic measurement optimization, the algorithm needs to search a large number of areas for path planning, the efficiency is low, after the dynamic measurement optimization is added, redundant search nodes are not generated except for necessary paths and obstacle detection requirements, the optimization effect is obvious, and the algorithm efficiency is greatly improved.

Fig. 11 and 12 are schematic diagrams illustrating path planning before and after re-search optimization, where the region a in fig. 11 is the problem of excessive turning of the trajectory mentioned above, and the region B in fig. 11 is the limitation unit length mentioned above, and when the target node is far away, the slope change of the connection line between two nodes and the target node is small, and is not enough to identify the angle change perpendicular to the connection line, a suboptimal path is generated. After the re-search algorithm is optimized, the track is as shown by a black path in fig. 12, both the broken line part of the area A and the suboptimal path of the area B are optimized, and the algorithm successfully generates the shortest path.

The final full segment path planning effect is shown in fig. 13.

Taking a certain type of airplane as an example, a kinematics model is established by the airplane, an optimal control method and a multi-scenario path planning simulation experiment combining a heuristic method and an optimal control algorithm are carried out, and the experimental result is analyzed.

The simulation experiment selects a single key point, the narrow space platform is in a full-weave arrangement state, the airplane is a large-sized fixed wing airplane, the simulation experiment of each scene only changes the arrangement conditions of an initial parking position, a target parking position and an obstacle airplane, various parameters and constraint conditions of the airplane and the tractor are kept unchanged, and each parameter value is p-3 and L-3 in the formula (6)₁＝5.88m、L₂＝2.4m、β_1max＝π/4、-1m/s≤v₂≤1m/s、-1m/s²≤u₂≤1m/s²、-π≤θ₁≤π、-π≤θ₂Less than or equal to pi, and the distance between the articulated point of the tractor and the center of the rear wheel of the tractor is very small, so that M is taken₀＝0、-1≤u₁Not more than 1, i.e., -pi/4 not more than beta₂≤π/4。

Table 3 comparison of simulation experiment results in scene 1

Fig. 14 is a track diagram for planning a route of an aircraft dispatch by an optimal control algorithm, fig. 15 is a track diagram for planning a route by combining a heuristic algorithm and an optimal control algorithm, and comparison of the two shows that both algorithms can effectively avoid obstacles, but the track diagram obtained by the algorithm is smoother than the track obtained by a pure optimal control algorithm, and for further analysis, a control quantity U ═ U is calculated₁,u₂]^TAnd the change curve of the airplane moving speed along with the time is analyzed, and fig. 16 and 17 are shown.

In both figures, (a) is the control quantity u₁I.e. the change curve of the steering angle of the tractor, can be obtained from a graph, and the algorithm in the text is used for controlling the quantity u₁The fluctuation amplitude and the frequency of the control quantity are obviously reduced, wherein the reduction value on the fluctuation amplitude can reach 45 percent, which shows that the improved algorithm enables the process of searching the target to be more stable, the searching efficiency is higher, and the variation trend of the control quantity is consistent with the turning condition of the airplane, namely u₁Greater than 0 left turn u of the aircraft₁The control effect is good when the airplane turns right less than 0.

In the two graphs, (b) is a control quantity u2, namely a change curve of the acceleration of the tractor, and can be obtained from the graphs, the stability of the result obtained by the algorithm is obviously better than that obtained by only using an optimal control algorithm, the aircraft only has the acceleration in the initial stage and the deceleration in the final stage, the speed of the aircraft in the middle process of the motion is kept unchanged, the aircraft runs stably, and the algorithm is better than the optimal control algorithm in combination with the graphs (c) and is difficult to converge in the motion process due to the fluctuation of the acceleration, so that the effect obtained by the algorithm on the one hand is very obvious, and the problem of wrong planning caused by the fact that the target distance or the obstacle situation is complex is effectively avoided.

Table 4 comparison of simulation experiment results in scene 2

As shown in fig. 18 to 21, comparing the simulation results of the two algorithms in the scene 2, the difference between the four types of data in table 4 is not large, but comparing fig. 18 and fig. 19, it can be found that the occupation of the path trajectory space planned by the algorithm is far smaller than that of the optimal control algorithm, the shortest path is more fitted, the dispatching process is concentrated on the lower half of the platform, and the upper half is basically unoccupied. In such narrow spaces, the improvement of the space utilization rate has important significance on the dispatching of the airplane fleet, the algorithm ensures the space utilization rate of the platform to the maximum extent, and a sufficient safety channel is reserved for the dispatching of other airplanes, so that the method has practical significance.

For the obstacle complex situation, as shown in the obstacle situation of scene 3 in fig. 22, the optimal control algorithm cannot converge to obtain the optimal path and cannot find the optimal solution because the target distance is too far and the obstacle situation is complex, and the algorithm can still avoid the complex obstacle to reach the target station and plan the optimal path, and the transformation curves of (a), (b) and (c) in fig. 23 show that the aircraft motion state is stable, the variation trend of the controlled variable is consistent with the aircraft turning situation, and the control effect is good.

Through simulation experiments of three types of scenes, compared with the traditional optimal control algorithm, the following advantages of the algorithm are verified: firstly, the problem of initial value sensitivity of an optimal control algorithm in a complex obstacle environment is effectively solved; secondly, the path is more fit with the shortest path, the time required by the airplane dispatching is effectively shortened, the space limitation of the platform is considered, and enough safe channels are reserved for the platform; and fluctuation of the airplane transferring track is reduced, the track is smoother, and the stability of airplane transferring is enhanced.

The method comprises the steps of establishing a convex hull obstacle expansion model aiming at a complex arrangement environment, introducing dynamic weighing factors into an A-x algorithm, designing a track re-search algorithm, solving key points of the shortest path, then resolving the motion states of the key points, and planning and integrating the segmented paths among the key points by combining an optimal control algorithm. And moreover, a path planning simulation experiment under a typical platform environment is also carried out, and the superiority of the method is verified by comparing the result with the simulation experiment result of the optimal control algorithm. The method improves the A-algorithm, combines the optimal control algorithm, establishes the shortest path by improving the A-algorithm, selects the key points, carries out key point segmentation processing on the long path, carries out path planning by utilizing the optimal control algorithm in each segment, ensures that the path is the shortest path, fully considers kinematics and terminal pose constraints in the airplane dispatching and transporting process, avoids the problem of initial value sensitivity in a complex obstacle environment, and effectively improves the optimization performance of airplane dispatching and transporting.

In one embodiment, as shown in fig. 24, there is provided an aircraft traction path planning apparatus combining heuristic and optimal control, including: an obtaining module 2402, an initial path establishing module 2404, a key point set establishing module 2406, a model establishing module 2408 and an optimal path establishing module 2410, wherein:

an obtaining module 2402, configured to obtain a path planning task for dispatching and transporting an aircraft on a platform; the path planning task comprises the following steps: an initial position of the aircraft, a target position of the aircraft, and an obstacle;

an initial path establishing module 2404, configured to perform path planning for avoiding an obstacle from an initial position to a target position of an aircraft by using an a-x algorithm, so as to obtain an initial path, where the initial path includes a plurality of nodes;

a keypoint set establishing module 2406, configured to re-search each node in the initial path, starting from the first node; when an obstacle exists in a preset range of a path between a first node and a second node, the second node is taken as a key point, otherwise, whether the obstacle exists in the preset range of the path between the first node and a third node is judged, and until whether the obstacle exists in the preset range of the path between the last node and an adjacent node is judged, a key point set is obtained;

the model establishing module 2408 is used for establishing a kinematic model for the process of debugging and transporting the airplane on the platform, and meeting obstacle constraints, kinematic constraints and terminal pose constraints to obtain an optimal control model; converting the optimal control model to obtain a nonlinear programming model;

an optimal path establishing module 2410, configured to select more than one keypoint in the keypoint set for geometric solution to obtain a corresponding keypoint posture; and obtaining an optimal path according to the key point posture and the nonlinear programming model.

For specific limitations of the aircraft traction path planning device combining the heuristic and the optimal control, reference may be made to the above limitations of the aircraft traction path planning method combining the heuristic and the optimal control, and details thereof are not described here. The various modules in the above-described apparatus may be implemented in whole or in part by software, hardware, and combinations thereof. The modules can be embedded in a hardware form or independent from a processor in the computer device, and can also be stored in a memory in the computer device in a software form, so that the processor can call and execute operations corresponding to the modules.

The technical features of the above embodiments can be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the above embodiments are not described, but should be considered as the scope of the present specification as long as there is no contradiction between the combinations of the technical features.

The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is specific and detailed, but not to be understood as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims

1. The aircraft traction path planning method combining heuristic and optimal control is characterized by comprising the following steps of:

establishing a kinematic model for the process of debugging and transporting the airplane on the platform, and satisfying obstacle constraint, kinematic constraint and terminal pose constraint to obtain an optimal control model; converting the optimal control model to obtain a nonlinear programming model;

2. The method of claim 1, wherein planning a path of the aircraft from the initial position to the target position avoiding the obstacle using an a-x algorithm, the obtaining the initial path comprising:

3. The method of claim 2, wherein planning a path of the aircraft from the initial position to the target position avoiding the obstacle using an a-x algorithm, the obtaining the initial path further comprising:

4. The method according to claim 3, wherein the dynamic scaling operator is equal to or greater than one and gradually decreases from the initial stage to the final stage of the A-x algorithm.

5. The method according to any one of claims 1 to 4, wherein the A-algorithm satisfies a barrier convex hull expansion constraint;

expanding the convex shell model outwards by a certain safe buffer distance by adopting a polygonal expansion algorithm to obtain a convex shell transition model;

6. The method according to any one of claims 1 to 4, wherein selecting more than one keypoint for geometric solution to obtain corresponding keypoint poses comprises:

7. The method of any one of claims 1 to 4, wherein deriving an optimal path from the keypoint poses and the nonlinear programming model comprises:

8. The method according to any one of claims 1 to 4, wherein the kinematic constraints and the end pose constraints comprise:

9. Method according to any of claims 1 to 4, wherein the transformation of the optimal control model uses Radau pseudo-spectral algorithm.

10. An aircraft traction path planning device combining heuristic and optimal control is characterized by comprising the following steps:

a key point set building module, configured to re-search each node in the initial path starting from the first node; when an obstacle exists in a preset range of a path between a first node and a second node, the second node is taken as a key point, otherwise, whether the obstacle exists in the preset range of the path between the first node and a third node is judged, and until whether the obstacle exists in the preset range of the path between the last node and an adjacent node is judged, a key point set is obtained;