A method and device for removing redundant points in robot path planning

Abstract

This invention discloses a method and apparatus for removing redundant points in robotic arm path planning. The method includes: acquiring a sequence of original points for the robotic arm's path planning; calculating the shortest distance between each intermediate point in the original path planning sequence and a reference straight line based on the start and end points of the original path planning sequence; constructing a key point set from all original path planning points whose shortest distance values ​​are greater than a preset residual threshold; if the key point set is empty, retaining the endpoints of the current path sequence as feature points; if it is not empty, selecting the optimal segmentation point based on weight parameters, segmenting the current path sequence into subsequences and recursively processing them until all subsequences can no longer be segmented, retaining their endpoints as feature points; and obtaining a set of retained path planning points after removing redundant points based on all feature points. This significantly optimizes the spatial distribution of path points while preserving the original path's key features, providing well-distributed path point input for trajectory planning methods such as multinomial interpolation.

Description

Technical Field

[0001] This invention relates to the field of robotic arm control technology, and in particular to a method and apparatus for removing redundant points in robotic arm path planning. Background Technology

[0002] In the field of robotic arm path planning technology, to improve trajectory generation efficiency, redundant points on the original path are typically removed. Currently, commonly used methods for redundant point removal mainly include triangulation and the Douglas-Peucker algorithm. Triangulation reduces the number of path points to the minimum by detecting line collisions between path points segment by segment. However, this method completely ignores the geometric features of the path when removing redundant points, and oversimplification may lead to the loss of critical path information. For example, when the simplified straight path crosses an obstacle area, the robotic arm will face the risk of collision or the path may become unreachable due to inverse kinematics failure.

[0003] While the Douglas-Peucker algorithm can preserve path features through the residual threshold ε, it has significant limitations. This algorithm selects points to retain based solely on the perpendicular distance from the path point to the baseline, resulting in a severely uneven spatial distribution of path points after processing. This non-uniform distribution negatively impacts subsequent trajectory planning—when using conventional methods such as polynomial interpolation, NURBS curves, or Bezier curves for trajectory planning, a relatively uniform distribution of path points is required. Path points that are too close together can cause local curvature abrupt changes in the interpolation curve (i.e., the Runge phenomenon), leading to robotic arm motion jitter and severely affecting trajectory stability.

[0004] The fundamental flaws of existing technologies lie in the fact that the triangular pruning method, with its sole objective of minimizing the number of path points, sacrifices the integrity of path features; while the Douglas-Peucker algorithm, although preserving features, disrupts the uniformity of distribution. Neither method addresses the dual requirements of feature preservation and distribution optimization, leading to curvature control challenges in subsequent trajectory planning, ultimately affecting the stability of the robotic arm's motion and the reliability of obstacle avoidance. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for removing redundant points in robotic arm path planning. While retaining the key features of the original path (such as key turning points for obstacle avoidance), it significantly optimizes the spatial distribution of path points, providing well-distributed path point inputs for trajectory planning methods such as polynomial interpolation, thereby ensuring the smoothness, stability, and obstacle avoidance reliability of the robotic arm's motion trajectory.

[0006] To address the aforementioned technical problems, a first aspect of this invention provides a method for removing redundant points in robotic arm path planning, comprising the following steps:

[0007] Step S100: Obtain the original point sequence for the path planning of the robotic arm;

[0008] Step S200: Calculate the shortest distance between each intermediate point of the original path planning point sequence and the reference straight line based on the start and end points of the original path planning point sequence; and form a key point set by all original path planning points whose shortest distance value is greater than a preset residual threshold.

[0009] Step S300: If the key point set is empty, the endpoints of the current path sequence are retained as feature points. If it is not empty, the optimal split point is selected by adjusting the weight parameters, the current path sequence is split into subsequences and recursively processed until all subsequences can no longer be split, and their endpoints are retained as feature points. Based on all feature points, the path planning retained point set after removing redundant points is obtained.

[0010] Further, the step S300, which states that if the set of key points is empty, the endpoints of the current path sequence are retained as feature points, includes:

[0011] Step S311: If the set of key points is empty, then the starting point and ending point of the original point sequence of the current path planning are taken as feature points.

[0012] Further, in step S300, if the condition is not empty, the optimal split point is selected by adjusting the weight parameters, the current path sequence is divided into subsequences and recursively processed until all subsequences can no longer be divided. Then, their endpoints are retained as feature points. Based on all feature points, a set of path planning retained points after removing redundant points is obtained, including:

[0013] Step S321: If the set of key points is not empty, calculate the distance values ​​between each key point and the starting point and the ending point respectively, and calculate the target value of each key point by combining the straight line distance weight and the point distance weight.

[0014] Step S322: Take the key point with the largest target value in the current path planning original point sequence as the split point, and divide the current path planning original point sequence into two sub-sequences;

[0015] Step S323: Return each of the subsequences to step S200 until the set of key points of all subsequences in step S200 is empty, and list the start and end points of the subsequences as feature points, and obtain the set of path planning retained points after removing redundant points based on all feature points.

[0016] Furthermore, the formula for calculating the target value is as follows:

[0017]

[0018] Among them, w dThe straight-line distance weight value, d i w represents the shortest distance from the i-th keypoint in the current path sequence to the baseline. m The distance to the point is the weight value. This represents the straight-line distance from the i-th keypoint in the current path sequence to the starting point of the current path sequence. This is the straight-line distance from the i-th key point in the current path sequence to the end point of the current path sequence.

[0019] Further, in step S323, each of the subsequences is returned to step S200 until the key point set of all subsequences in step S200 is empty, and the start and end points of the subsequences are listed as feature points. Based on all feature points, a path planning retained point set after removing redundant points is obtained, including:

[0020] Step S3231: Take the segmented first subsequence as the current path sequence, return to step S200, and recalculate the key point set of the first subsequence;

[0021] Step S3232: If the set of key points of the first subsequence is not empty, then select a new splitting point for secondary splitting to generate a secondary subsequence, and recursively execute step S3231.

[0022] Step S3233: If the key point set of the first subsequence is empty, add the start and end points of the first subsequence to the feature point set;

[0023] Step S3234: Repeat steps S3231-S3233 for the second subsequence after segmentation;

[0024] Step S3235: When the key point set after the segmentation step of all subsequences is empty, terminate the recursion and output the feature point set. After deduplicating the feature point set, obtain the path planning retained point set.

[0025] Furthermore, after obtaining the set of path planning retained points after removing redundant points in step S300, the method further includes:

[0026] Step S410: Obtain the rate of curvature change of the set of retained points for path planning;

[0027] Step S420: When the rate of change of curvature is greater than the first preset curvature threshold, the preset residual threshold is reduced according to the first preset ratio.

[0028] Step S430: When the rate of change of curvature is less than the second preset curvature threshold, the preset residual threshold is increased according to the second preset ratio.

[0029] Wherein, the first preset curvature threshold and the second preset curvature threshold are the maximum and minimum values ​​of the preset curvature range, respectively.

[0030] Furthermore, the formula for calculating the rate of curvature change σ is:

[0031]

[0032] Where N is the number of path points in the current path sequence, θ k The turning angle of the k-th path point in the current path sequence. It is the average turning angle of several path points in the current path sequence.

[0033] Furthermore, after obtaining the set of path planning retained points after removing redundant points based on all feature points in step S300, the method further includes:

[0034] Step S510: Detect the distance between two adjacent path planning reserved points in the path planning reserved point set;

[0035] Step S520: If the distance between two adjacent path planning reserved points is greater than a first preset multiple of the average distance between all two adjacent path planning reserved points in the path planning reserved point set, then an interpolation point is inserted between the two adjacent path planning reserved points so that the distance between each pair of adjacent path planning reserved points is less than a second preset multiple of the average distance.

[0036] Accordingly, a second aspect of the present invention provides a robotic arm path planning redundancy point removal device, which removes redundant points in the original point sequence of the robotic arm path planning based on the above-described robotic arm path planning redundancy point removal method, including:

[0037] The data acquisition module is used to acquire the original point sequence for the path planning of the robotic arm;

[0038] A set construction module is used to calculate the shortest distance between each intermediate point of the original point sequence of the path planning and the reference straight line based on the start and end points of the original point sequence of the path planning, and to form a key point set of all original points of the path planning with the shortest distance value greater than a preset residual threshold.

[0039] The recursive processing module is used to retain the endpoints of the current path sequence as feature points if the key point set is empty, and to select the optimal split point by combining the weight parameters if it is not empty. The current path sequence is then divided into subsequences and recursively processed until all subsequences can no longer be divided, at which point their endpoints are retained as feature points. Based on all feature points, a set of path planning retained points after removing redundant points is obtained.

[0040] Accordingly, a third aspect of the present invention provides an electronic device, including: at least one processor; and a memory connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the above-described robotic arm path planning redundancy point removal method.

[0041] Accordingly, a fourth aspect of the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-described method for removing redundant points in robotic arm path planning.

[0042] The above-described technical solutions of the embodiments of the present invention have the following beneficial technical effects:

[0043] 1. Through an innovatively designed dual-weight objective function, the algorithm retains the path feature extraction capabilities of the traditional Douglas-Peucker algorithm while achieving proactive control over the uniformity of point distribution for the first time. When the point distance weight is increased, the algorithm prioritizes path points with relatively balanced distances from the beginning and end points as split points, macroscopically promoting a more uniform spatial distribution of the retained point sequence. By adjusting the straight-line distance weight, it can still ensure that key points that significantly contribute to the geometric features of the path (such as obstacle avoidance turning points) are retained first. The above-mentioned collaborative mechanism fundamentally overcomes the contradiction that "feature retention" and "uniform distribution" cannot be achieved simultaneously in traditional algorithms.

[0044] 2. Because the optimized path point set has both feature integrity and uniform distribution, it provides ideal input conditions for subsequent trajectory planning; by suppressing the problem of excessively small spacing between adjacent path points, it completely avoids the phenomenon of local curvature increase caused by uneven point distribution (i.e., Runge phenomenon) in methods such as polynomial interpolation and spline curves; even if the residual is increased to retain more features, the path points after removing redundancy can still maintain a smooth curvature transition after cubic spline interpolation, thereby ensuring the stability and continuity of the robotic arm's end effector motion;

[0045] 3. Based on the dual guarantee of feature point preservation and distribution optimization, two types of motion failure problems caused by path simplification are avoided from the root: First, by preserving key obstacle avoidance feature points, the simplified path is prevented from intruding into the obstacle area and causing collisions; second, the uniform point distribution ensures smooth joint motion after trajectory interpolation, avoiding robotic arm shaking or inverse solution failure caused by curvature abrupt changes; further, the curvature feedback is used to adjust the residual threshold and path point density to form a closed-loop optimization mechanism, ultimately improving the reliability and safety of the motion trajectory. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the triangular pruning method for removing redundant points in existing technology;

[0047] Figure 2 This is a schematic diagram of the Dougla-Peucker algorithm for removing redundant points in existing technology;

[0048] Figure 3 This is a schematic diagram illustrating excessive curvature caused by overfitting in the existing Douglas-Peucker algorithm.

[0049] Figure 4 This is a flowchart of the method for removing redundant points in robotic arm path planning provided in an embodiment of the present invention;

[0050] Figure 5a This is a schematic diagram of the original path points of the robotic arm without removing redundant points, provided in an embodiment of the present invention.

[0051] Figure 5b This is a schematic diagram of the change of a robotic arm joint over time without removing redundant points, provided in an embodiment of the present invention.

[0052] Figure 6a This is a schematic diagram of the original path points of the robotic arm corresponding to the first residual value, provided in an embodiment of the present invention.

[0053] Figure 6b This is a schematic diagram of the change of the robotic arm joint corresponding to the first residual value over time, provided in an embodiment of the present invention.

[0054] Figure 7a This is a schematic diagram of the original path points of the robotic arm corresponding to the second residual value provided in an embodiment of the present invention;

[0055] Figure 7b This is a schematic diagram of the change of the robotic arm joints corresponding to the second residual value over time, provided in an embodiment of the present invention.

[0056] Figure 8a This is a schematic diagram of the original path points of the robotic arm corresponding to the third residual value provided in an embodiment of the present invention;

[0057] Figure 8b This is a schematic diagram of the change of the robotic arm joints corresponding to the third residual value over time, provided in an embodiment of the present invention.

[0058] Figure 9 This is a block diagram of the robotic arm path planning redundancy point removal device module provided in an embodiment of the present invention.

[0059] Figure label:

[0060] 1. Data acquisition module, 2. Set construction module, 3. Recursive processing module. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. It should be understood that these descriptions are merely exemplary and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0062] like Figure 1 As shown, the triangular pruning method is a commonly used method for removing redundant points. It mainly connects the current starting point to the current point. If the two lines do not collide, the current point is updated to the next point. If a collision occurs, the current starting point is updated to the previous point, and so on, until the current point has traversed all path points. For example, initially, the current starting point is path point 1, and the current point is path point 2. It checks if 1 and 2 collide. If no collision occurs, the current point is updated from path point 2 to path point 3. It continues checking if 1 and 3 collide, until the current point is 6. When a collision occurs between 1 and 6, the current starting point is recorded and changed from 1 to 5, and so on. The triangular pruning algorithm for removing redundant points ends when the current point has finished traversing. As shown in the figure, the number of path points is reduced from 8 to 3, minimizing the number of path points and reducing the algorithm's time consumption for subsequent trajectory planning. It can be seen that the triangular pruning method is very effective in removing redundant points. However, because the retained path points lack the characteristics of the original path points (such as the path 1-2-3-4-5 and the path 1-5, which lack the upward feature of path point 3), the robotic arm can guarantee the movement of the 1-2-3-4-5 path, but cannot guarantee the straight-line movement from 1-5. This is because during the straight-line movement from 1-5, the robotic arm body may collide with obstacles, or the robotic arm may not be able to reach a certain position on this straight line (inverse solution failure).

[0063] like Figure 2As shown, the Douglas-Peucker algorithm is another commonly used method for removing redundant points. It first sets a residual ε (the smaller the ε, the higher the accuracy and the fewer redundant points removed). A straight line connects path point 1 and path point 8. The distance from the intermediate path point between 1 and 8 to this straight line is calculated, and the maximum distance is found to be d5. The algorithm then compares d5 with ε. If ε > d5, the straight line connecting 1 and 8 represents the characteristics of this curve. If ε ≤ d5, the straight line does not represent the characteristics of this curve and further subdivision is needed. Path point 5 is used as the intermediate point, connecting 1 and 5, and 5 and 8. The maximum distance between the path points in these two sets of points and the curves at both ends is calculated, and the comparison with a threshold is repeated. Finally, based on the threshold, the path points with the retained indices are 1-3-5-8. Compared to the triangular pruning method, this algorithm can retain the characteristics of the original path points based on the magnitude of the residual. After removing redundant points using the Douglas-Peucker algorithm, it can be seen that the path points retain the characteristics of the original path points, but the distance between each point is not equal. For such path points, the above curve interpolation method will result in a very large curvature between points that are very close to each other, which is the Runge phenomenon, and is not friendly to the end effector motion of the robotic arm. Figure 3 The curve is the interpolation curve of the cubic spline function on the path points. It can be seen that the curvature between path points 1 and 3 is too large due to the small distance between them, which is the Runge phenomenon.

[0064] Please refer to 4. A first aspect of the present invention provides a method for removing redundant points in robotic arm path planning, including the following steps:

[0065] Step S100: Obtain the original point sequence for the path planning of the robotic arm.

[0066] The original discrete path point sequence of the robotic arm's motion trajectory is obtained through environmental sensing devices or upper-level planning systems. These original path points carry key information such as environmental obstacle avoidance constraints and motion geometry features. Their distribution density directly affects the subsequent computational efficiency and feature preservation integrity. When the original point set is too dense, it will increase the burden of redundant processing, while when the point set is too sparse, it may lead to feature loss problems such as those encountered in the triangular pruning method. The above steps maintain the integrity of the original data without preprocessing, laying the foundation for accurate extraction of path geometry features in the subsequent process.

[0067] Step S200: Calculate the shortest distance between each intermediate point of the original path planning point sequence and the baseline straight line based on the start and end points of the original path planning point sequence, and form a key point set of all original path planning points whose shortest distance value is greater than the preset residual threshold.

[0068] An improvement upon the Douglas-Peucker algorithm framework is made by constructing a baseline line by connecting the first and last endpoints of the current path subsequence. The perpendicular distance from each intermediate point to this line is calculated to measure the saliency of its path features. A filtering mechanism using a preset residual threshold retains only path points whose deviation from the baseline line exceeds the threshold, forming a keypoint set. These selected keypoints are essentially turning points in the path with high geometric feature contributions (such as key obstacle avoidance locations). The residual threshold plays a crucial regulatory role here: increasing the threshold improves the redundancy removal rate but may weaken the ability to capture detailed features, while decreasing the threshold enhances feature preservation but reduces path compression efficiency.

[0069] Step S300: If the key point set is empty, retain the endpoints of the current path sequence as feature points. If it is not empty, combine the weight parameters to select the optimal split point, divide the current path sequence into subsequences and recursively process them until all subsequences can no longer be divided, then retain their endpoints as feature points. Based on all feature points, obtain the path planning retained point set after removing redundant points.

[0070] First, the state of the key point set is determined: if the set is empty, the endpoints of the current path segment are directly retained; if the set is not empty, a dual-weight control mechanism is used to achieve synergy between feature retention and distribution optimization. Specifically, an objective function that integrates the feature intensity weight and distance balance weight of path points is used to dynamically evaluate the comprehensive value of each key point. The feature intensity weight ensures that key features such as obstacle avoidance turning points are not missed, while the distance balance weight promotes the uniformity of the spatial distribution of path points. Based on the segmentation points selected by the objective function, the current path segment is divided into two subsequences, and the subsequences are optimized step by step through recursive processing. The above mechanism fundamentally solves the contradiction between "feature retention" and "uniform distribution" in traditional algorithms: it avoids the risk of obstacle avoidance failure of the robotic arm due to feature loss, and eliminates the Runge phenomenon in trajectory interpolation caused by uneven point distribution (manifested as abrupt changes in curvature between adjacent points), ultimately forming an optimized path point set that combines feature integrity and motion stability.

[0071] Furthermore, in step S300, if the set of key points is empty, the endpoints of the current path sequence are retained as feature points, including:

[0072] Step S311: If the key point set is empty, then the starting point and ending point of the original point sequence of the current path planning are taken as feature points.

[0073] When the keypoint set is empty, it indicates that the vertical distance from all intermediate points in the current path subsequence to the first and last endpoints does not exceed the residual threshold. That is, the path segment has the geometric characteristics of an approximately straight line, and there are no feature points that significantly deviate from the straight trajectory (such as turning points or curvature abrupt changes required for obstacle avoidance). In this case, the first and last endpoints are retained as feature points, following the optimization principle of path simplification: representing the geometric essence of the path with the fewest possible keypoints.

[0074] Further, in step S300, if the value is not empty, the optimal split point is selected by adjusting the weight parameters, and the current path sequence is divided into subsequences and processed recursively until all subsequences can no longer be divided. Then, their endpoints are retained as feature points. Based on all feature points, a set of path planning retained points after removing redundant points is obtained, including:

[0075] Step S321: If the set of key points is not empty, calculate the distance values ​​between each key point and the starting point and the ending point, and calculate the target value of each key point by combining the straight-line distance weight and the point distance weight.

[0076] When the keypoint set is not empty, a collaborative optimization process for feature preservation and distribution balancing is initiated. For each keypoint in the set, two core indicators are calculated simultaneously: the vertical distance from the point to the baseline (representing the strength of its geometric features deviating from the straight path) and the difference in straight-line distances from the point to the first and last endpoints (reflecting the spatial distribution balance). By introducing a dynamic adjustment mechanism for feature strength weights and distance balance weights, these two indicators are integrated into a single target value. The feature strength weight prioritizes the preservation of high-feature contribution points such as obstacle avoidance keypoints, while the distance balance weight promotes the uniformity of the spatial distribution of path points. The weight allocation is flexibly adapted to different scenario requirements; the distance balance weight can be increased when motion stability needs to be enhanced, and the feature strength weight can be increased when complex path features need to be guaranteed.

[0077] Step S322: Take the key point with the largest target value in the current path planning original point sequence as the split point, and divide the current path planning original point sequence into two sub-sequences.

[0078] Based on the target value calculated in step S321, the key point with the best comprehensive evaluation is selected as the split point. Maximizing the target value means that the point simultaneously satisfies two conditions: it is both the most geometrically significant turning point in the current path segment (such as a key obstacle avoidance location) and relatively close to the central region of the beginning and end endpoints in spatial distribution (optimizing the uniformity of point spacing). After selecting the split point, the current path segment is divided into two sub-sequences. The path is split by feature-significant points to ensure that key features such as obstacle avoidance turning points are preserved. Feature points with central positions are preferentially selected for splitting, which makes the lengths of the subsequently recursively generated sub-sequences approach similar, laying the foundation for a uniform distribution of path points.

[0079] Step S323: Return each subsequence to step S200 until the key point set of all subsequences in step S200 is empty, and list the start and end points of the subsequences as feature points. Based on all feature points, obtain the path planning retained point set after removing redundant points.

[0080] Construct a complete recursive processing loop: Treat the segmented subsequences as new processing units, and re-execute feature point selection (step S200) and dual-weight optimization (steps S321-S322). The recursion depth is determined by the geometric complexity of the path. For feature-rich path segments, segmentation continues until the keypoint set is empty; for near-straight path segments, endpoints are directly retained (step S311). When all subsequences cannot be further segmented, the endpoints and segmentation points retained at each level are integrated to form the final feature point set.

[0081] This recursive divide-and-conquer structure achieves local optimization accumulation by decomposing the path sequence step by step: each subsequence independently performs feature point selection and dual-weight optimization, ensuring that the local path segment has both feature integrity and point distribution uniformity; at the same time, the recursion depth and path geometric complexity are adaptively matched, and the near-straight line segments with sparse features quickly converge to the endpoints for simplification, while the feature-dense segments are deeply segmented to retain key turning points, significantly improving computational efficiency; the final integrated feature point set achieves dual protection at the motion planning level: it not only completely retains all obstacle avoidance key feature points in the original path, but also provides ideal input conditions for trajectory interpolation through global uniform distribution, thereby forming a highly reliable robotic arm motion trajectory.

[0082] Furthermore, the formula for calculating the target value is:

[0083]

[0084] Among them, w d The straight-line distance weight value, d i w represents the shortest distance from the i-th keypoint in the current path sequence to the baseline. m The distance to the point is the weight value. This represents the straight-line distance from the i-th keypoint in the current path sequence to the starting point of the current path sequence. This is the straight-line distance from the i-th key point in the current path sequence to the end point of the current path sequence.

[0085] The above target value calculation formula achieves synergistic optimization of path feature preservation and point distribution balance through a dual-weight control mechanism: the product of feature intensity weight and the perpendicular distance from the key point to the baseline line strengthens the priority of preserving feature contribution points of equal height at obstacle avoidance turning points (solving the feature loss defect of the traditional triangular pruning method); the product of distance balance weight and the difference in distance from the key point to the beginning and end endpoints drives the algorithm to prioritize the selection of centrally located feature points as split points, macroscopically promoting a more uniform spatial distribution of the preserved point sequence (overcoming the Runge phenomenon caused by uneven point spacing in the traditional Douglas-Peucker algorithm). The dynamic adjustment of the two weight parameters forms a flexible adaptability—increasing the feature intensity weight can adapt to complex obstacle environments and ensure motion safety, while increasing the distance balance weight optimizes the trajectory interpolation input conditions; the competitive evaluation framework constructed by the subtraction operation of the two fundamentally solves the inherent contradiction between feature integrity and distribution uniformity in path simplification, and finally outputs an optimized point set that both preserves the geometric essence of the original path and meets the requirements of trajectory planning stability.

[0086] Further, in step S323, each subsequence is returned to step S200 until the key point set of all subsequences in step S200 is empty, and the start and end points of the subsequences are listed as feature points. Based on all feature points, a path planning retained point set after removing redundant points is obtained, including:

[0087] Step S3231: Take the segmented first subsequence as the current path sequence, return to step S200, and recalculate the key point set of the first subsequence.

[0088] Taking the first subsequence as the new current path sequence and returning to perform keypoint detection (step S200) is essentially a refined processing of the local features of the path. Here, a keypoint selection algorithm based on minimum relative distance is recursively invoked: the vertical distance from all points in the subsequence to the line connecting the first and last ends is calculated, and combined with the difference in distance from that point to both ends, the optimal segmentation point is dynamically selected through a weighted objective function. This recursive hierarchical approximation mechanism ensures that the final retained points reflect both the path's turning features and avoid local point clustering.

[0089] In step S3232, if the set of key points of the first subsequence is not empty, a new splitting point is selected for secondary splitting to generate a secondary subsequence, and step S3231 is executed recursively.

[0090] When the set of key points in a subsequence is not empty, it indicates that there are still insufficiently expressed local features in that path segment. At this point, a new split point is selected for secondary segmentation, generating finer-grained secondary subsequences, and triggering recursion again. This process continues until the termination condition is met. Its core value lies in forcibly dispersing dense path points through multi-level segmentation. Especially when the weight of intermediate points is dominant, the algorithm tends to select points with close distances to the beginning and end as split points, thereby promoting a uniform distribution of retained points in geometric space and fundamentally avoiding Runge's phenomenon in subsequent trajectory interpolation.

[0091] Step S3233: If the key point set of the first subsequence is empty, then add the start and end points of the first subsequence to the feature point set.

[0092] When the set of key points for a subsequence is empty, it indicates that the path segment can be considered an approximately straight line segment, and there is no need to retain intermediate points. In this case, only the starting and ending points are included in the feature point set, significantly reducing redundant data. This rule directly echoes the technical effect described in this application: for straight path segments, traditional algorithms may retain too many meaningless points, while intelligent compression is achieved through recursive verification, which reduces the computational load of subsequent trajectory planning and avoids the loss of obstacle avoidance key points due to oversimplification.

[0093] Step S3234: Repeat steps S3231-S3233 for the second subsequence after segmentation.

[0094] Repeat the aforementioned recursive operation for the second subsequence to ensure the integrity of the segmentation process. It is worth noting that the recursion of the two subsequences is independent of each other but shares the same set of feature points. This allows the path segmentation process to be parallelized, ensuring that the uniformity standard of each part of the path curve is consistent, avoiding the introduction of new distribution imbalance points due to segmentation, and providing a globally coordinated node foundation for subsequent spline interpolation.

[0095] Step S3235: When the key point set after the segmentation step of all subsequences is empty, terminate the recursion and output the feature point set. After deduplication of the feature point set, obtain the path planning retained point set.

[0096] The recursion terminates and outputs the feature point set when the keypoint sets of all subsequences are empty. The final deduplication operation solves the problem of duplicate endpoint records that may be caused by multiple segmentations (such as shared endpoints between adjacent subsequences). This step marks that the algorithm has achieved its dual objectives: first, controlling the feature fidelity of retained points through recursion depth; second, suppressing curvature abrupt changes through a uniformly distributed point set. The output can be directly used in trajectory planning methods such as polynomial interpolation without additional point distribution optimization.

[0097] In the above implementation, after the original path is divided into two subsequences through intermediate points, each subsequence needs to be re-evaluated to see if there are any key points that need to be retained. This recursive process ensures that path features can be captured at multiple levels: if a subsequence still has points that significantly deviate from the path trend (i.e., the set of key points is not empty), then the subsequence is further divided; conversely, if the subsequence is sufficiently smooth (the set of key points is empty), then only its starting and ending points are retained as feature points. This design directly serves the core innovation of this application—optimizing the uniformity of point distribution while retaining path features.

[0098] Furthermore, after obtaining the set of path planning retained points after removing redundant points in step S300, the process also includes:

[0099] Step S410: Obtain the rate of curvature change of the set of retained points for path planning.

[0100] After removing redundant points, a curvature change rate analysis is performed on the set of retained points in the path planning. The curvature change rate reflects the drastic change in path direction and is a core indicator for measuring trajectory smoothness. In this application, the curvature change rate is calculated based on the feature point sequence formed after removing redundant points. Discrete point differential geometry methods (such as the three-point circle method or parametric equation differentiation) are used to quantify the rate of change of curvature in the local path. A high curvature change rate indicates abrupt changes in the trajectory, which may lead to sudden acceleration changes in the robotic arm joints, causing vibration or tracking errors; a low curvature change rate indicates that the path is too straight, potentially indicating insufficient redundancy compression.

[0101] Step S420: When the rate of change of curvature is greater than the first preset curvature threshold, the preset residual threshold is reduced according to the first preset ratio.

[0102] When the rate of curvature change exceeds a first preset threshold, it indicates that the current path segment has a sharp turn or abrupt change in direction. At this point, the preset residual threshold is reduced by a first preset ratio, and the feature point density of this local path is enhanced. A smaller residual threshold allows the recursive segmentation algorithm to retain more points deviating from the straight path in step S200, thus more finely characterizing the path curvature features. This dynamic adjustment effectively solves the key contradiction pointed out in this application, achieving a balance between preserving path features and ensuring uniform distribution. The above operation, by increasing the number of feature points, distributes the path description burden in high curvature change areas, fundamentally suppressing curvature spikes (Runge phenomenon) that may occur in subsequent trajectory interpolation, ensuring smooth movement of the robotic arm during complex turns.

[0103] Step S430: When the rate of change of curvature is less than the second preset curvature threshold, the preset residual threshold is increased by the second preset ratio. The first preset curvature threshold and the second preset curvature threshold are the maximum and minimum values ​​of the preset curvature interval, respectively.

[0104] When the rate of change of curvature is lower than the second preset threshold, it means that the path segment is approximately a straight line or a gradually changing curve. At this time, the residual threshold is increased by the second preset ratio, triggering further simplification of redundant points. Smooth path segments do not require too many feature points to maintain trajectory fidelity. After increasing the residual threshold, the recursive segmentation algorithm will reduce the retention of intermediate points in step S200, and preferentially merge them into points with similar beginning and end distances. This not only reduces the computational complexity of trajectory planning, but also optimizes the spatial distribution of the point set, avoiding the retention of densely adjacent points in straight areas, thereby preventing local curvature distortion caused by excessively small point spacing. The above mechanism and step S420 form a closed-loop control, enabling the algorithm to dynamically adjust the allocation of accuracy resources according to the geometric characteristics of the path.

[0105] Furthermore, the formula for calculating the rate of change of curvature σ is:

[0106]

[0107] Where N is the number of path points in the current path sequence, θ k The turning angle of the k-th path point in the current path sequence. It is the average turning angle of several path points in the current path sequence.

[0108] The formula for calculating the rate of curvature change quantifies the fluctuation intensity of path curvature characteristics by statistically analyzing the dispersion of the turning angles of path points from their average values. It uses the variance of the turning angles as a proxy for the rate of curvature change. The turning angles directly reflect the degree of local directional change at a path point, while the variance calculation captures the uniformity of these directional changes across the entire path. When there are sharp turns in the path (such as sharp bends required for obstacle avoidance), the turning angles of some path points will deviate significantly from the average, leading to an increase in the rate of curvature change. In this case, step S420 lowers the residual threshold to force the retention of more feature points, thereby finely characterizing high-curvature regions. Conversely, when the path is gentle, the turning angles tend to be consistent, and the rate of curvature change decreases, triggering step S430 to increase the residual threshold to simplify the number of feature points and avoid redundant point aggregation that could cause curvature distortion in subsequent interpolation. This feedback mechanism based on geometric feature statistics dynamically optimizes the density distribution of feature point sets, overcoming the uneven point distribution defect of the traditional Douglas-Peucker algorithm and avoiding the contradiction between feature fidelity and distribution uniformity caused by a fixed residual threshold. Ultimately, it provides a path foundation for trajectory planning that combines motion stability and environmental adaptability.

[0109] Furthermore, after obtaining the set of path planning retained points after removing redundant points based on all feature points in step S300, the process also includes:

[0110] Step S510: Detect the distance between two adjacent path planning reserved points in the path planning reserved point set.

[0111] After removing redundant points, the set of retained points in the path planning is analyzed for the distance between adjacent points. This identifies potential local sparse regions in the path, where the abnormally large distance between points is caused by oversimplification of smooth path segments or insufficient segmentation of complex path segments in the recursive segmentation algorithm. When the distance between adjacent feature points is significantly greater than the average distance of the entire path, it indicates that the granularity of the path description in that interval is insufficient. This may force subsequent trajectory interpolation to use high-order polynomials to fit long-distance paths in this interval, leading to curvature instability (such as the Runge phenomenon) or discontinuous robot arm motion. By quantifying the Euclidean distance of each pair of adjacent points and comparing it with the global average distance, a data foundation is provided for subsequent adaptive interpolation.

[0112] Step S520: If the distance between two adjacent path planning reserved points is greater than a first preset multiple of the average distance between all two adjacent path planning reserved points in the path planning reserved point set, then an interpolation point is inserted between the two adjacent path planning reserved points so that the distance between each pair of adjacent path planning reserved points is less than a second preset multiple of the average distance.

[0113] When the distance between adjacent points exceeds a first preset multiple of the average distance (i.e., it is determined to be an abnormally sparse interval), an interpolation point is automatically inserted into that interval. The insertion strategy must ensure that the distance between adjacent points after the addition does not exceed a second preset multiple of the average distance. Essentially, this achieves global equalization of the path description granularity by forcibly constraining the maximum distance. Interpolation points are generated only based on existing retained points (such as linear interpolation or low-order polynomial interpolation), without introducing new path features, thus avoiding the destruction of key turning points retained by the original algorithm. By suppressing local maximum distances, the spatial distribution of the entire point set approaches uniformity, overcoming the uneven point set density defect that may occur in the traditional Douglas-Peucker algorithm. The above steps provide a node sequence with coordinated spacing for subsequent spline interpolation, ensuring that the length ratio of adjacent interpolation intervals is controllable, fundamentally eliminating curvature oscillations caused by abrupt changes in node distribution. This post-processing operation, together with the aforementioned curvature adaptive adjustment (steps S420-S430), provides a dual guarantee: curvature adjustment solves the feature density problem, and spacing adjustment solves the geometric distribution problem, jointly ensuring that the output point set simultaneously meets the requirements of motion stability and environmental adaptability.

[0114] like Figure 5a , Figure 5b , Figure 6a , Figure 6b , Figure 7a , Figure 7b , Figure 8a and Figure 8bAs shown, by increasing the residual ε, the characteristics of the original path points can be better preserved. It can also be seen that after removing redundant points and performing cubic spline interpolation, the robotic arm model does not exhibit Runge phenomenon. Even when increasing the residual ε to preserve the characteristics of the original path points to a greater extent, there is still no Runge phenomenon caused by uneven distribution of path points.

[0115] Accordingly, please refer to Figure 9 A second aspect of the present invention provides a device for removing redundant points in robotic arm path planning, which removes redundant points in the original point sequence of the robotic arm's path planning based on the above-described method for removing redundant points in robotic arm path planning, including:

[0116] Data acquisition module 1 is used to acquire the original point sequence for the path planning of the robotic arm;

[0117] Set construction module 2 is used to calculate the shortest distance between each intermediate point of the path planning original point sequence and the reference straight line based on the start and end points of the path planning original point sequence, and to form a key point set of all path planning original points whose shortest distance value is greater than a preset residual threshold.

[0118] The recursive processing module 3 is used to retain the endpoints of the current path sequence as feature points if the key point set is empty, and to select the optimal split point by combining the weight parameters if it is not empty, to split the current path sequence into subsequences and perform recursive processing until all subsequences can no longer be split, and to retain their endpoints as feature points. Based on all feature points, a set of path planning retained points after removing redundant points is obtained.

[0119] Accordingly, a third aspect of the present invention provides an electronic device, including: at least one processor; and a memory connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the above-described robotic arm path planning redundancy point removal method.

[0120] Accordingly, a fourth aspect of the present invention provides a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the above-described method for removing redundant points in robotic arm path planning.

[0121] The embodiments of the present invention aim to protect a method and apparatus for removing redundant points in robotic arm path planning, which has the following effects:

[0122] 1. Through an innovatively designed dual-weight objective function, the algorithm retains the path feature extraction capabilities of the traditional Douglas-Peucker algorithm while achieving proactive control over the uniformity of point distribution for the first time. When the point distance weight is increased, the algorithm prioritizes path points with relatively balanced distances from the beginning and end points as split points, macroscopically promoting a more uniform spatial distribution of the retained point sequence. By adjusting the straight-line distance weight, it can still ensure that key points that significantly contribute to the geometric features of the path (such as obstacle avoidance turning points) are retained first. The above-mentioned collaborative mechanism fundamentally overcomes the contradiction that "feature retention" and "uniform distribution" cannot be achieved simultaneously in traditional algorithms.

[0123] 2. Because the optimized path point set has both feature integrity and uniform distribution, it provides ideal input conditions for subsequent trajectory planning; by suppressing the problem of excessively small spacing between adjacent path points, it completely avoids the phenomenon of local curvature increase caused by uneven point distribution (i.e., Runge phenomenon) in methods such as polynomial interpolation and spline curves; even if the residual is increased to retain more features, the path points after removing redundancy can still maintain a smooth curvature transition after cubic spline interpolation, thereby ensuring the stability and continuity of the robotic arm's end effector motion;

[0124] 3. Based on the dual guarantee of feature point preservation and distribution optimization, two types of motion failure problems caused by path simplification are avoided from the root: First, by preserving key obstacle avoidance feature points, the simplified path is prevented from intruding into the obstacle area and causing collisions; second, the uniform point distribution ensures smooth joint motion after trajectory interpolation, avoiding robotic arm shaking or inverse solution failure caused by curvature abrupt changes; further, the curvature feedback is used to adjust the residual threshold and path point density to form a closed-loop optimization mechanism, ultimately improving the reliability and safety of the motion trajectory.

[0125] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0126] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0127] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0128] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0129] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A method for removing redundant points in robotic arm path planning, characterized in that, Includes the following steps: Step S100: Obtain the original point sequence for the path planning of the robotic arm; Step S200: Calculate the shortest distance between each intermediate point of the original path planning point sequence and the reference straight line based on the start and end points of the original path planning point sequence; and form a key point set by all original path planning points whose shortest distance value is greater than a preset residual threshold. Step S300: If the key point set is empty, the endpoints of the current path sequence are retained as feature points. If it is not empty, the optimal split point is selected by adjusting the weight parameters, the current path sequence is split into subsequences and recursively processed until all subsequences can no longer be split, and their endpoints are retained as feature points. Based on all feature points, the path planning retained point set after removing redundant points is obtained.

2. The method for removing redundant points in robotic arm path planning according to claim 1, characterized in that, The step S300, which states that if the key point set is empty, the endpoints of the current path sequence are retained as feature points, includes: Step S311: If the set of key points is empty, then the starting point and ending point of the original point sequence of the current path planning are taken as feature points.

3. The method for removing redundant points in robotic arm path planning according to claim 1, characterized in that, If the condition in step S300 is not empty, the optimal split point is selected by adjusting the weight parameters, the current path sequence is divided into subsequences and processed recursively until all subsequences can no longer be divided. Then, their endpoints are retained as feature points. Based on all feature points, a set of path planning retained points after removing redundant points is obtained, including: Step S321: If the set of key points is not empty, calculate the distance values ​​between each key point and the starting point and the ending point respectively, and calculate the target value of each key point by combining the straight line distance weight and the point distance weight. Step S322: Take the key point with the largest target value in the current path planning original point sequence as the split point, and divide the current path planning original point sequence into two sub-sequences; Step S323: Return each of the subsequences to step S200 until the set of key points of all subsequences in step S200 is empty, and list the start and end points of the subsequences as feature points, and obtain the set of path planning retained points after removing redundant points based on all feature points.

4. The method for removing redundant points in robotic arm path planning according to claim 3, characterized in that, The formula for calculating the target value is: Among them, w d The straight-line distance weight value, d i w represents the shortest distance from the i-th keypoint in the current path sequence to the baseline. m The distance to the point is the weight value. This represents the straight-line distance from the i-th keypoint in the current path sequence to the starting point of the current path sequence. This is the straight-line distance from the i-th key point in the current path sequence to the end point of the current path sequence.

5. The method for removing redundant points in robotic arm path planning according to claim 3, characterized in that, Step S323 involves returning each subsequence to step S200 until the key point set of all subsequences in step S200 is empty, and listing the start and end points of the subsequences as feature points. Based on all feature points, a path planning retained point set after removing redundant points is obtained, including: Step S3231: Take the segmented first subsequence as the current path sequence, return to step S200, and recalculate the key point set of the first subsequence; Step S3232: If the set of key points of the first subsequence is not empty, then select a new splitting point for secondary splitting to generate a secondary subsequence, and recursively execute step S3231. Step S3233: If the key point set of the first subsequence is empty, then add the start and end points of the first subsequence to the feature point set. Step S3234: Repeat steps S3231-S3233 for the second subsequence after segmentation; Step S3235: When the key point set after the segmentation step of all subsequences is empty, terminate the recursion and output the feature point set. After deduplication of the feature point set, obtain the path planning retained point set.

6. The method for removing redundant points in robotic arm path planning according to claim 1, characterized in that, After obtaining the set of path planning retained points after removing redundant points in step S300, the method further includes: Step S410: Obtain the rate of curvature change of the set of retained points for path planning; Step S420: When the rate of change of curvature is greater than the first preset curvature threshold, the preset residual threshold is reduced according to the first preset ratio. Step S430: When the rate of change of curvature is less than the second preset curvature threshold, the preset residual threshold is increased according to the second preset ratio. Wherein, the first preset curvature threshold and the second preset curvature threshold are the maximum and minimum values ​​of the preset curvature range, respectively.

7. The method for removing redundant points in robotic arm path planning according to claim 6, characterized in that, The formula for calculating the rate of change of curvature σ is: Where N is the number of path points in the current path sequence, θ k The turning angle of the k-th path point in the current path sequence. It is the average turning angle of several path points in the current path sequence.

8. The method for removing redundant points in robotic arm path planning according to any one of claims 1-7, characterized in that, After obtaining the set of path planning retained points after removing redundant points based on all feature points in step S300, the method further includes: Step S510: Detect the distance between two adjacent path planning reserved points in the path planning reserved point set; Step S520: If the distance between two adjacent path planning reserved points is greater than a first preset multiple of the average distance between all two adjacent path planning reserved points in the path planning reserved point set, then an interpolation point is inserted between the two adjacent path planning reserved points so that the distance between each pair of adjacent path planning reserved points is less than a second preset multiple of the average distance.

9. A device for removing redundant points in robotic arm path planning, characterized in that, The redundant points in the original point sequence of the robotic arm path planning are removed based on the method for removing redundant points in robotic arm path planning as described in any one of claims 1-8, including: The data acquisition module is used to acquire the original point sequence for the path planning of the robotic arm; A set construction module is used to calculate the shortest distance between each intermediate point of the original point sequence of the path planning and the reference straight line based on the start and end points of the original point sequence of the path planning, and to form a key point set of all original points of the path planning with the shortest distance value greater than a preset residual threshold. The recursive processing module is used to retain the endpoints of the current path sequence as feature points if the key point set is empty, and to select the optimal split point by combining the weight parameters if it is not empty. The current path sequence is then divided into subsequences and recursively processed until all subsequences can no longer be divided, at which point their endpoints are retained as feature points. Based on all feature points, a set of path planning retained points after removing redundant points is obtained.

10. An electronic device, characterized in that, include: At least one processor; And a memory connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to cause the at least one processor to perform the robotic arm path planning redundancy point removal method as described in any one of claims 1-8.

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