Industrial robot calibration method and system based on elastic static flexibility calibration

Abstract

The invention discloses an industrial robot calibration method and system based on elastic static flexibility calibration. The method comprises the steps that an elastic static calibration rigidity model considering elastic deformation of all connecting rods and joint flexibility of a robot is established; based on machining technological process characteristics and geometric and physical limitations of working units, an artificial intelligence algorithm is used for screening the optimal measurement pose and load combination of the robot; in the optimal measurement pose and load combined state, external force is applied to an end effector of the robot, actual pose data before and after the external force is applied are obtained through high-precision measurement equipment, and the pose deviation of the end effector and the magnitude of the external force are recorded; identifying unknown elastic static stiffness parameters in the robot elastic static calibration stiffness model by using a numerical optimization algorithm; and applying the identified elastic statics rigidity parameter to a correction robot kinematics model, calculating a pose error caused by elastic deformation, and compensating the pose error to a control instruction of the robot with the pose error so as to improve the positioning precision of the robot.

Description

Technical Field

[0001] The present invention belongs to the technical field of industrial robot calibration, and more specifically, relates to an industrial robot calibration method and system based on elastic static compliance calibration. Background Art

[0002] The long-term use of industrial robots may cause their accuracy to decrease due to wear. In addition, due to the influence of the fixed characteristics of the serial structure of industrial-grade robots, their stiffness is insufficient. The weak-rigidity structural characteristics result in low tolerance of industrial robots to working loads, which will affect the machining trajectory accuracy and product surface quality of the robots, and it is difficult to meet the manufacturing and assembly requirements of high-value-added products with high precision requirements and complex assembly processes. The pose error of industrial robots will gradually increase with the increase of service time, resulting in the inability of the robots to accurately reach the predetermined position when performing tasks, affecting the machining accuracy and assembly effect. The existing control algorithms have deficiencies in trajectory planning and servo control, and it is difficult to meet the requirements of high-precision machining and complex trajectory control.

[0003] The serial structure of industrial robots results in low stiffness. Especially when subjected to external forces during the machining process, they are prone to deformation and vibration, affecting the machining accuracy and stability. The stiffness of the robots will change with the change of joint angles and loads, and this dynamic change further exacerbates the instability and accuracy problems during the machining process.

[0004] There are many problems in the domestic industrial robot standard system, such as standard cross-repetition, and some traditional robot standards lagging behind the industrial development, etc., resulting in the lack of unified specifications and guidance for enterprises in the production and application processes. The standard formulation of new robot products and technologies lags far behind the development and application of products. For example, the standards in fields such as mobile manipulator composite robots and service robots are missing, affecting the healthy development of the industry. The existing standards have deficiencies in accuracy requirements and cannot meet the needs of high-precision machining and complex assembly tasks, resulting in uneven product quality and performance. Summary of the Invention

[0005] In view of the above deficiencies or improvement requirements of the prior art, the present invention provides an industrial robot calibration method and system based on elastic static compliance calibration. By constructing an elastic static calibration stiffness model that takes into account the elastic deformation of each link of the robot and the joint flexibility, the present invention accurately describes the elastic static characteristics of the robot and the positioning deviation of the end effector under external forces. Taking the characteristics of the machining process, the geometric and physical limitations of the work cell as performance indicators, an artificial intelligence algorithm is used to screen out the optimal measurement poses and load combinations, reducing the number of experiments and maximizing the data information content. An external force is applied to the end effector of the robot under the selected pose and load combination, and actual pose data before and after the application of the external force is obtained using a high-precision measurement device, recording the pose deviation of the end effector and the magnitude of the external force. A numerical optimization algorithm is used, with the measured pose deviation and external force data as inputs, to identify the unknown elastic static stiffness parameters in the elastic static calibration stiffness model of the robot, and to evaluate the accuracy of the identification and the positioning accuracy. The identified elastic static stiffness parameters are applied to correct the kinematic model of the robot, calculate the pose error caused by elastic deformation, and compensate the error into the control command of the robot, significantly improving the accuracy and efficiency of industrial robot calibration, while reducing the computational amount and the number of experiments, enhancing the applicability and flexibility of the calibration method, and meeting the requirements of high-precision machining and complex assembly tasks.

[0006] To achieve the above object, one aspect of the present invention provides an industrial robot calibration method based on elastic static compliance calibration, including the following steps:

[0007] S1: Establish an elastic static calibration stiffness model of the robot that takes into account the elastic deformation of each link of the robot and the joint flexibility;

[0008] S2: Taking the characteristics of the machining process, the geometric and physical limitations of the work cell as performance indicators, use an artificial intelligence algorithm to screen out the optimal measurement poses and load combinations of the robot;

[0009] S3: Apply an external force to the end effector of the robot in the state of the optimal measurement poses and load combinations of the robot obtained in step S2, use a high-precision measurement device to obtain the actual pose data of the robot before and after the application of the external force, and record the pose deviation of the end effector and the magnitude of the external force;

[0010] S4: Use a numerical optimization algorithm, with the pose deviation and external force data obtained in step S3 as inputs, to identify the unknown elastic static stiffness parameters in the elastic static calibration stiffness model of the robot, and at the same time evaluate the accuracy of the identification of the elastic static stiffness parameters and the positioning accuracy;

[0011] S5: Apply the elastostatic stiffness parameters identified in step S4 to correct the kinematic model of the robot, calculate the pose error caused by elastic deformation, and compensate the pose error into the control command of the robot to improve the positioning accuracy of the robot.

[0012] Further, step S2 includes an experimental planning method using a linear regression model. According to optimality principles such as A-optimization and D-optimization, the best combination is selected from a large number of possible measurement poses and load combinations, and then the experimental planning scheme is determined.

[0013] Further, the mechanical processing technological process features in step S2 include blank manufacturing, grasping or handling; the artificial intelligence algorithms include genetic algorithms and particle swarm algorithms.

[0014] Further, applying an external force to the robot end effector in step S3 includes installing a force sensor on the robot end effector or adding a counterweight with a known mass to the end effector.

[0015] Further, step S3 also includes measuring the pose of the robot twice before and after applying an external force to the robot end effector, measuring the actual pose of the robot under different external forces using a high-precision measuring device; arranging multiple measurement points in the robot motion space, recording the pose data of the robot at each measurement point, and calculating the deviation of the end effector according to the difference.

[0016] Further, in the robot elastostatic calibration stiffness model in step S4, the relationship between the displacement of the robot end effector under an external force, the elastic characteristics of each part of the robot, and the external force applied to the robot end effector is expressed by Equation (1):

[0017] ΔP = K -1 ·F + ∈ (1)

[0018] Where, ΔP is the displacement of the robot end effector under an external force; K is the stiffness matrix, which is used to describe the elastic characteristics of each part of the robot; F is the external force applied to the robot end effector; ∈ is the measurement noise and model error.

[0019] Further, step S4 includes reducing the parameters in the robot elastostatic calibration stiffness model by the following methods before parameter identification:

[0020] 1) Order reduction processing: Before applying the least squares method for parameter identification, reduce the order of the robot stiffness model, eliminate redundant parameters, and ensure the invertibility of the information matrix;

[0021] 2) Remove unimportant parameters among the remaining non-redundant parameters;

[0022] 3) Optimize the number of matrix parameters according to the basic attributes of the information matrix.

[0023] Further, the optimization of the number of matrix parameters according to the basic attributes of the information matrix includes:

[0024] Based on the symmetry characteristics of the compliance matrix, merge the parameter pairs with symmetric relationships into a single parameter;

[0025] Based on the geometric characteristics and material properties of the robotic arm links, pre-define the sparse pattern of the stiffness matrix, and achieve dimensionality reduction by excluding the parameters corresponding to zero elements;

[0026] Realize parameter integration through the structural adjustment of the compliance matrix and the optimization of the observation matrix.

[0027] The second aspect of the present invention provides an industrial robot calibration system based on elastic static compliance calibration for implementing the industrial robot calibration method based on elastic static compliance calibration, including a first main module, a second main module, a third main module, a fourth main module, and a fifth main module; wherein,

[0028] The first main module is used to establish a robot elastic static calibration stiffness model considering the elastic deformation of each link of the robot and joint flexibility by improving and supplementing the robot base elastic statics model;

[0029] The second main module is used to screen the optimal measurement pose and load combination of the robot by using artificial intelligence algorithms with the performance indicators of the mechanical processing process characteristics, the geometry and physical limitations of the work cell;

[0030] The third main module is used to apply an external force to the robot end effector in the state of the optimal measurement pose and load combination of the robot obtained by the second main module, use high-precision measurement equipment to obtain the actual pose data of the robot before and after applying the external force, and record the pose deviation of the end effector and the magnitude of the external force;

[0031] The fourth main module is used to use numerical optimization algorithms (such as intelligent optimization algorithms like genetic algorithms, particle swarm algorithms, etc.), take the pose deviation and external force data obtained by the third main module as input, identify the unknown elastic static stiffness parameters in the robot elastic static calibration stiffness model, and at the same time evaluate the accuracy and positioning accuracy of the identification of the elastic static stiffness parameters;

[0032] The fifth main module is used to apply the elastic static stiffness parameters identified by the fourth main module to correct the kinematic model of the robot, calculate the pose error caused by elastic deformation, and compensate the pose error into the control instruction of the robot to improve the positioning accuracy of the robot.

[0033] The third aspect of the present invention provides an electronic device, including a processor and a memory, and the processor and the memory are interconnected;

[0034] The memory is used for storing a computer program;

[0035] The processor is configured to execute the industrial robot calibration method based on elastic static compliance calibration when calling the computer program.

[0036] Generally speaking, compared with the prior art by the above technical solutions conceived by the present invention, the following beneficial effects can be achieved:

[0037] (1) For the industrial robot calibration method and system based on elastic static compliance calibration of the present invention, by establishing a more accurate elastic static calibration stiffness model of the robot, considering factors such as elastic deformation of each link of the robot and joint flexibility, etc., it can more accurately describe the elastic deformation characteristics of the robot under static external forces. The unknown elastic statics stiffness parameters in the model are identified through numerical optimization algorithms (such as genetic algorithms, particle swarm algorithms), ensuring the accuracy and reliability of the parameters. In addition, through the experimental planning method of the linear regression model, the best measurement poses and load combinations are screened out, reducing the number of experiments, while maximizing the data information volume, and further improving the calibration accuracy.

[0038] (2) For the industrial robot calibration method and system based on elastic static compliance calibration of the present invention, a series of methods are proposed to reduce the number of parameters in the stiffness model, including order reduction processing, removing unimportant parameters, and optimizing based on the basic attributes of the information matrix. These methods significantly reduce the number of parameters to be identified, while maintaining the integrity of the physical meaning. Through these optimizations, the calculation amount is greatly reduced, and the calibration process is more efficient. In addition, this application compares various numerical optimization algorithms and finds that the numerical optimization algorithms based on artificial intelligence (such as genetic algorithms and particle swarm algorithms) can significantly shorten the calculation time and improve the convergence speed while ensuring the calibration accuracy, further optimizing the calibration efficiency.

[0039] (3) For the industrial robot calibration method and system based on elastic static compliance calibration of the present invention, the calibration method is applicable to a variety of industrial robots and different working environments. By considering performance indicators such as mechanical processing process characteristics, geometric and physical limitations of the work cell, etc., this method can adapt to different application requirements, such as grasping, moving, machining of large-sized workpieces, etc. In addition, through the combination of experimental planning and parameter identification in this application, the reliability and stability of the calibration results are ensured, improving the overall performance and application range of the robot. Description of the Drawings

[0040] Figure 1Schematic flowchart of a calibration method for an industrial robot based on elastic static compliance calibration according to an embodiment of the present invention;

[0041] Figure 2 Test schematic diagram of the optimal measurement pose of an industrial robot according to an embodiment of the present invention;

[0042] Figure 3 Schematic structural diagram of a calibration system for an industrial robot based on elastic static compliance calibration according to an embodiment of the present invention;

[0043] Figure 4 Schematic structural diagram of an electronic device according to an embodiment of the present invention. Detailed implementation manners

[0044] In order to make the objectives, technical solutions and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0045] As Figure 1 shown, one aspect of the present invention provides a calibration method for an industrial robot based on elastic static compliance calibration, including the following steps:

[0046] S1: Establish a robot elastic static calibration stiffness model considering the elastic deformation of each link and joint flexibility of the robot by improving and supplementing the robot basic elastic statics model;

[0047] S2: Use artificial intelligence algorithms to screen the optimal measurement pose and load combination of the robot with the characteristics of the machining process, geometric and physical limitations of the work cell as performance indicators;

[0048] S3: Apply an external force to the end effector of the robot in the state of the optimal measurement pose and load combination of the robot obtained in step S2, use a high-precision measurement device to obtain the actual pose data of the robot before and after applying the external force, and record the pose deviation of the end effector and the magnitude of the external force;

[0049] S4: Use numerical optimization algorithms (such as intelligent optimization algorithms like genetic algorithms, particle swarm algorithms, etc.), take the pose deviation and external force data obtained in step S3 as input, identify the unknown elastic static stiffness parameters in the robot elastic static calibration stiffness model, and at the same time evaluate the accuracy and positioning accuracy of the identification of the elastic static stiffness parameters;

[0050] The unknown elastic static stiffness parameters in step S4 refer to the elastic static stiffness parameters used to describe the elastic static parameters of each link and joint of the robot when subjected to force in the elastic static calibration stiffness model of the robot. These parameters are unknown in the early stage of model establishment and need to be determined through experiments and parameter identification steps to accurately reflect the actual elastic static characteristics of the robot;

[0051] S5: Apply the elastic static stiffness parameters obtained by step S4 to modify the kinematic model of the robot, calculate the posture error caused by elastic deformation, and compensate the posture error into the control instructions of the robot to improve the positioning accuracy of the robot.

[0052] Furthermore, step S1 includes improving and supplementing the basic elastic statics model according to the structural characteristics of the industrial robot, taking into account factors such as the elastic deformation of each link of the robot and the flexibility of the joints, and establishing a more accurate elastic static calibration stiffness model of the robot; the elastic static calibration stiffness model of the robot correctly describes the elastic static characteristics of the robot and the positioning deviation of the robot end effector under external force, providing a theoretical basis for subsequent calibration; according to the robot structure, combined with the theory of material mechanics and elastic mechanics, the static equation considering elastic deformation and joint flexibility is derived. The accuracy of the model is verified by means of theoretical analysis and finite element analysis.

[0053] Furthermore, the core goal of step S2 is to reduce the number of experiments and maximize the amount of data information. The best measurement posture and load combination are selected through artificial intelligence algorithms, the number of experiments is reduced by dozens of times, and the required positioning accuracy is achieved using the least number of calibration experiments. Step S2 uses the characteristics of the machining process, the geometry of the work unit, and the physical limitations as performance indicators, uses artificial intelligence algorithms to select the best measurement posture and load combination, and uses the experimental planning method of the linear regression model. According to the optimality principles such as A optimization and D optimization, the best combination is selected from a large number of possible measurement postures and load combinations, and then the experimental planning scheme is determined. The combination can maximize the amount of data information while reducing the number of experiments, providing optimal conditions for subsequent data measurement; the characteristics of the machining process include blank manufacturing, grasping or handling; the artificial intelligence algorithm includes genetic algorithm and particle swarm algorithm.

[0054] Furthermore, in robot calibration, model construction and parameter accuracy are the core basis for achieving high precision. Although the model structure of the robot is known in actual engineering, identifying the parameters of this model requires a large amount of experimental work, and the accuracy of the calibration results highly depends on the pose of the robot. Step S2 proposes a method to improve the accuracy of parameter identification by correctly selecting the best measurement pose; the best measurement pose in Step S2 is obtained by using a linear regression model; the experimental planning method based on the linear regression model can improve the accuracy of parameter identification. For example, the optimality principles corresponding to A optimization, T optimization, D optimization, G optimization, and E optimization in linear regression analysis. See Table 1. Among them, A optimization and T optimization operate on the trace of the covariance matrix and the information matrix respectively. Both of these methods minimize the average variance of the estimated parameters, but this method is unreliable because the elements of the off-diagonal information matrix are not included in the objective function. Additionally, if the units of the parameters are different, it is difficult to apply these two criteria.

[0055] D optimization is to maximize the determinant of the information matrix. This optimization tends to attach extremely great importance to the most sensitive parameters of the model.

[0056] G optimization is to seek to minimize the largest diagonal element in the covariance matrix.

[0057] E optimization is to minimize the largest eigenvalue of the covariance matrix. The purpose is to minimize the largest dispersion of all possible standard linear combination parameter evaluations.

[0058] Table 1 Objective functions for experimental planning in classical regression analysis

[0059]

[0060]

[0061] Industrial robots usually operate with limited configurations, and the goal of calibration is to ensure the best accuracy of the robot in a specific state. The objective functions of all the linear regression optimization criteria listed in Table 1 can be easily adapted to various applications where positioning accuracy is crucial. For example, for grasping and moving operations, when the robot only performs tasks at two target positions, using these two measurement poses is sufficient to achieve the best accuracy after compensating for elastic errors. Similarly, for machining large-sized workpieces, multiple measurement pose points can be introduced.

[0062] Further, in step S3, based on the optimal measurement pose and load combination obtained in step S2, a calibration experiment is carried out to obtain multiple sets of data including the pose deviation of the end effector and the magnitude of the external force, providing a basis for subsequent parameter identification. Specifically, known external forces are applied to the robot end effector in various ways, such as force sensors or counterweights. The force sensor is installed on the robot end effector, and the force is applied through the contact between the robot and the external environment, and the magnitude and direction of the force are measured in real time. Or add a counterweight with a known mass to the end effector and use gravity as the external force. In this step, the pose of the robot is measured twice before and after applying the external force to the robot end effector, and a high-precision measurement device, such as a laser tracker, is used to measure the actual pose of the robot under different external forces. Multiple measurement points are arranged in the robot motion space, the pose data of the robot at each measurement point are recorded, and the deviation of the end effector is calculated based on the difference. In addition, a force sensor is used to measure the magnitude of the applied external load. The result of this step is to record multiple sets of data on the pose deviation and external force magnitude of the end effector.

[0063] Further, the main purpose of parameter identification in step S4 is to obtain the elastic static stiffness parameters required for the robot elastic static calibration stiffness model through experiments. This step takes the pose deviation and external force data collected in step S3 as the input (i.e., the extended elastic static model), and uses a numerical optimization algorithm (such as intelligent optimization algorithms like genetic algorithms, particle swarm algorithms, etc.) to identify the unknown elastic static stiffness parameters in the robot elastic static calibration stiffness model; at the same time, evaluate the accuracy of the identification of the unknown elastic static stiffness parameters and the positioning accuracy.

[0064] The relationship between the displacement of the robot end effector under the action of an external force, the elastic characteristics of each part of the robot, and the external force applied to the robot end effector in the robot elastic static calibration stiffness model is expressed by Equation (1):

[0065] ΔP = K -1 ·F + ∈ (1)

[0066] Where, ΔP is the displacement of the robot end effector under the action of an external force; K is the stiffness matrix, which is used to describe the elastic characteristics of each part of the robot; F is the external force applied to the robot end effector; ∈ is the measurement noise and model error; the significance of Equation (1) is to solve the unknown parameters in the stiffness matrix K by measuring the displacement of the end effector and the applied external force using numerical methods.

[0067] Furthermore, the main difficulty in the elastic static calibration in step S5 lies in the large number of parameters and large computational amount of the robot's elastic static calibration stiffness model, which is not conducive to practical applications. In order to obtain a reliable stiffness model suitable for rapid calibration, before the parameter identification in step S4, the parameters in the robot's elastic static calibration stiffness model are reduced by the following methods:

[0068] 1) Order reduction processing: Before applying the least squares method for parameter identification, reduce the order of the robot's stiffness model to eliminate redundant parameters to ensure the invertibility of the information matrix; the information matrix includes the observation matrix or the Jacobian matrix; the observation matrix is used to map the signal from a high-dimensional space to a low-dimensional space while retaining the key information of the signal, so that the original signal can be accurately restored during the subsequent signal reconstruction process; in compressive sensing, the observation matrix is used for the sparse representation and reconstruction of the signal, and by designing an observation matrix that meets specific conditions, efficient sampling and accurate reconstruction of the signal can be achieved; in the engineering field, such as robotics, the Jacobian matrix is used to describe the influence of the change in the robot's joint angles on the pose of the end effector.

[0069] For example, the link stiffness matrix consists of a 6x6 matrix containing 36 parameters. According to the energy conservation principle of conservative systems, the stiffness matrix needs to satisfy symmetry and positive definiteness, so the 36 parameters can be reduced to 21. If further considering material isotropy or specific process constraints, the parameters can be reduced to 9 - 12;

[0070] 2) Remove unimportant parameters: Among the remaining non-redundant parameters, there are many unimportant parameters with relatively small absolute values, low identification accuracy, and negligible influence on the calibration result of the entire robot. These parameters can be removed from the stiffness model to further reduce the number of parameters.

[0071] 3) Optimize the number of matrix parameters according to the basic properties of other related matrices (such as compliance matrix, template matrix) of the stiffness model.

[0072] Furthermore, the method of optimizing the number of matrix parameters according to the basic properties of other related matrices (such as compliance matrix, template matrix) of the stiffness model specifically includes:

[0073] Merge parameters using the symmetry of the compliance matrix: Based on the symmetry characteristics of the compliance matrix, merge the parameter pairs with symmetric relationships into a single parameter. For example, the cross terms kij and kji in the compliance matrix can be simplified to the same parameter through geometric constraint relationships. This method can reduce the parameter dimension by about 50%.

[0074] Using a template matrix to exclude redundant parameters: Based on the geometric features and material properties of the robotic arm links, a sparse pattern of the stiffness matrix (i.e., the "template matrix") is predefined, and dimensionality reduction is achieved by excluding the parameters corresponding to zero elements. For example, the axial stiffness characteristics of a cylindrical link of a robotic arm can generate a diagonally dominant template matrix.

[0075] Structural adjustment of the compliance matrix and optimization of the observation matrix to achieve parameter integration: In the elastic statics modeling of robots, the coupling characteristics of joint compliance parameters lead to parameter redundancy and difficult identification. Parameter integration is achieved through the structural adjustment of the compliance matrix and the optimization of the observation matrix. For example, diagonal element integration, where some of the parameters of the diagonal elements in the current link compliance matrix are merged into the compliance matrix of the previous link.

[0076] The model parameter reduction method proposed above significantly reduces the number of parameters to be identified while maintaining the integrity of the physical meaning. However, the simplified stiffness model may still have redundancy. At the same time, due to the insufficient rank of the observation matrix, there may be multiple feasible solutions for the identification of stiffness parameters in the redundant robotic arm stiffness model. Therefore, an optimization algorithm is still needed to screen the optimal solution. The present invention uses a numerical optimization method to solve this problem, minimizing the calculation time and improving the convergence speed while meeting the calibration accuracy requirements.

[0077] Furthermore, the kinematic model of the robot in step S5 is represented by equation (2):

[0078] p = f(q i ) (2)

[0079] where p represents the position of the robot end effector in the Cartesian coordinate system, and this position can be used to determine the distance of the robot relative to the safety fence or other reference points; f is a function representing the forward kinematic model of the robot.

[0080] Furthermore, based on two evaluation criteria: calculation time and the ability to find the optimal solution, the present invention studied and compared two traditional algorithms: random search and gradient search, and two artificial intelligence algorithms: genetic algorithm and particle swarm algorithm. The results are shown in Table 3. The algorithms were verified using Matlab 2020, and the programs were run on a computer with an i7-8750H processor and 30G of memory.

[0081] The following takes the ABB6700 industrial robot as an example to illustrate the calibration method of the present invention, which specifically includes the following process:

[0082] The first step is to establish a robotic arm elastic static calibration stiffness model, including:

[0083] Simulating the displacement and rotation of the flexible link through six-degree-of-freedom springs, corresponding to a 6×6 link stiffness matrix;

[0084] The flexible joint is simulated by a single-degree-of-freedom spring, corresponding to a 1x6 joint stiffness matrix;

[0085] By combining the local stiffness matrices of each flexible link and flexible joint in the global coordinate system according to the kinematic chain, the equivalent stiffness model of the robot is obtained, that is, the stiffness matrix Kf ∈ R of the robot system is obtained; 42×42 ;

[0086] As Figure 2 shown, the robot includes a fixed base 1, a plurality of flexible links provided on the fixed base 1, flexible joints provided between the plurality of flexible links, and an end effector 3 for contacting a workpiece. The robot is in the process of machining the mechanical blank of the workpiece 6, and an external force F is applied to the end effector of the robot. In order to establish a complete robot stiffness model, the flexible link is simulated by a six-degree-of-freedom spring (3 for simulating displacement + 3 for simulating rotation), corresponding to a 6×6 link stiffness matrix, and the flexible joint is simulated by a single-degree-of-freedom spring, corresponding to a 1x6 joint stiffness matrix. The global stiffness matrix is obtained by combining the local stiffness matrices of each link and joint in the global coordinate system according to the kinematic chain, and then the equivalent stiffness model of the robot is established. On this basis, the stiffness matrix Kf ∈ R of the robot system is obtained; 42×42 . The dimension of the 42×42 stiffness matrix comes from the total degrees of freedom of the robot system: each of the 6 flexible joints contributes 1 degree of freedom, and each of the 6 flexible links contributes 6 degrees of freedom (a total of 36), and the total degrees of freedom is 6 + 36 = 42.

[0087] In the second step, constraints are configured for the robot; the configuration constraints of the robot include joint physical limitations, safety fence limitations, and end external force limitations;

[0088] The physical limitation q of each robot joint low < q i < q hi , q low represents the minimum position limit of the joint, that is, the minimum angle or position that the joint can reach; q hi represents the maximum position limit of the joint, that is, the maximum angle or position that the joint can reach; q i represents the actual position or angle of joint i, which is the specific state of the joint when the robot is in motion. This value must always be between q low and q hi to ensure the safe and stable operation of the robot; these limitations can be obtained from the robot manual;

[0089] The distance of the robot relative to the safety fence can be calculated from the direct kinematics of the robot p = f(q i); p represents the position p of the robot end - effector in the Cartesian coordinate system, which can be used to determine the distance of the robot relative to the safety fence or other reference points; f(q i ) represents a function that calculates the position p of the robot end - effector in the Cartesian coordinate system based on the angles or positions q of each joint of the robot i of the robot. The function f represents the forward kinematic model of the robot;

[0090] The external force limits at the robot end include the external force wF and the external torque wM acting on the end - effector or the robot flange. These limits can also be obtained from the allowable load parameter values of the robot in the robot manual.

[0091] The third step is to apply and measure the external force on the robot

[0092] The external force wi = [wF wM]T acting on the robot end - effector, where wF and wM are the external force and external torque acting on the end - effector or the robot flange respectively, including gravity. For example, in the experiment, a standard weight 4 is suspended at the end of the robot flange. The external force wF and the external torque wM are generated by the standard weight suspended at the end, as Figure 2 shown. Before and after applying the external force, a laser tracker 5 (AT960) is used to record the actual displacement of the end of the robot flange. The accuracy of this laser tracker AT960 can reach the micron level (such as ±5μm), which is sufficient to capture small elastic deformations.

[0093] The fourth step is to determine the target trajectory and the measured pose

[0094] Select a square with a side length of 50 cm as the target trajectory of the robot end - effector; select the center of this square as the measured pose;

[0095] The fifth step is to select the objective function and experimental planning in sequence;

[0096] Before comparing numerical optimization algorithms, it is important to select an appropriate objective function. In numerical optimization, the objective function can be selected according to the actual situation as one of the methods described in Table 2; use the objective function in Table 2 and the measured pose obtained in the fourth step during the experimental planning stage;

[0097] Table 2 Calibration results of experimental planning using different objective functions

[0098] Serial number Method Average deviation (mm) 1 A optimization 1.07 2 D optimization 0.88 3 G optimization 0.96 4 E optimization 1.23 5 Optimal measurement pose 0.66

[0099] The sixth step is to use numerical optimization methods such as genetic algorithms to identify and optimize the parameters for the total number of measured poses;

[0100] Table 3 compares the final accuracy of the calibrated robot system. The subsequent numerical optimization algorithm uses the genetic algorithm, and the total number of measured poses m = 4;

[0101] Comparison of calibration results using various numerical optimization algorithms and the total number of experimental configurations

[0102]

[0103] The first algorithm in Table 3 is to select an optimal solution from a group of randomly generated solutions. This algorithm outputs results very quickly and can find the optimal solution in less than 10 minutes. However, the optimal solution obtained by this method is worse in calibration accuracy than the solutions obtained by other algorithms. The second algorithm is to use gradient search. This algorithm has a high calibration accuracy, but the calculation time is too long and it is not convenient for practical application in engineering. The third genetic algorithm used in the present invention has a population size of 200. This algorithm can obtain a high final accuracy after calibration, and the convergence speed is also relatively fast. When the number of measured poses increases by 4 times, the search time only increases by 2 times. The present invention also compares and uses the particle swarm algorithm. The difference between this algorithm and other optimization algorithms is that it only requires the objective function and does not depend on the gradient or differential form of the problem. The number of particles used is 400. The calibration result of this algorithm is close to that of the genetic algorithm, but this algorithm has a faster convergence speed.

[0104] From the perspective of the final accuracy rate and search time, the present invention recommends using numerical optimization algorithms based on artificial intelligence, such as genetic algorithms or particle swarm algorithms. Compared with traditional search algorithms, both of these methods can shorten the time to search for the optimal value by dozens of times at the same or higher accuracy.

[0105] The present invention uses numerical optimization methods such as genetic algorithms to perform parameter identification and optimization for the case where the total number of measured poses is 4; according to the optimization results, it can be seen that the method of measuring poses based on the above numerical optimization algorithm can achieve the best accuracy of the target trajectory of the robot end effector, thereby proving the effectiveness of the proposed method.

[0106] Through the method of the present invention, elastic static calibration of industrial robots can be effectively carried out, and the positioning accuracy of the robots can be improved. Especially in the parameter identification step, through numerical optimization algorithms and appropriate order reduction processing, the amount of calculation can be significantly reduced and the calibration efficiency can be improved. Using artificial intelligence-based methods to expand the search range of parameter values and the number of model parameters improves the efficiency and accuracy of obtaining robot precision calibration and improves production efficiency.

[0107] As Figure 3As shown in the figure, the second aspect of the present invention provides an industrial robot calibration system based on elastic static compliance calibration for implementing the industrial robot calibration method based on elastic static compliance calibration, including a first main module, a second main module, a third main module, a fourth main module, and a fifth main module; wherein,

[0108] The first main module is used to establish a robot elastic static calibration stiffness model considering the elastic deformation of each link of the robot and joint flexibility by improving and supplementing the robot basic elastic statics model;

[0109] The second main module is used to screen the optimal measurement pose and load combination of the robot by using artificial intelligence algorithms with the performance indicators of the mechanical processing process characteristics, the geometry and physical limitations of the work cell;

[0110] The third main module is used to apply an external force to the robot end effector in the state of the optimal measurement pose and load combination of the robot obtained by the second main module, use a high-precision measurement device to obtain the actual pose data of the robot before and after applying the external force, and record the pose deviation of the end effector and the magnitude of the external force;

[0111] The fourth main module is used to use numerical optimization algorithms (such as intelligent optimization algorithms like genetic algorithms, particle swarm algorithms, etc.), with the pose deviation and external force data obtained by the third main module as inputs, to identify the unknown elastic static stiffness parameters in the robot elastic static calibration stiffness model, and at the same time evaluate the accuracy and positioning accuracy of the identification of the elastic static stiffness parameters;

[0112] The fifth main module is used to apply the elastic static stiffness parameters identified by the fourth main module to correct the kinematic model of the robot, calculate the pose error caused by elastic deformation, and compensate the pose error into the control command of the robot to improve the positioning accuracy of the robot.

[0113] It should be noted that the industrial robot calibration system based on elastic static compliance calibration provided in this embodiment can be a computer program (including program code) running in a computer device. For example, the industrial robot calibration system based on elastic static compliance calibration is an application software; the industrial robot calibration system based on elastic static compliance calibration can be used to execute the corresponding steps in the above method provided in the embodiments of the present application.

[0114] In some feasible embodiments, the industrial robot calibration system provided in this embodiment based on elastic static compliance calibration can be implemented in a combination of software and hardware. As an example, the industrial robot calibration system provided in the embodiments of the present application can be a processor in the form of a hardware decoding processor, which is programmed to execute the industrial robot calibration method based on elastic static compliance calibration provided in the embodiments of the present application. For example, the processor in the form of a hardware decoding processor can adopt one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), or other electronic components.

[0115] In some feasible embodiments, the industrial robot calibration system provided in this embodiment based on elastic static compliance calibration can be implemented in software, which can be software in the form of programs and plugins, and includes a series of modules, such as a first main module, a second main module, a third main module, and a fourth main module, to implement the industrial robot calibration method based on elastic static compliance calibration provided in the embodiments of the present invention.

[0116] The industrial robot calibration system provided in this embodiment, by establishing an elastic static calibration stiffness model considering the elastic deformation of each link of the robot and joint flexibility, using artificial intelligence algorithms to screen the optimal measurement poses and load combinations, adopting numerical optimization algorithms to identify unknown elastic statics stiffness parameters, and performing order reduction processing and parameter optimization on the model, significantly improves the accuracy and efficiency of industrial robot calibration, while reducing the computational amount and the number of experiments, enhancing the applicability and flexibility of the calibration method, and meeting the requirements of high-precision machining and complex assembly tasks.

[0117] The third aspect of the present invention further provides an electronic device. Figure 4 is a schematic structural diagram of the electronic device of this embodiment, as Figure 4As shown in the figure, the electronic device 1000 in this embodiment may include: a processor 1001, a network interface 1004, and a memory 1005. In addition, the above-mentioned electronic device 1000 may further include: a user interface 1003 and at least one communication bus 1002. Among them, the communication bus 1002 is used to realize the connection and communication between these components. Among them, the user interface 1003 may include a display screen (Display) and a keyboard (Keyboard). Optionally, the user interface 1003 may further include a standard wired interface and a wireless interface. The network interface 1004 may optionally include a standard wired interface and a wireless interface (such as a WI-FI interface). The memory 1005 may be a high-speed RAM memory or a non-volatile memory, such as at least one disk memory. Optionally, the memory 1005 may also be at least one storage device located far from the aforementioned processor 1001. As Figure 4 shown, the memory 1005, as a computer-readable storage medium, may include an operating system, a network communication module, a user interface module, and a device control application program.

[0118] As Figure 4 shown in the electronic device 1000, the network interface 1004 can provide network communication functions; while the user interface 1003 is mainly used to provide an input interface for users; and the processor 1001 can be used to call the device control application program stored in the memory 1005 to achieve:

[0119] By improving and supplementing the robot's basic elastic static model, a robot elastic static calibration stiffness model considering the elastic deformation of each link of the robot and joint flexibility is established;

[0120] Taking the characteristics of the machining process, the geometry and physical limitations of the work unit as performance indicators, an artificial intelligence algorithm is used to screen the best measurement pose and load combination of the robot;

[0121] An external force is applied to the robot end effector in the state of the best measurement pose and load combination of the robot obtained by the second main module. Using a high-precision measurement device, the actual pose data of the robot before and after the external force is applied is obtained, and the pose deviation of the end effector and the magnitude of the external force are recorded;

[0122] Using a numerical optimization algorithm (such as intelligent optimization algorithms like genetic algorithms and particle swarm algorithms), taking the pose deviation and external force data obtained by the third main module as input, the unknown elastic static stiffness parameters in the robot elastic static calibration stiffness model are identified, and at the same time, the accuracy and positioning accuracy of the identification of the elastic static stiffness parameters are evaluated;

[0123] Apply the elastostatic stiffness parameters identified by the fourth main module to correct the kinematic model of the robot, calculate the pose error caused by elastic deformation, and compensate the pose error into the control command of the robot to improve the positioning accuracy of the robot.

[0124] It should be understood that in some feasible embodiments, the above-mentioned processor 1001 may be a central processing unit (CPU), and this processor may also be other general-purpose processors, DSPs, ASICs, FPGAs or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or this processor may also be any conventional processor, etc. The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A part of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0125] In specific implementation, the above-mentioned electronic device 1000 may execute the implementation manners provided in each step as described above Figure 1 through each built-in functional module thereof. For specific details, reference may be made to the implementation manners provided in each step as described above, which will not be elaborated herein.

[0126] The electronic device provided in this embodiment establishes an elastic static calibration stiffness model considering the elastic deformation of each link of the robot and the joint flexibility, uses an artificial intelligence algorithm to screen the optimal measurement pose and load combination, uses a numerical optimization algorithm to identify unknown elastostatic stiffness parameters, and performs order reduction processing and parameter optimization on the model, significantly improving the accuracy and efficiency of industrial robot calibration. At the same time, it reduces the computational amount and the number of experiments, enhances the applicability and flexibility of the calibration method, and meets the requirements of high-precision machining and complex assembly tasks.

[0127] This application embodiment also provides a computer-readable storage medium storing a computer program, which is executed by a processor to implement Figure 1 the methods provided in each step as described above. For specific details, reference may be made to the implementation manners provided in each step as described above, which will not be elaborated herein.

[0128] The computer-readable storage medium provided in this embodiment establishes an elastic static calibration stiffness model considering the elastic deformation of each link of the robot and the joint flexibility, uses an artificial intelligence algorithm to screen the optimal measurement pose and load combination, uses a numerical optimization algorithm to identify unknown elastostatic stiffness parameters, and performs order reduction processing and parameter optimization on the model, significantly improving the accuracy and efficiency of industrial robot calibration. At the same time, it reduces the computational amount and the number of experiments, enhances the applicability and flexibility of the calibration method, and meets the requirements of high-precision machining and complex assembly tasks.

[0129] Any reference to memory, storage, database, or other media used in the embodiments provided in this application may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0130] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the present invention and is not used to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. An industrial robot calibration method based on elastic static compliance calibration, characterized in that: The steps include: S1: Establish a robot elastic static calibration stiffness model that takes into account the elastic deformation of each link and the flexibility of the joints of the robot; S2: Taking the robot machining process characteristics, work unit geometry and physical limitations as performance indicators, artificial intelligence algorithms are used to select the best measurement posture and load combination of the robot; S3: applying an external force to the robot end effector in the optimal measurement posture and load combination state of the robot obtained in step S2, obtaining the actual posture data of the robot before and after the external force is applied using a high-precision measuring device, and recording the posture deviation of the end effector and the magnitude of the external force; S4: using a numerical optimization algorithm, taking the posture deviation and external force data obtained in step S3 as input, identifying unknown elastic static stiffness parameters in the elastic static calibration stiffness model of the robot, and evaluating the accuracy of the elastic static stiffness parameter identification and the positioning accuracy; S5: Apply the elastic static stiffness parameters obtained by step S4 to modify the kinematic model of the robot, calculate the posture error caused by elastic deformation, and compensate the posture error into the control instructions of the robot to improve the positioning accuracy of the robot.

2. The industrial robot calibration method based on elastic static compliance calibration according to claim 1, characterized in that: Step S2 includes using the experimental planning method of the linear regression model to select the best combination from a large number of possible measurement postures and load combinations according to optimality principles such as A optimization and D optimization, and then determine the experimental planning scheme.

3. The industrial robot calibration method based on elastic static compliance calibration according to claim 1, characterized in that: The machining process features in step S2 include blank manufacturing, grasping or handling; the artificial intelligence algorithm includes genetic algorithm and particle swarm algorithm.

4. The industrial robot calibration method based on elastic static compliance calibration according to claim 1, characterized in that: Applying an external force to the robot end effector in step S3 includes installing a force sensor on the robot end effector, or adding a counterweight of known mass to the end effector.

5. The industrial robot calibration method based on elastic static compliance calibration according to claim 4, characterized in that: Step S3 also includes measuring the robot's posture twice before and after the robot's end effector applies external force, using high-precision measuring equipment to measure the robot's actual posture under different external forces; arranging multiple measurement points in the robot's motion space, recording the robot's posture data at each measurement point, and calculating the end effector deviation based on the difference.

6. An industrial robot calibration method based on elastic static compliance calibration according to any one of claims 1 to 5, characterized in that: In step S4, the relationship between the displacement of the robot end effector under the action of external force, the elastic characteristics of each part of the robot, and the external force applied to the robot end effector in the robot elastic static calibration stiffness model is expressed by formula (1): ΔP=K -1 ·F+∈ (1) Among them, ΔP is the displacement of the robot end effector under the action of external force; K is the stiffness matrix, which is used to describe the elastic characteristics of each part of the robot; F is the external force applied to the robot end effector; ∈ is the measurement noise and model error.

7. An industrial robot calibration method based on elastic static compliance calibration according to any one of claims 1 to 5, characterized in that: Step S4 includes reducing the parameters in the robot elastic static calibration stiffness model by the following method before parameter identification: 1) Order reduction: Before applying the least squares method for parameter identification, the stiffness model of the robot is reduced to eliminate redundant parameters to ensure the reversibility of the information matrix; 2) Remove unimportant parameters from the remaining non-redundant parameters; 3) Optimize the matrix parameters according to the basic properties of the compliance matrix and template matrix of the stiffness model.

8. The industrial robot calibration method based on elastic static compliance calibration according to claim 7, characterized in that: The optimization of matrix parameters according to the basic properties of the compliance matrix and the template matrix of the stiffness model includes: Based on the symmetry characteristics of the compliance matrix, the parameter pairs with symmetric relationship are merged into a single parameter; Based on the geometric characteristics and material properties of the robot arm connecting rod, the template matrix of the stiffness matrix is ​​predefined, and the dimension reduction is achieved by excluding the parameters corresponding to the zero elements; Parameter integration is achieved through structural adjustment of the compliance matrix and optimization of the observation matrix.

9. An industrial robot calibration system based on elastic static compliance calibration, characterized in that: The method for calibrating an industrial robot based on elastic static compliance calibration according to any one of claims 1 to 8 comprises a first main module, a second main module, a third main module, a fourth main module and a fifth main module; wherein: The first main module is used to establish a robot elastic static calibration stiffness model that takes into account the elastic deformation of each link and joint flexibility of the robot by improving and supplementing the basic elastic static model of the robot; The second main module is used to select the best measurement posture and load combination of the robot using artificial intelligence algorithms based on the machining process characteristics, work unit geometry and physical limitations as performance indicators; The third main module is used to apply external force to the robot end effector under the best measured posture and load combination state of the robot obtained by the second main module, obtain the actual posture data of the robot before and after the external force is applied by using high-precision measuring equipment, and record the posture deviation of the end effector and the magnitude of the external force; The fourth main module is used to use a numerical optimization algorithm (such as a genetic algorithm, a particle swarm algorithm, or other intelligent optimization algorithms) to identify unknown elastic static stiffness parameters in the elastic static calibration stiffness model of the robot using the posture deviation and external force data obtained by the third main module as input, and to evaluate the accuracy of the elastic static stiffness parameter identification and the positioning accuracy. The fifth main module is used to apply the elastic static stiffness parameters identified by the fourth main module to modify the robot's kinematic model, calculate the posture error caused by elastic deformation, and compensate the posture error into the robot's control instructions to improve the robot's positioning accuracy.

10. An electronic device, characterized in that: comprising a processor and a memory, wherein the processor and the memory are connected to each other; The memory is used to store computer programs; The processor is configured to execute the industrial robot calibration method based on elastic static compliance calibration according to any one of claims 1 to 8 when calling the computer program.

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