A robot calibration method based on LM and ARO algorithms

Abstract

The present invention discloses a robot calibration method for LM and ARO algorithms, comprising step S1, establishing a robot kinematic error model using an MDH model; step S2, obtaining robot joint data and laser tracker measurement data of sampling points; step S3, calculating the distance values ​​between two points corresponding to the robot end points, and establishing an objective function through the distance difference between the two points; step S4: performing parameter iterative optimization on the objective function of step S3 using the LM‑ARO algorithm to obtain a robot kinematic parameter error value that satisfies the minimum objective function value. The present invention solves the rounding error of high-order terms of the single LM algorithm, and also overcomes the problem of slow search speed and low efficiency caused by the large search range of the single ARO algorithm. No constraints of standard parts are required. At the same time, the calibration cost is low, and the robot kinematic parameter error can be effectively calibrated, significantly improving the accuracy level of the robot.

Description

Technical Field

[0001] The present invention relates to the field of robots, and in particular to a robot calibration method based on LM and artificial rabbit optimization algorithms. Background Art

[0002] Today's manufacturing industry is moving toward intelligent manufacturing. Robots, as a crucial component of intelligent manufacturing, are widely used in aerospace, automotive, automated production, consumer electronics, defense, military, and healthcare. At the same time, the transformation and upgrading of the manufacturing industry, driven by demands for improved product quality and production efficiency, is accelerating demand for robots, while also placing higher demands on robot precision.

[0003] Due to the errors in the production, processing and assembly of robot parts and the deformation errors of the connecting rods during the movement of the robot, errors will occur between the theoretical design values ​​and actual values ​​of the robot's kinematic parameters, thereby affecting the positioning accuracy of the robot. The current methods to improve the robot's positioning accuracy include: (1) Improving the processing technology and manufacturing accuracy during the production, processing and assembly of robot parts. Reducing errors from the source, but this requires high production and processing technology and increases the production cost of the robot. (2) Improving the robot's positioning accuracy by calibrating the robot's kinematic parameter errors. The robot's kinematic parameter error calibration is divided into four steps: modeling, measurement, calibration and compensation. By introducing standard parts or higher-precision measuring instruments, the error between the actual measurement value and the robot model calculation value is obtained. Based on this, the objective function is established, and the kinematic parameter errors of each robot are obtained through the calibration algorithm. These kinematic parameter error values ​​are compensated to the corresponding parameters of the robot's kinematic model to improve the robot's positioning accuracy. This method is relatively simple, efficient and low-cost.

[0004] Robot calibration algorithms are a key component in calibrating robot kinematic parameter errors. Basic algorithms include the LM algorithm and the extended Kalman filter. While these algorithms can effectively improve robot positioning accuracy, they require solving the Jacobian matrix, making them complex in practice. Furthermore, the calibration capabilities of these algorithms are limited by the nonlinearity and complexity of robot kinematic models.

[0005] Evolutionary algorithms are effective in solving nonlinear problems in robot kinematic models, but a single evolutionary algorithm cannot simultaneously meet the calibration accuracy and efficiency requirements for robot parameter calibration. Therefore, there is an urgent need to propose an efficient and high-precision calibration algorithm.

[0006] In view of the above-mentioned deficiencies in the prior art, the present invention is proposed. Summary of the Invention

[0007] The purpose of the present invention is to propose a robot calibration method based on LM and artificial rabbit optimization (ARO) algorithms to improve the calibration efficiency and accuracy of robot kinematic parameter errors.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is: a robot calibration method based on LM and ARO algorithms, which specifically includes the following steps:

[0009] Step S1, using the MDH model to establish a robot kinematic error model;

[0010] Step S2, obtaining robot joint data and laser tracker measurement data of the sampling points;

[0011] Select several points evenly spaced in the robot's workspace, and move the robot to these points in sequence. Record the robot's joint angles at these points, and simultaneously use a laser tracker to measure the coordinates of the robot's end points.

[0012] Step S3: Substitute the joint rotation angle value obtained in step S2 into the MDH model in step S1 to calculate the distance between any two points measured by the robot. Simultaneously, calculate the distance between the two points corresponding to the robot end points measured by the laser tracker obtained in step S2, and establish the objective function based on the distance difference between the two points.

[0013] Step S4: Use the LM-ARO algorithm to iteratively optimize the parameters of the objective function of step S3 to obtain the robot kinematic parameter error value that satisfies the minimum objective function value;

[0014] The specific steps for calibrating the robot using the LM-ARO algorithm are as follows:

[0015] Step S40, initial rapid calibration of the LM algorithm;

[0016] Step S400, initializing LM algorithm parameters;

[0017] Step S401, calculating the Jacobian matrix;

[0018] Step S402, calculating a system of linear equations;

[0019] Step S403, obtaining the robot kinematic parameter error;

[0020] Step S404, determine whether it is within the allowable error range, if not, change the estimated parameters, return to step S401 and iterate again, if yes, stop the iteration and return the robot kinematic parameter error after iteration;

[0021] Step S41, ARO algorithm precise calibration;

[0022] Step S410, initializing ARO algorithm parameters;

[0023] The robot kinematic parameter error value obtained by the LM algorithm calibration in step S40 is used as the center value of the initial range of kinematic parameters searched by the ARO algorithm to initialize the parameters of the ARO algorithm;

[0024] Step S411, calculating the energy factor A(t) to determine whether the rabbit is foraging or hiding randomly;

[0025] Step S412, calculating the fitness function and continuously updating the position of the rabbit;

[0026] Step S413, determining whether the global optimal position is found;

[0027] Determine whether the global optimal value is found or the maximum number of iterations is reached. If not, return to step S411. If yes, obtain the optimal kinematic parameter error of the robot.

[0028] Step S5: Compensate the robot kinematic parameter error values ​​obtained in step S4 into the robot model and conduct experimental verification.

[0029] The preferred technical solution provided by the present invention is:

[0030] In step S1, the specific method of using the MDH model to establish the robot kinematic error model is:

[0031] According to the MDH model, the transformation relationship between adjacent joints of the robot can be expressed as:

[0032]

[0033] Among them, θ i d i 、a i and α i Represent the joint angle, link offset distance, link length, and link torsion angle α respectively i , cθ i =cosθ i , sθ i = sinθ i .

[0034] The present invention further provides the following preferred technical solutions:

[0035] The robot is a UR5 robot with six degrees of freedom, and its end position is expressed as:

[0036]

[0037] Then the transformation matrix error between joints can be expressed by formula (3):

[0038]

[0039] Where Δθ i , Δd i , Δa i , Δα i and Δβ i is the error of each kinematic parameter;

[0040] The end position of the robot is further expressed as:

[0041]

[0042] The positioning error Δp ​​at the end of the robot is expressed as:

[0043]

[0044] Where J is the Jacobian matrix and ΔX is the robot kinematic parameter error, which consists of Δθ, Δd, Δa, Δα, and Δβ.

[0045] The more preferred technical solution provided by the present invention is:

[0046] In step S411, determining whether the rabbit is foraging or hiding randomly is specifically represented as follows:

[0047]

[0048] Where r is a random number in (0,1), T represents the maximum number of iterations, and t is the current number of iterations;

[0049] Circuitous foraging can be expressed by formula (8):

[0050]

[0051] Random hiding can be expressed by formula (9):

[0052]

[0053] in, represents the candidate position of the i-th rabbit at iteration t+1; represents the position of the i-th rabbit in iteration t; i, j = 1,…, n and j ≠ i; r1 is a random number in the interval (0, 1); n1 obeys the standard normal distribution N(0, 1); R represents the operator that simulates the movement characteristics of the rabbit.

[0054] Compared with the prior art, the present invention has the following advantages:

[0055] The robot calibration method based on the LM and ARO algorithms described in the present invention solves the rounding error of high-order terms of the LM algorithm alone, and also overcomes the problems of slow search speed and low efficiency caused by the large search range of the ARO algorithm alone.

[0056] The robot calibration method based on the LM and ARO algorithms described in this paper is relatively simple, does not require the constraints of standard components, and is low-cost. It can effectively calibrate the robot's kinematic parameter errors and significantly improve the robot's accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention;

[0058] Figure 1 Schematic diagram of the robot kinematic parameter error calibration process;

[0059] Figure 2 Schematic diagram of robot positioning error before and after verification of different algorithm calibrations. DETAILED DESCRIPTION

[0060] The present invention will be further clearly and completely described below with reference to the accompanying drawings and embodiments.

[0061] A robot calibration method based on LM and ARO algorithms is used to improve the positioning accuracy of the robot. The calibration process is as follows Figure 1 As shown, the specific steps include:

[0062] Step S1, using the MDH model to establish a robot kinematic error model;

[0063] According to the MDH model, the transformation relationship between adjacent joints of the robot can be expressed as:

[0064]

[0065] Among them, θ i d i 、a i and α i Represent the joint angle, link offset distance, link length, and link torsion angle α respectively i , cθ i =cosθ i , sθ i = sinθ i .

[0066] The robot uses a UR5 robot with six degrees of freedom, and its end position is expressed as:

[0067]

[0068] Due to the influence of errors in processing and assembly on the robot, there is a certain error between the actual value and the theoretical value of the robot's kinematic parameters. The transformation matrix error between the joints can be expressed by formula (3):

[0069]

[0070] Where Δθ i , Δd i , Δa i , Δα i and Δβ i is the error of each kinematic parameter;

[0071] Therefore, the end position of the robot is further expressed as:

[0072]

[0073] The positioning error Δp ​​at the end of the robot is expressed as:

[0074]

[0075] Where J is the Jacobian matrix and ΔX is the robot kinematic parameter error, which consists of Δθ, Δd, Δa, Δα, and Δβ.

[0076] Step S2, obtaining robot joint data and laser tracker measurement data of the sampling points;

[0077] Select several points evenly in the robot workspace, and the robot moves in the workspace to reach these points in turn. Record the joint angles θ of the robot at these points i , and use a laser tracker to measure the coordinates of the robot's end point.

[0078] Step S3: Substitute the joint rotation angle value obtained in step S2 into the MDH model in step S1 to calculate the distance between any two points measured by the robot. Simultaneously, calculate the distance between the two points corresponding to the robot end points measured by the laser tracker obtained in step S2, and establish the objective function based on the distance difference between the two points.

[0079] Step S4: Use the LM-ARO algorithm to iteratively optimize the parameters of the objective function of step S3 to obtain the robot kinematic parameter error value that satisfies the minimum objective function value;

[0080] The specific steps for calibrating the robot using the LM-ARO algorithm are as follows:

[0081] Step S40, initial rapid calibration of the LM algorithm;

[0082] Step S400, initializing LM algorithm parameters;

[0083] Step S401, calculating the Jacobian matrix;

[0084] Step S402, calculating a system of linear equations;

[0085] Step S403, obtaining the robot kinematic parameter error;

[0086] Step S404, determine whether it is within the allowable error range, if not, change the estimated parameters, return to step S401 and iterate again, if yes, stop the iteration and return the robot kinematic parameter error after iteration;

[0087] Step S41, ARO algorithm precise calibration;

[0088] Step S410, initializing ARO algorithm parameters;

[0089] The robot kinematic parameter error value obtained by the LM algorithm calibration in step S40 is used as the center value of the initial range of kinematic parameters searched by the ARO algorithm to initialize the parameters of the ARO algorithm;

[0090] Step S411, calculating the energy factor A(t) to determine whether the rabbit is foraging or hiding randomly;

[0091] The specific method to judge whether the rabbit is foraging or hiding randomly is:

[0092]

[0093] Where r is a random number in (0,1), T represents the maximum number of iterations, and t is the current number of iterations;

[0094] Circuitous foraging can be expressed by formula (8):

[0095] in, represents the candidate position of the i-th rabbit at iteration t+1; represents the position of the i-th rabbit in iteration t; i, j = 1, ..., n and j ≠ i; r1 is a random number in the interval (0, 1); n1 follows the standard normal distribution N(0, 1); R represents the operator that simulates the movement characteristics of the rabbit;

[0096] Random hiding can be expressed by formula (9):

[0097]

[0098] Step S412, calculating the fitness function and continuously updating the position of the rabbit, i.e., the kinematic parameter error value;

[0099]

[0100] Step S413, determining whether the global optimal position is found;

[0101] Determine whether the global optimal value is found or the maximum number of iterations is reached. If not, return to step S411. If yes, obtain the optimal kinematic parameter error of the robot.

[0102] Step S5: Compensate the robot kinematic parameter error values ​​obtained in step S4 into the robot model and conduct experimental verification.

[0103] Step 5: Compensate the robot kinematic parameter error values ​​obtained in step 4 into the robot model and conduct experimental verification.

[0104] According to the above calibration principle, a UR5 robot was used to conduct a calibration experiment to verify the effectiveness of the LM-ARO algorithm. In order to verify the accuracy of the calibration results, 101 points were randomly selected from the robot workspace to form 100 groups of distances for verification. The distance L between the points was calculated using the robot kinematic model. i , and the corresponding distance measured using a laser tracker Calculate the positioning error before compensation, the result is as follows Figure 2 shown.

[0105] Although both the ARO algorithm and the LM-ARO algorithm can obtain the optimal value of the kinematic parameter error, the LM-ARO algorithm converges faster, has higher algorithm efficiency, and higher accuracy. Therefore, when calibrating the robot's kinematic parameter error, the LM-ARO algorithm can be used to calibrate the motion parameter error to improve the robot's positioning accuracy.

[0106] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A robot calibration method based on LM and ARO algorithms, characterized in that: The following steps are involved: Step S1, using the MDH model to establish a robot kinematic error model; Step S2, obtaining robot joint data and laser tracker measurement data of the sampling points; Select several points evenly in the robot's workspace. The robot moves in the workspace to reach these points in sequence. The joint angles of the robot at these points are recorded. At the same time, a laser tracker is used to measure the coordinates of the robot's end points. Step S3: Substitute the joint rotation angle value obtained in step S2 into the MDH model in step S1 to calculate the distance between any two points measured by the robot. Simultaneously, calculate the distance between the two points corresponding to the robot end points measured by the laser tracker obtained in step S2, and establish the objective function based on the distance difference between the two points. Step S4: Use the LM-ARO algorithm to iteratively optimize the parameters of the objective function of step S3 to obtain the robot kinematic parameter error value that satisfies the minimum objective function value; The specific steps for calibrating the robot using the LM-ARO algorithm are as follows: Step S40, initial rapid calibration of the LM algorithm; Step S400, initializing LM algorithm parameters; Step S401, calculating the Jacobian matrix; Step S402, calculating a system of linear equations; Step S403, obtaining the robot kinematic parameter error; Step S404, determine whether it is within the allowable error range, if not, change the estimated parameters, return to step S401 and iterate again, if yes, stop the iteration and return the robot kinematic parameter error after iteration; Step S41, ARO algorithm precise calibration; Step S410, initializing ARO algorithm parameters; The robot kinematic parameter error value obtained by the LM algorithm calibration in step S40 is used as the center value of the initial range of kinematic parameters searched by the ARO algorithm to initialize the parameters of the ARO algorithm; Step S411, calculating the energy factor A(t) to determine whether the rabbit is foraging or hiding randomly; Step S412, calculating the fitness function and continuously updating the position of the rabbit; Step S413, determining whether the global optimal position is found; Determine whether the global optimal value is found or the maximum number of iterations is reached. If not, return to step S411. If yes, obtain the optimal kinematic parameter error of the robot. Step S5: Compensate the robot kinematic parameter error values ​​obtained in step S4 into the robot model and conduct experimental verification.

2. A robot calibration method based on LM and ARO algorithms as claimed in claim 1, characterized in that: In step S1, the specific method of using the MDH model to establish the robot kinematic error model is: According to the MDH model, the transformation relationship between adjacent joints of the robot can be expressed as: Among them, θ i d i 、a i and α i Represent the joint angle, link offset distance, link length, and link torsion angle α respectively i , cθ i =cosθ i , sθ i = sinθ i .

3. A robot calibration method based on LM and ARO algorithms as claimed in claim 2, characterized in that: The robot is a UR5 robot with six degrees of freedom, and its end position is expressed as: Then the transformation matrix error between joints can be expressed by formula (3): Where Δθ i , Δd i , Δa i , Δα i and Δβ i is the error of each kinematic parameter; The end position of the robot is further expressed as: The positioning error Δp ​​at the end of the robot is expressed as: Where J is the Jacobian matrix and ΔX is the robot kinematic parameter error, which consists of Δθ, Δd, Δa, Δα, and Δβ.

4. A robot calibration method based on LM and ARO algorithms as claimed in claim 1, characterized in that: In step S411, determining whether the rabbit is foraging or hiding randomly is specifically represented as follows: Where r is a random number in (0,1), T represents the maximum number of iterations, and t is the current number of iterations; Circuitous foraging can be expressed by formula (8): Random hiding can be expressed by formula (9): in, represents the candidate position of the i-th rabbit at iteration t+1; represents the position of the i-th rabbit in iteration t; i, j = 1,…, n and j ≠ i; r1 is a random number in the interval (0, 1); n1 obeys the standard normal distribution N(0, 1); R represents the operator that simulates the movement characteristics of the rabbit.

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