Automatic guided vehicle (AGV) trajectory planning method and system with continuous curvature

Abstract

The invention provides a curvature-continuous AGV trajectory planning method and system, and relates to the technical field of trajectory planning. The method comprises the following steps: firstly, establishing a two-dimensional coordinate system taking a starting point as an original point, and acquiring a final position and angle information; based on the data, the system determines proper basic trajectory path types from a preset trajectory classification library, including straight lines, various curves and the like. Then, the basic track is segmented, and the basic track is divided into a combination of a straight line segment, a gradual change curve segment and an arc segment; and a track information packet containing complete attribute information is formed by calculating gradual change curve parameters and integrating all sections of routes. And finally, the system performs trafficability verification on the track to ensure that the finally generated track meets the movement requirement of the AGV. According to the method, the gradual change curve is introduced to serve as the transition section, and continuous and smooth change of the track curvature is achieved.

Description

Technical Field

[0001] This application relates to the technical field of trajectory planning, and particularly to a method and system for AGV trajectory planning with continuous curvature. Background Art

[0002] With the continuous improvement of industrial automation level, AGV (Automated Guided Vehicle) has been widely used in scenarios such as intelligent factories and automated warehouses. In practical applications, AGV needs to flexibly plan its trajectory according to the working environment to achieve precise motion control from the starting point to the ending point.

[0003] Currently, the commonly used trajectory planning methods in the industry mainly adopt the arc transition method, that is, connecting between straight line segments through arcs. This method calculates the intersection point between two straight lines, constructs an arc with a specific radius centered at the intersection point, and uses the arc as the transition curve to connect adjacent straight line segments, thereby forming the motion trajectory of AGV.

[0004] However, due to the sudden change in curvature between the arc and the straight line, there will be an instantaneous acceleration change when AGV transitions from the straight line segment to the arc segment, resulting in unstable phenomena such as jitter and skidding during vehicle driving. This instability will reduce the running accuracy of AGV, increase wheel wear, and may cause damage to the carried items. Summary of the Invention

[0005] This application provides a method and system for AGV trajectory planning with continuous curvature, which is used to solve the problem of sudden change in curvature at the connection between the straight line segment and the arc segment of the existing AGV.

[0006] In a first aspect, this application provides a method for AGV trajectory planning with continuous curvature, which is applied to a trajectory planning system. The method includes: constructing a two-dimensional environmental coordinate system with the starting point as the origin; obtaining the coordinate data and angle data of the trajectory end point, where the angle data takes the driving direction of the starting point as the positive direction of the X-axis; combining the end point coordinate data and the angle data, and determining the basic trajectory path according to a preset trajectory classification library, where the basic trajectory path includes straight lines, right-angle bends, acute-angle bends, obtuse-angle bends, S-bends, and flat-angle bends; performing curve segmentation on the basic trajectory path to obtain corresponding multiple segments of routes, where the multiple segments of routes at least include straight line segments, gradual change curve segments, and arc segments; combining the end point coordinate data and the angle data to calculate the gradual change curve parameters; integrating the multiple segments of routes to obtain a preliminary trajectory information package containing attribute information, where the attribute information at least includes route type information, the end point coordinates, the angle data, and the gradual change curve parameters; checking the passability of the preliminary trajectory information package to determine the final trajectory information package.

[0007] By adopting the above technical solutions, a two-dimensional environmental coordinate system with the starting point as the origin is first constructed, and the end point coordinates and angle data are obtained, laying a foundation for subsequent trajectory planning. Combining these data, the system can accurately identify the most suitable basic trajectory path type from the preset trajectory classification library. By segmenting the basic trajectory into curves and introducing a gradual change curve segment as a transition between the straight line segment and the arc segment, the curvature can change smoothly and continuously. The introduction of this gradual change curve, combined with reasonable parameter calculation, effectively eliminates the problem of sudden curvature change at the connection between the arc and the straight line in the traditional solution, thus avoiding the jitter and skidding phenomena caused by the instantaneous acceleration change during the driving process of the AGV, and realizing the stable operation of the AGV.

[0008] In combination with some embodiments of the first aspect, in some embodiments, in the step of determining the basic trajectory path according to the preset trajectory classification library by combining the end point coordinate data and the angle data, it specifically includes: If , meters and meters, then the basic trajectory path is a straight line; if , meters and meters, then the basic trajectory path is an S-curve; if , and meters, then the basic trajectory path is an acute-angle bend; if , and meters, then the basic trajectory path is a right-angle bend; if , the preset minimum allowable radius, and meters, then the basic trajectory path is an obtuse-angle bend; if , the preset minimum allowable radius, then the basic trajectory path is a flat-angle bend; where is the angle data, is the abscissa of the trajectory end point, is the ordinate of the trajectory end point.

[0009] By adopting the above technical solutions, a complete set of trajectory type determination criteria is established. Through the specific numerical ranges of the end point coordinates and the angle data, the system can accurately judge which basic path type the trajectory should adopt. This classification method based on specific parameters makes the determination of different types of trajectories such as straight lines, S-curves, acute-angle bends, right-angle bends, obtuse-angle bends, and flat-angle bends more accurate and reliable. By setting constraint conditions such as the minimum allowable radius, it ensures that the generated trajectory meets the kinematic characteristics of the AGV, providing a reliable prerequisite for realizing curvature continuous trajectory planning, and further ensuring the stability of the AGV operation.

[0010] In some embodiments in combination with some embodiments of the first aspect, it further includes: setting the end point of the trajectory as P and the starting point as O; determining the straight-line equation L1 in the moving direction of the starting point O and the straight-line equation L2 in the moving direction of the end point P; determining the coordinates of the intersection point N in combination with the straight-line equation L2, and calculating the symmetric line equation L3 of the straight-line equation L1 and the straight-line equation L2; if the basic trajectory path is an acute bend, a right-angle bend or an obtuse bend, determining the symmetric point Q of the end point P with respect to the symmetric line equation L3; if there is a gradually changing curve segment in the curve PQ, the curve function of the gradually changing curve segment is: , where is a preset trajectory smoothness value, is a parameter of the gradually changing curve; if there is an arc segment in the curve PQ, the curve function of the arc segment is: , where .

[0011] By adopting the above technical solution, the straight-line equations L1, L2 and the symmetric line equation L3 are introduced, and a complete mathematical model is constructed. By determining the coordinates of the intersection point N and the symmetric point Q, an accurate spatial position reference is provided for the construction of the gradually changing curve. In particular, by introducing the gradually changing curve function and the arc segment function, the curvature of the curve can change continuously and smoothly. The curve function of the gradually changing curve segment contains a preset trajectory smoothness value, which can adjust the smoothness of the curve according to actual needs, effectively solving the problem of sudden change of curvature in the traditional solution.

[0012] In some embodiments in combination with some embodiments of the first aspect, if the basic trajectory path is an acute bend, a right-angle bend or an obtuse bend, after the step of determining the symmetric point Q of the end point P with respect to the symmetric line equation L3, it further includes: if the basic trajectory path is an S bend, calculating the relative driving angle of the midpoint T of the OP line segment; splitting the basic trajectory path into two mirror-image acute bends or right-angle bends according to the relative driving angle.

[0013] By adopting the above technical solution, when dealing with an S-shaped bend, by calculating the relative driving angle of the midpoint T of the OP line segment, the complex S-bend trajectory is decomposed into two simple bends that can be mirror-processed. This decomposition method enables the system to reuse the existing processing logic for acute bends or right-angle bends, simplifies the calculation process while ensuring the continuity of the trajectory. This modular processing method not only improves the calculation efficiency of the system but also ensures the smooth transition of the curvature of the entire S-bend trajectory.

[0014] In combination with some embodiments of the first aspect, in some embodiments, the step of segmenting the base trajectory path into curves to obtain corresponding multi-segment routes specifically includes: if the base trajectory path is a right-angle bend, determining QP as a gradually changing curve segment; if the base trajectory path is an S-bend, determining OT and TP as two mirror-image gradually changing curve segments; if the base trajectory path is an obtuse-angle bend, determining that QP includes two gradually changing curve segments with an angle change of 45° and an arc segment.

[0015] By adopting the above technical solution, corresponding curve segmentation strategies are adopted for different types of base trajectory paths. A single gradually changing curve segment is used for a right-angle bend, two mirror-image gradually changing curve segments are used for an S-bend, and a combination of two gradually changing curve segments and an arc segment is used for an obtuse-angle bend. This differential segmentation strategy ensures that the optimal curvature transition can be achieved for each type of trajectory. Especially in the case of a large turning angle, an arc segment is introduced to maintain a stable turning curvature.

[0016] In combination with some embodiments of the first aspect, in some embodiments, the step of, if the base trajectory path is an S-bend, determining OT and TP as two mirror-image gradually changing curve segments specifically includes: calculating the coordinates and relative driving angle of the midpoint T of the OP line segment ; if the relative driving angle < 90°, then the base trajectory path can be regarded as composed of two mirror-image acute-angle bends; if the relative driving angle = 90°, then the base trajectory path can be regarded as composed of two mirror-image right-angle bends; determining OT and TP as two mirror-image gradually changing curve segments.

[0017] By adopting the above technical solution, the relative driving angle is introduced as the judgment basis for S-bend classification, realizing the precise classification and processing of S-bends. When is less than 90°, the processing method for an acute-angle bend is adopted, and when is equal to 90°, the processing method for a right-angle bend is adopted. This angle-based classification method ensures that the system can generate the most suitable combination of gradually changing curve segments for different types of S-bends. Through the splicing of two mirror-image gradually changing curve segments, a smooth transition of the entire S-bend trajectory is achieved.

[0018] In connection with some embodiments of the first aspect, in some embodiments, for the step of determining that the QP includes two gradually changing curve segments and one circular arc segment when the basic trajectory path is an acute bend or an obtuse bend, it specifically includes: calculating the coordinates of the intersection point N of L1 and L2; if the line segment ON > PN, determining that there is a straight line segment at the starting point; if the line segment ON < PN, determining that there is a straight line segment at the ending point; determining the symmetric point Q of the ending point P with respect to the straight line L3; there are points M1 and M2 in the curve QP that are symmetric with respect to the straight line equation L3, and the relative traveling angle of point Z is 45°; determining that QM1 and PM2 are gradually changing curve segments and M1M2 is a circular arc segment.

[0019] By adopting the above technical solution, when dealing with acute bends and obtuse bends, the existence position of the straight line segment is reasonably determined by comparing the length relationship between ON and PN. By introducing the symmetric point Q and the key points M1 and M2, the system can accurately locate the starting and ending positions of the gradually changing curve segments and the circular arc segment. In particular, by ensuring that the relative traveling angle of point Z is 45°, the transition between the gradually changing curve segment and the circular arc segment is made smoother, thereby further optimizing the running stability of the AGV during the turning process.

[0020] In a second aspect, the present application provides a trajectory planning system, which includes: one or more processors and a memory; the memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code includes computer instructions, and the one or more processors call the computer instructions to enable the trajectory planning system to execute the method described in the first aspect and any possible implementation manner in the first aspect.

[0021] In a third aspect, the present application provides a computer-readable storage medium, including instructions, when the instructions run on the trajectory planning system, enabling the trajectory planning system to execute the method described in the first aspect and any possible implementation manner in the first aspect.

[0022] In a fourth aspect, the present application provides a computer program product, when the computer program product runs on the trajectory planning system, enabling the trajectory planning system to execute the method described in the first aspect and any possible implementation manner in the first aspect.

[0023] One or more technical solutions provided in the embodiments of the present application have at least the following technical effects or advantages: 1. By adopting the above technical solution, due to the two key technical means of determining the basic trajectory path based on the preset trajectory classification library and introducing a gradual change curve segment as the transition between the straight line segment and the arc segment, the problem of sudden curvature change at the connection between the straight line segment and the arc segment of the AGV in the prior art is effectively solved. Furthermore, it is realized that the AGV avoids jitter and skidding caused by instantaneous acceleration changes during the driving process, ensuring the smoothness and stability of the AGV operation, and improving the operation efficiency and safety of the AGV.

[0024] 2. By adopting the above technical solution, due to the two key technical means of establishing a mathematical model including the straight line equations L1, L2 and the symmetry line equation L3 and introducing a gradual change curve function with an adjustable smoothness parameter, the technical problem that the curvature cannot be continuously and smoothly transitioned in the prior art is effectively solved. Furthermore, the continuous and controllable change of the trajectory curvature is realized, ensuring that the AGV can maintain smooth operation on any type of trajectory, and greatly improving the motion performance and operation stability of the AGV.

[0025] 3. By adopting the above technical solution, due to the two key technical means of formulating a differential curve segmentation strategy for different types of trajectories and introducing a combination of an arc segment and a double gradual change curve segment at large-angle turns, the technical problem of discontinuous curvature transition of different types of trajectories in the prior art is effectively solved. Furthermore, the optimal curvature transition of various types of trajectories is realized, enabling the AGV to maintain a stable operation state even during complex turning processes, and significantly improving the motion control accuracy of the AGV. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 is a flowchart of a method for AGV trajectory planning with continuous curvature in an embodiment of the present application; Figure 2 is a schematic diagram of curve segmentation of a 90-degree bend in a method for AGV trajectory planning with continuous curvature in an embodiment of the present application; Figure 3 is a schematic diagram of curve segmentation of an S-degree bend in a method for AGV trajectory planning with continuous curvature in an embodiment of the present application; Figure 4 is a schematic diagram of curve segmentation of an obtuse bend in a method for AGV trajectory planning with continuous curvature in an embodiment of the present application; Figure 5 is a schematic diagram of the structure of an entity device of a trajectory planning system in an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0027] The terms used in the following embodiments of the present application are only for the purpose of describing specific embodiments and are not intended to limit the present application. As used in the specification and appended claims of the present application, the singular forms "a", "an", "the", "above-mentioned", "said", "this" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It should also be understood that the term "and / or" used in the present application refers to and includes any or all possible combinations of one or more of the listed items.

[0028] Hereinafter, the terms "first" and "second" are only used for descriptive purposes and should not be construed as implying or suggesting relative importance or implicitly indicating the quantity of the indicated technical features. Thus, features defined with "first" and "second" may explicitly or implicitly include one or more of such features. In the description of the embodiments of the present application, unless otherwise specified, the meaning of "a plurality" is two or more.

[0029] For ease of understanding, the method provided in this embodiment is described in terms of a process below. Please refer to Figure 1 , which is a schematic flowchart of a curvature continuous AGV trajectory planning method in an embodiment of the present application.

[0030] S101. Construct a two-dimensional environmental coordinate system with the starting point as the origin; Among them, the starting point represents the position point where the AGV is currently located; the origin refers to the reference point of the coordinate system for determining the position of the coordinate system; the two-dimensional environmental coordinate system refers to a rectangular coordinate system established in a plane for describing the position relationship within the AGV movement plane.

[0031] Specifically, before the AGV starts trajectory planning, the trajectory planning system first needs to establish a unified reference coordinate system. The system sets the current position of the AGV as the coordinate origin (0, 0), takes the current driving direction of the AGV as the positive direction of the X-axis, and the direction perpendicular to the driving direction and to the left as the positive direction of the Y-axis, thereby establishing a right-handed coordinate system. The coordinate system established in this way can intuitively express the position relationship of the AGV relative to the target point, facilitating subsequent path planning calculations. In practical applications, the system will consider the attitude information of the AGV, including position coordinates and heading angles, and combine with the environmental map information to ensure that the established coordinate system matches the actual movement environment. At the same time, the system also needs to convert the coordinate information of all environmental elements such as obstacles and channel boundaries into this unified coordinate system.

[0032] In some embodiments, the construction of the coordinate system can be achieved in the following manner: Optionally, the system first obtains the real-time position information and attitude information of the AGV, obtains the surrounding environment information through the sensor system, and then uses the coordinate transformation matrix to transform the position information in the global coordinate system into the local coordinate system with the AGV as the origin; Optionally, the system can also directly establish a local coordinate system with the current position of the AGV as the origin and the current orientation as the reference direction based on the data provided by the AGV's positioning system. It can be understood that during the construction of the coordinate system, the kinematic constraints and dynamic characteristics of the AGV also need to be considered to ensure that the established coordinate system can accurately reflect the actual movement ability of the AGV.

[0033] S102. Obtain the coordinate data of the trajectory end point and the angle data, where the angle data takes the driving direction at the starting point as the positive direction of the X-axis; Among them, the coordinate data of the trajectory end point represents the coordinate values of the target position that the AGV needs to reach in the established two-dimensional coordinate system; the angle data represents the desired orientation angle of the AGV at the end point; the driving direction refers to the movement direction of the AGV at the starting point; the positive direction of the X-axis is used as the reference benchmark for angle calculation to unify the angle measurement standard.

[0034] Specifically, after establishing the coordinate system, the trajectory planning system needs to obtain the position and attitude information of the target point. The system first receives the target point information from the task scheduling module, including the position coordinates of the target point in the global coordinate system. Then, the system transforms these global coordinates into the coordinate values in the local coordinate system with the current position of the AGV as the origin through coordinate transformation. For the angle data, the system takes the current driving direction of the AGV as the positive direction of the X-axis (0 degrees), and uses the angle measurement method with the counterclockwise direction as positive and the clockwise direction as negative to calculate the included angle between the desired orientation of the AGV at the target point and the positive direction of the X-axis.

[0035] S103. Combine the coordinate data of the end point and the angle data, and determine the basic trajectory path according to the preset trajectory classification library. The basic trajectory path includes straight lines, right-angle turns, acute-angle turns, obtuse-angle turns, S-turns, and flat-angle turns; Among them, the preset trajectory classification library represents a set of various basic trajectory types predefined by the system; the basic trajectory path refers to the basic movement path type of the AGV from the starting point to the end point; path types such as straight lines and right-angle turns refer to different basic trajectory forms.

[0036] Specifically, after obtaining the end position and angle data, the system needs to determine the most suitable basic trajectory type based on these data. The system first analyzes the positional relationship and angular difference of the end point relative to the start point, including calculating parameters such as distance and azimuth angle. Then, the system matches these parameters with the preset trajectory classification rules to determine which basic trajectory path should be adopted. For example, when the end point is approximately on the same straight line as the start point and the angle is close, the system will select a straight-line path; when the end point position and angle present a specific relationship, the system will select the corresponding type of curved path. During the classification process, the system will consider the kinematic constraints of the AGV to ensure that the selected path type meets the AGV's turning radius, speed and other limiting conditions.

[0037] More specifically, during the AGV trajectory planning process, the system needs to determine the most suitable basic trajectory type based on the end position and orientation. This determination process is mainly based on three key parameters: the desired orientation angle dw at the end point, the lateral position dx of the end point, and the longitudinal position dy. The system adopts a step-by-step judgment strategy, gradually transitioning from the simplest situation to the complex situation to ensure that the most suitable trajectory type can be accurately selected. First, the system will judge the most basic straight-line driving situation. When the end point orientation is the same as the start point orientation (dw = 0°), and the end point mainly reflects the longitudinal distance (dx >> 0.01 m), while the lateral deviation is extremely small (dy ≤ 0.01 m), the system will select a straight-line trajectory. In this case, the AGV can directly drive along a straight line to the target point, which is the simplest and most energy-efficient motion mode.

[0038] If the end point also maintains the same orientation as the start point (dw = 0°), but there is an obvious lateral offset (dy > 0.01 m), and there is still a significant longitudinal distance (dx >> 0.01 m), the system will determine that an S-shaped trajectory is needed. This situation usually occurs in scenarios where lateral displacement is required but the start and end points need to maintain the same orientation, such as lane-changing actions between shelves. When the end point orientation turns relative to the start point, the system will select different trajectory types according to the size of the turning angle: For small-angle turns (0° < dw < 90°), when ensuring that the end point is in front (dx > 0) and there is enough lateral distance (dy > 0.01 m), the system selects an acute-angle curved trajectory, which can complete the turn with a relatively gentle curvature.

[0039] When a 90-degree turn (dw = 90°) is required, if the end point is also in front and there is enough lateral distance, the system will select a standard right-angle curved trajectory.

[0040] For large-angle turns (90° < dw < 180°), the system will select an obtuse-angle turn trajectory on the premise of ensuring sufficient turning space (dy is greater than the preset minimum allowable radius). This trajectory usually requires more movement space but can ensure the smooth completion of large-angle turns by the AGV.

[0041] In extreme cases, if a complete U-turn (dw = 180°) is required, as long as the lateral space meets the minimum turning radius requirement, the system will select a flat-angle turn trajectory. This classification and determination method not only considers geometric features but also fully takes into account the motion characteristics of the AGV and actual application requirements, and can effectively generate basic trajectories that meet the needs of various scenarios. Through this systematic judgment process, it can be ensured that the AGV can select the most suitable motion trajectory in various situations, which not only guarantees the smoothness of motion but also improves the operation efficiency.

[0042] S104. Segment the path of the basic trajectory to obtain corresponding multiple segments of routes, and these multiple segments of routes at least include straight segments, gradually changing curve segments, and arc segments; Curve segmentation means dividing the complete path into different types of sub-segments according to geometric features. The straight segment represents the part of the path where the AGV moves along a straight line; the gradually changing curve segment represents the transition path with gradually changing curvature; the arc segment represents the turning path with a constant curvature.

[0043] Specifically, after determining the type of the basic trajectory, the system needs to decompose it into a combination of path segments that can be actually executed. The system first analyzes the geometric features of the path and identifies the key points that need to be smoothly transitioned. For a right-angle turn, the system plans the entire turning process as a single gradually changing curve segment to ensure that the AGV can smoothly complete a 90-degree turn. For an S-shaped path, the system splits it into two mirror-image gradually changing curve segments to enable the AGV to achieve continuous S-shaped movement. For an obtuse-angle turn, the system adopts a more complex combination, dividing it into two 45-degree gradually changing curve segments and an intermediate arc segment. This combination can ensure the stable motion state of the AGV during large-angle turns. Each segment needs to consider the motion constraints of the AGV, including the minimum turning radius, maximum motion speed, etc., to ensure that the combined path after segmentation meets the motion capabilities of the AGV.

[0044] S105. Combine the end coordinate data and angle data to calculate the gradually changing curve parameters; Among them, the gradually changing curve parameters represent the key numerical values that define the shape and characteristics of the curve; the end coordinate data refers to the spatial position information of the target position; the angle data represents the desired orientation angle at the end point; the calculation process refers to the mathematical operations to determine the specific shape of the gradually changing curve.

[0045] Specifically, after completing the path segmentation, the system needs to accurately calculate the specific parameters of each gradual change curve. For the gradual change curve segment, its mathematical expression is , where k is the trajectory smoothness parameter and C is the curve characteristic parameter. The system first establishes a system of linear equations containing the starting motion direction (L1) and the ending motion direction (L2) according to the ending coordinates and angle requirements. Then it calculates the coordinates of the intersection point N of these two lines and solves the equation of their symmetry line L3. Based on the symmetry line L3, the system can determine the positions of the key control points, including the symmetry point Q and the starting and ending points of the gradual change curve. For different types of paths, the system adopts different parameter calculation strategies: for a right-angle bend, a single gradual change curve is used, and its parameters are mainly determined by the turning radius; for an S-shaped path, the parameters of two mirror-image gradual change curves need to be calculated to ensure smooth connection of the two curves; for an obtuse-angle bend, the parameter matching of two gradual change curve segments and the intermediate circular arc segment needs to be considered simultaneously. The system also needs to ensure that the calculated parameters meet the motion constraints of the AGV, including limitations such as the minimum turning radius and the maximum curvature change rate.

[0046] S106. Integrate the multi-segment route to obtain a preliminary trajectory information packet containing attribute information, where the attribute information at least includes route type information, the ending coordinates, the angle data, and the gradual change curve parameters; Among them, the multi-segment route represents a segmented trajectory composed of straight line segments, gradual change curve segments, and circular arc segments; integration means connecting and combining each segmented trajectory into a complete trajectory; attribute information represents various parameter data used to describe the trajectory characteristics; the preliminary trajectory information packet is a data set containing complete trajectory information; the route type information is used to identify the basic type of the trajectory; the ending coordinates are used to determine the target position of the trajectory; the angle data is used to determine the orientation of the AGV at the end point; the gradual change curve parameters are used to define the geometric characteristics of the gradual change curve segment.

[0047] Specifically, after completing the segmentation of the basic trajectory and the calculation of the gradual change curve parameters, the trajectory planning system needs to integrate these scattered trajectory information into a complete trajectory information packet. The system first arranges each segmented trajectory in the order of its position in the complete trajectory to ensure the continuity of the connection point coordinates and tangent directions between adjacent segments. For each segment of the trajectory, the system records its type (straight line segment, gradual change curve segment, or circular arc segment), starting coordinates, ending coordinates, length, and other basic information. In particular, for the gradual change curve segment, characteristic parameters such as its curvature change parameter and transition length also need to be recorded. The system packs these segmented information together with the global information (such as the overall trajectory type, ending position and orientation, total trajectory length, etc.) to form a preliminary trajectory information packet containing complete attribute information. This information packet not only contains the geometric characteristics of the trajectory but also all the data required to ensure the continuity of the trajectory.

[0048] During the process of integrating trajectory information, a core issue is how to ensure smooth connection between adjacent trajectory segments. To solve this problem, the system adopts a connection point processing method based on tangent continuity and curvature continuity. Specifically, at each connection point, the system calculates the tangent directions and curvature values of the front and rear trajectory segments, and makes these geometric features achieve continuous transition at the connection point by adjusting the parameters of the gradual change curve. If a discontinuity is found at a certain connection point, the system will automatically insert a transition curve of appropriate length and adjust the parameter data in the trajectory information packet accordingly to ensure the continuity of the entire trajectory.

[0049] S107. Check the passability of the preliminary trajectory information packet to determine the final trajectory information packet.

[0050] Among them, passability indicates whether the trajectory meets the AGV motion constraints and environmental constraints; checking means verifying various features of the trajectory; the final trajectory information packet refers to a complete trajectory data set that can be actually executed after verification.

[0051] Specifically, after generating the preliminary trajectory information packet, the trajectory planning system needs to conduct a comprehensive feasibility verification on the trajectory. The system first checks whether the geometric characteristics of the trajectory meet the kinematic constraints of the AGV, including the minimum turning radius, maximum curvature change rate, etc. Then it verifies whether there is a collision risk between the trajectory and static obstacles in the environment, which requires considering the actual size of the AGV and the safety margin. The system also needs to check the dynamic characteristics of the trajectory to ensure that the AGV can execute this trajectory smoothly at the expected speed. For trajectory segments that do not meet the constraint conditions, the system will give specific default situations, including default positions, default degrees and other information. Based on these inspection results, the system may need to make local adjustments or re-plan the trajectory until a completely feasible trajectory plan is obtained. The finally determined trajectory information packet will be used as the input data for the AGV execution module.

[0052] In some embodiments, the passability check of the trajectory can be achieved in multiple ways: Optionally, the system adopts a hierarchical inspection strategy. First, it quickly checks the geometric characteristics of the trajectory, including calculating the curvature values and curvature change rates of each point to verify whether they exceed the motion constraints of the AGV. Then it conducts collision detection, simplifies the AGV into a geometric shape, and judges the collision of the sampling points on the trajectory. Finally, it conducts dynamic verification, simulates the motion process of the AGV on this trajectory, and calculates whether the speeds and accelerations of each point meet the requirements. Optionally, the system adopts a sampling-based verification method, uniformly samples a series of control points on the trajectory, and comprehensively checks the states at each control point, including position reachability, attitude rationality and dynamic feasibility, and determines the overall feasibility of the trajectory through statistical analysis. It can be understood that other verification methods can also be adopted, which are not limited here.

[0053] In the embodiments of the present application, due to the adoption of the full-process technical system of two-dimensional coordinate system construction, trajectory classification library matching, gradient curve segmentation, parameter calculation, and passability verification, the basic trajectory type can be accurately matched according to the end point coordinates and angle data. By introducing a gradient curve segment, the curvature is continuously transitioned, and through a mathematical model and parameter adjustment, the trajectory is ensured to be smooth and controllable. Effectively solving the problems of driving jitter, slipping, and insufficient control accuracy caused by the sudden change of curvature at the connection of straight lines and arc segments in the existing AGV trajectory planning, and then realizing the continuous and smooth change of curvature of AGV in various curves (right-angle curves, acute-angle curves, obtuse-angle curves, S-curves, etc.), improving the driving stability, reducing mechanical wear, and meeting the high-precision motion control requirements in complex industrial scenarios.

[0054] The following describes the specific curve segmentation method for a 90-degree bend. Please refer to Figure 2 , which is a schematic diagram of the curve segmentation of a 90-degree bend in the AGV trajectory planning method with continuous curvature in the embodiments of the present application.

[0055] In Figure 2 , first, two key points are determined in the two-dimensional coordinate system: the starting point O is located at the origin of the coordinate, and the position of the end point P is given by the specific task requirements. As can be seen from the figure, L1 is a straight line extending along the moving direction of the starting point O, which appears as a horizontal line coinciding with the x-axis in the figure; L2 is a straight line extending along the moving direction of the end point P, which appears as a vertical line in the figure. The setting of these two straight lines lays the foundation for constructing a smooth trajectory. By extending L1 and L2, their intersection point N can be obtained. As can be clearly seen in the figure, point N is located on the x-axis. Next, the system calculates the symmetry line L3 of L1 and L2. The symmetry line L3 is a straight line passing through the intersection point N and having equal angles with L1 and L2. Geometrically, L3 bisects the angle between L1 and L2, and this symmetry line plays an important role in determining the key points of the trajectory subsequently. When an acute-angle bend, a right-angle bend, or an obtuse-angle bend needs to be planned, the system determines the symmetric point Q of the end point P with respect to the symmetry line L3. As can be seen from the figure, point Q is located on the x-axis and to the right of the starting point O. The determination of point Q provides an important geometric reference for constructing the gradient curve. By obtaining point Q through the symmetry of point P with respect to L3, the symmetry of the finally generated trajectory is ensured. In the gradient curve segment in the curve PQ, a special curve function is adopted: , in this function, k is a preset value for the trajectory smoothness, which is used to control the smoothness of the curve; C is a parameter of the gradual change curve, which determines the specific shape of the curve. As can be seen from the figure, the gradual change curve segments (blue and green parts) achieve a smooth transition from the straight line segment to the circular arc segment, ensuring a continuous change in curvature. If the curve PQ contains a circular arc segment, the standard circular arc equation: x² + (R - y)² = R² is used, where R = C. This ensures a smooth connection between the circular arc segment and the gradual change curve segment, because the parameter C of the gradual change curve directly determines the radius R of the circular arc. As can be observed from the figure, there may be a circular arc between the gradual change curve segments (the curve segment near point M in the figure), and this circular arc maintains a constant curvature.

[0056] Among them, the method for calculating the parameters of the gradual change curve in the above process is as follows: Taking the first quadrant as an example, the curve function of QM is , the angle of the curve at M , so the slope of the curve at M can be obtained . (The degree k of the curve > 2. By adjusting the value of k, the smoothness of the trajectory can be controlled. In actual engineering, k can be selected in the range of 2.5 - 4) Taking the derivative of the function gives: (Equation 1) Normalize the curve function. After normalization, the curve function is: (Equation 2) After the curve is normalized The slope of the point remains unchanged and is still , combining Equation 1 and Equation 2, it can be obtained that after normalization The formula for the x-axis coordinate of the point: (Equation 3) y’ is the tangent slope of the curve at this point, that is, tan (the angle of this point). After normalization, the angle of the curve at M remains unchanged, so it can be based on Obtain , combining Equation 3, the x-axis coordinate of the point after normalization can be obtained .

[0057] Through Equation 2 and Equation 3, the y-axis coordinate of the point M’ after normalization can be obtained: (Equation 4) According to the coordinates of the point after normalization , calculate the coordinates of the point after normalization , so as to calculate the length of the line segment after normalization . The parameters of the gradual change curve can be obtained: As can be clearly seen from the figure, the complete trajectory consists of three parts: a straight line segment (red) starting from the origin O, the first gradual curve (green), a possible circular arc segment, the second gradual curve (blue) until the end point P. This combination ensures the curvature continuity of the entire trajectory and avoids the sudden change problems in traditional trajectory planning. By introducing the gradual curve and a reasonable geometric construction method, the continuous change of curvature is achieved; through the symmetry design, the calculation process of the trajectory is simplified; by adjusting the parameter k, the smoothness of the trajectory can be flexibly controlled. The entire construction process not only ensures the mathematical rigor but also meets the requirements for trajectory smoothness in practical applications.

[0058] For the specific curve segmentation method of the S-degree bend, please refer to Figure 3 , which is the schematic diagram of the S-degree bend curve segmentation of the AGV trajectory planning method with continuous curvature in the embodiment of the present application.

[0059] If the basic trajectory path is a right-angle bend, then QP is determined as the gradual curve segment; if the basic trajectory path is an S-bend, then OT and TP are determined as two mirror-image gradual curve segments. Among them, the gradual curve segment represents the part of the trajectory with continuous curvature change; the basic trajectory path refers to the basic path type of the AGV movement; the right-angle bend refers to the trajectory with a steering angle of 90 degrees; the S-bend refers to a composite curve including two turns in opposite directions, and points Q and P represent the starting point and the end point of the gradual curve respectively; the mirror image means that the two curves have symmetry properties.

[0060] For the S-degree bend, assuming it is defined in the starting point coordinate system and the end point coordinate is P, first calculate the coordinates of the midpoint T of the OP line segment and the angle . Among them, the OP line segment represents the straight connection from the starting point to the end point; the midpoint T refers to the geometric center point of the OP line segment; The function refers to an improved version of the arctangent function, which is used to calculate the angle of point T relative to the starting point; represents the included angle between the tangent direction of point T and the positive x-axis direction. Specifically, after the trajectory planning system determines the starting point O and the end point P, it first needs to determine the position and direction of the key turning point T of the S-bend. The system first calculates the coordinates of the midpoint T through the coordinates of the starting point O(0, 0) and the end point P(xp, yp): = xp / 2, = yp / 2. Then use the atan2 function to calculate the relative angle θT of point T, which reflects the overall inclination of the OP line segment. The atan2 function has better quadrant judgment ability than the ordinary arctangent function and can accurately handle any position in the coordinate plane. This angle information plays a crucial role in subsequent judgment of the type and decomposition method of the S-curve. By calculating the precise position and direction of the midpoint T, it lays the foundation for subsequent trajectory segmentation and parameter calculation.

[0061] Figure 4 Two different types of S-shaped trajectories are shown: the left figure shows an S-curve with a larger turning angle, and the right figure shows an S-curve with a smaller turning angle. Both figures adopt a symmetric design centered on point T, and different parts of the trajectory are marked with different colors, reflecting the segmented characteristics of the trajectory.

[0062] Based on the calculated relative driving angle θT, the system adopts different processing strategies: When θT < 90° (as shown in the right figure), the trajectory is regarded as a combination of two mirror-image acute-angle bends When θT = 90° (as shown in the left figure), the trajectory is regarded as a combination of two mirror-image right-angle bends. This classification method ensures the rationality and feasibility of the trajectory planning. Different segments of the trajectory are marked with different colors in the figure: green segment: starting segment, achieving a smooth start from the horizontal direction; blue segment: first turning segment, achieving the initial turn; red and yellow segments: intermediate transition segments, achieving the direction conversion; light blue segment: ending segment, achieving a smooth transition to the target point. The two gradient curves have the same geometric characteristics but opposite directions. The symmetric design simplifies the calculation process, and only the parameters of half of the trajectory need to be calculated. Each turning part adopts a gradient curve to ensure the continuous change of curvature, avoid mutations, and achieve a smooth transition of speed and acceleration.

[0063] Please refer to FIG. 4 below for the schematic diagram of the obtuse-angle bend curve segmentation of the AGV trajectory planning method with continuous curvature in the embodiment of the present application.

[0064] In the trajectory planning of AGVs, obtuse-angle turns are a common and complex form of motion. As can be seen from the figure, the entire trajectory planning process is first established in a standard rectangular coordinate system, where the starting point O is located at the origin of the coordinates, the positive x-axis direction is the initial driving direction, and the end point P is located in the first quadrant with its precise coordinates and driving angle known. The entire trajectory consists of a red starting straight-line segment, green and blue gradually changing curve segments, and a yellow arc transition segment. This combined design ensures the smoothness and controllability of the AGV's motion. The planning process begins with the determination of the straight-line equation. Based on the coordinates of the end point P and the predetermined driving angle, the system calculates the equation of the straight line L2, which represents the expected motion direction of the AGV at the end point. Subsequently, by calculating the intersection point N of this straight line and the horizontal line L1 (i.e., the x-axis), a key reference position is determined. The determination of this intersection point N is crucial for the subsequent trajectory design, as it not only demarcates the range of turning but also provides a benchmark for the symmetry of the trajectory. On this basis, the system calculates the angle bisector L3 of L1 and L2. This line serves as the axis of symmetry for the entire trajectory and is of great guiding significance for the subsequent path generation.

[0065] The judgment of the trajectory type is the next key step. By comparing the lengths of ON and PN, the system can determine whether a straight-line segment is required at the starting point or the end point. When ON is greater than PN, it indicates that the starting point should be on the straight-line segment; when ON is less than PN, the end point should be on the straight-line segment; and when ON is equal to PN, no straight-line segment is required in the trajectory. This judgment directly affects the specific shape of the subsequent trajectory. Taking the case where the starting point is on the straight-line segment as an example, the system will calculate the symmetric point Q of the end point P with respect to the symmetry line L3 and determine OQ as the actual straight-line segment.

[0066] After determining the basic framework, the design of the gradually changing curve becomes crucial. The system decomposes the entire turning process into two gradually changing curves (QM1 and PM2) and an arc transition (M1M2). Each gradually changing curve undertakes an angular change of 45 degrees. This design not only ensures the smoothness of turning but also avoids excessive instantaneous curvature changes. The two gradually changing curves are symmetric with respect to L3. This symmetry not only simplifies the calculation process but also ensures the geometric beauty of the trajectory. The key parameter of the gradually changing curve is the curve angle at point M1 , which is fixed at 45 degrees. Based on this angle, the characteristic parameter C of the gradually changing curve QM1 can be calculated.

[0067] The middle arc transition segment M1M2 uses the standard arc equation x²+(R - y)² = R², where the radius R is equal to the gradually changing curve parameter C. This design ensures that the curvature at point M1 exactly matches that of the gradually changing curve segment, thus achieving a completely smooth transition. The arc segment undertakes the remaining angular change and provides stable motion characteristics through a turn with a constant curvature.

[0068] The trajectory planning system decomposes the complete trajectory into multiple basic line segments through the aforementioned steps. Each line segment needs to be encapsulated into a standardized information packet for subsequent trajectory execution and control. The design of this information packet adopts a unified data structure, ensuring the consistent processing and smooth connection of different types of line segments. Specifically, the information packet of each line segment contains four core elements: the line segment type identifier. The system defines four basic line segment types: straight line segment: representing a uniform motion segment with a constant direction; gradual curve segment: representing a transition segment with continuous curvature change; arc segment: representing a turning segment with a constant curvature; gradual curve symmetric segment: representing a curve segment that is mirror-symmetric to the reference gradual curve. This type classification ensures that the system can correctly identify and process trajectory segments with different characteristics. It also includes global starting point information, including recording the complete state of the line segment starting point in the environmental coordinate system: starting point coordinates (x0, y0): defining the starting position of the line segment; starting point angle θ0: representing the motion direction at the starting point. These global information are used to ensure the spatial continuity of the overall trajectory and provide an absolute position reference for trajectory execution. Through this standardized information packet design, the system can transform complex trajectory planning results into clear execution instructions, providing a reliable data basis for the actual motion control of the AGV.

[0069] The following describes the trajectory planning system in the embodiment of the present invention application from the perspective of hardware processing. Please refer to Figure 5 , which is a schematic structural diagram of an entity device of the trajectory planning system in the embodiment of the present application.

[0070] It should be noted that Figure 5 the structure of the trajectory planning system shown is only an example and should not impose any limitations on the functions and usage scope of the embodiments of the present invention.

[0071] As Figure 5 shown, the trajectory planning system includes a Central Processing Unit (CPU) 501, which can execute various appropriate actions and processes according to the program stored in the Read-Only Memory (ROM) 502 or the program loaded from the storage section 508 into the Random Access Memory (RAM) 506, such as executing the method described in the above embodiments. In the RAM 506, various programs and data required for system operation are also stored. The CPU 501, ROM 502, and RAM 506 are connected to each other through the bus 504. The Input / Output (I / O) interface 505 is also connected to the bus 504.

[0072] The following components are connected to the I / O interface 505: an input section 506 including an audio input device, a button switch, etc.; an output section 507 including a liquid crystal display (LCD), an audio output device, an indicator light, etc.; a storage section 508 including a hard disk, etc.; and a communication section 509 including a network interface card such as a LAN (Local Area Network) card, a modem, etc. The communication section 509 performs communication processing via a network such as the Internet. The drive 510 is also connected to the I / O interface 505 as needed. A removable medium 511, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 510 as needed so that a computer program read from it can be installed into the storage section 508 as needed.

[0073] Specifically, according to an embodiment of the present invention, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present invention includes a computer program product that includes a computer program carried on a computer-readable medium, and the computer program contains a computer program for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through the communication section 509, and / or installed from the removable medium 511. When the computer program is executed by the central processing unit (CPU) 501, various functions defined in the present invention are executed.

[0074] It should be noted that specific examples of the computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a flash memory, an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present invention, the computer-readable storage medium can be any tangible medium that contains or stores a program, and the program can be used by or in combination with an instruction execution system, device, or apparatus.

[0075] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of systems, methods, and computer program products according to various embodiments of the present invention. Among them, each block in the flowchart or block diagram may represent a module, a program segment, or a part of code, and the above-mentioned module, program segment, or part of code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order from that marked in the accompanying drawings.

[0076] Specifically, the trajectory planning system of this embodiment includes a processor and a memory. A computer program is stored on the memory. When the computer program is executed by the processor, it implements the curvature - continuous AGV trajectory planning method provided in the above - mentioned embodiment.

[0077] On the other hand, the present invention also provides a computer - readable storage medium. This storage medium may be included in the trajectory planning system described in the above - mentioned embodiment; or it may exist separately and not be assembled into the trajectory planning system. The above - mentioned storage medium carries one or more computer programs. When the above - mentioned one or more computer programs are executed by a processor of the trajectory planning system, the trajectory planning system is enabled to implement the curvature - continuous AGV trajectory planning method provided in the above - mentioned embodiment.

[0078] As mentioned above, the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the various embodiments of the present application.

[0079] As used in the above - mentioned embodiments, depending on the context, the term "when..." can be interpreted to mean "if...", or "after...", or "in response to determining...", or "in response to detecting...". Similarly, depending on the context, the phrase "when determining..." or "if detecting (the stated condition or event)" can be interpreted to mean "if determining...", or "in response to determining...", or "when detecting (the stated condition or event)", or "in response to detecting (the stated condition or event)".

[0080] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by relevant hardware instructed by a computer program. This program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the above method embodiments. The foregoing storage medium includes various media that can store program codes, such as ROM, random access memory (RAM), magnetic disks, or optical discs.

Claims

1. A method for AGV trajectory planning with continuous curvature, which is applied to a trajectory planning system, is characterized in that, The method includes: Construct a two-dimensional environmental coordinate system with the starting point as the origin; Obtain the coordinate data of the trajectory end point and the angle data, where the angle data takes the driving direction of the starting point as the positive X-axis direction; Combine the end point coordinate data and the angle data, and determine the basic trajectory path according to a preset trajectory classification library. The basic trajectory path includes a straight line, a right-angle bend, an acute-angle bend, an obtuse-angle bend, an S-bend, and a flat-angle bend; Perform curve segmentation on the basic trajectory path to obtain corresponding multiple segments of routes. The multiple segments of routes at least include straight-line segments, gradient curve segments, and arc segments; Combine the end point coordinate data and the angle data to calculate the gradient curve parameters; Integrate the multiple segments of routes to obtain a preliminary trajectory information packet containing attribute information. The attribute information at least includes route type information, the end point coordinates, the angle data, and the gradient curve parameters; Check the passability of the preliminary trajectory information packet to determine the final trajectory information packet.

2. The method according to claim 1, wherein In the step of combining the end point coordinate data and the angle data and determining the basic trajectory path according to a preset trajectory classification library, it specifically includes: If , meters and meters, then the basic trajectory path is a straight line; If , meters and meters, then the basic trajectory path is an S-curve; If , and meters, then the basic trajectory path is an acute bend; If , and meters, then the basic trajectory path is a right-angle bend; If , is the preset minimum allowable radius, and meters, then the basic trajectory path is an obtuse bend; If , is the preset minimum allowable radius, then the basic trajectory path is a flat-angle bend, where is the angle data, is the abscissa of the trajectory end point, is the ordinate of the trajectory end point.

3. The method according to claim 1, wherein It also includes: Set the trajectory end point as P and the starting point as O; Determine the straight-line equation L1 in the movement direction of the starting point O and the straight-line equation L2 in the movement direction of the end point P; Combine the straight-line equation L2 to determine the coordinates of the intersection point N, and calculate the symmetric line equation L3 of the straight-line equation L1 and the straight-line equation L2; If the basic trajectory path is an acute-angle bend, a right-angle bend, or an obtuse-angle bend, then determine the symmetric point Q of the end point P relative to the symmetric line equation L3; If there is a gradient curve segment in the curve PQ, then the curve function of the gradient curve segment is: , where is a preset value of the trajectory smoothness, is a parameter of the gradient curve; If there is an arc segment in the curve PQ, then the curve function of the arc segment is: , where .

4. The method according to claim 3, characterized in that, If the basic trajectory path is an acute-angle bend, a right-angle bend, or an obtuse-angle bend, after the step of determining the symmetric point Q of the end point P relative to the symmetric line equation L3, it further includes: If the basic trajectory path is an S-bend, then calculate the relative driving angle of the midpoint T of the OP line segment; Split the basic trajectory path into two mirror-image acute-angle bends or right-angle bends according to the relative driving angle.

5. The method according to claim 1, characterized in that In the step of performing curve segmentation on the basic trajectory path to obtain corresponding multiple segments of routes, it specifically includes: If the basic trajectory path is a right-angle bend, then determine QP as a gradient curve segment; If the basic trajectory path is an S-bend, then determine OT and TP as two mirror-image gradient curve segments; If the basic trajectory path is an obtuse-angle bend, then determine that QP contains two gradient curve segments with an angle change of 45° and an arc segment; 6. The method according to claim 5, wherein In the step of determining OT and TP as two mirror-image gradient curve segments if the basic trajectory path is an S-bend, it specifically includes: Calculate the coordinates of the midpoint T of the OP line segment and the relative driving angle ; If the relative traveling angle is less than 90°, the basic trajectory path can be regarded as composed of two mirror-image acute bends If the relative traveling angle = 90°, then the basic trajectory path can be regarded as composed of two mirror-image right-angle bends spliced together; Determine OT and TP as two mirror-image gradient curve segments.

7. The method according to claim 5, characterized in that In the step of determining that QP contains two gradient curve segments and an arc segment if the basic trajectory path is an acute-angle bend or an obtuse-angle bend, it specifically includes: Calculate the coordinates of the intersection point N of L1 and L2; If the line segment ON > PN, then determine that there is a straight-line segment at the starting point; If the line segment ON < PN, then determine that there is a straight-line segment at the end point; Determine the symmetric point Q of the end point P relative to the straight line L3; There exist points M1 and M2 on the curve QP that are symmetric with respect to the straight-line equation L3, and the relative traveling angle of point Z is 45°; Determine that QM1 and PM2 are gradually changing curve segments, and M1M2 is an arc segment.

8. A trajectory planning system, characterized in that, The trajectory planning system includes: one or more processors and a memory; the memory is coupled to the one or more processors, the memory is used to store computer program code, the computer program code includes computer instructions, and the one or more processors call the computer instructions to cause the trajectory planning system to execute the method according to any one of claims 1-7.

9. A computer-readable storage medium, comprising instructions, characterized in that, When the instructions run on the trajectory planning system, cause the trajectory planning system to execute the method according to any one of claims 1-7.

10. A computer program product, characterized in that, When the computer program product runs on the trajectory planning system, cause the trajectory planning system to execute the method according to any one of claims 1-7.

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