Robot grading calibration method based on distance error model

Abstract

The invention discloses a robot grading calibration method based on a distance error model, and belongs to the field of industrial robot calibration. Firstly, a robot distance error model is established based on a D-H method; constructing a fitness function based on a distance error model; optimizing and identifying the connecting rod parameter error by adopting an improved particle swarm algorithm; and the obtained connecting rod parameter error is compensated to a robot controller to complete geometric factor error compensation of the robot. Secondly, cube grid division is conducted on the working space of the robot, errors of all vertexes of a cube are measured, and non-geometric errors, caused by environment factors such as temperature rise and humidity and loads, of the robot are compensated based on spatial interpolation; according to the method, the distance error model is adopted, so that errors caused by coordinate system conversion can be effectively avoided, and non-geometric factor errors can be compensated. Compared with a traditional least square method parameter identification process, the problem that errors are large due to complex matrix calculation and matrix singularity can be solved, and the parameter identification precision is improved.

Description

Technical Field

[0001] The present invention relates to the field of industrial robot calibration, and in particular to a robot hierarchical calibration method based on a distance error model. Background Art

[0002] With the continuous advancement of industrialization, robots have been widely used in industrial production, aerospace, medical, service and other fields. Although robots have high repeatability, their absolute positioning accuracy often does not meet industrial requirements. In addition, due to robot processing errors, assembly errors and mechanical wear during use, the absolute positioning accuracy of robots cannot be guaranteed.

[0003] At present, most of the robot calibration methods are single-level calibration, which only considers the errors caused by the robot's geometric factors, but not the errors caused by the robot's non-geometric factors. Moreover, most of them establish the robot's error model based on the position error, so coordinate transformation is required. Since coordinate transformation is difficult to complete accurately and the operation is complicated, it will bring new errors. For example, the Chinese patent with publication number CN118752481A only calibrates the robot's geometric factors based on position errors. For another example, the publication number CN118061181A, named a robot calibration method, system and device based on a gravitational search algorithm, and the announcement number CN117325156B, named a parallel robot kinematic calibration method and device based on an improved gray wolf algorithm, the disclosed solutions are only for the robot's geometric factor errors. The publication number is CN114406991A, and its name is Industrial Robot Calibration and Spatial Position Measurement Method Based on Cable Encoder. It uses a three-station cable encoder to measure data and uses the least squares method to identify the connecting rod parameters. It is difficult to avoid the matrix singularity problem of the least squares parameter identification method during the calculation process, which affects the identification accuracy. Summary of the invention

[0004] The purpose of the present invention is to provide a robot hierarchical calibration method based on a distance error model, to perform geometric factor calibration based on the distance error model to avoid introducing additional errors, to design a normal distribution curve to control the change of the algorithm's inertia coefficient, and to introduce a control factor to improve the particle position update formula to improve the particle swarm algorithm, thereby achieving the purpose of avoiding local optimal solutions. Based on spatial interpolation, the robot is compensated for errors caused by non-geometric factors caused by environmental factors (such as temperature rise, humidity, etc.) and load. In summary, a comprehensive and high-precision robot accuracy calibration is achieved.

[0005] The technical solution adopted by the present invention is: a robot classification calibration method based on a distance error model, comprising the following steps:

[0006] S1: Construct robot distance error model based on DH method;

[0007] S2: Define the algorithm to identify the fitness function;

[0008] S3: Improve the particle swarm algorithm to find the optimal identification of the connecting rod parameter error and obtain the connecting rod parameter error of the robot;

[0009] S4: Correct the link parameter error data to the robot controller to complete the robot geometric factor calibration.

[0010] S5: Divide the robot workspace into a cube grid, measure and calculate the errors of the grid vertices.

[0011] S6: Error compensation is performed based on spatial interpolation to complete the calibration of non-geometric factors.

[0012] Furthermore, the robot distance error model constructed based on the DH method is:

[0013] ΔL=L r -L n

[0014]

[0015]

[0016] Where, L r is the distance between two actual points of the robot, L n is the distance between two theoretical points of the robot, ΔL is the actual distance minus the theoretical distance, is the actual distance between the robot’s i-th point and the i+1-th point, is the theoretical distance between the i-th point and the i+1-th point of the robot. is the theoretical spatial position of the robot's i-th point and i+1-th point obtained by the DH model, is the actual spatial position of the robot's i-th point and i+1-th point. i=l,2,…,N. N is the number of measurement points.

[0017] Furthermore, the fitness function is defined as:

[0018]

[0019] Wherein, N is the number of measurement points. The device is used to measure the distance between spatial points and calculate the fitness function f expression.

[0020] Furthermore, the specific process of optimizing and identifying the connecting rod parameter error using the improved particle swarm algorithm is as follows:

[0021] Step 1: Set the initial parameters of the algorithm, including the search space, the boundary value of the search speed, the population size, and the maximum number of iterations k max ;

[0022] Step 2: Use tent chaotic mapping to initialize the population position. First, generate a chaotic sequence in the search space [0,1], and then complete the population initialization, as shown in the following formula;

[0023]

[0024] x i =f(x n )·(ub-lb)+lb, i=1,2,3...N

[0025] Where α is an arbitrary value in the search space, ub and lb are the upper and lower limits of the search space. i represents the initial position of the particle after the tent chaos mapping, x n is the initial value of the system.

[0026] Step 3: Calculate the inertia weight coefficient w to control the size of the inertia direction in the next iteration direction;

[0027]

[0028] In the formula, w max 、w min is the maximum and minimum value of the inertia coefficient, k is the current iteration number, k max is the maximum number of iterations, η is used to describe the degree of dispersion of the normal distribution, and its value is 0.4433.

[0029] Step 4: Change the particle speed v i (k), we get v i (k+1), perform an iterative optimization; r 1 、r 2 is a random number between [-1,1], x i (k)=[△θ 1 … △θ 6 △a 1 … △a 6 △α 1 … Δα 6 Δd 1 … Δd 6 ], is the robot geometric parameter error; P best,i (k) is the optimal position of the i-th particle; G best is the optimal position of the population.

[0030] v i (k+1)=ωv i(k)+c 1 r 1 (P best，i (k)-x i (k))+c 2 r 2 (G best -x i (k))

[0031]

[0032] x i (k+1)=x i (k)+λv i (k+1)

[0033] In the formula, c 1 、c 2 are self-cognition factors and social cognition factors, respectively. 1 =2, c 2 =2, λ is the control factor; f(x i ) is the fitness value of the ith particle, is the average value of all current particle fitness.

[0034] Step 5: Calculate the value of the fitness function f of the updated particle;

[0035] Step 6: Update the particle's own historical optimal position;

[0036] Step 7: Determine whether the maximum number of iterations k has been reached max If it is not reached, go back to step 3; if it is reached, go to step 8;

[0037] Step 8: Output the current optimal particle, and the algorithm terminates.

[0038] Furthermore, the specific process of performing error compensation based on spatial interpolation and completing non-geometric factor calibration is as follows:

[0039] The robot's workspace is divided into cube grids according to a certain step distance. Figure 2 As shown, the theoretical spatial position P of all 8 vertices of the cube is calculated. n , measure the actual spatial position P of each vertex of the cube r , then the position error corresponding to each vertex of the cube is:

[0040] ΔP i =P r -P n =[Δx i Δy i Δz i ]

[0041] In the formula, Δx i , Δy i , Δz i It is the position error of the robot in the x-axis, y-axis and z-axis directions.

[0042] Then the position error of the robot's target point in the cube grid is estimated. First, the eight vertices P of the cube grid are calculated. i (x i ,y i , z i ) on the position error of the target point P(x, y, z) i :

[0043]

[0044]

[0045] Among them, d i is the robot's target point and the vertices P of the cube i The distance between them is calculated, and then the position error AP (Δx, Δy, △z) of the target point is calculated according to the following formula:

[0046]

[0047]

[0048]

[0049] The calculated position error is used to correct the target point, and the corrected value is used to control the robot movement, thereby improving the robot's movement accuracy.

[0050] The beneficial effects of the present invention are as follows: 1) The geometric factor calibration is performed based on the distance error model to avoid the additional error introduced by the new coordinate conversion. 2) The particle swarm algorithm is improved, a normal distribution curve is designed to control the change of the algorithm inertia coefficient, and a control factor is introduced to improve the particle position update formula to improve the accuracy of the connecting rod parameter identification. 3) The error caused by the non-geometric factors of the robot is compensated based on spatial interpolation to further improve the calibration accuracy of the robot. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Flow chart of the method of the present invention.

[0052] Figure 2 Schematic diagram of grid space division of the present invention.

[0053] Figure 3 This is the spatial grid compensation principle of the present invention.

[0054] Figure 4 This is a schematic diagram of the dimensions of a robot according to the present invention. DETAILED DESCRIPTION

[0055] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0056] A robot classification calibration method based on a distance error model, the specific steps of the method are as follows:

[0057] S1: Construct robot distance error model based on DH method.

[0058] First, create the robot DH parameter table. Figure 4 As an example, according to the robot shown in Figure 4 The robot size parameters are shown, and the robot DH parameter table is established as follows:

[0059]

[0060]

[0061] Then, based on the DH model, the homogeneous transformation matrix T between adjacent joints is established i i-1 , as shown below:

[0062]

[0063] Among them, Z i , X i are the Z axis and X axis of the i-th coordinate system.

[0064] Secondly, the transformation relationship T between the robot terminal coordinate system and the base coordinate system is constructed 0 6 , as shown below:

[0065]

[0066] Among them, α i is the member torsion angle, θ i is the joint angle, d i is the joint length, a i is the length of the rod, n is the representation of the x-axis of the sixth link coordinate system in the base coordinate system, o and a are the representations of the y and z-axes of the sixth link coordinate system in the base coordinate system, and p is the representation of the origin of the sixth link coordinate system in the base coordinate system. The theoretical position T of the robot is obtained. n :

[0067]

[0068] Among them, R n is the robot theoretical posture, Pn is the theoretical spatial position of the robot. Since the robot's link parameters have an error Δα i , △θ i , △d i , △a i , get the actual position T of the robot r :

[0069]

[0070] Among them, Rr is the actual posture of the robot, and Pr is the actual spatial position of the robot.

[0071] Therefore, the distance error model of the robot is:

[0072] ΔL=L r -L n

[0073]

[0074]

[0075] In the formula, ΔL is the actual distance minus the theoretical distance, is the actual distance between the robot’s i-th point and the i+1-th point, is the theoretical distance between the i-th point and the i+1-th point of the robot. is the theoretical spatial position of the robot's i-th point and i+1-th point obtained by the DH model, is the actual spatial position of the robot's i-th point and i+1-th point. i=1,2,…,N. N is the number of measurement points.

[0076] S2: The fitness function is defined as:

[0077]

[0078] Wherein, N is the number of measurement points. The device is used to measure the distance between spatial points and calculate the fitness function f expression.

[0079] S3: The specific process of optimizing and identifying the connecting rod parameter error using the improved particle swarm algorithm is as follows:

[0080] Step 1: Set the initial parameters of the algorithm, including the search space, the boundary value of the search speed, the population size, and the maximum number of iterations k max ;

[0081] Step 2: Use tent chaotic mapping to initialize the population position. First, generate a chaotic sequence in the search space [0,1], and then complete the population initialization, as shown in the following formula;

[0082]

[0083] x i =f(x n )·(ub-lb)+lb, i=1, 2, 3...N

[0084] Where α is an arbitrary value in the search space, ub and lb are the upper and lower limits of the search space. i represents the initial position of the particle after the tent chaos mapping, x n is the initial value of the system.

[0085] Step 3: Calculate the inertia weight coefficient w to control the size of the inertia direction in the next iteration direction;

[0086]

[0087] In the formula, w max 、w min is the maximum and minimum value of the inertia coefficient, k is the current iteration number, k max is the maximum number of iterations, η is used to describe the degree of dispersion of the normal distribution, and its value is 0.4433.

[0088] Step 4: Change the particle speed v i (k), we get v i (k+1), perform an iterative optimization; r 1 、r 2 is a random number between [-1, 1], x i (k)=[△θ 1 … △θ 6 △a 1 … △a 6 △α 1 … Δα 6 Δd 1 … Δd 6 ], is the robot geometric parameter error; P best，i (k) is the optimal position of the i-th particle; G best is the optimal position of the population.

[0089] v i (k+1)=ωv i (k)+c 1 r 1 (P best，i (k)-x i (k))+c 2 r 2 (G best -x i (k))

[0090]

[0091] x i (k+1)=x i (k)+λv i (k+1)

[0092] In the formula, c 1 、c 2 are self-cognition factors and social cognition factors, respectively. 1 =2, c 2 =2, λ is the control factor; f(x i ) is the fitness value of the ith particle, is the average value of all current particle fitness.

[0093] Step 5: Calculate the value of the fitness function f of the updated particle;

[0094] Step 6: Update the particle's own historical optimal position;

[0095] Step 7: Determine whether the maximum number of iterations k has been reached max If it is not reached, go back to step 3; if it is reached, go to step 8;

[0096] Step 8: Output the current optimal particle, and the algorithm terminates.

[0097] S4: The identified error data of the 24 links of the robot's six-link parameters are compensated to the robot controller to complete the robot's geometric factor error calibration.

[0098] S5: Error compensation based on spatial interpolation and the specific process of completing non-geometric factor calibration are as follows:

[0099] First, determine the optimal step length, and randomly select about 15 test points in the robot workspace according to the average distribution. Construct multiple cubic grids with each test point as the center and a step length of 10mm, ranging from 10mm to 300mm. Then use the above-mentioned method based on spatial interpolation to perform error compensation, measure the accuracy of the test points under different step lengths after compensation, and determine the step length with the highest accuracy as the optimal step length.

[0100] The robot's workspace is divided into cube grids according to the optimal step size, such as Figure 2 shown.

[0101] Calculate the theoretical spatial position P of all 8 vertices of the cube n , measure the actual spatial position P of each vertex of the cube r , then the position error corresponding to each vertex of the cube is:

[0102] ΔP i =Pr -P n =[Δx i Δy i Δz i ]

[0103] In the formula, Δx i , Δy i , △z i It is the position error of the robot in the x-axis, y-axis and z-axis directions.

[0104] Then the robot's target point position error in the cube grid is estimated. Figure 3 As shown, P is the target point that the robot wants to reach, P i (i=1, 2...8) are the 8 vertices of the cube mesh. First, calculate the 8 vertices P of the cube mesh. i (x i ,y i , z i ) on the position error of the target point P(x, y, z) i :

[0105]

[0106]

[0107] Among them, d i is the robot's target point P and the cube's vertices P i The distance between (i=1, 2…8) is calculated, and then the position error △P (△x, △y, △z) of the target point is calculated according to the following formula:

[0108]

[0109]

[0110]

[0111] The calculated position error is used to correct the target point, and the corrected value is used to control the robot movement, thereby improving the robot's movement accuracy.

[0112] The present invention provides a more comprehensive and accurate robot calibration method. Most current robot calibration methods are based on single geometric factor error calibration based on position error models. The present invention uses a distance error model to effectively avoid errors caused by coordinate system conversion and can compensate for non-geometric factor errors. Compared with the traditional least squares parameter identification process, the present invention can solve the problem of large errors caused by complex matrix calculations and matrix singularity, and improve the accuracy of parameter identification.

[0113] The above is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited to the above content. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A robot hierarchical calibration method based on a distance error model, characterized in that: The steps include: S1: Construct robot distance error model based on DH method; S2: Define the fitness function to be identified by the improved particle swarm algorithm according to the distance error model; S3: The improved particle swarm algorithm is used to optimize and identify the connecting rod parameter error to obtain the connecting rod parameter error of the robot; S4: Correct the link parameter error data to the robot controller to complete the robot geometric factor calibration; S5: Divide the robot workspace into a cube grid, measure and calculate the errors of the grid vertices; S6: Error compensation is performed based on spatial interpolation to complete the calibration of non-geometric factors.

2. The robot hierarchical calibration method based on the distance error model according to claim 1 is characterized in that: The robot distance error model constructed based on the DH method in S1 is: ΔL=L r -L n Where, L r is the distance between two actual points of the robot, L n is the distance between two theoretical points of the robot, ΔL is the actual distance minus the theoretical distance, is the actual distance between the robot’s i-th point and the i+1-th point, is the theoretical distance between the robot’s i-th point and the i+1-th point, is the theoretical spatial position of the robot's i-th point and i+1-th point obtained by the DH model, is the actual spatial position of the robot's i-th point and i+1-th point, i=1, 2,…, N, where N is the number of measurement points.

3. The robot hierarchical calibration method based on the distance error model according to claim 2 is characterized in that: The fitness function in S2 is f:

4. The robot hierarchical calibration method based on the distance error model according to claim 1 is characterized in that: The specific process of optimizing and identifying the connecting rod parameter error using the improved particle swarm algorithm in S3 is as follows: Step 1: Set the initial parameters of the algorithm, including the search space, the boundary value of the search speed, the population size, and the maximum number of iterations k max ; Step 2: Use tent chaotic mapping to initialize the population position: First, generate a chaotic sequence in the search space [0, 1], and then complete the population initialization, as shown in the following formula; x i =f(x n )·(ub-lb)+lb,i=1,2,3…N In the formula, α is any value in the search space, ub and lb are the upper and lower limits of the search space, and x i represents the initial position of the particle after the tent chaos mapping, x n is the initial value of the system; Step 3: Calculate the inertia weight coefficient w to control the size of the inertia direction in the next iteration direction; In the formula, w max 、w min is the maximum and minimum value of the inertia coefficient, k is the current iteration number, k max is the maximum number of iterations, and η is used to describe the degree of dispersion of the normal distribution; Step 4: Change the particle speed v i (k), we get v i (k+1), perform an iterative optimization; r1, r2 are random numbers between [-1,1], x i (k) = [Δθ1…Δθ6 Δa1…Δa6 Δα1…Δα6 Δd1…Δd6], is the robot geometric parameter error; P best，i (k) is the optimal position of the i-th particle; G best is the optimal position of the population; v i (k+1)=ωv i (k)+c1r1(P best，i (k)-x i (k))+c2r2(G best -x i (k)) x i (k+1)=x i (k)+λv i (k+1) In the formula, c1 and c2 are self-cognition factors and social cognition factors respectively, so that c1 = 2, c2 = 2, and λ is the control factor; f(x i ) is the fitness value of the ith particle, is the average value of the fitness of all particles at present; Step 5: Calculate the value of the fitness function f of the updated particle; Step 6: Update the particle's own historical optimal position; Step 7: Determine whether the maximum number of iterations k has been reached max If it is not reached, go back to step 3; if it is reached, go to step 8; Step 8: Output the current optimal particle, and the algorithm terminates.

5. The robot hierarchical calibration method based on the distance error model according to claim 1, characterized in that: The method for performing error compensation based on spatial interpolation in S6 is: The robot's workspace is divided into cube grids according to the set step length, and the theoretical spatial positions P of all 8 vertices of the cube are calculated. n , measure the actual spatial position P of each vertex of the cube r , then the position error corresponding to each vertex of the cube is: ΔP i =P r -P n =[Δx i Δy i Δz i ] In the formula, Δx i , Δy i , Δz i is the position error of the robot's spatial position in the x-axis, y-axis, and z-axis directions; Then the position error of the robot's target point in the cube grid is estimated. First, the eight vertices P of the cube grid are calculated. i (x i ,y i , z i ) on the position error of the target point P(x, y, z) i : Among them, d i is the robot's target point and each vertex P of the cube i The distance between them is then used to calculate the position error ΔP (Δx, Δy, Δz) of the target point according to the following formula: The calculated position error is used to correct the target point, and the corrected value is used to control the robot movement, thereby improving the robot's movement accuracy.

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