A path planning method and system for frequent reversing working conditions of a forklift, an electronic device, and a storage medium

Abstract

The application discloses a forklift frequent reversing working condition-oriented path planning method and system, electronic equipment and a storage medium, and the method comprises the following steps: acquiring an initial path point set and heading information; performing preliminary smoothing processing on the initial path; identifying all reversing points, and performing geometric constraint adjustment on the path at the reversing points based on the minimum turning radius of the forklift; dividing the one-way driving sub-sections by taking the adjusted reversing points as boundaries, generating local trajectories by adopting B-spline curve fitting based on a sliding window, and achieving the continuity of position, tangent direction and curvature of adjacent local trajectories at the reversing points by sharing control points to obtain an overall spliced trajectory; finally, in combination with the maximum steering angular velocity and the maximum linear velocity constraint, the overall trajectory is nonlinearly optimized with the maximum running speed as the target to generate a feasible trajectory meeting the kinematic constraint. The application can realize efficient, continuous and safe automatic operation of the forklift under the frequent reversing working condition.

Description

Technical Field

[0001] This application relates to the field of intelligent forklift control technology, and in particular to a path planning method, system, electronic device and storage medium for forklifts in frequent reversing conditions. Background Technology

[0002] In modern warehousing and logistics systems, automated guided vehicles (AGVs) are widely used for handling and stacking goods. During operation (such as moving in and out of racks, turning in narrow aisles), forklifts often need to frequently switch directions of travel (i.e., alternating between forward and reverse), and this kind of action is called "reversing".

[0003] Existing forklift path planning technologies have the following shortcomings:

[0004] 1. Sharp angles in the path lead to unnecessary stops and repeated adjustments: Traditional path planning algorithms (such as Dijkstra's or A* algorithms) typically generate polylines composed of multiple straight line segments. Although the path is spatially continuous (i.e., connected), abrupt changes in heading angle occur at nodes (especially reversal points), causing discontinuities in the first derivative (tangent direction) of the path, forming sharp angles. As a nonholonomic constraint system, the forklift's direction of movement must be consistent with its vehicle orientation. It cannot smoothly pass through such abrupt directional changes at a non-zero speed and must stop and adjust. Therefore, after reaching a reversal point, the forklift not only needs to perform the necessary direction change and stop but also must stop additionally and make multiple fine adjustments to align with the direction of the next path segment. This process significantly increases operation time and reduces overall efficiency.

[0005] 2. Global smoothing methods fail at reversing points: When the path includes a reversing operation from forward to reverse (or from reverse to forward), if a single global curve fitting method (such as global B-spline) is used, it will fail to adapt to the reversal of the driving direction because the method assumes that the path evolves smoothly in a single direction. This often leads to geometric distortions such as trajectory self-intersection, local loops, or severe bending in the reversing area, making it difficult to control the forklift or even causing it to go out of control.

[0006] 3. Ignoring the actual movement limitations of the forklift: Many existing smoothing algorithms only focus on the geometric smoothness of the trajectory, without considering the physical limitations of the forklift itself, such as the minimum turning radius and maximum steering angular velocity. Although the generated trajectory may appear smooth, it exceeds the actual execution capability of the forklift, making the trajectory infeasible in actual operation and unable to be reliably tracked. This may also force the forklift to decelerate or stop to correct its movement.

[0007] Therefore, there is an urgent need for a path planning method for forklifts that frequently change direction during operation. This method should be able to generate feasible trajectories at the reversal points with smooth transitions in heading angle and no abrupt changes in curvature, while strictly satisfying kinematic constraints such as the forklift's minimum turning radius and maximum steering angular velocity. This would eliminate unnecessary stops and repeated adjustments caused by discontinuous path geometry, allowing the forklift to continue operating efficiently and smoothly with only one necessary direction change operation. Summary of the Invention

[0008] To overcome the problems of sharp path corners, trajectory distortion at reversal points, and neglect of kinematic constraints in existing technologies, this application proposes a path planning method, system, electronic device, and storage medium for frequent reversal conditions of forklifts. The aim is to generate a highly efficient and feasible trajectory that can smoothly transition reversals and meet the physical limits of forklifts by segmented identification of reversal points, adjustment of geometric constraints, segmented B-spline splicing, and joint optimization.

[0009] The first objective of this application is to provide a path planning method for forklifts operating under frequent reversing conditions.

[0010] The aforementioned objective of this application is achieved through the following technical solution:

[0011] A path planning method for forklifts operating in frequent reversing conditions, the method comprising the following steps:

[0012] S1, Obtain the initial path point set for forklift operation, wherein each path point in the initial path point set contains position coordinates and the corresponding expected heading angle;

[0013] S2, perform preliminary smoothing processing on the initial path point set to obtain a smoothed path point set;

[0014] S3, based on the smooth path point set, traverse and identify all reversal points, and adjust the path at each reversal point geometrically according to the minimum turning radius of the forklift;

[0015] S4. Using each reversal point as a boundary, the path after geometric constraint adjustment is divided into multiple continuous one-way driving segments. For each one-way driving segment, a B-spline curve fitting method based on a sliding window is used to generate a local trajectory. At each reversal point, by sharing control points, the positions, tangent directions, and curvatures of adjacent local trajectories at that point are continuous, achieving smooth splicing and obtaining the overall spliced ​​trajectory.

[0016] S5. Based on the forklift's maximum steering angular velocity and maximum linear velocity constraints, speed planning and nonlinear optimization are performed on the overall splicing trajectory to generate a feasible trajectory that satisfies the kinematic constraints.

[0017] Preferably, in step S2, the preliminary smoothing process of the initial path point set to obtain a smoothed path point set specifically includes:

[0018] The initial path point set is denoised using a least-squares smoothing method, which suppresses path jitter caused by sensor noise or path planning algorithms while preserving the original path geometry.

[0019] The least squares smoothing method obtains the smoothed path point set by constructing an optimization model that balances path fidelity and smoothness, and solving the linear equations corresponding to the optimization model.

[0020] Preferably, in step S3, the step of identifying all reversal points based on the smooth path point set specifically includes:

[0021] Traverse the set of smooth path points, and for each path point, calculate the displacement vector from the current path point to the next path point, and obtain the heading vector of that path point;

[0022] Calculate the dot product of the displacement vector and the heading vector to obtain the dot product corresponding to the current path point;

[0023] When it is detected that the dot product corresponding to the current path point has the opposite sign to the dot product corresponding to the previous path point, the current path point is determined to be a reversal point.

[0024] Preferably, in step S3, adjusting the path at each reversing point based on the forklift's minimum turning radius specifically includes:

[0025] Based on each reversal point, the forward path tangent and the backward path tangent at the current reversal point are determined based on the continuous path point sequence before and after the current reversal point, respectively.

[0026] Based on the minimum turning radius of the forklift, the forklift is offset outward along the forward path tangent and the backward path tangent, respectively, so that the radius of the inscribed circle between the two offset tangents is not less than the minimum turning radius.

[0027] Calculate the intersection of the two offset tangents and use this intersection as the adjusted reversal point;

[0028] Specifically, for reversing points adjacent to the target location of the forklift operation, their geometric adjustment range is limited to preserve the path space required for the forklift to adjust the picking angle before operation.

[0029] Preferably, in step S4, generating a local trajectory for each unidirectional travel segment using a B-spline curve fitting method based on a sliding window specifically includes:

[0030] The path points of each one-way travel segment are divided into multiple local windows using a sliding window method, and each window contains several consecutive path points.

[0031] For each path point within a local window, a parameterized representation of the B-spline curve is constructed using uniform B-spline basis functions;

[0032] An optimization objective is constructed based on the parametric representation of the B-spline curve, and the control polygon vertices of the B-spline curve are determined by solving the optimization objective.

[0033] The optimization objective comprehensively considers the geometric proximity between the B-spline curve and the original path points within the corresponding window, as well as the smoothness of the curve curvature.

[0034] Preferably, in step S4, the step of ensuring the continuity of the position, tangent direction, and curvature of adjacent local trajectories at each reversal point by sharing a control point specifically includes:

[0035] The last control point of the B-spline curve corresponding to the last local window covering the reversal point in the previous one-way travel segment is set to the same set of control points as the starting control point of the B-spline curve corresponding to the first local window covering the reversal point in the next one-way travel segment. This forces the two adjacent one-way travel segments to achieve continuity in position, tangent direction, and curvature at the reversal point.

[0036] Preferably, in step S5, the speed planning and nonlinear optimization of the overall splicing trajectory based on the forklift's maximum steering angular velocity and maximum linear velocity constraints specifically includes:

[0037] Calculate the curvature of each point on the overall splicing trajectory;

[0038] Based on the curvature and the forklift’s maximum steering angular velocity, kinematic feasibility constraints are constructed.

[0039] With the goal of maximizing the forklift's running speed along the trajectory, the B-spline control points of the overall spliced ​​trajectory are used as optimization variables. A nonlinear optimization algorithm is employed to adjust the trajectory shape and generate the speed-optimal trajectory that satisfies the kinematic feasibility constraints.

[0040] The second objective of this application is to provide a path planning system for forklifts operating under frequent reversing conditions.

[0041] The second objective of this application is achieved through the following technical solution:

[0042] A path planning system for forklifts operating in frequent direction-changing conditions, the system comprising:

[0043] The initial path acquisition module is used to acquire the initial path point set for forklift operations. Each path point in the initial path point set contains position coordinates and the corresponding expected heading angle.

[0044] The path preliminary optimization module is used to perform preliminary smoothing processing on the initial path point set to obtain a smoothed path point set.

[0045] The reversing point identification and geometric adjustment module is used to identify all reversing points based on the smooth path point set, and to adjust the geometric constraints of the path at each reversing point according to the minimum turning radius of the forklift.

[0046] The segmented trajectory generation and splicing module is used to divide the geometrically constrained path into multiple continuous one-way driving segments with each reversal point as the boundary. For each one-way driving segment, a B-spline curve fitting method based on a sliding window is used to generate a local trajectory. At each reversal point, by sharing control points, the positions, tangent directions, and curvatures of adjacent local trajectories at that point are continuous, so as to achieve smooth splicing and obtain the overall spliced ​​trajectory.

[0047] The trajectory optimization module is used to perform velocity planning and nonlinear optimization on the overall spliced ​​trajectory based on the forklift's maximum steering angular velocity and maximum linear velocity constraints, generating a feasible trajectory that satisfies kinematic constraints.

[0048] Preferably, when the path preliminary optimization module performs preliminary smoothing processing on the initial path point set to obtain a smoothed path point set, it is specifically used for:

[0049] The initial path point set is denoised using a least-squares smoothing method, which suppresses path jitter caused by sensor noise or path planning algorithms while preserving the original path geometry.

[0050] The least squares smoothing method obtains the smoothed path point set by constructing an optimization model that balances path fidelity and smoothness, and solving the linear equations corresponding to the optimization model.

[0051] Preferably, when the reversing point identification and geometric adjustment module performs traversal identification of all reversing points based on the smooth path point set, it is specifically used for:

[0052] Traverse the set of smooth path points, and for each path point, calculate the displacement vector from the current path point to the next path point, and obtain the heading vector of that path point;

[0053] Calculate the dot product of the displacement vector and the heading vector to obtain the dot product corresponding to the current path point;

[0054] When it is detected that the dot product corresponding to the current path point has the opposite sign to the dot product corresponding to the previous path point, the current path point is determined to be a reversal point.

[0055] Preferably, when the reversing point identification and geometric adjustment module performs geometric constraint adjustment on the path at each reversing point based on the minimum turning radius of the forklift, it is specifically used for:

[0056] Based on each reversal point, the forward path tangent and the backward path tangent at the current reversal point are determined based on the continuous path point sequence before and after the current reversal point, respectively.

[0057] Based on the minimum turning radius of the forklift, the forklift is offset outward along the forward path tangent and the backward path tangent, respectively, so that the radius of the inscribed circle between the two offset tangents is not less than the minimum turning radius.

[0058] Calculate the intersection of the two offset tangents and use this intersection as the adjusted reversal point;

[0059] Specifically, for reversing points adjacent to the target location of the forklift operation, their geometric adjustment range is limited to preserve the path space required for the forklift to adjust the picking angle before operation.

[0060] Preferably, when the segmented trajectory generation and splicing module performs speed planning and nonlinear optimization on the overall spliced ​​trajectory based on the forklift's maximum steering angular velocity and maximum linear velocity constraints, it is specifically used for:

[0061] The path points of each one-way travel segment are divided into multiple local windows using a sliding window method, and each window contains several consecutive path points.

[0062] For each path point within a local window, a parameterized representation of the B-spline curve is constructed using uniform B-spline basis functions;

[0063] An optimization objective is constructed based on the parametric representation of the B-spline curve, and the control polygon vertices of the B-spline curve are determined by solving the optimization objective.

[0064] The optimization objective comprehensively considers the geometric proximity between the B-spline curve and the original path points within the corresponding window, as well as the smoothness of the curve curvature.

[0065] Preferably, when the segmented trajectory generation and splicing module performs the operation of sharing control points at each reversal point to ensure the continuity of position, tangent direction, and curvature of adjacent local trajectory segments at that point, it is specifically used for:

[0066] The last control point of the B-spline curve corresponding to the last local window covering the reversal point in the previous one-way travel segment is set to the same set of control points as the starting control point of the B-spline curve corresponding to the first local window covering the reversal point in the next one-way travel segment. This forces the two adjacent one-way travel segments to achieve continuity in position, tangent direction, and curvature at the reversal point.

[0067] Preferably, when the trajectory optimization module performs speed planning and nonlinear optimization on the overall spliced ​​trajectory based on the forklift's maximum steering angular velocity and maximum linear velocity constraints, it is specifically used for:

[0068] Calculate the curvature of each point on the overall splicing trajectory;

[0069] Based on the curvature and the forklift’s maximum steering angular velocity, kinematic feasibility constraints are constructed.

[0070] With the goal of maximizing the forklift's running speed along the trajectory, the B-spline control points of the overall spliced ​​trajectory are used as optimization variables. A nonlinear optimization algorithm is employed to adjust the trajectory shape and generate the speed-optimal trajectory that satisfies the kinematic feasibility constraints.

[0071] The third objective of this application is to provide an electronic device.

[0072] The aforementioned objective three of this application is achieved through the following technical solution:

[0073] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the path planning method for frequent forklift reversing conditions as described in any of the first objectives of this application.

[0074] The fourth objective of this application is to provide a computer-readable storage medium.

[0075] The fourth objective of this application is achieved through the following technical solution:

[0076] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the path planning method for frequent forklift reversing conditions as described in any of the first objectives of this application.

[0077] Compared with the prior art, this application has the following beneficial effects:

[0078] 1. By splicing segmented B-spline curves and forcibly sharing control points at reversing points, the position, tangent direction, and curvature of adjacent trajectory segments at reversing points are ensured to be continuous. This allows forklifts to smoothly enter the next travel segment without needing to make additional attitude adjustments or start and stop multiple times due to discontinuous path geometry during reversing. They only need to complete the necessary direction switching operation, which significantly improves the continuity and efficiency of operations.

[0079] 2. This application introduces geometric constraint adjustment based on minimum turning radius in the early stage of path planning to ensure the geometric feasibility of the path; in the later stage, it combines maximum steering angular velocity and maximum linear velocity for joint optimization. The trajectory generated by this dual guarantee mechanism is entirely within the physical capabilities of the forklift, ensuring the executability of the trajectory and the reliability of tracking.

[0080] 3. In the final stage of path planning, this application performs nonlinear optimization with the goal of maximizing operating speed, fully exploring the performance potential of the forklift on road sections with different curvatures. At the same time, for the reversing points of adjacent work targets, the geometric adjustment range is specifically limited, preserving the path space required for the forklift to adjust its picking posture, demonstrating a deep adaptation to actual working conditions.

[0081] 4. A sliding window mechanism is employed for local B-spline fitting, decomposing the large-scale global optimization problem into multiple small-scale local optimization problems, significantly improving computational efficiency and making it suitable for forklift control systems with high real-time requirements. Simultaneously, preliminary smoothing effectively filters out noise interference, enhancing the robustness of the entire planning process. Attached Figure Description

[0082] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0083] Figure 1 This is a flowchart illustrating a path planning method for frequent forklift reversal scenarios in one embodiment of this application.

[0084] Figure 2 This is a schematic diagram of forklift trajectory segmentation and B-spline curve splicing in one embodiment of this application;

[0085] Figure 3 In one embodiment of this application, a maximum speed curve is obtained after speed planning for the forward trajectory.

[0086] Figure 4This is a maximum speed curve obtained after speed planning for the reversing trajectory in one embodiment of this application;

[0087] Figure 5 This is a schematic diagram of the path planning system for frequent forklift reversal scenarios in one embodiment of this application.

[0088] Figure 6 This is a schematic diagram of the structure of an electronic device in one embodiment of this application. Detailed Implementation

[0089] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0090] In the embodiments provided in this application, it should be understood that the disclosed methods and systems can be implemented in other ways. The system embodiments described below are merely illustrative. For example, the division of units and modules is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or modules can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling, direct coupling, or communication connection between the various components shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or modules, and can be electrical, mechanical, or other forms.

[0091] In addition, each functional unit in the various embodiments of this application can be integrated into a single processor, or each unit can be a separate device, or two or more units can be integrated into a single device; each functional unit in the various embodiments of this application can be implemented in hardware or in the form of hardware plus software functional units.

[0092] Those skilled in the art will understand that all or part of the steps of the following method embodiments can be implemented by program instructions and related hardware. The aforementioned program instructions can be stored in a computer-readable storage medium. When the program instructions are executed, they perform the steps of the following method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), magnetic disks, or optical disks.

[0093] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this application, "a plurality of" or "several" means two or more, unless otherwise explicitly specified.

[0094] This application provides a path planning method for frequent forklift reversing operations, such as... Figure 1 As shown, the method may include the following steps:

[0095] S1, obtain the initial path point set for the forklift operation. Each path point in the initial path point set contains the position coordinates and the corresponding expected heading angle.

[0096] In this embodiment, taking the cargo handling scenario of an automated warehouse as an example: an automated guided vehicle (AGV Forklift) needs to move goods from starting point A to target shelf B in a narrow aisle. During the task, it needs to enter and exit the aisle multiple times and frequently switch between forward and reverse modes.

[0097] The upper-level scheduling system generates an initial path for the forklift, consisting of discrete waypoints, based on the warehouse map and task requirements. This path can be obtained through manual teaching, high-level path planning algorithms (such as the A* algorithm), or a navigation system. Each waypoint contains not only two-dimensional location coordinates but also a desired heading angle, specifying the ideal orientation of the forklift at that point. For example, when approaching the target rack B, the heading angle is precisely set to align with the fork insertion point to ensure smooth loading and unloading.

[0098] The position coordinates of all the aforementioned points along with their corresponding expected heading angles together constitute the initial path point set, which serves as the original input data for subsequent path smoothing and reversal optimization.

[0099] S2, perform preliminary smoothing on the initial path point set to obtain a smoothed path point set.

[0100] Due to sensor noise or the discretization characteristics of high-level planning algorithms, the initial path point set may contain high-frequency jitter or minute jagged edges. These irregularities can interfere with subsequent judgments of changes in driving direction. Therefore, this step performs preliminary smoothing on the initial path to filter out these noises, resulting in a smoother path point set. This step ensures the quality of the path data and lays the foundation for accurate identification of changeover points.

[0101] S3 identifies all reversal points by traversing the smooth path point set, and adjusts the path at each reversal point geometrically according to the minimum turning radius of the forklift.

[0102] Forklifts frequently switch between forward and reverse during operation. This step first analyzes the relationship between the displacement direction and heading information of smoothed path points to accurately identify the key locations where the travel direction reverses, i.e., reversal points. However, directly using these reversal points may cause the path to form sharp angles at these locations, exceeding the physical limits of the forklift. Therefore, this step further reconstructs the geometry of each reversal point based on the forklift's own minimum turning radius parameters, ensuring that the adjusted path has sufficient space in the reversal area for the forklift to turn safely, thereby guaranteeing the geometric feasibility of the path.

[0103] S4. Using each reversal point as a boundary, the path adjusted by geometric constraints is divided into multiple continuous one-way driving segments. For each one-way driving segment, a B-spline curve fitting method based on a sliding window is used to generate a local trajectory. At each reversal point, by sharing control points, the positions, tangent directions, and curvatures of adjacent local trajectories at that point are continuous, achieving smooth splicing and obtaining the overall spliced ​​trajectory.

[0104] In this step, the geometrically constrained reversal point is first used as the dividing point to divide the entire continuous path into multiple unidirectional driving segments containing only forward or only reverse motion. Then, a local trajectory is generated independently for each segment using a sliding window-based B-spline curve fitting method. More importantly, at the crucial connection point of the reversal point, by forcing the B-spline curves of the two segments to share a set of control points, the spliced ​​overall trajectory at that point is not only connected in position but also has the same tangent direction and equal curvature value. This fundamentally eliminates the sharp corner problem of traditional polyline paths and the distortion that may occur at reversal points in global smoothing methods, generating a globally C² continuous (or at least G² continuous) smooth trajectory.

[0105] S5, based on the forklift's maximum steering angular velocity and maximum linear velocity constraints, performs velocity planning and nonlinear optimization on the overall splicing trajectory to generate a feasible trajectory that satisfies kinematic constraints.

[0106] The overall spliced ​​trajectory obtained by piecing together piecewise B-spline curves and forcibly sharing control points at reversal points is already a geometrically perfect and smooth trajectory. However, whether this trajectory can be physically executed by the forklift still needs to consider its dynamic capabilities. This step combines the forklift's maximum steering angular velocity and maximum linear velocity to perform velocity planning on the overall spliced ​​trajectory and to perform final nonlinear optimization of the trajectory shape. The final output trajectory is not only geometrically smooth, but also strictly meets the physical constraints of the forklift at any given time, making it a truly executable and highly efficient feasible trajectory.

[0107] As can be seen from the above scheme, this embodiment solves multiple bottlenecks in the prior art, such as sharp path corners, distortion at reversing points, and neglect of kinematic constraints, through the coordinated work of reversing point identification, geometric constraint adjustment, segmented B-spline splicing, and joint kinematic optimization. First, geometric constraint adjustment ensures the physical feasibility of the path; second, the segmented B-spline splicing and control point sharing mechanism achieves high-order continuity at reversing points, avoiding unnecessary stopping and repeated adjustments caused by path discontinuities; finally, joint optimization ensures the dynamic executability of the trajectory and maximizes operational efficiency. In summary, the method of this embodiment enables forklifts to achieve efficient, stable, and safe fully automated operation in complex working conditions such as narrow aisles with frequent reversals.

[0108] like Figure 2 The image shows a schematic diagram of the forklift trajectory segmentation and the stitching of B-spline curves. (The image is presented in the original text.) Figure 2 As can be clearly seen, this application successfully transforms an originally impassable path with sharp reversals into a feasible trajectory that meets the minimum turning radius limit for forklifts and is highly smooth at the reversal points. This smoothness allows forklifts to pass smoothly through the reversal area at higher speeds without requiring additional stopping and attitude adjustments due to path discontinuity, thereby significantly improving operational efficiency and driving safety.

[0109] In one embodiment, step S2 involves performing preliminary smoothing on the initial path point set to obtain a smoothed path point set, specifically including:

[0110] The least squares smoothing method is used to denoise the initial path point set, suppressing path jitter caused by sensor noise or path planning algorithms while preserving the original path geometry.

[0111] Among them, the least squares smoothing method constructs an optimization model that takes into account both path fidelity and smoothness, and solves the corresponding linear equation system to obtain the smooth path point set.

[0112] In practical applications, the initial path point set of a forklift typically originates from manual teaching or high-level path planning algorithms. Taking manual teaching as an example, the operator drives the forklift along the desired route, and the onboard sensors record a series of discrete position coordinates and corresponding heading angles, forming the initial path point set. However, due to sensor noise, road vibration, or the discretization effect of the algorithm, the original trajectory corresponding to the initial path point set often contains high-frequency jitter or slight bends. While these irregularities do not affect the overall direction, they can severely interfere with the subsequent accurate judgment of changes in driving direction.

[0113] To address this issue, this embodiment employs a smoothing method based on a least-squares framework. Its core lies in constructing an optimization model that achieves the best balance between faithfully adhering to the main geometric features of the original path (fidelity) and pursuing the overall smoothness of the path (smoothness).

[0114] Specifically, the original trajectories corresponding to the initial path point set and the optimized trajectories corresponding to the smoothed path point set are each organized into N×2 matrices. and Construct the following objective function:

[0115]

[0116] Among them, the first item The first term is the data fidelity term, used to maintain the geometric consistency between the smoothed trajectory and the original trajectory; the second term... It is a curvature change penalty term that, by constraining the second-order difference of the trajectory, effectively suppresses local oscillations and sharp turns in the path, thereby improving the geometric smoothness of the trajectory. It is a second-order difference matrix; The smoothing weight coefficient (configurable parameter) is used to adjust the trade-off between fidelity and smoothness; It is the Frobenius norm.

[0117] Regarding the objective function Taking the derivative and setting the gradient to zero, we obtain a large system of sparse linear equations:

[0118]

[0119] in, It is an N×N identity matrix.

[0120] This system of linear equations can be solved quickly using efficient numerical methods (such as the conjugate gradient method), thereby obtaining the globally optimal set of smooth path points. .

[0121] The advantage of this method lies in its adjustable parameters and high computational efficiency. When the task path contains many fine turns (such as navigating dense shelving), the parameters can be appropriately reduced. The value is increased to make the result closer to the original teaching trajectory; when the path is relatively open and the main goal is to eliminate jitter, the value can be increased. To achieve a smoother result, adjust the value.

[0122] More importantly, this initial smoothing process provides a high-quality data foundation for subsequent reversal point identification. If the original path has minor oscillations due to noise, the sign of the dot product of the displacement vector and the heading vector may frequently and incorrectly change, resulting in a large number of false reversal points. After this step, the path becomes clean and stable, enabling accurate and reliable identification of reversal points truly caused by operational requirements (rather than noise), rather than false reversal points caused by sensor noise or path jitter. This greatly improves the robustness and accuracy of the entire planning process.

[0123] In one embodiment, step S3, identifying all reversal points based on the smooth path point set traversal, specifically includes:

[0124] Traverse the set of smooth path points. For each path point, calculate the displacement vector from the current path point to the next path point, and obtain the heading vector of that path point.

[0125] Calculate the dot product of the displacement vector and the heading vector to obtain the dot product corresponding to the current path point;

[0126] When it is detected that the dot product corresponding to the current path point has the opposite sign to the dot product corresponding to the previous path point, the current path point is determined to be a reversal point.

[0127] In complex scenarios such as automated warehousing, forklifts need to frequently switch between forward and reverse modes to complete operations such as picking up and placing goods and turning around in aisles. These reversal points (i.e., reversal points) are key features for path planning. However, directly using the original trajectory to identify reversal points is susceptible to noise interference, leading to misjudgments; while relying solely on the geometric inflection points of the position sequence cannot distinguish between pure turns and forward / reverse switching.

[0128] Therefore, this embodiment proposes a robust reversal point discrimination method that integrates position and heading information, namely, identifying reversal behavior by judging the consistency change between the direction of movement and the vehicle's orientation:

[0129] When the forklift moves forward, its instantaneous displacement direction is basically consistent with the vehicle's heading (angle < 90°).

[0130] When the forklift reverses, the direction of displacement is opposite to the vehicle's heading (angle > 90°).

[0131] Therefore, a change in the direction of travel must be accompanied by a reversal of the sign of the dot product of the displacement vector and the heading vector.

[0132] The specific implementation steps are as follows:

[0133] 1. For each path point in the smooth path point set, calculate the displacement vector from the current point to the next path point. This vector reflects the actual direction of movement of the forklift on that path segment.

[0134] 2. Obtain the heading vector of the current path point (that is, convert the heading angle of the current path point into a unit heading vector), which represents the orientation of the forklift at that point.

[0135] 3. Calculate the dot product and determine the sign: Calculate the dot product of the displacement vector and the heading vector. If the dot product > 0, the angle between the displacement direction and the heading is less than 90°, and it is determined to be in a forward state; if the dot product < 0, the angle between the displacement direction and the heading is greater than 90°, and it is determined to be in a reverse state.

[0136] 4. Detect sign reversal and locate the reversal point: Traverse all dot product sequences. When the signs of the dot products of two adjacent path points are reversed, determine the latter of these two path points as the reversal point.

[0137] This embodiment uses the displacement-heading dot product sign detection method to achieve automatic, accurate, and robust identification of reversing points under frequent reversing conditions of forklifts. This lays a key foundation for subsequent geometric constraint adjustment and smooth segment splicing of the path, significantly improving the reliability and execution efficiency of the overall path planning.

[0138] In one embodiment, step S3 involves adjusting the geometric constraints of the path at each reversing point based on the forklift's minimum turning radius, specifically including:

[0139] Based on each reversal point, the forward path tangent and the backward path tangent at the current reversal point are determined based on the continuous path point sequence before and after the current reversal point, respectively.

[0140] Based on the minimum turning radius of the forklift, the tangents along the forward path and the backward path are offset outwards respectively, so that the radius of the inscribed circle between the two offset tangents is not less than the minimum turning radius.

[0141] Calculate the intersection of the two offset tangents and use this intersection as the adjusted reversal point;

[0142] Specifically, for reversing points adjacent to the target location of the forklift operation, their geometric adjustment range is limited to preserve the path space required for the forklift to adjust the picking angle before operation.

[0143] As a non-holonomically constrained vehicle, the forklift's steering capability is limited by its minimum turning radius. If the planned path forms a sharp angle (such as the vertex of a broken line) at a reversal point, its local curvature will tend towards infinity, far exceeding the forklift's physical limits, rendering the trajectory unexecutable. Especially in narrow aisle scenarios with frequent reversals, unadjusted reversal points are highly likely to cause path collisions or execution failures. Therefore, it is essential to reconstruct the geometric feasibility of identified reversal points to ensure that the path satisfies the vehicle's kinematic constraints.

[0144] This embodiment proposes a geometric adjustment method based on the intersection of tangent offset and ray, the core idea of ​​which is:

[0145] 1. Preserve the overall directional trend of the path near the reversal point;

[0146] 2. By expanding the tangent and finding its intersection, construct a new reversal point that satisfies the minimum turning radius constraint;

[0147] 3. Introduce adjustment limits in key areas (such as near the target of the operation) to balance feasibility and operational flexibility.

[0148] The specific implementation steps are as follows:

[0149] 1. Determine the preceding and following path tangents in the neighborhood of the reversal point:

[0150] For each identified original reversal point, several consecutive points to its front are taken, and the forward path tangent direction is obtained through linear fitting or difference calculation; similarly, several consecutive points to its rear are taken, and the backward path tangent direction is obtained. These two tangents represent the driving direction trends before and after the reversal, respectively.

[0151] 2. Tangent offset based on minimum turning radius:

[0152] Along the forward tangent direction, starting from the reversal point, translate a certain distance outward (i.e., away from the inside of the angle between the two tangents) to generate a first offset ray; similarly, along the backward tangent direction, generate a second offset ray.

[0153] The design principle for the offset distance is to ensure that the radius of the inscribed circle between the first and second offset rays is exactly equal to or greater than the minimum turning radius of the forklift. .

[0154] If the angle between the two rays is Then the required offset distance .

[0155] Specifically, the offset distance refers to the vertical distance by which the original front and rear path tangents are translated along their respective outward normals (i.e., the vertical distance from the original tangent to the corresponding offset ray, used to control curvature feasibility), and its value is based on the forklift's minimum turning radius. Angle with two tangents Confirmed, satisfied To ensure that the area between the two rays after the offset can accommodate a radius not less than The incircle, that is, at the bend of the original path, is a segment with a radius of curvature ≥ When using an arc to smoothly connect two straight lines, the arc must lie entirely within the feasible path defined by the offset ray. In other words, the offset operation is to make room for the arc with the minimum turning radius.

[0156] 3. Calculate the new reversing point:

[0157] Find the intersection point of the first offset ray and the second offset ray, and use this intersection point as the adjusted reversal point.

[0158] 4. Adjustment limits for special areas:

[0159] If the reversing point is expanded outward without restriction to a location close to the target (such as a rack insertion point), the new reversing point may be too far from the target, depriving the forklift of the space to fine-tune its posture during final alignment.

[0160] Therefore, this embodiment introduces an adaptive constraint mechanism:

[0161] Set a maximum allowable offset threshold (e.g., 50cm); if the calculated offset distance is greater than the maximum allowable offset threshold, then forcibly truncate the offset distance to the maximum allowable offset threshold and recalculate the intersection point;

[0162] Alternatively, the Euclidean distance between the new reversing point and the original point can be directly limited to a preset value.

[0163] This adaptive constraint mechanism preserves the flexibility of end-point operations while ensuring basic feasibility.

[0164] This embodiment achieves physically feasible reconstruction of the reversing point through a tangent offset-ray intersection geometric strategy, fundamentally solving the path infeasibility problem caused by the minimum turning radius limitation of forklifts. Simultaneously, by introducing an adjustment range limitation mechanism for the target's neighboring region, it balances path feasibility with end-operation flexibility. This method provides a safe, reasonable, and executable geometric foundation for subsequent high-order smooth splicing and speed optimization.

[0165] In one embodiment, step S4 involves generating a local trajectory for each unidirectional travel segment using a sliding window-based B-spline curve fitting method, specifically including:

[0166] The path points of each one-way travel segment are divided into multiple local windows using a sliding window method, and each window contains several consecutive path points.

[0167] For each path point within a local window, a parameterized representation of the B-spline curve is constructed using uniform B-spline basis functions;

[0168] An optimization objective is constructed based on the parametric representation of B-spline curves, and the vertices of the control polygons of the B-spline curves are determined by solving the optimization objective.

[0169] The optimization objective comprehensively considers the geometric proximity between the B-spline curve and the original path points within the corresponding window, as well as the smoothness of the curve curvature.

[0170] In this embodiment, a local B-spline fitting method based on sliding windows is used to perform high-order smoothing on each unidirectional driving sub-segment (i.e., a pure forward or pure reverse sub-path). Specifically, the sequence of path points in the sub-segment is divided into multiple overlapping or continuous local windows, each containing several continuous points (e.g., 5–7) to ensure the controllability of the local trajectory and computational efficiency. For each window, a parametric curve model is constructed using uniform B-spline basis functions, and the generated B-spline curve is geometrically closely fitted to the original path points and has good curvature continuity by optimizing the control polygon vertices. This method avoids the problems of oscillation, overfitting, or high computational complexity that easily occur with global fitting on long paths.

[0171] The sliding window mechanism of this scheme decomposes large-scale trajectories into small-scale sub-problems, significantly reducing the scale of a single optimization and making it suitable for real-time operation in vehicle-mounted embedded systems. Simultaneously, by constraining both proximity (data fidelity) and curvature smoothness (e.g., minimizing the rate of curvature change) in the optimization objective, the generated local B-spline curves are not only visually smooth but also exhibit continuous and abrupt curvature changes, naturally meeting the forklift's requirements for smooth steering commands. More importantly, this local fitting method provides the structural foundation for subsequent G² continuous splicing at reversing points through shared control points, thereby ensuring high quality for each trajectory segment while achieving a globally smooth transition of the overall path.

[0172] In one embodiment, in step S4, at each reversal point, by sharing control points, the position, tangent direction, and curvature of two adjacent local trajectory segments are made continuous at that point. Specifically, this includes:

[0173] The last control point of the B-spline curve corresponding to the last local window covering the reversal point in the previous one-way travel segment is set to the same set of control points as the starting control point of the B-spline curve corresponding to the first local window covering the reversal point in the next one-way travel segment. This forces the two adjacent one-way travel segments to achieve continuity in position, tangent direction, and curvature at the reversal point.

[0174] In this embodiment, to ensure high-order geometric continuity of the forklift trajectory at frequent reversing points, a control point sharing mechanism is employed at the junctions of adjacent unidirectional travel segments (such as forward and reverse segments). Specifically, for each reversing point, firstly, the last local B-spline window in the preceding segment and the first local B-spline window in the following segment are identified (both windows cover the reversing point). Subsequently, the coordinate values ​​of several control points at the end of the preceding B-spline curve (which can be the last three, corresponding to the position, first derivative, and second derivative information of the uniform cubic B-spline at the endpoints) are forcibly set to the same coordinate values ​​as those of several control points at the beginning of the following B-spline curve. Since the geometric properties of the B-spline curve are uniquely determined by its control polygon, this sharing operation directly constrains the two curve segments to have the same position, tangent direction (first derivative), and curvature (determined by the second derivative) at the connection point, thereby achieving G² geometric continuity (or C² continuity when parameterization is consistent).

[0175] This method fundamentally eliminates the sharp corners, inflection points, or curvature jumps common in traditional piecewise fitting, enabling forklifts to continuously and smoothly switch between forward and reverse directions without stopping to adjust their posture. Secondly, compared to global B-spline fitting, the local window + control point sharing strategy balances computational efficiency and local controllability, avoiding optimization difficulties caused by global coupling on long paths. More importantly, this mechanism is inherently compatible with the sliding window fitting framework, achieving high-order continuous stitching through structural constraints alone without adding extra optimization variables, significantly improving the algorithm's robustness and real-time performance. The resulting overall trajectory not only satisfies kinematic constraints such as the forklift's minimum turning radius but also possesses excellent curvature continuity, providing a high-quality geometric foundation for high-speed, safe, and low-impact automated operation in the subsequent speed planning stage.

[0176] In one embodiment, step S5 involves speed planning and nonlinear optimization of the overall splicing trajectory based on the forklift's maximum steering angular velocity and maximum linear velocity constraints, specifically including:

[0177] Calculate the curvature of each point on the overall stitching trajectory;

[0178] Based on the curvature and the forklift’s maximum steering angular velocity, kinematic feasibility constraints are constructed.

[0179] With the goal of maximizing the forklift's running speed along the trajectory, the B-spline control points of the overall spliced ​​trajectory are used as optimization variables. A nonlinear optimization algorithm is employed to adjust the trajectory shape and generate the speed-optimal trajectory that satisfies the kinematic feasibility constraints.

[0180] In this embodiment, based on the obtained globally smooth stitched trajectory, velocity-geometry joint optimization is further performed by combining the actual kinematic capabilities of the forklift. First, discrete sampling is performed along the overall stitched trajectory, and the curvature at each point is calculated. (Unit: m) -1 Based on the vehicle's kinematics, using the forklift's maximum given steering angular velocity... (Unit: rad) and maximum linear velocity (Unit: m / s) Strict kinematic feasibility constraints are established: for any point on the trajectory, the forklift's travel speed... (Unit: m / s) must meet the following requirements This constraint ensures that, at any curvature, the forklift can safely track the trajectory by appropriately allocating speed and steering commands.

[0181] To improve operational efficiency, this embodiment uses maximizing overall operating speed (e.g., minimizing travel time or maximizing average speed) as the objective function, and innovatively uses the control points of the B-spline curve as adjustable optimization variables, rather than only adjusting the speed profile. Through nonlinear optimization algorithms (such as sequential quadratic programming (SQP) or the interior point method), while satisfying the aforementioned kinematic constraints, the local shape of the trajectory is fine-tuned. For example, the path is appropriately straightened in high-curvature regions to reduce curvature, thereby allowing for higher throughput speeds. This collaborative optimization mechanism of trajectory shape and speed overcomes the limitations of the traditional two-stage method of first determining the shape and then adjusting the speed. The resulting final trajectory is not only geometrically smooth and kinematically feasible, but also close to optimal in terms of time or efficiency, significantly improving the forklift's operating cycle time and smoothness in complex and frequent reversing scenarios, while ensuring driving safety and mechanical lifespan.

[0182] like Figure 3 and Figure 4 The figures show the maximum speed curves obtained after applying the speed planning described above for the forward and reverse sections of the trajectory. The horizontal axis represents the path length along the trajectory, and the vertical axis represents the maximum allowable operating speed at that location. As can be seen from the figures, in areas with significant trajectory curvature (such as turns), the corresponding maximum speed is automatically limited to a lower level; while in areas with straight trajectories and near-zero curvature, the forklift can accelerate to its maximum linear speed. This adaptive velocity profile ensures that the forklift's steering action at any given moment will not exceed its physical limits (i.e., the steering angular velocity will not exceed...). This ensures the accuracy and safety of trajectory tracking during high-speed operation.

[0183] In summary, this embodiment, through the technical approach of reversal point identification, geometric constraint adjustment, segmented B-spline splicing, and joint kinematic optimization, collaboratively solves multiple bottlenecks in the prior art, such as path sharp angles, reversal point distortion, and neglect of kinematic constraints, and achieves efficient, continuous, and safe automatic operation of forklifts under frequent reversal conditions.

[0184] like Figure 5 As shown in the figure, this application embodiment also provides a path planning system for frequent forklift reversing conditions, the system may include:

[0185] The initial path acquisition module 201 is used to acquire the initial path point set for forklift operation. Each path point in the initial path point set contains position coordinates and the corresponding expected heading angle.

[0186] The path preliminary optimization module 202 is used to perform preliminary smoothing on the initial path point set to obtain a smoothed path point set.

[0187] The reversing point identification and geometric adjustment module 203 is used to identify all reversing points based on the smooth path point set traversal, and to adjust the path at each reversing point geometrically according to the minimum turning radius of the forklift.

[0188] The segmented trajectory generation and splicing module 204 is used to divide the geometrically constrained path into multiple continuous one-way driving segments with each reversal point as the boundary. For each one-way driving segment, a local trajectory is generated using a B-spline curve fitting method based on a sliding window. At each reversal point, by sharing control points, the positions, tangent directions, and curvatures of adjacent local trajectories at that point are continuous, achieving smooth splicing and obtaining the overall spliced ​​trajectory.

[0189] The trajectory optimization module 205 is used to perform velocity planning and nonlinear optimization on the overall splicing trajectory based on the forklift's maximum steering angular velocity and maximum linear velocity constraints, generating a feasible trajectory that meets the kinematic constraints.

[0190] In one embodiment, when the path preliminary optimization module 202 performs preliminary smoothing processing on the initial path point set to obtain a smoothed path point set, it is specifically used for:

[0191] The least squares smoothing method is used to denoise the initial path point set, suppressing path jitter caused by sensor noise or path planning algorithms while preserving the original path geometry.

[0192] Among them, the least squares smoothing method constructs an optimization model that takes into account both path fidelity and smoothness, and solves the corresponding linear equation system to obtain the smooth path point set.

[0193] In one embodiment, when the reversing point identification and geometry adjustment module 203 performs the identification of all reversing points based on smooth path point set traversal, it is specifically used for:

[0194] Traverse the set of smooth path points. For each path point, calculate the displacement vector from the current path point to the next path point, and obtain the heading vector of that path point.

[0195] Calculate the dot product of the displacement vector and the heading vector to obtain the dot product corresponding to the current path point;

[0196] When it is detected that the dot product corresponding to the current path point has the opposite sign to the dot product corresponding to the previous path point, the current path point is determined to be a reversal point.

[0197] In one embodiment, when the reversing point identification and geometry adjustment module 203 performs geometric constraint adjustment of the path at each reversing point based on the minimum turning radius of the forklift, it is specifically used for:

[0198] Based on each reversal point, the forward path tangent and the backward path tangent at the current reversal point are determined based on the continuous path point sequence before and after the current reversal point, respectively.

[0199] Based on the minimum turning radius of the forklift, the tangents along the forward path and the backward path are offset outwards respectively, so that the radius of the inscribed circle between the two offset tangents is not less than the minimum turning radius.

[0200] Calculate the intersection of the two offset tangents and use this intersection as the adjusted reversal point;

[0201] Specifically, for reversing points adjacent to the target location of the forklift operation, their geometric adjustment range is limited to preserve the path space required for the forklift to adjust the picking angle before operation.

[0202] In one embodiment, when the segmented trajectory generation and splicing module 204 performs speed planning and nonlinear optimization on the overall spliced ​​trajectory based on the forklift's maximum steering angular velocity and maximum linear velocity constraints, it is specifically used for:

[0203] The path points of each one-way travel segment are divided into multiple local windows using a sliding window method, and each window contains several consecutive path points.

[0204] For each path point within a local window, a parameterized representation of the B-spline curve is constructed using uniform B-spline basis functions;

[0205] An optimization objective is constructed based on the parametric representation of B-spline curves, and the vertices of the control polygons of the B-spline curves are determined by solving the optimization objective.

[0206] The optimization objective comprehensively considers the geometric proximity between the B-spline curve and the original path points within the corresponding window, as well as the smoothness of the curve curvature.

[0207] In one embodiment, when the segmented trajectory generation and splicing module 204 performs the operation of sharing control points at each reversal point to ensure that the position, tangent direction, and curvature of adjacent local trajectory segments are continuous at that point, it is specifically used for:

[0208] The last control point of the B-spline curve corresponding to the last local window covering the reversal point in the previous one-way travel segment is set to the same set of control points as the starting control point of the B-spline curve corresponding to the first local window covering the reversal point in the next one-way travel segment. This forces the two adjacent one-way travel segments to achieve continuity in position, tangent direction, and curvature at the reversal point.

[0209] In one embodiment, when the trajectory optimization module 205 performs speed planning and nonlinear optimization on the overall spliced ​​trajectory based on the forklift's maximum steering angular velocity and maximum linear velocity constraints, it is specifically used for:

[0210] Calculate the curvature of each point on the overall stitching trajectory;

[0211] Based on the curvature and the forklift’s maximum steering angular velocity, kinematic feasibility constraints are constructed.

[0212] With the goal of maximizing the forklift's running speed along the trajectory, the B-spline control points of the overall spliced ​​trajectory are used as optimization variables. A nonlinear optimization algorithm is employed to adjust the trajectory shape and generate the speed-optimal trajectory that satisfies the kinematic feasibility constraints.

[0213] like Figure 6 As shown in the illustration, this application also provides an electronic device, which may include:

[0214] The system includes a memory 301, a processor 302, and a computer program 303 stored in the memory 301 and executable on the processor 302. The memory 301 and the processor 302 communicate with each other via a bus 304. When the processor 302 executes the computer program 303, it implements the steps of the path planning method for frequent forklift reversing conditions as described in the above-described method embodiments of this application.

[0215] Specifically, the electronic device 3 can be an intelligent device with memory and processor, such as an industrial control computer, PC, or smart mobile terminal, or a computer component with memory and processor, such as a CPU or GPU.

[0216] In this embodiment, electronic device 3 is an on-board controller or robot motion controller installed on the forklift body.

[0217] This application also provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the steps of the path planning method for frequent forklift reversing conditions described in the above embodiments.

[0218] In this embodiment, the computer-readable storage medium facilitates the storage and dissemination of computer programs, enabling the path planning method for frequent forklift reversing conditions to be easily ported and used across different electronic devices, thus improving the method's versatility and scalability. Storing the program on the storage medium also allows for backup and updates, ensuring the program's security and integrity. This storage medium provides a convenient carrier for implementing the path planning method for frequent forklift reversing conditions, which is beneficial for the widespread application of this method.

[0219] It should be noted that the path planning system, electronic device and computer-readable storage medium for frequent forklift reversing conditions in the above embodiments have the same working principle and technical effect as the path planning method for frequent forklift reversing conditions in the above embodiments, and will not be repeated here.

[0220] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0221] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Those skilled in the art can implement the described functions using different methods for each specific application, but such implementations should not be considered beyond the scope of this application.

[0222] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0223] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. This application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A path planning method for frequent forklift reversing operations, characterized in that, The method includes the following steps: S1, Obtain the initial path point set for forklift operation, wherein each path point in the initial path point set contains position coordinates and the corresponding expected heading angle; S2, perform preliminary smoothing processing on the initial path point set to obtain a smoothed path point set; S3, based on the smooth path point set, traverse and identify all reversal points, and adjust the path at each reversal point geometrically according to the minimum turning radius of the forklift; S4. Using each reversal point as a boundary, the path after geometric constraint adjustment is divided into multiple continuous one-way driving segments. For each one-way driving segment, a B-spline curve fitting method based on a sliding window is used to generate a local trajectory. At each reversal point, by sharing control points, the positions, tangent directions, and curvatures of adjacent local trajectories at that point are continuous, achieving smooth splicing and obtaining the overall spliced ​​trajectory. S5. Based on the forklift's maximum steering angular velocity and maximum linear velocity constraints, speed planning and nonlinear optimization are performed on the overall splicing trajectory to generate a feasible trajectory that satisfies the kinematic constraints.

2. The path planning method for frequent forklift reversing operations according to claim 1, characterized in that, In step S2, the preliminary smoothing process of the initial path point set to obtain a smoothed path point set specifically includes: The initial path point set is denoised using a least-squares smoothing method, which suppresses path jitter caused by sensor noise or path planning algorithms while preserving the original path geometry. The least squares smoothing method obtains the smoothed path point set by constructing an optimization model that balances path fidelity and smoothness, and solving the linear equations corresponding to the optimization model.

3. The path planning method for frequent forklift reversing operations according to claim 1, characterized in that, In step S3, the step of traversing and identifying all reversal points based on the smooth path point set specifically includes: Traverse the set of smooth path points, and for each path point, calculate the displacement vector from the current path point to the next path point, and obtain the heading vector of that path point; Calculate the dot product of the displacement vector and the heading vector to obtain the dot product corresponding to the current path point; When it is detected that the dot product corresponding to the current path point has the opposite sign to the dot product corresponding to the previous path point, the current path point is determined to be a reversal point.

4. The path planning method for frequent forklift reversing operations according to claim 1, characterized in that, In step S3, adjusting the path at each reversing point based on the forklift's minimum turning radius specifically includes: Based on each reversal point, the forward path tangent and the backward path tangent at the current reversal point are determined based on the continuous path point sequence before and after the current reversal point, respectively. Based on the minimum turning radius of the forklift, the forklift is offset outward along the forward path tangent and the backward path tangent, respectively, so that the radius of the inscribed circle between the two offset tangents is not less than the minimum turning radius. Calculate the intersection of the two offset tangents and use this intersection as the adjusted reversal point; Specifically, for reversing points adjacent to the target location of the forklift operation, their geometric adjustment range is limited to preserve the path space required for the forklift to adjust the picking angle before operation.

5. The path planning method for frequent forklift reversing operations according to claim 1, characterized in that, In step S4, the speed planning and nonlinear optimization of the overall splicing trajectory based on the forklift's maximum steering angular velocity and maximum linear velocity constraints specifically includes: The path points of each one-way travel segment are divided into multiple local windows using a sliding window method, and each window contains several consecutive path points. For each path point within a local window, a parameterized representation of the B-spline curve is constructed using uniform B-spline basis functions; An optimization objective is constructed based on the parametric representation of the B-spline curve, and the control polygon vertices of the B-spline curve are determined by solving the optimization objective. The optimization objective comprehensively considers the geometric proximity between the B-spline curve and the original path points within the corresponding window, as well as the smoothness of the curve curvature.

6. The path planning method for frequent forklift reversing operations according to claim 5, characterized in that, In step S4, the step of ensuring the continuity of position, tangent direction, and curvature of adjacent local trajectories at each reversal point by sharing control points specifically includes: The last control point of the B-spline curve corresponding to the last local window covering the reversal point in the previous one-way travel segment is set to the same set of control points as the starting control point of the B-spline curve corresponding to the first local window covering the reversal point in the next one-way travel segment. This forces the two adjacent one-way travel segments to achieve continuity in position, tangent direction, and curvature at the reversal point.

7. The path planning method for frequent forklift reversing operations according to claim 1, characterized in that, In step S5, the speed planning and nonlinear optimization of the overall splicing trajectory based on the forklift's maximum steering angular velocity and maximum linear velocity constraints specifically includes: Calculate the curvature of each point on the overall splicing trajectory; Based on the curvature and the forklift’s maximum steering angular velocity, kinematic feasibility constraints are constructed. With the goal of maximizing the forklift's running speed along the trajectory, the B-spline control points of the overall spliced ​​trajectory are used as optimization variables. A nonlinear optimization algorithm is employed to adjust the trajectory shape and generate the speed-optimal trajectory that satisfies the kinematic feasibility constraints.

8. A path planning system for frequent forklift reversing operations, characterized in that, The system includes: The initial path acquisition module is used to acquire the initial path point set for forklift operation. Each path point in the initial path point set contains position coordinates and the corresponding expected heading angle. The path preliminary optimization module is used to perform preliminary smoothing processing on the initial path point set to obtain a smoothed path point set. The reversing point identification and geometric adjustment module is used to identify all reversing points based on the smooth path point set, and to adjust the geometric constraints of the path at each reversing point according to the minimum turning radius of the forklift. The segmented trajectory generation and splicing module is used to divide the geometrically constrained path into multiple continuous one-way driving segments with each reversal point as the boundary. For each one-way driving segment, a B-spline curve fitting method based on a sliding window is used to generate a local trajectory. At each reversal point, by sharing control points, the positions, tangent directions, and curvatures of adjacent local trajectories at that point are continuous, so as to achieve smooth splicing and obtain the overall spliced ​​trajectory. The trajectory optimization module is used to perform velocity planning and nonlinear optimization on the overall spliced ​​trajectory based on the forklift's maximum steering angular velocity and maximum linear velocity constraints, generating a feasible trajectory that satisfies kinematic constraints.

9. An electronic device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the path planning method for frequent forklift reversing conditions as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the path planning method for frequent forklift reversing conditions as described in any one of claims 1-7.

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