A robot workspace partitioning method based on non-probabilistic reliability

Abstract

The application discloses a robot workspace partitioning method based on non-probability reliability, and belongs to the technical field of industrial robot calibration.The application adopts a partitioning optimization design method of a fuzzy C-means clustering algorithm combined with a genetic algorithm according to the non-probability reliability difference of a robot end position in different workspace ranges, and performs two-stage hierarchical partitioning on a robot Cartesian full workspace domain, including hierarchical partitioning and interval re-subdivision under the hierarchical partitioning.The application can improve the absolute positioning accuracy of a large workspace robot, and provide a theoretical basis for formulating classification calibration and error compensation strategies under different work partitions.The application partitions a robot Cartesian three-dimensional workspace, and the partitioning is detailed and reasonable, and the partitioning result is intuitive, so that the application is convenient for understanding and subsequent fine and accurate calibration and compensation, and can effectively improve the reliability and spatial adaptability of subsequent parameter calibration and compensation in a full workspace domain of the robot, and improve the absolute positioning accuracy of the robot.

Description

Technical Field

[0001] This invention belongs to the field of industrial robot calibration technology. Specifically, it relates to a partitioning optimization design method that combines fuzzy C-means clustering algorithm with genetic algorithm to partition the robot's Cartesian full workspace domain into a two-stage hierarchical partitioning method, including hierarchical division and further subdivision of intervals under each hierarchical layer, based on the non-probabilistic reliability differences of the robot's end-effector pose in different workspace ranges. This provides a basis for subsequent partitioning calibration compensation. Background Technology

[0002] With the rapid development of the intelligent manufacturing industry, replacing manual labor with robots to complete tasks is a major development direction for industrial transformation and upgrading. However, due to uncertainties, the insufficient absolute positioning accuracy of robot end-effectors has become the biggest obstacle to their application in high-end manufacturing. Currently, the repeatability of industrial robots has reached a very high level, and their development is most limited by absolute positioning accuracy. Lower absolute positioning accuracy will have a huge negative impact on the efficiency, accuracy, and stability of component processing and assembly, resulting in failure to meet operational requirements. Therefore, research on the reliability of industrial robot positional accuracy is of profound significance.

[0003] Extensive research has been conducted by scholars both domestically and internationally on the topic of positional accuracy and reliability of industrial robots. Regarding the handling of robot uncertainties and reliability analysis, Zhang Xiaojin et al. conducted motion reliability analysis on an arc welding robot based on the Mean Value First Order Second Moment (MVFOSM) method. However, due to the high nonlinearity of the robot's kinematic model, the MVFOSM analysis has low accuracy. Zhang reduced the position variables of the end effector to a function of three independent standard normal variables to represent the error, and applied the DR-saddlepoint approximation (SPA) method to analyze reliability. Wu et al., on the other hand, used a point estimation method to calculate the first four moments of the positioning point to determine the probability density function of the position error. Chen Huiqing constructed a motion reliability model to address the impact of various motion failure modes and their correlations during the operation of palletizing robots, and proposed a reliability solution method based on variable state space; Jiang Wensong attempted to construct a mathematical relationship between uncertain parameter components and the robotic arm model through large-scale Monte Carlo stochastic numerical simulation, and realized a method for evaluating parameter calibration uncertainty; Tang considered the interval uncertainty of joint gaps and proposed a non-probabilistic positioning accuracy reliability measurement method for robot end effectors, analyzed the displacement error interval and motion reliability of end effectors in different workspace areas, but did not further study the non-probabilistic reliability calibration of robots.

[0004] Regarding parameter identification and calibration reliability, Naveen established a linear regression model based on the conservation of momentum and angular momentum, and applied the recursive least squares method to identify the inertial parameters of a 12-DOF on-orbit service dual-arm space robot; Wei accurately identified the parameters of a 2-DOF flexible joint robot dynamic model by setting a compact series of elastic actuators on each joint; Icli et al. used the "TriCal" measurement device to achieve automatic calibration of all kinematic and joint stiffness parameters of the robot; Li Jun proposed a parameter identification method based on feature vector selection multi-output support vector machine for strongly coupled and highly nonlinear robot identification problems; Zhang Chuntao focused on "zero To address the "drift" interference, an online calibration method for a six-dimensional force sensor of a robot was proposed; Zhang Chenglin et al. used the damped least squares method for robot calibration; Jiang Xiaocan analyzed the relationship between the magnitude of parameter error and the reliability of robot pose accuracy based on the MD-H model; Cui Weixiang et al. studied the reliability of robot calibration based on the Monte Carlo method; Zhao Bin, considering the randomness of the actual zero-position parameters of the robot, proposed a zero-position parameter calibration method based on spatial clustering, which improved the reliability of calibration; Sun Jianping et al., comprehensively considering the influence of the interval uncertainty of the parameters of each link of the robot on the pose accuracy, proposed a new method for robot positioning accuracy and non-probabilistic reliability of calibration, but did not further propose the idea of ​​zonal calibration of the entire workspace.

[0005] Large, high-end equipment robots perform precision operations within extremely large workspaces and are subject to numerous uncertainties. These uncertainties influence the robot's pose, exhibiting non-uniform spatial distribution, ultimately stemming from differences in model parameter identification. Current robot parameter identification and error compensation methods are largely based on deterministic, probabilistic, or fuzzy approaches. Deterministic methods ignore the impact of uncertainties in the robot system; probabilistic or fuzzy methods often suffer from insufficient statistical samples in engineering, making it impossible to know the probability distribution or fuzzy membership degree beforehand, and thus difficult to accurately define the probabilistic or fuzzy model, resulting in insufficient accuracy in parameter identification and error compensation. In contrast, interval non-probabilistic methods only require knowledge of the upper and lower bounds of uncertain parameter values, making them more advantageous for uncertainty analysis in situations with small samples and limited information.

[0006] Xu Changjun (Xu Changjun. Research on Kinematic Calibration Technology of Industrial Robots Based on MDH Model [D]. Harbin: Harbin Institute of Technology, 2017.) conducted calibration experiments in a small local workspace and found that reducing the calibration space can improve the absolute positioning accuracy of the robot within the calibration space. However, current calibration methods almost all focus on the global workspace and treat the robot's kinematic parameters in the entire workspace domain as the same constant. They do not consider the differences in the impact of uncertainties on the robot's pose accuracy in different local workspace domains, nor do they consider that the kinematic parameters may vary within a certain range due to the combined effects of uncertainties. Only Li Jituo et al. of Zhejiang University (CN 114714348 A) proposed a calibration compensation method based on joint space partitioning. This method starts from the joint space perspective, analyzes the impact of various errors on the end-effector position error in the joint space, and uses the relationship between the robot joint angle and residual error to cluster points with similar joint space distances and error values ​​to guide the division of joint space regions, achieving a better calibration compensation effect. However, Li Jituo et al.'s method, based on joint space partitioning, requires a precise description of the motion state of each joint of the robot. The description method is complex and not intuitive enough, and it is not convenient to observe and analyze the robot's motion state in three-dimensional space. More importantly, this method does not start from improving the robot's positioning accuracy and calibration non-probabilistic reliability, analyze the difference in the impact of uncertainty parameters on the robot's end-effector positioning accuracy in different workspace domains under the Cartesian coordinate system, and partition the entire workspace domain according to the non-probabilistic reliability index of positioning accuracy. As a result, their method is insufficient in improving the spatial adaptability of the robot's positioning accuracy non-probabilistic reliability. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the existing technology. Considering the differences in the impact of uncertain parameters on the positioning accuracy of the robot end effector in different workspace domains, which will cause differences in the range of coordinate point position errors and the reliability of positioning accuracy in different workspace domains, this invention proposes a robot workspace partitioning method based on nonprobabilistic reliability.

[0008] This invention focuses on the set of spatial points reachable by the robot's end effector within its entire workspace. It investigates a non-probabilistic reliability measurement method for the actual positional accuracy of these points. Based on the differences in non-probabilistic reliability of the robot's end effector pose across different workspace regions, a partitioning optimization design method combining fuzzy C-means clustering and genetic algorithms is employed. This method partitions the robot's Cartesian workspace domain in a two-stage hierarchical manner, including hierarchical division and further subdivision of intervals within each hierarchical layer. This ensures that the impact of the robot's uncertain parameters on the end effector position, the range of positional errors, and the reliability of positioning accuracy are similar within the same sub-workspace domain after partitioning. This provides a basis for more accurate calibration and compensation within each sub-workspace under the workspace partitioning framework. This invention is of significant value in reducing end effector position errors across the entire workspace and improving the reliability and spatial adaptability of parameter calibration and compensation within the robot's entire workspace domain.

[0009] This invention is achieved through the following technical solutions.

[0010] The robot workspace partitioning method based on non-probabilistic reliability described in this invention includes the following steps:

[0011] Step S1: Establish the kinematic model of the industrial robot based on the DH parameter method;

[0012] Step S2: Considering the influence of uncertainties, set parameterized variables for joint shaft hole fit clearance and link length and offset distance to establish a robot parameterized model;

[0013] Step S3: Obtain the robot workspace cloud map using the Monte Carlo method, and select an appropriate number of coordinate points in the workspace based on the optimal Latin hypercube.

[0014] Step S4: Obtain the position error data of the coordinate points through the parameterized model, and measure the reliability of the position accuracy of the coordinate points according to the non-probability interval theory.

[0015] Step S5: Solve for the non-probabilistic reliability index of the coordinate point location;

[0016] Step S6: Based on the non-probabilistic reliability of the robot's end-effector position, a partitioning optimization design method combining fuzzy C-means clustering algorithm and genetic algorithm is adopted to realize the first stage of stratification in the robot's workspace partitioning;

[0017] Step S7: For each layer of the workspace after hierarchical division, based on the non-probabilistic reliability of the robot end position point, a partition optimization design method combining fuzzy C-means clustering algorithm and genetic algorithm is adopted to realize the further subdivision of the interval under the second stage of hierarchical division in the robot workspace partitioning.

[0018] Step S8: Position accuracy reliability analysis and effect verification under workspace partitioning.

[0019] Furthermore, the step S1, which establishes the kinematic model of the industrial robot based on the DH parameter method, specifically includes:

[0020] Based on the DH parameter method, taking links i-1 and i as examples, the link parameters are defined as follows: link length a i For from z i-1 axis to z i axis along x i The distance between axes; the torsion angle α of the connecting rod. i For z i-1 axis to z i Axis around x i The angle of rotation around the axis is defined as about x. i Right-hand rotation of the axis is positive; offset distance d i For x i-1 axis to x i axis along z i-1 Distance between axes; joint rotation angle θ i For x i-1 axis to x i Axis around z i-1 The angle of rotation around the axis is defined as about z. i-1 A right-handed rotation of the axis is positive.

[0021] Let A be the transformation matrix from joint i-1 to joint i. i Then the homogeneous transformation matrix of the robot is:

[0022] A = A1A2…A i

[0023] The coordinate system from joint i-1 to joint i can be obtained by revolving around z. i axis and x i It is described by a combination of axis translation and rotation, with the specific transformation matrix using... express:

[0024]

[0025] The pose information of the robot's end effector in the base coordinate system is:

[0026]

[0027] In the above formula, (n x ,n y ,n z ) T , (o x ,o y ,o z ) T ,(a x ,ay ,a z ) T These represent the direction vectors of the robot's end effector in the x, y, and z directions in the base coordinate system, respectively; (p x ,p y ,p z ) T Let be the position vector of the robot's end effector in the base coordinate system.

[0028] Furthermore, in step S2, considering the influence of uncertainties, parameterized variables are set for the joint shaft hole fit clearance and link size to establish a robot parameterized model, specifically including:

[0029] Due to numerous uncertainties such as manufacturing and installation errors, elastic deformation, kinematic pair clearances, friction, and chatter, industrial robots experience subtle deviations during movement, affecting the absolute positioning accuracy and reliability of the robot's end effector. Conventional robot dynamics models have fixed structural dimensions, making it impossible to simulate and analyze the impact of these uncertainties on the end effector's position error. Therefore, this invention proposes a parametric modeling method for uncertainty. Specifically, at the joint connections of the model, circular rings and cylinders coaxial with the revolute joints are established to simulate mating holes and shafts. Boolean operations are then used to integrate the newly created components with the robot model, and the joint hole radius, link length, and offset distance are set as parametric variables with a certain error range. The advantage of this parametric modeling method is that by controlling the relationships or values ​​between parametric variables, the model's joint hole radius and link length and offset distance can be driven to change, thereby generating robot dynamics simulation models with different mating relationships and different link lengths and offset distances, providing a model foundation for subsequent dynamics analysis. The parametric processing of robot joint clearances and link dimensions is crucial.

[0030] There are many reasons for joint clearance. For example, in order to achieve flexible rotation, robot joints are designed with clearance fit from the beginning. Manufacturing or assembly errors, wear and tear between parts, etc. can all cause changes in clearance. Figure 3 The diagram shows the vector image of the gap at a certain joint connection. It can be seen that the axis position has shifted. Assuming p is the center of the axis (hole) at the joint connection, and o is the center of the hole at the previous joint connection, then op is the ideal rod length. However, in actual operation, the axis center p will randomly shift during rotation. The shifted axis center is c, and the maximum shift is pc. Therefore, the actual rod length from the previous joint to this joint after the shift can be considered as oc. This refers to the error vector generated by the joint clearance during motion. The link parameter error caused by the joint clearance can be expressed as a formula:

[0031]

[0032] In the formula, L is the actual link length affected by the joint clearance; l is the theoretical link length; and x and y are the components of the vector decomposition of the joint clearance.

[0033] x 2 +y 2 ≤|a| 2

[0034] Due to the influence of joint clearance, the length of pc cannot be ignored, and since the center c of the axis is randomly distributed within the error circle, the clearance vector of each joint... They are also different; the randomness of the joint gaps will inevitably lead to the randomness of the execution endpoint.

[0035] Figure 4 (a) shows a schematic diagram of the joints of an industrial robot. The robot’s movement in space depends on the cooperation of the six joints. By inputting the rotation angle of each joint, the robot end can be driven to reach the specified position. Figure 4 (b) represents the positional error of the robot's end effector in space under the influence of joint clearance errors. It can be seen that the clearance error at each joint causes changes in the position and length of the links relative to the ideal state. The cumulative effect is ultimately reflected in the positional error of the end effector point P1 relative to the theoretical point P0. Let the clearance vectors offset at each joint be s1, s2, s3, s4, s5, and s6, then we can obtain:

[0036]

[0037] In the formula, The positional error of the end effector is obtained by summing the gap vectors of the six joints. This formula reveals the influence of joint gaps on the reliability of the robot's end effector positioning accuracy.

[0038] For a 6-joint robot, there are 6 joints, so 12 parameterized axes and holes need to be created. Specifically, at each joint connection point of the model, a ring and a cylinder coaxial with the revolute joint are created to simulate the mating holes and shafts. Boolean operations are used to integrate the newly created parts with the robot model, and the radius dimensions of the parts are set as variables with an error range. For a 6-joint robot, 12 parameterized axes and holes need to be created, with the radius variables represented by DV1 to DV12 respectively. See details... Figure 5 After establishing six sets of parameterized models for joint clearances, the radius variables of each joint shaft hole are given. Based on the process and precision requirements for robots in the equipment manufacturing industry, the joint adopts the H6 / h5 standard for hole basis and sets the specific values ​​of the variables.

[0039] Similarly, for all links in the robot model, add link length and offset distance as parameterized variables, see details below. Figure 5 The specific values ​​of a1, d1, a2, a3, d4, and d6, the link length and offset distance variables, should be set based on the nominal values, taking into account manufacturing tolerances.

[0040] The specific robot parameterization model established is as follows: Figure 5 As shown.

[0041] Once the parametric model is built, simulation analysis of the robot can be performed. By connecting each joint with a revolute joint and simulating a more realistic simulation environment by treating the contact force as the contact friction between the shaft and the hole, the simulation environment can be improved.

[0042] Furthermore, in step S3, the Monte Carlo method is used to obtain the robot's workspace cloud map, and an appropriate number of coordinate points are selected in the workspace based on the optimal Latin hypercube. Specifically, this includes:

[0043] When a robot's joints perform all possible movements within their rotational range, the set of spatial points reached by these movements is considered the robot's workspace. The actual workspace is quite complex and requires experimental design to determine its specific range. By deriving the forward kinematics formula in step S1, the pose information of the robot's end effector can be obtained, where [p x ,p y ,p z ] T This refers to the end position information, specifically the x, y, and z coordinates of the end in the Cartesian coordinate system.

[0044]

[0045] The Monte Carlo method is used to randomly select values ​​for the rotation angles of the six joints to obtain the end-effector coordinates. Theoretically, as long as the number of times the values ​​are taken is large enough and non-repeating, the set of different end-effector coordinates obtained can be considered as an approximately complete workspace. The specific operation is implemented in MATLAB. First, the range of rotation angles on each joint is limited. After the given range, the rand function is used to randomly select values ​​for the joint angles.

[0046] θ i =θ i min +(θ i max -θ i min rand(N,1)(i=1,…,6)

[0047] In the formula, θ i max θ i minLet $\mathbf{i}$ and $\mathbf{i}$ represent the maximum and minimum values ​​of the range of rotation angles of joint $i$, respectively; $N$ is the number of iterations.

[0048] The obtained workspace range is imported into the Isight software, and the coordinate points within the workspace are sampled using the optimal Latin hypercube.

[0049] Furthermore, in step S4, the position error data of the coordinate points are obtained through a parameterized model, and the reliability of the position accuracy of the coordinate points is measured according to the non-probability interval theory, specifically including:

[0050] The algebraic method is used to obtain multiple sets of inverse solutions for the coordinate points extracted in the workspace, and the optimal inverse solution is obtained by the "shortest stroke" rule. The corresponding robot joint angles are input into the parameterized model for multiple solutions to obtain the actual coordinate value range of the coordinate points. The results are exported and the difference is calculated with the theoretical coordinate values ​​to obtain the position error range of the sampled coordinate points.

[0051] In actual work, robots are affected by many non-probabilistic uncertainties, so the non-probabilistic interval theory is used to measure the obtained interval error parameters.

[0052] The reliability model for the position accuracy of the robot end effector based on non-probabilistic interval theory is shown below:

[0053]

[0054] In the formula, r u r is the maximum permissible value for position error. l s is the minimum permissible value for position error. u s represents the maximum position error. l This represents the minimum positional error. R set ∈[0,1] represents the reliability of the coordinate point position accuracy. The closer the value is to 1, the higher the reliability, and vice versa.

[0055] Furthermore, the non-probabilistic reliability index for solving the coordinate point position in step S5 specifically includes:

[0056] During robot movement, the position of its end effector constantly changes due to numerous uncertainties, resulting in varying positional errors and consequently, inconsistent reliability of the robot's positioning accuracy. The reliability evaluation metrics for robot positional accuracy can be appropriately selected based on operational needs. Taking the errors in the three coordinate components (x, y, z) and distance of the end effector as an example, based on a given permissible error range, the errors ΔX, ΔY or ΔZ of the three coordinate components and the distance error are evaluated. Substitute the reliability model of the robot end effector position accuracy based on the non-probabilistic interval theory constructed in step S4 into the non-probabilistic reliability calculation to obtain the non-probabilistic reliability index of the coordinate point position.

[0057] In specific operational situations, the position offset error in a single spatial coordinate direction or two coordinate directions can also be considered in particular.

[0058] Furthermore, in step S6, based on the non-probabilistic reliability of the robot's end-effector position, a partitioning optimization design method combining fuzzy C-means clustering and genetic algorithms is used to achieve the first-stage stratification in the robot's workspace partitioning, specifically including:

[0059] The distribution of a robot's workspace significantly impacts the positioning accuracy of the end effector. Therefore, researching reasonable workspace partitioning is crucial for developing classification error compensation strategies for different partitions. Thus, employing a fuzzy C-clustering mean algorithm with non-probabilistic characteristics, combined with a genetic algorithm for partition optimization design, is a good choice. This partitioning is achieved by introducing a membership index. Let... For the dataset, V = {v1, v2, ..., v...} C} are the cluster centers, there are c in total, and x are the samples. j (j = 1, 2, ..., n) for cluster centers v i The membership matrix of (i = 1, 2, ..., c) is u = {u ij} c×n ∈M fcn v i ∈R s , 2≤c <n;

[0060] All datasets are divided into c cluster centers using a clustering algorithm, and the membership degree of each dataset to its respective cluster center is u. ij ∈[0,1],u ij The larger the value, the higher the similarity of the data information;

[0061] Its clustering partitioning optimization model is defined as:

[0062]

[0063]

[0064] In the formula, m is a fuzzy weight exponent that controls the clustering results, and 1 <m<+∞;d ij ΔR represents the Euclidean distance between the j-th sample and the i-th cluster center; Xset(ij) ΔR Yset(ij) ΔR Zset(ij) ΔR Dset(ij)Let limΔR be the difference in nonprobabilistic reliability of the j-th sample relative to the i-th cluster center in the three coordinate directions and the distance direction, respectively; Xset ,limΔR Yset 、imΔR Zset ,limΔR Dset These are the permissible values ​​for the differences in nonprobabilistic reliability in the three coordinate directions and the distance direction, respectively.

[0065] Cluster center v i and membership matrix u ij The calculation formula is as follows:

[0066]

[0067]

[0068] To achieve detailed partitioning of the workspace, this invention employs a two-stage hierarchical partitioning method, consisting of a stratified layer and further subdivisions of intervals within that stratified layer. Step S6 first uses the non-probabilistic reliability values ​​of each spatial coordinate point, based on the constructed clustering partitioning optimization model, and employs a fuzzy C-means clustering algorithm combined with a genetic algorithm to divide all coordinate points into several layers, thus achieving the first stage of the two-stage hierarchical partitioning method: stratification.

[0069] Furthermore, in step S7, for each layer of the hierarchically divided workspace, based on the non-probabilistic reliability of the robot's end-effector position points, a partitioning optimization design method combining fuzzy C-means clustering and genetic algorithms is used to achieve further subdivision of the intervals under the second-stage hierarchical partitioning of the robot's workspace. Specifically, this includes:

[0070] Based on the first stage of stratification of the entire workspace in step S6, the fuzzy C-means clustering algorithm combined with the genetic algorithm is used again for each layer of the workspace to further refine the spatial coordinate points of each layer, thus completing the second stage of further refinement of the two-stage hierarchical partitioning of the robot's Cartesian full workspace domain.

[0071] To achieve further subdivision of the workspace, the limΔR constraint in the clustering partitioning optimization model is used. Xset ,limΔR Yset 、imΔR Zset ,limΔR Dset The values ​​should be appropriately reduced based on the workspace and the hierarchical data.

[0072] Furthermore, the positional accuracy reliability analysis and effect verification under the workspace partitioning scenario in step S8 specifically includes:

[0073] The feasibility of the proposed robot workspace partitioning method was experimentally verified. Coordinate points in each subspace were sampled using the optimal Latin hypercube. The joint angles corresponding to each set of coordinate points were input into a parameterized model for multiple solutions, obtaining actual spatial coordinates under the influence of multiple sets of uncertain parameters. These actual spatial coordinates were compared with theoretical coordinates to calculate the offset errors of the x, y, and z components. The straight-line distance error between the actual and theoretical coordinate points was also calculated. Finally, the reliability of the obtained positional accuracy was compared with the reliability of the subspace to verify the effectiveness of the proposed partitioning method. Furthermore, the error ranges in the x, y, and z directions were compared between partitioned calibration compensation and unified calibration compensation for the entire workspace, demonstrating the significant value of the proposed partitioning method in reducing end-effector position errors across the entire workspace and improving the reliability and spatial adaptability of parameter calibration and compensation within the robot's entire workspace.

[0074] Compared with the prior art, the present invention has the following beneficial technical effects:

[0075] 1) This invention provides a preprocessing technology for achieving fine and accurate calibration of robots. Based on the non-probabilistic reliability differences of robot end-effector poses in different workspaces, this method uses a partitioning optimization design method combining fuzzy C-means clustering algorithm and genetic algorithm to partition the robot's Cartesian full workspace domain in a two-stage hierarchical manner, including hierarchical division and further subdivision of intervals under each hierarchical division. This can improve the absolute positioning accuracy of robots with large workspaces and provide a theoretical basis for formulating classification, calibration and error compensation strategies under different workspace partitions. It can solve the problem of high repeatability accuracy but low absolute positioning accuracy of robots.

[0076] 2) This invention adopts a partitioning optimization design method that combines fuzzy C-means clustering algorithm with genetic algorithm to partition the robot’s Cartesian full workspace domain in a two-stage hierarchical manner, including hierarchical division and further subdivision of intervals under the hierarchical division. The partitioning is detailed and reasonable, which facilitates subsequent fine and accurate calibration and compensation.

[0077] 3) This invention partitions the robot's Cartesian three-dimensional workspace, and the partitioning results are highly intuitive and easy to understand;

[0078] 4) After partitioning, the subsequent partitioning calibration and compensation effectively reduces the end-effector position error in the entire working domain, and improves the reliability and spatial adaptability of parameter calibration and compensation in the entire working space of the robot. Attached Figure Description

[0079] Figure 1 This is a flowchart of the technical solution of the present invention.

[0080] Figure 2 This is a schematic diagram of the external shape of the object to be implemented in this invention and its connecting rod coordinate system.

[0081] Figure 3 Vector diagram of the joint space of this invention

[0082] Figure 4 This is a schematic diagram of the joint clearance of the mechanism of the object of the present invention. Among them, (a) is a schematic diagram of each joint of the industrial robot, and (b) is the positional error of the robot end effector in space under the influence of joint clearance error.

[0083] Figure 5 This is a schematic diagram of the parameterized model of the object of this invention.

[0084] Figure 6 This is a schematic diagram of the workspace of the object of this invention.

[0085] Figure 7 This is a schematic diagram of the sampling coordinate points.

[0086] Figure 8 This is a schematic diagram of the stratification of sampling coordinate points.

[0087] Figure 9 This is a schematic diagram of the first-level coordinate points obtained from the first stage of layering.

[0088] Figure 10 This is a schematic diagram of the first-level coordinate point clustering partitioning obtained from the first-stage stratification.

[0089] Figure 11 The diagrams show the clustering partitions of coordinate points at the second, third, and fourth levels obtained from the first stage of stratification. Specifically, (a) shows the clustering partitions at the second level, (b) shows the clustering partitions at the third level, and (c) shows the clustering partitions at the fourth level.

[0090] Figure 12 Error interval diagrams in the x, y, and z directions are shown for two scenarios: zonal calibration compensation and unified calibration compensation for the entire workspace. (a) shows the error interval diagram in the x direction, (b) shows the error interval diagram in the y direction, and (c) shows the error interval diagram in the z direction. Detailed Implementation

[0091] The invention will be further described below with reference to the accompanying drawings, using a six-DOF KR 1000Titan robot as the implementation object and in Adams software.

[0092] like Figures 1 to 12 As shown, this embodiment employs a fuzzy C-means clustering algorithm to rationally partition the robot's workspace based on the non-probabilistic reliability differences of coordinate points within different workspace ranges. This provides a theoretical basis for improving the absolute positioning accuracy of robots with large workspaces and for developing classification error compensation strategies under different workspace partitions. Specifically, the steps include the following:

[0093] Step S1: Establish the kinematic model of the industrial robot based on the DH parameter method:

[0094] Based on the DH parameter method, taking links i-1 and i as examples, the link parameters are defined as follows: link length a i For from z i-1 axis to z i axis along x i The distance between axes; the torsion angle α of the connecting rod. i For z i-1 axis to z i Axis around x i The angle of rotation around the axis is defined as about x. i Right-hand rotation of the axis is positive; offset distance d i For x i-1 axis to x i axis along z i-1 Distance between axes; joint rotation angle θ i For x i-1 axis to x i Axis around z i-1 The angle of rotation around the axis is defined as about z. i-1 A right-handed rotation of the axis is positive.

[0095] Let A be the transformation matrix from joint i-1 to joint i. i Then the homogeneous transformation matrix of the robot is:

[0096] A = A1A2…A i (1)

[0097] The coordinate system from joint i-1 to joint i can be obtained by revolving around z. i axis and x i It is described by a combination of axis translation and rotation, with the specific transformation matrix using... express:

[0098]

[0099] The pose information of the robot's end effector in the base coordinate system is:

[0100]

[0101] In equation (3), (n x ,n y ,n z ) T , (o x ,o y ,o z ) T ,(a x ,a y ,a z ) TThese represent the direction vectors of the robot's end effector in the x, y, and z directions in the base coordinate system, respectively; (p x ,p y ,p z ) T Let be the position vector of the robot's end effector in the base coordinate system.

[0102] The robot's shape and the link coordinate system established based on the DH parameter method are as follows: Figure 2 As shown in Table 1, the theoretical parameters of the connecting rod are as follows.

[0103] Table 1 Theoretical parameters of the connecting rod

[0104] 1 600 1100 -90 <![CDATA[θ1]]> 2 1400 0 0 <![CDATA[θ2]]> 3 65 0 -90 <![CDATA[θ3]]> 4 0 1200 90 <![CDATA[θ4]]> 5 0 0 -90 <![CDATA[θ5]]> 6 0 372 0 <![CDATA[θ6]]>

[0105] Step S2: Considering the influence of uncertainties, set parameterized variables for the joint shaft hole fit clearance and link dimensions to establish a parametric model of the robot:

[0106] Due to numerous uncertainties such as manufacturing and installation errors, elastic deformation, kinematic pair clearances, friction, and chatter, industrial robots experience subtle deviations during movement, affecting the absolute positioning accuracy and reliability of the robot's end effector. Conventional robot dynamics models have fixed structural dimensions, making it impossible to simulate and analyze the impact of these uncertainties on the end effector's position error. Therefore, this invention proposes a parametric modeling method for uncertainty. Specifically, at the joint connections of the model, circular rings and cylinders coaxial with the revolute joints are established to simulate mating holes and shafts. Boolean operations are then used to integrate the newly created components with the robot model, and the joint hole radius, link length, and offset distance are set as parametric variables with a certain error range. The advantage of this parametric modeling method is that by controlling the relationships or values ​​between parametric variables, the model's joint hole radius and link length and offset distance can be driven to change, thereby generating robot dynamics simulation models with different mating relationships and different link lengths and offset distances, providing a model foundation for subsequent dynamics analysis. The parametric processing of robot joint clearances and link dimensions is crucial.

[0107] There are many reasons for joint clearance. For example, in order to achieve flexible rotation, robot joints are designed with clearance fit from the beginning. Manufacturing or assembly errors, wear and tear between parts, etc. can all cause changes in clearance. Figure 3 The diagram shows the vector image of the gap at a certain joint connection. It can be seen that the axis position has shifted. Assuming p is the center of the axis (hole) at the joint connection, and o is the center of the hole at the previous joint connection, then op is the ideal rod length. However, in actual operation, the axis center p will randomly shift during rotation. The shifted axis center is c, and the maximum shift is pc. Therefore, the actual rod length from the previous joint to this joint after the shift can be considered as oc. This refers to the error vector generated by the joint clearance during motion. The link parameter error caused by the joint clearance can be expressed as a formula:

[0108]

[0109] In the formula, L is the actual link length affected by the joint clearance; l is the theoretical link length; and x and y are the components of the vector decomposition of the joint clearance.

[0110] x 2 +y 2 ≤|a| 2

[0111] Due to the influence of joint clearance, the length of pc cannot be ignored, and since the center c of the axis is randomly distributed within the error circle, the clearance vector of each joint... They are also different; the randomness of the joint gaps will inevitably lead to the randomness of the execution endpoint.

[0112] Figure 4 (a) shows a schematic diagram of the joints of an industrial robot. The robot’s movement in space depends on the cooperation of the six joints. By inputting the rotation angle of each joint, the robot end can be driven to reach the specified position. Figure 4 (b) represents the positional error of the robot's end effector in space under the influence of joint clearance errors. It can be seen that the clearance error at each joint causes changes in the position and length of the links relative to the ideal state. The cumulative effect is ultimately reflected in the positional error of the end effector point P1 relative to the theoretical point P0. Let the clearance vectors offset at each joint be s1, s2, s3, s4, s5, and s6, then we can obtain:

[0113]

[0114] In the formula, The positional error of the end effector is obtained by summing the gap vectors of the six joints. This formula reveals the influence of joint gaps on the reliability of the robot's end effector positioning accuracy.

[0115] For a 6-joint robot, there are 6 joints, so 12 parameterized axes and holes need to be created. Specifically, at each joint connection point of the model, a ring and a cylinder coaxial with the revolute joint are created to simulate the mating holes and shafts. Boolean operations are used to integrate the newly created parts with the robot model, and the radius dimensions of the parts are set as variables with an error range. For a 6-joint robot, 12 parameterized axes and holes need to be created, with the radius variables represented by DV1 to DV12 respectively. See details... Figure 5After establishing six sets of parameterized models of joint clearances, the radius variables of each joint shaft hole were given. Based on the process and precision requirements of robots in the equipment manufacturing industry, the joints adopted the H6 / h5 standard for hole basis. The specific values ​​of the variables are set as shown in Table 2.

[0116] Table 2 Parameter Variable Table

[0117]

[0118]

[0119] As can be seen from Table 2, each pair of variables corresponds to a set of joints, totaling 6 sets. The base and end effector each have only one variable, while the other link components each have two radius variables, which are connected to the adjacent components respectively.

[0120] Similarly, for all links in the robot model, add link length and offset distance as parameterized variables, see details below. Figure 5 The specific values ​​of a1, d1, a2, a3, d4, and d6, the link length and offset distance variables, should be set based on the nominal values, taking into account manufacturing tolerances.

[0121] Specific robot parameterization models, such as Figure 5 As shown.

[0122] Once the parametric model is built, simulation analysis of the robot can be performed. By connecting each joint with a revolute joint and simulating a more realistic simulation environment by treating the contact force as the contact friction between the shaft and the hole, the simulation environment can be improved.

[0123] Step S3: Obtain the robot workspace cloud map using the Monte Carlo method, and select an appropriate number of coordinate points in the workspace based on the optimal Latin hypercube:

[0124] When a robot's joints perform all possible movements within their range of rotation, the set of spatial points reached by these movements is considered the robot's workspace. The actual workspace is quite complex and requires experimental design to determine its specific range. By deriving the forward kinematics formula in step S1, the pose information of the robot's end effector can be obtained, where [p x ,p y ,p z ] T This refers to the end position information, specifically the x, y, and z coordinates of the end in the Cartesian coordinate system.

[0125]

[0126] The Monte Carlo method is used to randomly select values ​​for the rotation angles of the six joints to obtain the end-effector coordinates. Theoretically, as long as the number of times the values ​​are taken is large enough and non-repeating, the set of different end-effector coordinates obtained can be considered as an approximately complete workspace. The specific operation is implemented in MATLAB. First, the range of rotation angles on each joint is limited. After the given range, the rand function is used to randomly select values ​​for the joint angles.

[0127] θ i =θ i min +(θ i max -θ i min )*rand(N,1)(i=1,...,6) (5)

[0128] In the formula, θ i max θ i min represents the maximum and minimum values ​​of the range of motion angle of joint i, respectively; N is the number of iterations.

[0129] The robot's workspace is obtained using the Monte Carlo method, such as... Figure 6 As shown, the obtained workspace range was imported into the Isight software. The optimal Latin hypercube was used to sample the coordinate points within the workspace, resulting in the distribution of 120 sets of coordinate points within the workspace, as shown below. Figure 7 As shown.

[0130] Step S4: Obtain the position error data of the coordinate points through the parametric model, and measure the reliability of the position accuracy of the coordinate points according to the non-probability interval theory:

[0131] Multiple inverse solutions are obtained for the selected coordinate points in the workspace using an algebraic method. The optimal inverse solution is obtained using the "shortest stroke" rule. The corresponding robot joint angles are input into the ADAMS model for multiple solutions to obtain the actual coordinate value range of the coordinate points. The results are exported and the difference is calculated with the theoretical coordinate values ​​to obtain the position error range of the sampled coordinate points.

[0132] In actual operation, the joint clearance parameters of a robot exhibit non-probabilistic uncertainty characteristics. Therefore, the obtained interval error parameters are measured using the non-probabilistic interval theory.

[0133] The reliability model for the position accuracy of the robot end effector based on the non-probabilistic interval theory is shown below.

[0134]

[0135] In the formula, r u r is the maximum permissible value for position error. ls is the minimum permissible value for position error. u s represents the maximum position error. l This represents the minimum positional error. R set ∈[0,1] represents the reliability of the coordinate point position accuracy. The closer the value is to 1, the higher the reliability, and vice versa.

[0136] Step S5: Solve for the non-probabilistic reliability index of the coordinate point location:

[0137] During robot movement, the position of its end effector constantly changes due to numerous uncertainties, resulting in varying positional errors and consequently, inconsistent reliability of the robot's positioning accuracy. The reliability evaluation metrics for robot positional accuracy can be appropriately selected based on operational needs. Considering the errors in the three coordinate components (x, y, z) and distance of the end effector, specific operational scenarios may require focusing on positional offset errors in a single spatial coordinate direction or multiple directions. In such cases, based on a given permissible error range, the errors in the three coordinate components ΔX, ΔY, or ΔZ, as well as the distance error, can be evaluated. Substitute the reliability model of the robot end effector position accuracy based on the non-probability interval theory constructed in step S4 into the non-probability reliability calculation and solve for the non-probability reliability index of the coordinate point position.

[0138] This embodiment determines the permissible error range according to operational requirements, and calculates the non-probabilistic reliability R of the robot in the distance direction at each coordinate point based on the reliability model. Dset The results are shown in Table 3.

[0139] Table 3 Non-probabilistic reliability of robot workspace coordinates

[0140]

[0141]

[0142] Step S6: Based on the non-probabilistic reliability of the robot's end-effector position, a partitioning optimization design method combining fuzzy C-means clustering and genetic algorithm is used to achieve the first-stage stratification in the robot's workspace partitioning:

[0143] The distribution of a robot's workspace significantly impacts the positioning accuracy of the end effector. Therefore, researching reasonable workspace partitioning is crucial for developing classification error compensation strategies for different partitions. Thus, employing a fuzzy C-clustering mean algorithm with non-probabilistic characteristics, combined with a genetic algorithm for partition optimization design, is a good choice. This partitioning is achieved by introducing a membership index. Let... For the dataset, V = {v1, v2, ..., v...} C} are the cluster centers, there are c in total, and x are the samples.j (j = 1, 2, ..., n) for cluster centers v i The membership matrix of (i = 1, 2, ..., c) is u = {u ij} c×n ∈M fcn v i ∈R s , 2≤c <n;

[0144] All datasets are divided into c cluster centers using a clustering algorithm, and the membership degree of each dataset to its respective cluster center is u. ij ∈[0,1],u ij The larger the value, the higher the similarity of the data information;

[0145] Its clustering partitioning optimization model is defined as:

[0146]

[0147] In the formula, m is a fuzzy weight exponent that controls the clustering results, and 1 <m<+∞;d ij ΔR represents the Euclidean distance between the j-th sample and the i-th cluster center; Xset(ij) ΔR Yset(ij) ΔR Zset(ij) ΔR Dset(ij) Let limΔR be the difference in nonprobabilistic reliability of the j-th sample relative to the i-th cluster center in the three coordinate directions and the distance direction, respectively; Xset ,limΔR Yset 、imΔR Zset ,limΔR Dset These are the permissible values ​​for the differences in nonprobabilistic reliability in the three coordinate directions and the distance direction, respectively.

[0148] Cluster center v i and membership matrix u ij The calculation formula is as follows:

[0149]

[0150]

[0151] To achieve detailed partitioning of the workspace, this embodiment adopts a two-stage hierarchical partitioning approach, consisting of layering and further subdivision of intervals within each layer. Step S6 first uses the non-probabilistic reliability values ​​of each spatial coordinate point and, based on the clustering partitioning optimization model constructed above, employs a fuzzy C-means clustering algorithm combined with a genetic algorithm to divide all coordinate points into layers, thus achieving the first stage of the two-stage hierarchical partitioning method: layering.

[0152] Based on the above method, all coordinate points were divided into four levels, and the results are shown in Table 4.

[0153] Table 4. Stratification results of the first stage of the partitioning method

[0154]

[0155]

[0156] The spatial coordinate points in Table 4, after being layered, are represented in MATLAB software using different shapes, such as... Figure 8 The coordinates are represented by "*" for the first level, "·" for the second level, "○" for the third level, and "◇" for the fourth level. It is clear that the coordinates in the first level are concentrated in the center of the robot's workspace, close to the robot's initial position, indicating that the rotation angles of the joints are small during operation, and the impact of uncertain joint clearance parameters is minimal. The coordinates in the second, third, and fourth levels gradually move outwards, closer to the edge of the workspace, indicating that the reliability of the robot's end effector's positioning accuracy is related to its position within the workspace under the influence of uncertain joint clearance parameters. The farther away from the center of the workspace, the worse the reliability.

[0157] Step S7: For each layer of the partitioned workspace, based on the non-probabilistic reliability of the robot's end-effector position, a partitioning optimization design method combining fuzzy C-means clustering and genetic algorithm is used to achieve further subdivision of the intervals in the second stage of the robot workspace partitioning:

[0158] Based on the first-stage stratification of the entire workspace completed in step S6, for each layer of the workspace, based on the non-probabilistic reliability of the robot's end-effector position point, a partition optimization design method combining fuzzy C-means clustering algorithm and genetic algorithm is adopted to realize the further subdivision of the intervals in the second-stage stratification of the robot's workspace partitioning.

[0159] The first layer coordinates obtained from the first stage of layering are as follows: Figure 9 As shown, based on this, the first-level coordinate points are further subdivided into intervals, and the result is as follows. Figure 10 As shown. Similarly, the coordinate points of the second, third, and fourth levels obtained from the first stage of layering are also further subdivided into intervals, as shown in the figure. Figure 11 As shown, (a) is a schematic diagram of the second-level coordinate point clustering partition, (b) is a schematic diagram of the third-level coordinate point clustering partition, and (c) is a schematic diagram of the fourth-level coordinate point clustering partition.

[0160] This method features detailed and reasonable partitioning, which facilitates subsequent refined and accurate calibration and compensation.

[0161] Step S8: Position accuracy reliability analysis and effect verification under workspace partitioning:

[0162] The feasibility of the robot workspace partitioning method proposed in this embodiment was experimentally verified in ADAMS. The optimal Latin hypercube was used to sample coordinate points in each subspace, with 5 samples per subspace, for a total of 50 spatial coordinate points across 10 subspaces. The joint angles corresponding to each set of coordinate points were input into the ADAMS model and the simulation was repeated 10 times to obtain 10 sets of actual spatial coordinates under the influence of uncertain joint clearance parameters. These actual spatial coordinates were compared with the theoretical coordinates, and the offset errors of the x, y, and z directional components were calculated. The straight-line distance error between the actual and theoretical coordinate points was also obtained. Finally, the reliability of the obtained positional accuracy was compared with the reliability of the subspace, as shown in Table 5.

[0163] Table 5 Subspace Sampling Coordinates and Non-probability Reliability

[0164]

[0165] As shown in Table 5, the non-probabilistic reliability of the positional accuracy of coordinate points in all subspaces of the first level is 1, indicating that the motion range of this level of subspace is relatively concentrated, and its positional accuracy is less affected by the uncertain joint clearance parameters. The reliability ranges of coordinate points in other subspace levels vary. Specifically, the reliability of coordinate points in the two subspaces of the second level is relatively close, with roughly the same range, both falling between 0.9 and 1. The reliability of coordinate points in the third level subspace varies slightly more. The reliability of coordinate points in the fourth level subspace is significantly lower than other levels, with the highest reliability being only 0.738, less than 0.75. This indicates that the positional accuracy of coordinate points in this level of subspace is most affected by the uncertain joint clearance parameters, and should be given more consideration in subsequent error compensation. Furthermore, the reliability of coordinate points in all subspaces meets the variation range of non-probabilistic reliability within the corresponding hierarchical spatial domain, demonstrating the rationality and accuracy of the robot workspace partitioning based on non-probabilistic reliability. This verifies the feasibility of the method and provides a theoretical basis for improving the absolute positioning accuracy of large workspace robots and formulating classification error compensation strategies under different workspace partitions.

[0166] To further verify the effectiveness of the partitioning method in this embodiment in partition calibration and compensation, further experimental verification was conducted. Figure 12The diagram shows the results of partitioning the robot's workspace according to this embodiment. It compares the error ranges in the x, y, and z directions under two scenarios: partitioned calibration and compensation, and unified calibration and compensation for the entire workspace. Specifically, (a) shows the error range in the x direction, (b) shows the error range in the y direction, and (c) shows the error range in the z direction.

[0167] Figure 12 The red dashed rectangle representing the "Unified Calibration Compensation - Lower Boundary" and the green solid rectangle representing the "Unified Calibration Compensation - Upper Boundary" indicate the lower and upper bounds of the position error range for unified compensation across the entire workspace, respectively. The cyan dotted line representing the "Partial Calibration Compensation - Lower Boundary" and the red solid line representing the "Partial Calibration Compensation - Upper Boundary" indicate the lower and upper bounds of the position error range for partial compensation. As shown in the figure, after partial compensation, the errors in all three directions are significantly reduced, with the end-effector positioning error within ±1mm, and the minimum reaching below 0.2mm. Compared to unified compensation across the entire workspace, the average lower and upper bounds of the error ranges in the x, y, and z directions for partial compensation decreased by 21.19% and 46.33%, and 45.60% and 21.12%, and 40.60% and 13.60%, respectively. Further observation of the robot's response speed and motion stability after partial compensation reveals a fast response speed and minimal fluctuations during movement, demonstrating the effectiveness of the partial compensation method of this invention.

Claims

1. A robot workspace partitioning method based on nonprobabilistic reliability, characterized in that... Includes the following steps: Step S1: Establish the kinematic model of the industrial robot based on the DH parameter method; Step S2: Considering the influence of uncertainties, set parameterized variables for joint shaft hole fit clearance and link length and offset distance to establish a robot parameterized model; Step S3: Obtain the robot workspace cloud map using the Monte Carlo method, and select an appropriate number of coordinate points in the workspace based on the optimal Latin hypercube. Step S4: Obtain the position error data of the coordinate points through the parameterized model, and measure the reliability of the position accuracy of the coordinate points according to the non-probability interval theory. Step S5: Solve for the non-probabilistic reliability index of the coordinate point location; Step S6: Based on the non-probabilistic reliability of the robot's end-effector position, a partitioning optimization design method combining fuzzy C-means clustering algorithm and genetic algorithm is adopted to realize the first stage of stratification in the robot's workspace partitioning; Step S7: For each layer of the workspace after hierarchical division, based on the non-probabilistic reliability of the robot end position point, a partition optimization design method combining fuzzy C-means clustering algorithm and genetic algorithm is adopted to realize the further subdivision of the interval under the second stage of hierarchical division in the robot workspace partitioning. Step S8: Position accuracy reliability analysis and effect verification under workspace partitioning.

2. The robot workspace partitioning method based on non-probabilistic reliability according to claim 1, characterized in that, Step S1 specifically includes: Based on the DH parameter method, taking links i-1 and i as examples, the link parameters are defined as follows: link length a i For from z i-1 axis to z i axis along x i The distance between axes; the torsion angle α of the connecting rod. i For z i-1 axis to z i Axis around x i The angle of rotation around the axis is defined as about x. i Right-hand rotation of the axis is positive; offset distance d i For x i-1 axis to x i axis along z i-1 Distance between axes; joint rotation angle θ i For x i-1 axis to x i Axis around z i-1 The angle of rotation around the axis is defined as about z. i-1 Right-hand rotation of the axis is positive; Let A be the transformation matrix from joint i-1 to joint i. i Then the homogeneous transformation matrix of the robot is: The coordinate system from joint i-1 to joint i can be obtained by revolving around z. i axis and x i It is described by a combination of axis translation and rotation, with the specific transformation matrix using... express: The pose information of the robot's end effector in the base coordinate system is: In the above formula, (n x ,n y ,n z ) T , (o x ,o y ,o z ) T ,(a x ,a y ,a z ) T These represent the direction vectors of the robot's end effector in the x, y, and z directions in the base coordinate system, respectively; (p x ,p y ,p z ) T Let be the position vector of the robot's end effector in the base coordinate system.

3. The robot workspace partitioning method based on non-probabilistic reliability according to claim 1, characterized in that, Step S2 specifically includes: At the joint connection of the model, create a ring and a cylinder coaxial with the revolute joint to simulate the mating holes and shafts. Then, use Boolean operations to merge the newly created parts with the robot model. Set the joint hole shaft radius, link length and offset distance as parameterized variables with a certain error range. The error range should be determined according to the manufacturing tolerance of the relevant parts and the mating tolerance of the joint hole shaft.

4. The robot workspace partitioning method based on non-probabilistic reliability according to claim 1, characterized in that, Step S3 specifically includes: By deriving the forward kinematics formula in step S1, the pose information of the robot's end effector can be obtained, where [p x ,p y ,p z ] T End position information: The Monte Carlo method is used to randomly select values ​​for the rotation angles of the six joints to obtain the end-effector coordinate information. In MATLAB, the range of rotation angles on each joint is first limited, and then the rand function is used to randomly select values ​​for the joint angles within the given range. In the formula, , Let $\mathbf{i}$ and $\mathbf{i}$ represent the maximum and minimum values ​​of the range of rotation angles of joint $i$, respectively; $N$ is the number of iterations. The obtained workspace range is imported into the Isight software, and the coordinate points within the workspace are sampled using the optimal Latin hypercube.

5. The robot workspace partitioning method based on non-probabilistic reliability according to claim 1, characterized in that, Step S4 specifically includes: Multiple sets of inverse solutions are obtained for the coordinate points extracted in the workspace using an algebraic method, and the optimal inverse solution is obtained using the shortest stroke rule. The corresponding robot joint angles are input into the parameterized model for multiple solutions to obtain the actual coordinate value range of the coordinate points. The results are exported and the difference is calculated with the theoretical coordinate values ​​to obtain the position error range of the sampled coordinate points. The obtained interval error parameters are measured using methods based on nonprobabilistic interval theory; The reliability model for the position accuracy of the robot end effector based on non-probabilistic interval theory is shown below: In the formula, r u r is the maximum permissible value for position error. l s is the minimum permissible value for position error. u s represents the maximum position error. l This represents the minimum value of the position error; , which represents the reliability of the coordinate point's position accuracy. The closer the value is to 1, the higher the reliability, and vice versa.

6. The robot workspace partitioning method based on non-probabilistic reliability according to claim 1, characterized in that, Step S5 specifically includes: Based on the given permissible error range, the error of the three coordinate components. , or and distance error Substitute the reliability model of the robot end effector position accuracy constructed in step S4 based on the non-probability interval theory into the non-probability reliability calculation and solve for the non-probability reliability index of the coordinate point position.

7. The robot workspace partitioning method based on non-probabilistic reliability according to claim 1, characterized in that, Step S6 specifically includes: A fuzzy C-clustering mean algorithm with non-probabilistic characteristics is adopted and combined with a genetic algorithm to perform partition optimization design. The partitioning of the workspace is achieved by introducing a membership index. set up For the dataset, There are c cluster centers, and the samples are... Cluster centers The membership matrix is , , ; The clustering algorithm divides all dataset information into c cluster centers, and the membership degree of each dataset to its respective cluster center is given by... u ij The larger the value, the higher the similarity of the data information; Its clustering partitioning optimization model is defined as: In the formula, m is a fuzzy weighting index that controls the clustering results, and ;d ij This represents the Euclidean distance between the j-th sample and the i-th cluster center; , , , These are the differences in non-probabilistic reliability of the j-th sample relative to the i-th cluster center in the three coordinate directions and the distance direction, respectively. , , , These are the permissible values ​​for the differences in nonprobabilistic reliability in the three coordinate directions and the distance direction, respectively. Cluster center v i and membership matrix u ij The calculation formula is as follows: To achieve detailed partitioning of the workspace, a two-stage hierarchical partitioning method is adopted, consisting of a layered structure and further subdivision of intervals within each layer. First, based on the non-probabilistic reliability values ​​of each spatial coordinate point, and using the clustering partitioning optimization model constructed above, a fuzzy C-means clustering algorithm combined with a genetic algorithm is employed to divide all coordinate points into layers, thus achieving the first stage of the two-stage hierarchical partitioning method.

8. The robot workspace partitioning method based on non-probabilistic reliability according to claim 1, characterized in that, Step S7 specifically includes: Based on the first stage of stratification of the entire workspace in step S6, the fuzzy C-means clustering algorithm combined with the genetic algorithm is used again for each layer of the workspace to further refine the spatial coordinate points of each layer, thus completing the second stage of further refinement of the two-stage hierarchical partitioning of the robot's Cartesian full workspace domain. To achieve further subdivision of the workspace, the constraints of the clustering partitioning optimization model are... , , , The values ​​should be appropriately reduced based on the workspace and the hierarchical data.

9. The robot workspace partitioning method based on non-probabilistic reliability according to claim 1, characterized in that, Step S8 specifically includes: The optimal Latin hypercube is used to sample the coordinate points in each subspace. The joint angles corresponding to each set of coordinate points are input into the parameterized model for multiple solutions to obtain the actual spatial coordinates under the influence of multiple sets of uncertain parameters. The actual spatial coordinates are compared with the theoretical coordinates to calculate the offset errors of the x, y, and z components. The straight-line distance error between the actual and theoretical coordinates is also obtained. Finally, the reliability of the obtained positional accuracy is compared with the reliability of the subspace to verify the effectiveness of the partitioning method proposed in this invention. Furthermore, the error ranges of the x, y, and z directions are compared under two scenarios: partitioned calibration compensation and unified calibration compensation for the entire workspace.

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