A curvature-continuous agv trajectory planning method and system

Abstract

The application 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, a two-dimensional coordinate system with the starting point as the origin is established, and the terminal position and angle information are obtained. Based on these data, the system determines the appropriate basic trajectory path type from the preset trajectory classification library, including straight lines, various types of curves, etc. Then, the basic trajectory is segmented and divided into a combination of straight line segments, gradual curve segments and circular arc segments. By calculating the gradual curve parameters and integrating each segment of the route, a trajectory information package containing complete attribute information is formed. Finally, the system verifies the passability of the trajectory to ensure that the finally generated trajectory meets the motion requirements of the AGV. The above method realizes the continuous and smooth change of the trajectory curvature by introducing a gradual curve as a transition segment.

Description

Technical Field

[0001] This application relates to the field of trajectory planning technology, and in particular to a method and system for AGV trajectory planning with continuous curvature. Background Technology

[0002] With the continuous improvement of industrial automation, AGVs (Automated Guided Vehicles) have been widely used in smart factories, automated warehousing, and other scenarios. In practical applications, AGVs need to be flexibly planned according to the working environment to achieve precise motion control from the starting point to the destination.

[0003] Currently, the most commonly used trajectory planning method in the industry is the circular arc transition method, which connects straight line segments with circular arcs. This method calculates the intersection point between two straight lines, constructs an arc of a specific radius with the intersection point as the center, and uses the arc as a transition curve to connect adjacent straight line segments, thereby forming the AGV's motion trajectory.

[0004] However, due to the abrupt change in curvature between a circular arc and a straight line, the AGV experiences a momentary change in acceleration when transitioning from a straight segment to a circular arc, leading to instability such as shaking and slippage during vehicle operation. This instability reduces the AGV's operational accuracy, increases wheel wear, and may cause damage to the carried goods. Summary of the Invention

[0005] This application provides a curvature-continuous AGV trajectory planning method and system to solve the problem of curvature abrupt change at the connection between straight and circular arc segments in existing AGVs.

[0006] Firstly, this application provides a curvature-continuous AGV trajectory planning method, applied to a trajectory planning system. The method includes: constructing a two-dimensional environmental coordinate system with the starting point as the origin; acquiring trajectory endpoint coordinate data and angle data, wherein the angle data has the travel direction from the starting point as the positive X-axis; combining the endpoint coordinate data and the angle data, determining a basic trajectory path according to a preset trajectory classification library, wherein the basic trajectory path includes straight lines, right-angle bends, acute-angle bends, obtuse-angle bends, S-curves, and flat-angle bends; segmenting the basic trajectory path into curve segments to obtain corresponding multi-segment routes, wherein the multi-segment routes include at least straight line segments, gradient curve segments, and arc segments; calculating gradient curve parameters by combining the endpoint coordinate data and the angle data; integrating the multi-segment routes to obtain a preliminary trajectory information package containing attribute information, wherein the attribute information includes at least route type information, endpoint coordinates, angle data, and gradient curve parameters; and checking the traversability of the preliminary trajectory information package to determine the final trajectory information package.

[0007] By adopting the above technical solution, a two-dimensional environmental coordinate system with the starting point as the origin is first constructed to obtain the coordinates and angle data of the endpoint, laying the foundation for subsequent trajectory planning. Combining this data, the system can accurately identify the most suitable basic trajectory path type from a pre-defined trajectory classification library. By segmenting the basic trajectory into curves and introducing gradual curve segments as a transition between straight and circular segments, the curvature can change smoothly and continuously. The introduction of this gradual curve, combined with reasonable parameter calculations, effectively eliminates the problem of abrupt curvature changes at the connection between circular and straight lines in traditional solutions, thereby avoiding the shaking and slippage caused by instantaneous acceleration changes during AGV operation and achieving stable AGV operation.

[0008] In conjunction with some embodiments of the first aspect, in some embodiments, the step of determining the basic trajectory path based on a preset trajectory classification library by combining the endpoint coordinate data and the angle data specifically includes: if d w =0°, d x >>0.01 meters and d y If the distance is greater than 0.01 meters, then the basic trajectory path is a straight line; if d w =0°, d x >>0.01 meters and d y If the distance is greater than 0.01 meters, then the basic trajectory path is an S-curve; if 0° < d w <90°, d x >0 and d y If d > 0.01 meters, then the basic trajectory path is an acute-angle bend; if d w =90°, d x >0 and d y If the distance is greater than 0.01 meters, then the basic trajectory path is a right-angle bend; if 90° < d w <180°, d y >Preset minimum allowable radius, and d y If d > 0.01 meters, then the basic trajectory path is an obtuse-angle bend; if d w =180°, d y >If a minimum allowable radius is preset, then the basic trajectory path is a straight-angle bend; where d w For this angle data, d x Let d be the x-coordinate of the endpoint of the trajectory. y y is the ordinate of the endpoint of the trajectory.

[0009] By adopting the above technical solution, a complete set of trajectory type determination criteria was established. Based on the specific numerical range of the endpoint coordinates and angle data, the system can accurately determine the appropriate basic path type for the trajectory. This parameter-based classification method makes the determination of different trajectory types, such as straight lines, S-curves, acute-angle curves, right-angle curves, obtuse-angle curves, and flat-angle curves, more accurate and reliable. By setting constraints such as the minimum allowable radius, it is ensured that the generated trajectory meets the kinematic characteristics of the AGV, providing a reliable prerequisite for achieving curvature-continuous trajectory planning, thereby guaranteeing the stability of AGV operation.

[0010] In some embodiments, in conjunction with the first aspect, the method further includes: setting the endpoint of the trajectory as P and the starting point as O; determining the equation of a straight line L1 in the direction of motion of the starting point O and the equation of a straight line L2 in the direction of motion of the endpoint P; determining the coordinates of the intersection point N based on the equation of a straight line L2, and calculating the equation of a symmetrical line L3 of the equations of a straight line L1 and L2; if the basic trajectory path is an acute-angle bend, a right-angle bend, or an obtuse-angle bend, then determining the point Q symmetrical to the endpoint P relative to the equation of a symmetrical line L3; if the curve PQ contains a gradual curve segment, then the curve function of the gradual curve segment is: x k +(Cy) k =C k Where k is the preset trajectory smoothness value, and C is the parameter of the gradient curve; if the curve PQ contains an arc segment, then the curve function of that arc segment is: x 2 +(Ry) 2 =R 2 , where R = C.

[0011] By adopting the above technical solution, straight line equations L1 and L2 and symmetry line equation L3 are introduced, constructing a complete mathematical model. Determining the coordinates of the intersection point N and the symmetry point Q provides accurate spatial references for constructing the gradient curve. In particular, by introducing gradient curve functions and circular arc segment functions, the curvature of the curve can change continuously and smoothly. The curve function of the gradient curve segment includes preset trajectory smoothness values, which can adjust the smoothness of the curve according to actual needs, effectively solving the problem of abrupt curvature changes in traditional solutions.

[0012] In conjunction with some embodiments of the first aspect, in some embodiments, if the basic trajectory path is an acute-angle bend, a right-angle bend, or an obtuse-angle bend, after determining the symmetrical point Q of the endpoint P relative to the equation L3 of the symmetrical line, the method further includes: if the basic trajectory path is an S-curve, calculating the relative driving angle of the midpoint T of the OP line segment; and splitting the basic trajectory path into two mirrored acute-angle bends or right-angle bends according to the relative driving angle.

[0013] By adopting the above technical solution, when handling S-curves, the complex S-curve trajectory is decomposed into two simpler curves that can be mirrored by calculating the relative driving angle of the midpoint T of the OP segment. This decomposition method allows the system to reuse existing processing logic for acute or right-angle curves, simplifying the calculation process while ensuring the continuity of the trajectory. This modular processing approach not only improves the system's computational efficiency but also ensures a smooth curvature transition throughout the entire S-curve trajectory.

[0014] In conjunction with some embodiments of the first aspect, in some embodiments, the step of segmenting the basic trajectory path into curve segments to obtain corresponding multi-segment routes specifically includes: if the basic trajectory path is a right-angle bend, then QP is determined to be a gradual curve segment; if the basic trajectory path is an S-bend, then OT and TP are determined to be two mirrored gradual curve segments; if the basic trajectory path is an obtuse-angle bend, then QP is determined to contain two gradual curve segments with an angle change of 45° and one arc segment.

[0015] By adopting the above technical solution, corresponding curve segmentation strategies were employed for different types of basic trajectory paths. Right-angle turns used a single gradual curve segment, S-curves used two mirrored gradual curve segments, and obtuse-angle turns used a combination of two gradual curve segments and a circular arc segment. This differentiated segmentation strategy ensures that each type of trajectory can achieve optimal curvature transition, especially when the turning angle is large, by introducing a circular arc segment to maintain stable steering curvature.

[0016] In conjunction with some embodiments of the first aspect, in some embodiments, if the basic trajectory path is an S-curve, the step of determining OT and TP as two mirrored gradient curve segments specifically includes: calculating the coordinates of the midpoint T of the OP segment and the relative driving angle θ. T If the relative driving angle θ T If the angle is less than 90°, the basic trajectory path can be considered as the combination of two mirrored acute-angle bends; if the relative driving angle θ T =90°, then the basic trajectory path can be regarded as the combination of two mirror right-angle bends; determine OT and TP as two mirror gradient curve segments.

[0017] By adopting the above technical solution, a relative driving angle θ is introduced. T This serves as the criterion for classifying S-curves, enabling accurate classification and handling of S-curves. When θ T When the angle is less than 90°, an acute angle bend is used. T When the angle is equal to 90°, a right-angle bend is treated. This angle-based classification method ensures that the system can generate the most suitable combination of gradient curve segments for different types of S-curves. By splicing two mirrored gradient curve segments, a smooth transition of the entire S-curve trajectory is achieved.

[0018] In conjunction with some embodiments of the first aspect, in some embodiments, if the basic trajectory path is an acute-angle bend or an obtuse-angle bend, the step of determining that QP contains two gradual curve segments and one circular arc segment specifically includes: calculating the coordinates of the intersection point N of L1 and L2; if line segment ON > PN, then determining that the starting point has a straight line segment; if line segment ON < PN, then determining that the ending point has a straight line segment; determining the symmetrical point Q of the ending point P relative to the straight line L3; in the curve QP, there exist points M1 and M2 that are symmetrical about the straight line equation L3, and the relative driving angle of point Z is 45°; determining that QM1 and PM2 are gradual curve segments, and M1M2 are circular arc segments.

[0019] By adopting the above technical solution, when handling acute and obtuse angle bends, the location of the straight segment is reasonably determined by comparing the length relationship between ON and PN. By introducing symmetrical point Q and key points M1 and M2, the system can accurately locate the start and end positions of the gradual curve segment and the circular arc segment. In particular, by ensuring that the relative travel angle of point Z is 45°, the transition between the gradual curve segment and the circular arc segment is smoother, thereby further optimizing the AGV's operational stability during turning.

[0020] In a second aspect, this 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, which includes computer instructions, and the one or more processors call the computer instructions to cause the trajectory planning system to perform the method described in the first aspect and any possible implementation thereof.

[0021] Thirdly, this application provides a computer-readable storage medium including instructions that, when executed on a trajectory planning system, cause the trajectory planning system to perform the method described in the first aspect and any possible implementation thereof.

[0022] Fourthly, this application provides a computer program product that, when run on a trajectory planning system, causes the trajectory planning system to perform the method described in the first aspect and any possible implementation thereof.

[0023] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0024] 1. By adopting the above technical solution, the key technical means of determining the basic trajectory path based on a preset trajectory classification library and introducing a gradual curve segment as a transition between the straight segment and the arc segment are adopted. Therefore, the problem of curvature change at the connection between the straight segment and the arc segment in the existing technology is effectively solved. This enables the AGV to avoid shaking and slipping caused by instantaneous acceleration changes during operation, ensuring the smoothness and stability of the AGV operation and improving the operating efficiency and safety of the AGV.

[0025] 2. By adopting the above technical solution, the technical problem of being unable to achieve a continuous and smooth transition of curvature in the prior art is effectively solved by using two key technical means: establishing a mathematical model that includes the equations of straight lines L1, L2 and the equation of symmetric lines L3, and introducing a gradual curve function with adjustable smoothness parameters. This achieves continuous and controllable changes in trajectory curvature, ensuring that the AGV can maintain stable operation on any type of trajectory, and greatly improving the motion performance and operational stability of the AGV.

[0026] 3. By adopting the above technical solution, the technical problem of inconsistent curvature transition between different types of trajectories in the existing technology is effectively solved by adopting two key technical means: developing differentiated curve segmentation strategies for different types of trajectories and introducing a combination of circular arc segments and double gradual curve segments at large-angle turns. This achieves the optimal curvature transition for various types of trajectories, enabling the AGV to maintain a stable operating state even during complex turning processes, and significantly improving the motion control accuracy of the AGV. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating a curvature-continuous AGV trajectory planning method in an embodiment of this application; Figure 2 This is a schematic diagram of the 90-degree curved line segmentation of the AGV trajectory planning method with continuous curvature in the embodiments of this application; Figure 3 This is a schematic diagram of the S-degree curvature line segmentation of the AGV trajectory planning method with continuous curvature in the embodiments of this application; Figure 4 This is a schematic diagram of obtuse-angle curved line segmentation in the curvature-continuous AGV trajectory planning method in the embodiments of this application; Figure 5 This is a schematic diagram of the physical device structure of a trajectory planning system in the embodiments of this application. Detailed Implementation

[0028] The terminology used in the following embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application. As used in the specification and appended claims of this application, the singular expressions “a,” “an,” “the,” “the,” “the,” and “this” are intended to include the plural expressions as well, unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in this application refers to and includes any or all possible combinations of one or more of the listed items.

[0029] Hereinafter, the terms "first" and "second" are used for descriptive purposes only and should not be construed as implying or suggesting relative importance or implicitly indicating the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature, and in the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more.

[0030] For ease of understanding, the method provided in this implementation is described in process below. Please refer to [link / reference]. Figure 1 This is a flowchart illustrating a curvature-continuous AGV trajectory planning method in an embodiment of this application.

[0031] S101. Construct a two-dimensional environmental coordinate system with the starting point as the origin;

[0032] The starting point represents the current position of the AGV; the origin is the reference point of the coordinate system, used to determine the position of the coordinate system; the two-dimensional environment coordinate system is a rectangular coordinate system established in a plane, used to describe the positional relationship of the AGV in the plane of motion.

[0033] Specifically, before the AGV begins trajectory planning, the trajectory planning system first needs to establish a unified reference coordinate system. The system sets the AGV's current position as the origin (0, 0), uses the AGV's current direction of travel as the positive X-axis, and the direction perpendicular to the direction of travel to the left as the positive Y-axis, thus establishing a right-handed coordinate system. This coordinate system can intuitively express the AGV's positional relationship relative to the target point, facilitating subsequent path planning calculations. In practical applications, the system considers the AGV's attitude information, including position coordinates and heading angle, and combines this with environmental map information to ensure that the established coordinate system matches the actual movement environment. Simultaneously, the system also needs to transform the coordinate information of all environmental elements such as obstacles and channel boundaries into this unified coordinate system.

[0034] In some embodiments, the coordinate system can be constructed in the following ways: Optionally, the system first acquires the real-time position and attitude information of the AGV, obtains surrounding environment information through the sensor system, and then uses a coordinate transformation matrix to transform the position information in the global coordinate system to a 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 is understood that during the coordinate system construction process, the kinematic constraints and dynamic characteristics of the AGV also need to be considered to ensure that the established coordinate system accurately reflects the actual movement capabilities of the AGV.

[0035] S102. Obtain the coordinate data and angle data of the trajectory endpoint, with the positive X-axis direction of the driving direction from the starting point.

[0036] Among them, the trajectory endpoint coordinate data represents the coordinate value of the target position that the AGV needs to reach in the established two-dimensional coordinate system; the angle data represents the expected orientation angle of the AGV at the endpoint; the driving direction refers to the direction of movement of the AGV at the starting point; the positive X-axis direction is used as a reference benchmark for angle calculation to unify the measurement standard of the angle.

[0037] Specifically, after establishing the coordinate system, the trajectory planning system needs to acquire the position and attitude information of the target point. The system first receives target point information from the task scheduling module, including the target point's position coordinates in the global coordinate system. Then, the system transforms these global coordinates into coordinate values ​​in a local coordinate system with the AGV's current position as the origin. For angle data, the system uses the AGV's current travel direction as the positive X-axis (0 degrees), employing a counter-clockwise direction as positive and a clockwise direction as negative angle measurement method to calculate the angle between the desired AGV orientation at the target point and the positive X-axis.

[0038] S103. Combining the endpoint coordinate data and the angle data, determine the basic trajectory path according to the preset trajectory classification library. The basic trajectory path includes straight lines, right-angle bends, acute-angle bends, obtuse-angle bends, S-bends, and flat-angle bends.

[0039] 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 motion path type of the AGV from the starting point to the end point; straight line, right angle bend and other path types refer to different basic trajectory shapes.

[0040] Specifically, after obtaining the end - point position and angle data, the system needs to determine the most suitable basic trajectory type based on these data. The system first analyzes the position relationship and angular difference between the end - point and 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 judge which basic trajectory path should be adopted. For example, when the end - point and the start - point are approximately on the same straight line and the angles are 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 - line 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.

[0041] More specifically, during the AGV trajectory planning process, the system needs to determine the most suitable basic trajectory type according to the end - point 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 of the end - point. 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 is mainly characterized by 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 movement mode.

[0042] If the end - point also maintains a parallel orientation to 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 judge 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 magnitude of the turning angle:

[0043] 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.

[0044] 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.

[0045] 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 kind of trajectory usually requires more movement space, but can ensure that the AGV smoothly completes large-angle turns.

[0046] 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 ensures the smoothness of the motion, but also improves the operation efficiency.

[0047] S104. Segment the path of the basic trajectory into corresponding multiple segments, and the multiple segments at least include straight segments, gradually changing curve segments, and arc segments;

[0048] 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 transitional path with gradually changing curvature; the arc segment represents the turning path with a constant curvature.

[0049] 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 smooth transition. 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 that the AGV maintains a stable motion state 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.

[0050] S105. Combine the end coordinate data and angle data to calculate the gradually changing curve parameters;

[0051] Among them, the gradually changing curve parameters represent the key 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 expected orientation angle at the end; the calculation process refers to the mathematical operations to determine the specific form of the gradually changing curve.

[0052] Specifically, after completing the path segmentation, the system needs to accurately calculate the specific parameters of each gradient curve segment. For a gradient curve segment, its mathematical expression is x. k +(Cy) k =C k Where k is the trajectory smoothness parameter and C is the curve characteristic parameter. The system first establishes a system of straight line equations including the starting direction of movement (L1) and the ending direction of movement (L2) based on the endpoint coordinates and angle requirements. Then, it calculates the coordinates of the intersection point N of these two lines and solves for their symmetry line equation L3. Based on the symmetry line L3, the system can determine the location of key control points, including the symmetry point Q and the start and end points of the gradient curve. For different types of paths, the system adopts different parameter calculation strategies: right-angle bends use a single gradient curve, whose parameters are mainly determined by the turning radius; S-shaped paths require calculating the parameters of two mirrored gradient curves to ensure a smooth connection between the two curves; obtuse-angle bends require considering the parameter matching of both gradient curves and the intermediate arc segment. The system also needs to ensure that the calculated parameters meet the AGV's motion constraints, including minimum turning radius and maximum rate of curvature change.

[0053] S106. Integrate the multiple route segments to obtain a preliminary trajectory information package containing attribute information. This attribute information includes at least route type information, endpoint coordinates, angle data, and gradient curve parameters. The multiple route segments represent segmented trajectories composed of straight line segments, gradient curve segments, and circular arc segments. Integration refers to connecting and combining the various segmented trajectories into a complete trajectory. The attribute information represents the parameter data used to describe the trajectory characteristics. The preliminary trajectory information package is a data set containing complete trajectory information. The route type information is used to identify the basic type of the trajectory. The endpoint 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 endpoint. The gradient curve parameters are used to define the geometric characteristics of the gradient curve segments.

[0054] Specifically, after completing the segmentation of the basic trajectory and the calculation of the gradient curve parameters, the trajectory planning system needs to integrate these scattered trajectory information into a complete trajectory information package. The system first arranges each segmented trajectory according to its position in the complete trajectory, ensuring the continuity of the connection point coordinates and tangent directions between adjacent segments. For each trajectory segment, the system records its type (straight line segment, gradient curve segment, or circular arc segment), starting point coordinates, ending point coordinates, length, and other basic information. In particular, for gradient curve segments, it also needs to record characteristic parameters such as curvature change parameters and transition length. The system packages this segmented information together with global information (such as overall trajectory type, ending point position and orientation, total trajectory length, etc.) to form a preliminary trajectory information package containing complete attribute information. This information package not only contains the geometric features of the trajectory but also all the data required to ensure trajectory continuity.

[0055] A key challenge in trajectory information integration is ensuring smooth connections between adjacent trajectory segments. To address this, the system employs a connection point processing method based on tangent continuity and curvature continuity. Specifically, at each connection point, the system calculates the tangent direction and curvature value of the preceding and following trajectory segments, adjusting the gradient curve parameters to achieve a continuous transition of these geometric features. If a discontinuity is detected at a connection point, the system automatically inserts a transition curve of appropriate length and adjusts the parameter data in the trajectory information packet accordingly to ensure the continuity of the entire trajectory.

[0056] S107. Check the accessibility of the preliminary trajectory information packet to determine the final trajectory information packet.

[0057] Among them, practicability indicates whether the trajectory meets the AGV motion constraints and environmental constraints; inspection refers to verifying the various features of the trajectory; and the final trajectory information package refers to the complete trajectory dataset that has been verified to be actually executable.

[0058] Specifically, after generating the initial trajectory information package, the trajectory planning system needs to perform a comprehensive feasibility verification of the trajectory. The system first checks whether the trajectory's geometric characteristics meet the AGV's kinematic constraints, including minimum turning radius and maximum rate of curvature change. Then, it verifies whether the trajectory poses a collision risk with static obstacles in the environment. This requires considering the AGV's actual size and safety margin. The system also needs to check the trajectory's dynamic characteristics to ensure the AGV can smoothly execute the trajectory at the expected speed. For trajectory segments that do not meet the constraints, the system provides specific violation information, including the location and severity of the violation. Based on these checks, the system may need to make local adjustments or replan the trajectory until a fully feasible trajectory solution is obtained. The final determined trajectory information package will serve as input data for the AGV execution module.

[0059] In some embodiments, trajectory drivability checks can be implemented in several ways: Optionally, the system employs a hierarchical verification strategy. First, it performs a rapid check on the trajectory's geometric characteristics, including calculating the curvature values ​​and rate of change of curvature at each point to verify whether the motion constraints of the AGV are exceeded. Then, collision detection is performed, simplifying the AGV to its geometric shape and determining collisions at sampled points on the trajectory. Finally, dynamic verification is performed, simulating the AGV's motion on the trajectory and calculating whether the velocity and acceleration at each point meet the requirements. Optionally, the system employs a sampling-based verification method, uniformly sampling a series of control points on the trajectory and comprehensively checking the state at each control point, including positional reachability, posture rationality, and dynamic feasibility. Statistical analysis is then used to determine the overall feasibility of the trajectory. It is understood that other verification methods can also be used, and no limitations are imposed here.

[0060] In this embodiment, a complete technical system is adopted, including two-dimensional coordinate system construction, trajectory classification library matching, gradual curve segmentation, parameter calculation, and feasibility verification. Therefore, it can accurately match the basic trajectory type based on the endpoint coordinates and angle data. By introducing gradual curve segments, continuous curvature transition is achieved, and the trajectory is smooth and controllable through mathematical models and parameter adjustments. This effectively solves the problems of driving vibration, slippage, and insufficient control precision caused by abrupt curvature changes at the connection between straight lines and arc segments in existing AGV trajectory planning. As a result, the AGV can achieve continuous and smooth curvature changes in various curves (right-angle curves, acute-angle curves, obtuse-angle curves, S-curves, etc.), improving driving stability, reducing mechanical wear, and meeting the high-precision motion control requirements in complex industrial scenarios.

[0061] The following explains the specific method for segmenting a 90-degree bend. Please refer to [link / reference]. Figure 2 This is a schematic diagram of the 90-degree curved line segmentation of the AGV trajectory planning method with continuous curvature in the embodiments of this application.

[0062] exist Figure 2 First, two key points are determined in the two-dimensional coordinate system: the starting point O is located at the origin, and the position of the ending point P is given by the specific task requirements. As shown in the diagram, L1 is a straight line extending along the direction of movement from the starting point O, represented as a horizontal line coinciding with the x-axis; L2 is a straight line extending along the direction of movement from the ending point P, represented as a vertical line. The establishment of these two lines lays the foundation for constructing a smooth trajectory. By extending L1 and L2, their intersection point N can be obtained. As clearly seen in the diagram, point N is located on the x-axis. Next, the system calculates the line of symmetry L3 between L1 and L2. The line of symmetry L3 is a straight line passing through the intersection point N and making an angle equal to that between L1 and L2. Geometrically, L3 bisects the angle between L1 and L2, and this line of symmetry plays an important role in determining the key points of the trajectory. When planning acute-angle, right-angle, or obtuse-angle curves, the system determines the point Q, the symmetric point of the ending point P with respect to the line of symmetry L3. As shown in the diagram, point Q is located on the x-axis, to the right of the starting point O. Determining point Q provides an important geometric reference for constructing the gradient curve. Point Q is obtained by symmetrically altering point P about L3, ensuring good symmetry in the final generated trajectory. The gradient curve segment in curve PQ uses a special curve function: x k +(Cy) k =C k In this function, k is a preset trajectory smoothness value used to control the smoothness of the curve; C is a parameter of the gradient curve, determining the specific shape of the curve. As can be seen from the figure, the gradient curve segments (curves QM and MP) achieve a smooth transition from straight lines to circular arcs, ensuring continuous change in curvature. If curve PQ contains circular arcs, the standard circular arc equation is used: x2 +(Ry) 2 =R 2 Where R = C. This ensures a smooth connection between the arc segment and the gradient curve segment, because the parameter C of the gradient curve directly determines the radius R of the arc. As can be observed from the figure, there may be an arc between the gradient curve segments (the curve segment near point M in the figure), and this arc maintains a constant curvature.

[0063] The method for calculating the parameters of the gradient curve in the above process is as follows:

[0064] Taking the first quadrant as an example, the curve function of QM is x k +(Cy) k =C k The angle θ of the curve at point M M =0.5*θ P′ Therefore, the slope K of the curve at point M can be calculated. m (The degree of the curve k>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 to 4.)

[0065] Taking the derivative of the function, we get:

[0066]

[0067] The curve function is normalized, and the normalized curve function is as follows:

[0068]

[0069] After curve normalization, the slope at point M′ remains unchanged at K. m Combining Equations 1 and 2, we can derive the formula for the normalized x-axis coordinate of point M′:

[0070]

[0071] y' is the slope of the tangent line to the curve at that point, which is tan(the angle at that point). After normalization, the angle of the curve at point M remains unchanged, so it can be calculated using tan(θ). M′ Find y′ M′ By combining Equation 3, the x-axis coordinates of point M′ after normalization can be obtained.

[0072] Using equations 2 and 3, the normalized y-axis coordinates of point M' can be obtained:

[0073]

[0074] Based on the normalized coordinates of point M′, the coordinates of point P′ are calculated, and thus the length of the normalized line segment Q′P′ is determined. The parameters of the gradient curve can then be derived.

[0075]

[0076] As clearly seen in the diagram, the complete trajectory consists of three parts: a straight line segment (curve OQ) starting at point O, a first gradually changing curve (curve QM), a possible circular arc segment, and a second gradually changing curve (curve MP) leading to the endpoint P. This combination ensures the continuity of curvature throughout the trajectory, avoiding the abrupt changes common in traditional trajectory planning. By introducing gradually changing curves and a reasonable geometric construction method, continuous curvature variation is achieved; the symmetrical design simplifies the trajectory calculation process; and the smoothness of the trajectory can be flexibly controlled by adjusting the parameter k. The entire construction process ensures both mathematical rigor and meets the requirements for trajectory smoothness in practical applications.

[0077] For the specific curve segmentation method of the S-curve below, please refer to [link / reference]. Figure 3 This is a schematic diagram of the S-degree curvature line segmentation of the AGV trajectory planning method with continuous curvature in the embodiments of this application.

[0078] If the basic trajectory path is a right-angle bend, then QP is determined to be a gradual curve segment; if the basic trajectory path is an S-bend, then OT and TP are determined to be two mirrored gradual curve segments. Here, a gradual curve segment represents a trajectory portion with continuously changing curvature; the basic trajectory path refers to the basic path type of AGV movement; a right-angle bend refers to a trajectory with a turning angle of 90 degrees; an S-bend refers to a composite curve containing two turns in opposite directions, with points Q and P representing the start and end points of the gradual curve, respectively; mirroring indicates that the two curve segments have symmetrical properties.

[0079] For an S-degree curve, assuming the coordinates of the starting point and the ending point are P in the coordinate system, first calculate the coordinates of the midpoint T of the OP line segment (X...). T ,Y T ) and angle θ T =atan2(Y T ,X T Here, OP represents a straight line connecting the start and end points; the midpoint T is the geometric center of OP; the atan2 function is an improved version of the arctangent function, used to calculate the angle of point T relative to the start point; θ T This represents the angle between the tangent direction at point T and the positive x-axis. Specifically, after determining the starting point O and the ending point P, the trajectory planning system first needs to determine the position and direction of the key turning point T of the S-curve. The system first calculates the coordinates of the midpoint T using the coordinates of the starting point O (0, 0) and the ending point P (xp, yp): X T = xp / 2, Y T=yp / 2. Then, the atan2 function is used to calculate the relative angle θT of point T. This angle reflects the overall inclination of the OP line segment. Compared with the ordinary arctangent function, the atan2 function has better quadrant determination ability and can accurately handle any position in the coordinate plane. This angle information plays a key role in subsequent determination of the type and decomposition method of the S-curve. By calculating the precise position and direction of the midpoint T, the foundation is laid for subsequent trajectory segmentation and parameter calculation.

[0080] Figure 3 The image illustrates two different types of S-curves: the left image shows an S-curve with a large turning angle, and the right image shows an S-curve with a smaller turning angle. Both images employ a symmetrical design centered on point T, using different letters to label the various parts of the trajectory, reflecting the segmented nature of the trajectory.

[0081] Based on the calculated relative driving angle θT, the system employs different processing strategies:

[0082] When θT < 90° (as shown in the right figure), the trajectory is considered as a combination of two mirrored acute-angle bends;

[0083] When θT = 90° (as shown in the left figure), the classification method of considering the trajectory as a combination of two mirrored right-angle bends ensures the rationality and feasibility of trajectory planning. Different segments of the trajectory are labeled with different letters in the figure: Curve OM segment: the starting segment, achieving a smooth start from the horizontal direction; Curve MQ segment: the first turning segment, achieving the initial turn; Qa segment and Curve ab segment: intermediate transition segments, achieving the change of direction; Curve bP segment: the ending segment, achieving a smooth transition to the target point. The two gradient curves have the same geometric characteristics but opposite directions. The symmetrical design simplifies the calculation process, requiring only the calculation of half of the trajectory parameters. Each turning section uses a gradient curve to ensure continuous change in curvature, avoid abrupt changes, and achieve a smooth transition in velocity and acceleration.

[0084] Please refer to Figure 4 below, which is a schematic diagram of obtuse-angle curved line segmentation for the curvature-continuous AGV trajectory planning method in the embodiments of this application.

[0085] In AGV trajectory planning, obtuse-angle bends are a common and complex motion form. As shown in the diagram, the entire trajectory planning process is first established in a standard Cartesian coordinate system, where the starting point O is located at the origin, the initial travel direction is along the positive x-axis, and the ending point P is located in the first quadrant with known precise coordinates and travel angle. The entire trajectory consists of the initial straight segment OQ, the gradual curve segment QM1 and curve M2P, and the circular transition segment M1M2. This combination design ensures the smoothness and controllability of the AGV's motion. The planning process begins with determining the equation of the straight line. Based on the coordinates of the ending point P and the predetermined travel angle, the system calculates the equation of straight line L2, which represents the desired travel direction of the AGV at the ending point. Subsequently, by calculating the intersection point N of this straight line and the horizontal line L1 (i.e., the x-axis), a crucial reference position is determined. The determination of this intersection point N is critical for subsequent trajectory design because it both defines the turning range and provides a benchmark for the symmetry of the trajectory. Based on this, the system calculates the angle bisector L3 of L1 and L2. This line serves as the axis of symmetry for the entire trajectory and has important guiding significance for subsequent path generation.

[0086] Determining the trajectory type is the next crucial step. By comparing the lengths of ON and PN, the system can determine whether a straight segment is needed for the start or end point. When ON is greater than PN, the start point should be on a straight segment; when ON is less than PN, the end point should be on a straight segment; and when ON equals PN, a straight segment is not needed in the trajectory. This determination directly affects the specific shape of the subsequent trajectory. Taking the case where the start point is on a straight segment as an example, the system calculates the point Q symmetrical to the end point P about the line of symmetry L3 and determines OQ as the actual straight segment.

[0087] After establishing the basic framework, the design of the gradient curves becomes crucial. The system decomposes the entire steering process into two gradient curves (QM1 and PM2) and a circular transition (M1M2). Each gradient curve handles a 45-degree angle change, a design that ensures steering smoothness while avoiding excessive instantaneous curvature changes. The two gradient curves are symmetrical about L3; this symmetry simplifies the calculation process and ensures the geometric aesthetics of the trajectory. The key parameter of the gradient curves is the curve angle at point M1. With the angle fixed at 45 degrees, the characteristic parameter C of the gradient curve QM1 can be calculated based on this angle.

[0088] The intermediate circular transition segment M1M2 adopts the standard circular arc equation x 2 +(Ry) 2 =R 2The radius R is equal to the gradient curve parameter C. This design ensures that the curvature at point M1 perfectly matches the gradient curve segment, thus achieving a completely smooth transition. The circular arc segment bears the remaining angular change, providing stable motion characteristics through constant curvature steering.

[0089] 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 package to facilitate subsequent trajectory execution and control. This information package design employs a unified data structure to ensure consistent processing and smooth connection of different types of line segments. Specifically, each line segment's information package contains four core elements: a line segment type identifier (the system defines four basic line segment types: straight line segment (representing uniform motion in a constant direction); a gradient curve segment (representing a transition segment with continuously changing curvature); a circular arc segment (representing a turning segment with constant curvature); and a gradient curve symmetrical segment (representing a curve segment mirror-symmetrical to a reference gradient curve). This type classification ensures 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's starting point in the environmental coordinate system: starting point coordinates (x0, y0): defining the starting position of the line segment; and starting point angle θ0: representing the direction of motion at the starting point. This global information ensures the spatial continuity of the overall trajectory and provides an absolute position reference for trajectory execution. Through this standardized information package design, the system can transform complex trajectory planning results into clear execution instructions, providing a reliable data foundation for the actual motion control of AGVs.

[0090] The trajectory planning system in the embodiments of this invention is described below from the perspective of hardware processing. Please refer to [link / reference]. Figure 5 This is a schematic diagram of the physical device structure of a trajectory planning system in an embodiment of this application.

[0091] It should be noted that, Figure 5 The structure of the trajectory planning system shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of the present invention.

[0092] like Figure 5As shown, the trajectory planning system includes a Central Processing Unit (CPU) 501, which can perform various appropriate actions and processes based on a program stored in Read-Only Memory (ROM) 502 or a program loaded from storage section 508 into Random Access Memory (RAM) 506, such as performing the methods described in the above embodiments. The RAM 506 also stores various programs and data required for system operation. The CPU 501, ROM 502, and RAM 506 are interconnected via a bus 504. An Input / Output (I / O) interface 505 is also connected to the bus 504.

[0093] The following components are connected to I / O interface 505: input section 506 including audio input devices, push-button switches, etc.; output section 507 including a liquid crystal display (LCD) and audio output devices, indicator lights, etc.; storage section 508 including a hard disk, etc.; and communication section 509 including a network interface card such as a LAN (Local Area Network) card, modem, etc. Communication section 509 performs communication processing via a network such as the Internet. Drive 510 is also connected to I / O interface 505 as needed. Removable media 511, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., are installed on drive 510 as needed so that computer programs read from them can be installed into storage section 508 as needed.

[0094] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing computer programs for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 509, and / or installed from removable medium 511. When the computer program is executed by central processing unit (CPU) 501, it performs the various functions defined in the present invention.

[0095] It should be noted that specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, optical fiber, portable compact disc read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0096] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. Each block in a flowchart or block diagram may represent a module, program segment, or portion of code, which contains one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those shown in the drawings.

[0097] Specifically, the trajectory planning system of this embodiment includes a processor and a memory. The memory stores a computer program. When the computer program is executed by the processor, it implements the curvature continuous AGV trajectory planning method provided in the above embodiment.

[0098] In another aspect, the present invention also provides a computer-readable storage medium, which may be included in the trajectory planning system described in the above embodiments; or it may exist independently and not assembled into the trajectory planning system. The storage medium carries one or more computer programs that, when executed by a processor of the trajectory planning system, cause the trajectory planning system to implement the curvature-continuous AGV trajectory planning method provided in the above embodiments.

[0099] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

[0100] As used in the above embodiments, depending on the context, the term "when..." can be interpreted as meaning "if...", "after...", "in response to determining...", or "in response to detecting...". Similarly, depending on the context, the phrase "when determining..." or "if (the stated condition or event) is interpreted as meaning "if determining...", "in response to determining...", "when (the stated condition or event) is detected", or "in response to detecting (the stated condition or event)".

[0101] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. This program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as ROM or random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A curvature-continuous AGV trajectory planning method, applied to a trajectory planning system, characterized in that, The method includes: Construct a two-dimensional environment coordinate system with the starting point as the origin; Acquire the coordinate data of the trajectory endpoint and the angle data, wherein the angle data is taken with the driving direction of the starting point as the positive X-axis direction; Combining the endpoint coordinate data and the angle data, a basic trajectory path is determined according to a preset trajectory classification library. The basic trajectory path includes straight lines, right-angle bends, acute-angle bends, obtuse-angle bends, S-curves, and flat-angle bends. The basic trajectory path is segmented into curves to obtain corresponding multi-segment routes, which include at least straight line segments, gradual curve segments, and circular arc segments. Based on the endpoint coordinate data and angle data, calculate the gradient curve parameters; The multiple route segments are integrated to obtain a preliminary trajectory information package containing attribute information, which includes at least route type information, endpoint coordinates, angle data, and gradient curve parameters. The accessibility of the preliminary trajectory information packet is checked to determine the final trajectory information packet; Also includes: Let the endpoint of the trajectory be P, and the starting point be O; Determine the equation of the straight line L1 in the direction of motion of the starting point O and the equation of the straight line L2 in the direction of motion of the ending point P; Determine the coordinates of the intersection point N using the equation of the line L2, and calculate the equation of the line symmetry L3 between the equations of the lines L1 and L2. If the basic trajectory path is an acute-angle bend, a right-angle bend, or an obtuse-angle bend, then determine the point Q that is symmetrical to the endpoint P relative to the equation of the symmetry line L3; If curve PQ contains a gradually changing curve segment, then the curve function of that gradually changing curve segment is: x k +(Cy) k =C k , where k is the preset trajectory smoothness value, and C is the parameter of the gradient curve; If curve PQ contains circular arc segments, then the curve function of those circular arc segments is: x 2 +(Ry) 2 =R 2 , where R = C.

2. The method according to claim 1, characterized in that, The step of determining the basic trajectory path by combining the endpoint coordinate data and the angle data according to a preset trajectory classification library specifically includes: If d w =0°, d x >>0.01 meters and d y If the distance is ≤0.01 meters, then the basic trajectory path is a straight line; If d w =0°, d x >>0.01 meters and d y If the distance is greater than 0.01 meters, then the basic trajectory path is an S-curve; If 0° < d w <90°, d x >0 and d y If the distance is greater than 0.01 meters, then the basic trajectory path is an acute-angle bend; If d w =90°, d x >0 and d y If the distance is greater than 0.01 meters, then the basic trajectory path is a right-angle bend; If 90° < d w <180°, d y >Preset minimum allowable radius, and d y If the distance is greater than 0.01 meters, then the basic trajectory path is an obtuse-angle bend; If d w =180°, d y >If a minimum allowable radius is preset, then the basic trajectory path is a straight-angle bend, where d w For the angle data, d x Let d be the x-coordinate of the endpoint of the trajectory. y y is the ordinate of the endpoint of the trajectory.

3. The method according to claim 1, characterized in that, If the basic trajectory path is an acute-angle bend, a right-angle bend, or an obtuse-angle bend, then after determining the point Q symmetrical to the endpoint P relative to the equation L3, the method further includes: If the basic trajectory path is an S-curve, then calculate the relative driving angle of the midpoint T of the OP line segment; The basic trajectory path is divided into two mirrored acute-angle bends or right-angle bends based on the relative driving angle.

4. The method according to claim 1, characterized in that, The step of segmenting the basic trajectory path into curve segments to obtain corresponding multi-segment routes specifically includes: If the basic trajectory path is a right-angle bend, then QP is determined to be a gradual curve segment; If the basic trajectory path is an S-curve, then OT and TP are determined to be two mirrored gradient curve segments. If the basic trajectory path is an obtuse-angle bend, then QP is determined to contain two gradual curve segments with an angle change of 45° and one circular arc segment.

5. The method according to claim 4, characterized in that, If the basic trajectory path is an S-curve, then the steps to determine OT and TP as two mirrored gradient curve segments specifically include: Calculate the coordinates of the midpoint T of line segment OP and the relative driving angle θ. T ; If the relative driving angle θ T If the angle is less than 90°, the basic trajectory path can be considered as a combination of two mirrored acute-angle bends. If the relative driving angle θ T =90°, then the basic trajectory path can be regarded as the combination of two mirror right-angle bends; OT and TP are determined to be two mirrored gradient curve segments.

6. The method according to claim 4, characterized in that, If the basic trajectory path is an acute-angle bend or an obtuse-angle bend, the steps to determine that QP contains two gradual curve segments and one circular arc segment specifically include: Calculate the coordinates of the intersection point N of L1 and L2; If line segment ON > PN, then the starting point must contain a straight line segment. If line segment ON < PN, then the endpoint is determined to have a straight line segment. Determine the point Q that is symmetrical to the endpoint P relative to line L3; In curve QP, there exist points M1 and M2 that are symmetrical about the equation of line L3, and the relative travel angle of point Z is 45°. QM1 and PM2 are defined as gradient curve segments, and M1M2 is defined as circular arc segments.

7. 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 including computer instructions, and the one or more processors call the computer instructions to cause the trajectory planning system to perform the method as described in any one of claims 1-6.

8. A computer-readable storage medium comprising instructions, characterized in that, When the instructions are run on the trajectory planning system, the trajectory planning system performs the method as described in any one of claims 1-6.

9. A computer program product, characterized in that, When the computer program product is run on the trajectory planning system, the trajectory planning system performs the method as described in any one of claims 1-6.

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