Deformation error compensation method, device and electronic equipment based on error superposition

Abstract

The present invention relates to a deformation error compensation method, device and electronic device based on error superposition. The method comprises the following steps: decomposing the external force vector according to the robot joint angle through the robot forward kinematics to obtain the force weights in the directions of the first external force, the second external force and the third external force; predicting the first deformation error caused by the first external force according to the robot joint angle through the first deformation error prediction sub-model; predicting the second deformation error caused by the second external force according to the robot joint angle through the second deformation error prediction sub-model; predicting the third deformation error caused by the third external force according to the robot joint angle through the third deformation error prediction sub-model; superimposing the first deformation error, the second deformation error and the third deformation error according to the force weight to obtain the final predicted deformation error; and finally compensating according to the predicted deformation error. The present invention has high prediction accuracy and low training cost.

Description

Technical Field

[0001] The present invention relates to the field of robots, and in particular to a deformation error compensation method, device and electronic equipment based on error superposition. Background Art

[0002] With the reduction of manufacturing costs and the improvement of precision, robots have been widely used in various fields of society. With their high flexibility and versatility, robots have replaced CNC machine tools in some industrial processing fields.

[0003] When a robot carries a heavy load, its structure deforms due to the applied forces. If the robot's motion control algorithm still treats the robot structure as a rigid body and fails to account for this deformation error, the robot's trajectory will inevitably deviate from the intended path, affecting its accuracy and stability. Deformation error is particularly significant in robots with weak rigidity or open-chain serial structures. Therefore, how to compensate for deformation error is a problem that needs to be solved in the field of robotics.

[0004] Existing methods for compensating robot deformation errors primarily include: 1. Reducing deformation errors by optimizing the robot's structure; 2. Real-time online measurement and compensation of deformation errors; and 3. Offline prediction and compensation of deformation errors using mathematical models. The first two solutions are costly and difficult to implement. The third method, offline prediction and compensation using mathematical models, uses a pre-set mathematical model to predict robot deformation errors in advance. This error is then factored into the robot's motion control algorithm and compensated accordingly, thereby improving the robot's motion accuracy and stability. This method significantly reduces computational complexity compared to real-time online measurement, resulting in a highly cost-effective and feasible approach.

[0005] The existing offline deformation error prediction method based on a stiffness model exists. This stiffness model treats the connecting rod as a rigid body and the robot's deformation error as being entirely caused by the torsion of the joints. Existing offline deformation error prediction methods based on stiffness models collect a large amount of deformation error data corresponding to external forces through experiments. This deformation error data is then substituted into the stiffness model to calculate the joint stiffness coefficient. During use, the external force vector is substituted into the stiffness model based on the set joint stiffness coefficient to calculate the predicted deformation error.

[0006] This existing offline deformation error prediction method based on the stiffness model ignores the influence of the connecting rod stiffness and is only applicable to robots with strong connecting rod stiffness. Therefore, it has the defects of low prediction accuracy, poor prediction stability, and cannot be widely applied to most robots. In addition, a large amount of sample data needs to be collected to calculate the joint stiffness parameters, which has a high training cost. Summary of the Invention

[0007] Based on this, the purpose of the present invention is to provide a deformation error compensation method, device and electronic equipment based on error superposition, which has the advantages of high prediction accuracy, good prediction stability, wide applicability to most robots and low training cost.

[0008] A deformation error compensation method based on error superposition includes the following steps: predicting deformation error according to robot joint angle and external force vector to obtain predicted deformation error; compensating robot motion control algorithm according to the predicted deformation error; predicting deformation error according to robot joint angle and external force vector to obtain predicted deformation error, specifically including: decomposing the external force vector according to the robot joint angle through robot forward kinematics to obtain force weights in the directions of first external force, second external force and third external force; predicting the first deformation error caused by the first external force according to the robot joint angle through the first deformation error prediction submodel; predicting the first deformation error caused by the first external force according to the robot joint angle through the second deformation error prediction submodel , predict the second deformation error caused by the second external force; through the third deformation error prediction sub-model, according to the robot joint angle, predict the third deformation error caused by the third external force; according to the force weight, the first deformation error, the second deformation error and the third deformation error are superimposed to obtain the final predicted deformation error; the directions of the first external force, the second external force and the third external force depend on the robot joint angle and the special force conditions used to train the first deformation error prediction sub-model, the second deformation error prediction sub-model and the third deformation error prediction sub-model; the special force condition is the force condition in which the external force on the robot is determined by the robot joint angle; the first external force, the second external force and the third external force are linearly independent.

[0009] The deformation error prediction fusion model of the present invention has an average prediction deviation of 30 μm and a prediction accuracy of 93.7%. Compared with the traditional stiffness model, its prediction deviation is reduced by 63.8%. The deformation error prediction fusion model of the present invention is simple, practical, and widely applicable to most industrial robots. The establishment of the deformation error prediction fusion model does not require consideration of the robot configuration and connecting rod stiffness, nor does it require complex calculations like traditional stiffness models. The process of collecting deformation error data is simple, and no complex and expensive force measurement equipment is required.

[0010] Furthermore, the training method of the first deformation error prediction sub-model includes: STA1, obtaining the robot joint angle under a preset first special force condition, and measuring the first real deformation error corresponding to the robot joint angle; the first special force condition is: the robot is subjected to a first external force determined by the robot joint angle; STA2, inputting the robot joint angle into the first deformation error prediction sub-model to be trained; the first deformation error prediction sub-model outputs the predicted first deformation error; STA3, updating the parameters of the first deformation error prediction sub-model corresponding to the current robot joint angle by comparing the difference between the first deformation error and the first real deformation error; STA4, changing the robot joint angle, keeping the first special force condition unchanged, and repeating steps STA1-STA3, thereby updating the parameters of the first deformation error prediction sub-model corresponding to the new robot joint angle, until all robot joint angles within the preset range are traversed, and the trained first deformation error prediction sub-model is obtained.

[0011] Furthermore, the training method of the second deformation error prediction sub-model includes: STB1, obtaining the robot joint angle under a preset second special force condition, and measuring the second real deformation error corresponding to the robot joint angle; the second special force condition is: the robot is subjected to a second external force determined by the robot joint angle; STB2, inputting the robot joint angle into the second deformation error prediction sub-model to be trained; the second deformation error prediction sub-model outputs the predicted second deformation error; STB3, updating the parameters of the second deformation error prediction sub-model corresponding to the current robot joint angle by comparing the difference between the second deformation error and the second real deformation error; STB4, changing the robot joint angle, keeping the second special force condition unchanged, and repeating steps STB1-STB3, thereby updating the parameters of the second deformation error prediction sub-model corresponding to the new robot joint angle, until all robot joint angles within the set range are traversed, and the trained second deformation error prediction sub-model is obtained.

[0012] Furthermore, the training method of the third deformation error prediction sub-model includes: STC1, obtaining the robot joint angle under a preset third special force condition, and measuring the third real deformation error corresponding to the robot joint angle; the third special force condition is: the robot is subjected to a third external force determined by the robot joint angle; STC2, inputting the robot joint angle into the third deformation error prediction sub-model to be trained; the third deformation error prediction sub-model outputs a predicted third deformation error; STC3, updating the parameters of the third deformation error prediction sub-model corresponding to the current robot joint angle by comparing the difference between the third deformation error and the third real deformation error; STC4, changing the robot joint angle, keeping the third special force condition unchanged, and repeating steps STC1-STC3, thereby updating the parameters of the third deformation error prediction sub-model corresponding to the new robot joint angle, until all robot joint angles within the set range are traversed, and a trained third deformation error prediction sub-model is obtained.

[0013] Furthermore, the first special force condition, the second special force condition and the third special force condition are any one of the force conditions in which the force point of the robot coincides with the end point of the robot or is relatively stationary, the magnitude of the external force is constant, and the external force always points to a fixed point or a fixed direction.

[0014] Furthermore, the first special force condition is specifically as follows: the force point of the robot coincides with the end point of the robot, and the magnitude of the first external force is constant, and the first external force always points to the preset first fixed point; the second special force condition is specifically as follows: the force point of the robot coincides with the end point of the robot, and the magnitude of the second external force is constant, and the second external force always points to the preset second fixed point; the third special force condition is specifically as follows: the force point of the robot coincides with the end point of the robot, and the magnitude of the third external force is constant, and the third external force always points to the preset fixed direction.

[0015] Furthermore, the measurement methods of the first true deformation error, the second true deformation error and the third true deformation error all include: measuring the first position of the end point of the robot in the absence of external force load; measuring the second position of the end point of the robot under special force conditions; calculating the true deformation error based on the first position and the second position; the true deformation error is a vector with the first position as the starting point and the second position as the end point.

[0016] Based on the same inventive concept, the present invention also provides a deformation error compensation device based on error superposition, including: a data acquisition module for acquiring the robot joint angle and external force vector; a deformation error prediction fusion model for predicting the deformation error according to the robot joint angle and the external force vector to obtain the predicted deformation error; a compensation module for compensating the robot motion control algorithm according to the predicted deformation error; wherein, the deformation error prediction fusion model includes: an external force vector decomposition unit for decomposing the external force vector according to the robot joint angle through the robot forward kinematics to obtain the force weights in the directions of the first external force, the second external force and the third external force; a first deformation error prediction sub-model for predicting the first deformation error caused by the first external force according to the robot joint angle; a second ... An error prediction sub-model is used to predict the second deformation error caused by the second external force according to the joint angle of the robot; a third deformation error prediction sub-model is used to predict the third deformation error caused by the third external force according to the joint angle of the robot; an error superposition unit is used to perform error superposition on the first deformation error, the second deformation error and the third deformation error according to the force weight to obtain a final predicted deformation error; the directions of the first external force, the second external force and the third external force depend on the joint angle of the robot and the special force conditions used for training the first deformation error prediction sub-model, the second deformation error prediction sub-model and the third deformation error prediction sub-model; the special force condition is the force condition in which the external force acting on the robot is determined by the joint angle of the robot; the first external force, the second external force and the third external force are linearly independent.

[0017] Furthermore, the training method of the first deformation error prediction sub-model includes: STA1, obtaining the robot joint angle under a preset first special force condition, and measuring the first real deformation error corresponding to the robot joint angle; the first special force condition is: the robot is subjected to a first external force determined by the robot joint angle; STA2, inputting the robot joint angle into the first deformation error prediction sub-model to be trained; the first deformation error prediction sub-model outputs the predicted first deformation error; STA3, updating the parameters of the first deformation error prediction sub-model corresponding to the current robot joint angle by comparing the difference between the first deformation error and the first real deformation error; STA4, changing the robot joint angle, keeping the first special force condition unchanged, and repeating steps STA1-STA3, thereby updating the parameters of the first deformation error prediction sub-model corresponding to the new robot joint angle, until all robot joint angles within the preset range are traversed, and the trained first deformation error prediction sub-model is obtained.

[0018] Based on the same inventive concept, the present invention also provides an electronic device, comprising: a processor; a memory for storing a computer program executed by the processor; wherein, when the processor executes the computer program, it implements any one of the deformation error compensation methods based on error superposition described in claims 1-7.

[0019] For better understanding and implementation, the present invention is described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 Schematic diagram of a module of a robot deformation error compensation device based on error superposition according to the present invention;

[0021] Figure 2 Schematic diagram of the flow of the robot deformation error compensation method based on error superposition of the present invention;

[0022] Figure 3 Schematic diagram of the network structure of the extreme learning machine;

[0023] Figure 4 This is a schematic diagram of a special force situation in which the external force always points to a fixed point in the present invention;

[0024] Figure 5 This is a schematic diagram of a special force situation in which the external force always points to a fixed direction in the present invention;

[0025] Figure 6 Schematic diagram of the measurement position of the deformation error in the simulation experiment of the present invention;

[0026] Figure 7 Schematic diagram of the prediction deviation of the first deformation error prediction sub-model in the simulation experiment of the present invention;

[0027] Figure 8 Schematic diagram of the prediction deviation of the second deformation error prediction sub-model in the simulation experiment of the present invention;

[0028] Figure 9 Schematic diagram of the prediction deviation of the third deformation error prediction sub-model in the simulation experiment of the present invention;

[0029] Figure 10 Schematic diagram of the prediction deviation of the deformation error prediction fusion model in the simulation experiment of the present invention;

[0030] Figure 11 This is a comparison diagram of the actual deformation error and the predicted deformation error in the X direction of the deformation error prediction fusion model in the experiment of the present invention;

[0031] Figure 12 This is a comparison diagram of the actual deformation error and the predicted deformation error in the Y direction of the deformation error prediction fusion model in the experiment of the present invention;

[0032] Figure 13 This is a comparison diagram of the actual deformation error and the predicted deformation error in the Z direction of the deformation error prediction fusion model in the experiment of the present invention;

[0033] Figure 14 Schematic diagram of the prediction deviation of the deformation error prediction fusion model in the experiment of the present invention;

[0034] Figure 15 This is a comparison chart of the prediction deviations between the traditional stiffness model in the prior art and the deformation error prediction fusion model of the present invention. DETAILED DESCRIPTION

[0035] By analyzing the traditional robot joint stiffness model, the inventors found that under the same robot configuration, the deformation error x caused by any external force f can be converted into the superposition of the first deformation error x1, the second deformation error x2 and the third deformation error x3 caused by any three linearly independent first external forces f1, the second external force f2 and the third external force f3, without the need to calculate the actual stiffness matrix. Based on the above findings, the inventors proposed a deformation error compensation method based on error superposition, which sets three sub-models to predict the three deformation errors x1, x2, and x3 caused by three linearly independent external forces f1, f2, and f3 respectively, and obtains the final predicted deformation error x through error superposition, and finally performs error compensation based on the predicted deformation error. The present invention can train the deformation error prediction sub-model only based on the robot joint angle, without adding an external force vector as input for training, thereby reducing the difficulty of model training.

[0036] Specifically, the deformation error x caused by any external force f can be converted into the superposition of the first deformation error x1, the second deformation error x2, and the third deformation error x3 caused by any three linearly independent external forces f1, f2, and f3. The analysis process is as follows:

[0037] (1) Analysis of traditional robot joint stiffness model:

[0038] Industrial robots consist of connecting rods and joints. When a force is applied to the robot's endpiece, the non-rigid connecting rods and joints undergo elastic deformation, causing displacement and deformation errors. Because the stiffness of connecting rods is generally much greater than that of joints, traditional robot stiffness models treat connecting rods as rigid bodies and ignore their deformation under force. Consequently, the robot's deformation errors are entirely caused by the torsion caused by the joints.

[0039] Robot forward kinematics based on exponential product formula

[0040]

[0041] Among them, ξ iis the rotation of each joint.

[0042] According to the principle of virtual work, the relationship between the robot joint torque and the external force is:

[0043]

[0044] Where τ is the robot joint torque, J is the robot Jacobian matrix, and F s is the force screw, p f is the coordinate of the robot's force point, and f is the external force vector.

[0045] Relationship between robot end point velocity and joint angular velocity

[0046]

[0047] Among them, δp is the end point velocity, which can be regarded as a small displacement of the end point, and δθ is the robot joint angular velocity, which can be regarded as a small angular displacement of the joint. is the antisymmetric matrix of p.

[0048] Relationship between joint stiffness and joint torque

[0049] τ=K θ δθ (4)

[0050] where K θ is the joint stiffness diagonal matrix.

[0051] Combining equations (2)(3)(4) we can get

[0052]

[0053] Formula (5) is the relationship between the deformation error and the external force under the traditional robot stiffness model.

[0054] (2) Analysis of robot deformation error:

[0055] set up Then from formula (5) we can get

[0056]

[0057] where K f is the displacement stiffness matrix,

[0058] From formula (6), we can see that in the same robot position, the displacement of the robot end is linearly related to the external force. Even if other factors that cause the robot deformation error are considered, in practice, the robot deformation error and the external force are still approximately linearly related, that is,

[0059] x=K′ f f (7)

[0060] Where x is the deformation error, K′ f is the actual displacement stiffness matrix.

[0061] In a certain position of the robot, there are external force vectors f1, f2, f3 and their corresponding deformation errors x1, x2, x3, and f1, f2, f3 are linearly independent, then there exist a, b, c such that any external force vector f has

[0062]

[0063] where f λ =[f1,f2,f3], called the basis of the force vector, It is called force weight.

[0064] From formula (7), we can see that x1=K′ f f1,x2=K′ f f2,x3=K′ f f3, combined with formula (8), we have

[0065]

[0066] Where x is the deformation error corresponding to the external force vector f.

[0067] From the above analysis, it can be seen that under the same robot configuration, the deformation error x caused by any external force f can be converted into the superposition of the first deformation error x1, the second deformation error x2 and the third deformation error x3 caused by any three linearly independent first external forces f1, second external forces f2 and third external forces f3, without the need to calculate the actual stiffness matrix.

[0068] Example 1

[0069] See also Figure 1-2 , Figure 1 Schematic diagram of a module of a robot deformation error compensation device based on error superposition according to embodiment 1 of the present invention. Figure 2 Schematic diagram of the flow of the robot deformation error compensation method based on error superposition according to embodiment 1 of the present invention.

[0070] Based on the principle that the deformation error x caused by any external force f can be converted into the superposition of the first deformation error x1, the second deformation error x2 and the third deformation error x3 caused by any three linearly independent first external force f1, the second external force f2 and the third external force f3, the robot deformation error compensation device based on error superposition of the present invention includes: a data acquisition module 1, a deformation error prediction fusion model 2 and a compensation module 3.

[0071] The data acquisition module 1 is used to execute step S1: obtain the robot joint angle and external force vector. The robot joint angle refers to the angle between two adjacent links around the common axis in the robot's forward kinematics, which can be obtained by an encoder. Under the condition that the robot joint coordinates and the robot joint angle are known, the position coordinates of the robot end point can be directly calculated. The external force vector refers to the external force acting on the robot, including the magnitude of the external force and the direction of the external force. Obviously, the larger the magnitude of the external force vector, the greater the deformation error; the direction of the external force vector will also affect the deformation error. The robot deformation error compensation method based on error superposition of the present invention needs to predict the deformation error based on the robot joint angle and the external force vector, and finally compensate according to the predicted deformation error.

[0072] The deformation error prediction fusion model 2 is used to execute step S2: performing deformation error prediction according to the robot joint angle and the external force vector to obtain a predicted deformation error.

[0073] Specifically, the deformation error prediction fusion model 2 includes an external force vector decomposition unit 21 , a first deformation error prediction sub-model 22 , a second deformation error prediction sub-model 23 , a third deformation error prediction sub-model 24 and an error superposition unit 25 .

[0074] The external force vector decomposition unit 21 is configured to execute step S21: decomposing the external force vector according to the robot joint angles using robot forward kinematics to obtain force weights λ for the directions of the first external force f1, the second external force f2, and the third external force f3. The directions of the first external force, the second external force, and the third external force depend on the robot joint angles and the specific force conditions used to train the first deformation error prediction sub-model 22, the second deformation error prediction sub-model 23, and the third deformation error prediction sub-model 24. Details are described in detail below in the training method for the first deformation error prediction sub-model 22, the second deformation error prediction sub-model 23, and the third deformation error prediction sub-model 24.

[0075] The first deformation error prediction sub-model 22 is used to perform step S22: predicting a first deformation error x1 caused by a first external force f1 according to the robot joint angle.

[0076] The second deformation error prediction sub-model 23 is used to perform step S23: predicting a second deformation error x2 caused by a second external force f2 according to the robot joint angle.

[0077] The third deformation error prediction sub-model 24 is used to perform step S24: predicting a third deformation error x3 caused by a third external force f3 according to the robot joint angle.

[0078] The error superposition unit 25 is configured to execute step S25: performing error superposition on the first deformation error x1, the second deformation error x2, and the third deformation error x3 according to the force weight λ obtained in step S21 to obtain a final predicted deformation error x.

[0079] The compensation module 3 is used to execute step S3: compensating the robot motion control algorithm according to the predicted deformation error x, thereby improving the accuracy and stability of the robot motion.

[0080] In this embodiment, the first deformation error prediction sub-model 22, the second deformation error prediction sub-model 23, and the third deformation error prediction sub-model 24 are identical ELM (Extreme Learning Machine) models, which output three deformation errors caused by three linearly independent external forces based on the robot's joint angles. In other embodiments, other fitting models may be used in place of the ELM model, and this is not specifically limited by the present invention.

[0081] The working principle of the ELM model adopted in this embodiment is as follows:

[0082] See also Figure 3 , Figure 3 This figure shows the network structure of an extreme learning machine (ELM). The extreme learning machine (ELM) is a machine learning algorithm used to train single-hidden-layer feedforward neural networks. Unlike traditional neural network training algorithms based on gradient descent, the input layer weights and hidden layer biases of an ELM are randomly determined at the outset, while the output layer weights are determined by minimizing a loss function consisting of the error term and the regularization term of the output layer weight norm.

[0083] Let the training set be {x i ,t i |x i ∈R D ,t i ∈R m ,i=1,2,3,…,N}, where x i =[x i1 ,x i2 ,…,x iD ] T , t i =[t i1 ,t i2 ,…,t im ] T . Let the number of nodes in the hidden layer be L and the output of the hidden layer be H(x), then

[0084] H(x)=[h1(x),h2(x),…,h L (x)] (10)

[0085] where h j (x) = g(w j ,b j ,x)=g(w j x+b j ), g(w j x+b j ) is the activation function. The sigmoid function is used as the activation function, that is,

[0086]

[0087] From the above formula and Figure 3 The output of the network shown is

[0088]

[0089] where β=[β1,β2,…,β L ] T .

[0090] When ELM starts training, the input layer weights and hidden layer biases w,b are randomly determined, and the feedforward network output can be obtained through (11) and (12). The objective function is formed by the sum of the variances of the feedforward network output and the training sample output T, that is,

[0091]

[0092] Where H is the hidden layer output, β is the weight from the hidden layer to the output layer, and T is the sample label value. In order to improve the generalization ability of the ELM algorithm, L is introduced. 2 The regularization term regularizes the model, and the objective function becomes:

[0093]

[0094] When the number of hidden layer nodes is less than the number of training samples, the solution is obtained according to the ridge regression principle:

[0095] β=(H T H+cI) -1 H T T (15)

[0096] The first deformation error prediction sub-model 22, the second deformation error prediction sub-model 23, and the third deformation error prediction sub-model 24 are trained by deformation error data samples of the robot under preset special force conditions. The special force condition refers to a situation where the external force acting on the robot is determined by the joint angle of the robot. Specifically, the special force condition can be any one of the force conditions in which the force point of the robot coincides with the end point of the robot or is relatively stationary, and the magnitude of the external force is constant, and the external force always points to a fixed point or a fixed direction. Under this special force condition, the external force acting on the robot can be determined by the position of the end of the robot, that is, by the joint angle of the robot. Therefore, when training the first deformation error prediction sub-model 22, the second deformation error prediction sub-model 23, and the third deformation error prediction sub-model 24, it is no longer necessary to use the external force vector as the input of the sub-model. Instead, it is sufficient to input the joint angle of the robot, which greatly reduces the difficulty and cost of training the model.

[0097] Specifically, the training method of the first deformation error prediction sub-model 22 includes the following steps:

[0098] STA1, obtaining the robot joint angle under a preset first special force condition and measuring the first true deformation error corresponding to the robot joint angle. The first special force condition is: the robot is subjected to a first external force determined by the robot joint angle.

[0099] STA2, input the robot joint angle into the first deformation error prediction sub-model to be trained; the first deformation error prediction sub-model outputs the predicted first deformation error.

[0100] STA3, updating the parameters of the first deformation error prediction sub-model corresponding to the current robot joint angle by comparing the difference between the first deformation error and the first true deformation error.

[0101] STA4: Change the robot joint angle while maintaining the first special force condition. Repeat steps STA1-STA3 to update the parameters of the first deformation error prediction sub-model corresponding to the new robot joint angle. This process continues until all robot joint angles within the preset range have been traversed, resulting in a trained first deformation error prediction sub-model. "Maintaining the first special force condition" means that after changing the robot joint angle, the direction of the first external force may change with the change in the robot joint angle, but the first external force remains determined by the robot joint angle.

[0102] Specifically, the training method of the second deformation error prediction sub-model 23 includes:

[0103] STB1: Obtain the robot joint angle under a preset second special force condition and measure a second true deformation error corresponding to the robot joint angle. The second special force condition is that the robot is subjected to a second external force determined by the robot joint angle.

[0104] STB2, inputs the robot joint angle into the second deformation error prediction sub-model to be trained; the second deformation error prediction sub-model outputs the predicted second deformation error.

[0105] STB3: Update the parameters of the second deformation error prediction sub-model corresponding to the current robot joint angle by comparing the difference between the second deformation error and the second true deformation error.

[0106] STB4: Change the robot joint angle while maintaining the second special force condition. Repeat steps STB1-STB3 to update the parameters of the second deformation error prediction sub-model corresponding to the new robot joint angle. This process continues until all robot joint angles within the set range have been traversed, resulting in a trained second deformation error prediction sub-model. "Maintaining the second special force condition" means that after changing the robot joint angle, the direction of the second external force may change with the change in the robot joint angle, but the second external force remains determined by the robot joint angle.

[0107] Specifically, the training method of the third deformation error prediction sub-model 24 includes:

[0108] STC1: Obtain the robot joint angle under a preset third special force condition and measure the third true deformation error corresponding to the robot joint angle. The third special force condition is: the robot is subjected to a third external force determined by the robot joint angle.

[0109] STC2, inputting the robot joint angle into the third deformation error prediction sub-model to be trained; the third deformation error prediction sub-model outputs the predicted third deformation error.

[0110] STC3: updating the parameters of the third deformation error prediction sub-model corresponding to the current robot joint angle by comparing the difference between the third deformation error and the third true deformation error.

[0111] In step STC4, the robot joint angle is changed, while the third special force condition is maintained. Steps STC1-STC3 are repeated to update the parameters of the third deformation error prediction sub-model corresponding to the new robot joint angle. This process continues until all robot joint angles within the set range are traversed, resulting in a trained third deformation error prediction sub-model. "Maintaining the third special force condition" means that after changing the robot joint angle, the direction of the third external force may change with the change in the robot joint angle, but the third external force always remains determined by the robot joint angle.

[0112] The first, second, and third special force conditions can be any of the following: the force-bearing point of the robot coincides with the end point of the robot or is relatively stationary, the magnitude of the external force is constant, and the external force is always directed toward a fixed point or in a fixed direction. The directions of the first, second, and third external forces acting on the robot in the first, second, and third special force conditions are the same as the directions of the first, second, and third external forces in step S21. The first, second, and third external forces are linearly independent.

[0113] For example, see Figure 4 , Figure 4 This is a schematic diagram of a special force situation in the present invention where the external force always points to a fixed point. Assuming that the external force is constant and always points to a fixed point, the external force can be expressed by the following formula:

[0114] f=M(p c -p f ) (16)

[0115] Where M represents the magnitude of the external force, p c represents the fixed point to which the external force is directed, p f Indicates the end point of the robot.

[0116] In one embodiment, the first special force condition may be: the robot's force-bearing point coincides with the robot's end point, the first external force is of constant magnitude, and the first external force is always directed toward a predetermined first fixed point. In this case, the direction of the first external force is determined to be from the robot's end point toward the first fixed point. The position of the robot's end point is uniquely determined by the robot's joint angle, so the first external force is uniquely determined by the robot's joint angle. The second special force condition may be: the robot's force-bearing point coincides with the robot's end point, the second external force is of constant magnitude, and the second external force is always directed toward a predetermined second fixed point. The third special force condition may be: the robot's force-bearing point coincides with the robot's end point, the third external force is of constant magnitude, and the third external force is always directed toward a predetermined third fixed point. Similarly, the directions of the second and third external forces are determined to be from the robot's end point toward the second and third fixed points, respectively. The position of the robot's end point is uniquely determined by the robot's joint angle, so the second and third external forces are both uniquely determined by the robot's joint angle.

[0117] For example, see Figure 5 , Figure 5 This is a schematic diagram of a special force situation in the present invention where the external force always points in a fixed direction. Assuming that the external force is constant and always points in a fixed direction, the external force can be expressed by the following formula:

[0118] f=Mω (17)

[0119] Where M represents the magnitude of the external force, and ω represents the unit direction vector of the external force.

[0120] In one embodiment, the first special force condition may be: the force point of the robot coincides with the end point of the robot, the magnitude of the first external force is constant, and the first external force always points to a preset first fixed direction. In this case, the first external force is determined to point from the end point of the robot to the first fixed direction, that is, it is uniquely determined by the joint angle of the robot. The second special force condition may be: the force point of the robot coincides with the end point of the robot, the magnitude of the second external force is constant, and the second external force always points to a preset second fixed direction. The third special force condition may be: the force point of the robot coincides with the end point of the robot, the magnitude of the third external force is constant, and the third external force always points to a preset third fixed direction. Similar to the case of the first external force, the second and third external forces are also determined to point from the end point of the robot to the first fixed direction and the second fixed direction, respectively, and are also uniquely determined by the joint angle of the robot.

[0121] According to the principles of mechanics, if the robot's force-bearing point and its end point are relatively stationary, then the external force is equivalent to an external force caused by another force-bearing point coinciding with the robot's end point. Therefore, the special force situation where the robot's force-bearing point and end point are relatively stationary is essentially the same as the special force situation where the force-bearing point and end point coincide with each other. This disclosure will not further discuss the special force situation where the robot's force-bearing point and end point are relatively stationary.

[0122] Furthermore, the first, second, and third true deformation errors are measured using the same method, each including: measuring a first position of the robot's end point without an external load; measuring a second position of the robot's end point under a specific load; and calculating the true deformation error based on the first and second positions. The true deformation error is a vector starting from the first position and ending at the second position. In this embodiment, the first and second positions are measured using a laser tracker. In other embodiments, the laser tracker can be replaced with other position measurement instruments, such as a visual sensor, and the present invention is not limited thereto.

[0123] The beneficial effects of the present invention are described in detail below in combination with simulation analysis and experimental analysis.

[0124] 1. Simulation analysis

[0125] In the simulation experiments, we used the kinematic parameters of the IRB120 robot, assumed appropriate joint stiffness coefficients, and calculated deformation errors based on a traditional robot stiffness model. We also added a random error in the range of [-20, 20] μm to simulate the measurement noise in the experiment, ultimately generating simulated deformation error data. The kinematic parameters of the IRB120 robot are shown in Table 1, and the simulated joint stiffness coefficients are shown in Table 2.

[0126] Table 1 IRB120 robot kinematic parameters

[0127] Joint number Screw parameter 1 [0,0,1,0,0,0] 2 [0,1,0,-290,0,0] 3 [0,1,0,-560,0,0] 4 [1,0,0,0,630,0] 5 [0,1,0,-630,0,302] 6 [1,0,0,0,630,0] <![CDATA[g st (0)]]> [0,1.5708,0,-210.06,0,788.53]

[0128] Table 2 Simulated joint stiffness coefficient (N·mm / rad)

[0129] Joint number 1 2 3 4 5 6 Stiffness coefficient <![CDATA[1.35×10 7 ]]> <![CDATA[2.15×10 7 ]]> <![CDATA[2.76×10 8 ]]> <![CDATA[1.31×10 6 ]]> <![CDATA[2.35×10 6 ]]> <![CDATA[3.75×10 5 ]]>

[0130] The robot's common workspace is selected as the measurement space. When collecting training set data, the space is evenly divided according to the number of measurement positions to form multiple grids, and the grid vertices are used as the measurement positions of the robot's end deformation error, which is conducive to improving the generalization performance of the prediction model in the entire measurement space. The measurement positions of the test set are randomly distributed, which can better evaluate the prediction effect of the model. The measurement positions of the deformation error are as follows: Figure 6 Show.

[0131] In the simulation experiments, the robot was subjected to a uniform external force of 30 N. Using the robot's base coordinate system as the reference coordinate system, deformation error data was collected when the external force passed through fixed points P1 (800, -750, 150) and P2 (800, 750, 150). The first and second deformation error prediction sub-models were trained using ELM, respectively. Deformation error data was collected when the external force direction was fixed at (0, 0, 1), and the third deformation error prediction sub-model was trained using ELM. In this case, fixed point P1 (800, -750, 150) serves as the first fixed point in the first special force case, fixed point P2 (800, 750, 150) serves as the second fixed point in the second special force case, and the direction (0, 0, 1) serves as the third fixed direction in the third special force case.

[0132] The first, second, and third deformation error prediction sub-models are used to fuse the deformation error prediction fusion model. The prediction deviations of the three deformation error prediction sub-models and the deformation error prediction fusion model are calculated using the test set data to verify the prediction effect of the model. When collecting the test set data for the deformation error prediction fusion model, the external force applied to the robot is fixed at (20, 0, -20) N, which is different from the external force applied to the robot in the training set, to verify the fusion effect of the model. Prediction deviation e p for

[0133]

[0134] Where E is the actual deformation error, E p is the deformation error predicted by the model. The training data of the three deformation error prediction sub-models is 150. The number of hidden layer nodes of the more suitable ELM obtained by the traversal method is 70, and the regularization coefficient is 10-5. The prediction effects of the three deformation error prediction sub-models are as follows: Figure 7 、 8 , 9 and Table 3. The prediction effect of the deformation error prediction fusion model is as follows Figure 10 and Table 4.

[0135] Table 3 Prediction deviation evaluation table of deformation error prediction sub-model (μm)

[0136] Model average value Maximum Minimum Standard Deviation Accuracy A 25 64 4 12 95.2％ B 25 63 8 11 94.8％ C 20 40 2 9 94.7％

[0137] Models A, B, and C described in the table represent the first deformation error prediction sub-model, the second deformation error prediction sub-model, and the third deformation error prediction sub-model, respectively.

[0138] Table 4. Prediction deviation evaluation table of deformation error prediction fusion model (μm)

[0139] average value Maximum Minimum Standard Deviation Accuracy 24 39 8 8 86％

[0140] From the above results, it can be seen that the three fixed-load deformation error prediction sub-models can accurately and stably predict the robot's deformation error under special force conditions based on the joint angle. The average prediction deviation is less than 25μm, and the prediction accuracy is over 94%, which verifies the effectiveness of the fixed-load deformation error prediction sub-model.

[0141] Because the deformation error prediction fusion model is formed by fusing three constant-load deformation error prediction sub-models, its prediction performance depends on the performance of the constant-load deformation error prediction models. The above results show that the deformation error prediction fusion model can also accurately and stably predict the robot's deformation error, with an average prediction deviation of 24 μm and an accuracy of 86%. The reason for the decrease in accuracy is that the robot's deformation error under the external force of (20, 0, -20) N is smaller, but the average prediction deviation is almost the same as that of the deformation error prediction sub-models. These results verify the effectiveness of the deformation error prediction fusion model.

[0142] 2. Experimental analysis

[0143] The robot used in this experiment is an IRB 120 industrial robot with a payload of 3 kg and a repeatability of 0.01 mm. The measuring device is a laser tracker with an accuracy of 10 μm + 5 μm / m within a measurement range of 2.5 m × 5 m × 10 m.

[0144] The experimental measurement space is 200*400*400mm 3 The robot is a rectangular parallelepiped, and the external force on the robot is always 3kg. The deformation error of the robot is obtained by subtracting the coordinates of the end of the robot when it is under force from the coordinates of the end when it is not under force, that is,

[0145] E=P t ′-P t (19)

[0146] Where E is the deformation error, P t ′ is the coordinate of the end of the robot when it is subjected to force, P t is the coordinate of the end of the robot when no force is applied.

[0147] Similar to the simulation experiments, the number of training data sets for each fixed-load deformation error prediction model is 150, and their location distribution is based on Section 4.1. The training sets for the first and second deformation error prediction sub-models are the deformation error data when the external force passes through the fixed points P1 (881.35, 384.97, 99.42) mm and P2 (813.87, -767.08, 184.5) mm. The training set for the third deformation error prediction sub-model is the deformation error data when the external force direction is fixed at (0, 0, -1).

[0148] 25 measurement positions are randomly selected in the measurement space, and 25 deformation error data are collected when the external force passes through the fixed points P1, P2, and P3 (1070.55, -14.22, 97.4) mm and when the external force direction is fixed at (0, 0, -1). A total of 100 deformation error data under different forces are used as a test set to verify the effectiveness of the deformation error prediction fusion model.

[0149] When training the fixed load deformation error prediction sub-model, the number of hidden layer nodes of ELM is 150 and the regularization coefficient is 10 -5 The prediction effect of the deformation error prediction fusion model is as follows: Figure 11-14 and as shown in Table 5.

[0150] Table 5 Prediction deviation evaluation of deformation error prediction fusion model (μm)

[0151] average value Maximum Minimum Standard Deviation Accuracy 30 78 1 18 93.7％

[0152] From the above results, it can be seen that the deformation error prediction fusion model can accurately and stably predict the robot deformation error. The average prediction deviation is 30μm and the accuracy is 93.7%, which verifies the effectiveness and accuracy of the deformation error prediction fusion model.

[0153] In order to demonstrate the accuracy and superiority of the prediction method of the present invention, the traditional stiffness model is compared with the deformation error prediction fusion model of the present invention using the same deformation error data. The comparison results of the two models are as follows: Figure 15 and as shown in Table 6.

[0154] Table 6 Comparison of prediction deviations of the two methods (μm)

[0155] method average value Maximum Minimum Standard Deviation Accuracy Tradition 81 231 25 36 83.3％ The present invention 30 78 1 18 93.7％

[0156] From the above results, it can be seen that compared with the traditional stiffness model, the prediction accuracy of the deformation error prediction fusion model proposed in this invention is significantly improved. The average prediction deviation is reduced from 81μm to 30μm, a reduction of 63.8%; the maximum value is also reduced from 231μm to 78μm, a reduction of 66.2%.

[0157] The IRB120 robot used in the experiment is a lightweight robot with a long service life. Its connecting rod stiffness is relatively low, which cannot be ignored. Consequently, the prediction accuracy of traditional stiffness models is poor. The deformation error prediction fusion model proposed in this paper is formed by fusing three constant-load deformation error prediction sub-models. These constant-load deformation error prediction sub-models use ELM to directly fit the deformation error, which is not restricted by the robot's conditions and achieves higher prediction accuracy. Therefore, the deformation error prediction fusion model is widely applicable to most robots and has higher accuracy and robustness.

[0158] In summary, the present invention has the following beneficial effects: the deformation error prediction fusion model of the present invention can accurately predict the deformation error. Experimental results show that the average prediction deviation of the deformation error prediction fusion model is 30μm, and the prediction accuracy is 93.7%. Compared with the traditional stiffness model, its prediction deviation is reduced by 63.8%. The deformation error prediction fusion model of the present invention is simple and practical, and is widely applicable to most industrial robots. The establishment of the deformation error prediction fusion model does not require consideration of the robot configuration and connecting rod stiffness, nor does it require complex calculations like traditional stiffness models. The process of collecting deformation error data is simple and does not require complex and expensive force measurement equipment.

[0159] Based on the same inventive concept, the present application also provides an electronic device, which can be a terminal device such as a server, a desktop computing device, or a mobile computing device (e.g., a laptop computing device, a handheld computing device, a tablet computer, a netbook, etc.). The device includes one or more processors and a memory, wherein the processor is configured to execute a program to implement the deformation error compensation method based on error superposition according to an embodiment of the present invention; and the memory is configured to store a computer program executable by the processor.

[0160] Based on the same inventive concept, the present application also provides a computer-readable storage medium, corresponding to the embodiment of the aforementioned deformation error compensation method based on error superposition, wherein the computer-readable storage medium stores a computer program thereon, which, when executed by a processor, implements the steps of the deformation error compensation method based on error superposition recorded in any of the above embodiments.

[0161] The present application may take the form of a computer program product implemented on one or more storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing program code. Computer-usable storage media include permanent and non-permanent, removable and non-removable media, and information storage can be achieved by any method or technology. The information can be computer-readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include but are not limited to: phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, read-only compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices or any other non-transmission medium that can be used to store information that can be accessed by a computing device.

[0162] The above-described embodiments merely represent several implementations of the present invention. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous modifications and improvements without departing from the spirit of the present invention, and the present invention is intended to encompass such modifications and variations.

Claims

1. A deformation error compensation method based on error superposition, comprising the steps of: predicting deformation errors based on robot joint angles and external force vectors to obtain predicted deformation errors; and compensating the robot motion control algorithm based on the predicted deformation errors; characterized in that: Deformation error prediction is performed based on the robot joint angle and external force vector to obtain the predicted deformation error, which specifically includes: Decomposing the external force vector according to the robot joint angles through the robot forward kinematics to obtain force weights in the directions of the first external force, the second external force, and the third external force; Predicting a first deformation error caused by a first external force according to the robot joint angle using a first deformation error prediction sub-model; Predicting a second deformation error caused by a second external force according to the robot joint angle using a second deformation error prediction sub-model; Predicting a third deformation error caused by a third external force according to the robot joint angle using a third deformation error prediction sub-model; According to the force weight, performing error superposition on the first deformation error, the second deformation error, and the third deformation error to obtain a final predicted deformation error; The directions of the first external force, the second external force and the third external force depend on the joint angle of the robot and the special force conditions used to train the first deformation error prediction sub-model, the second deformation error prediction sub-model and the third deformation error prediction sub-model; the special force conditions are the force conditions in which the external force acting on the robot is determined by the joint angle of the robot; the first external force, the second external force and the third external force are linearly independent.

2. The deformation error compensation method based on error superposition according to claim 1, characterized in that: The training method of the first deformation error prediction sub-model includes: STA1, obtaining the robot joint angle under a preset first special force condition and measuring a first true deformation error corresponding to the robot joint angle; the first special force condition is: the robot is subjected to a first external force determined by the robot joint angle; STA2, inputting the robot joint angle into the first deformation error prediction sub-model to be trained; the first deformation error prediction sub-model outputs the predicted first deformation error; STA3, updating the parameters of the first deformation error prediction sub-model corresponding to the current robot joint angle by comparing the difference between the first deformation error and the first true deformation error; STA4, change the robot joint angle, keep the first special force condition unchanged, repeat steps STA1-STA3, and thus update the parameters of the first deformation error prediction sub-model corresponding to the new robot joint angle, until all robot joint angles within the preset range are traversed to obtain the trained first deformation error prediction sub-model.

3. The deformation error compensation method based on error superposition according to claim 2, characterized in that: The training method of the second deformation error prediction sub-model includes: STB1, obtaining a robot joint angle under a preset second special force condition and measuring a second true deformation error corresponding to the robot joint angle; the second special force condition is that the robot is subjected to a second external force determined by the robot joint angle; STB2, inputs the robot joint angle into the second deformation error prediction sub-model to be trained; the second deformation error prediction sub-model outputs the predicted second deformation error; STB3, by comparing the difference between the second deformation error and the second true deformation error, updating the parameters of the second deformation error prediction sub-model corresponding to the current robot joint angle; STB4, change the robot joint angle, keep the second special force condition unchanged, repeat steps STB1-STB3, and thus update the parameters of the second deformation error prediction sub-model corresponding to the new robot joint angle, until all robot joint angles within the set range are traversed to obtain the trained second deformation error prediction sub-model.

4. The deformation error compensation method based on error superposition according to claim 3, characterized in that: The training method of the third deformation error prediction sub-model includes: STC1, obtaining the robot joint angle under a preset third special force condition and measuring a third true deformation error corresponding to the robot joint angle; the third special force condition is: the robot is subjected to a third external force determined by the robot joint angle; STC2, inputting the robot joint angle into the third deformation error prediction sub-model to be trained; the third deformation error prediction sub-model outputs the predicted third deformation error; STC3, updating the parameters of the third deformation error prediction sub-model corresponding to the current robot joint angle by comparing the difference between the third deformation error and the third true deformation error; STC4, change the robot joint angle, keep the third special force condition unchanged, repeat steps STC1-STC3, and thus update the parameters of the third deformation error prediction sub-model corresponding to the new robot joint angle, until all robot joint angles within the set range are traversed to obtain the trained third deformation error prediction sub-model.

5. The deformation error compensation method based on error superposition according to claim 4, characterized in that: The first special force condition, the second special force condition and the third special force condition are any one of the force conditions in which the force point of the robot coincides with the end point of the robot or is relatively stationary, the magnitude of the external force is constant, and the external force always points to a fixed point or a fixed direction.

6. The deformation error compensation method based on error superposition according to claim 5, characterized in that: The first special force condition is specifically: the force-bearing point of the robot coincides with the end point of the robot, the magnitude of the first external force is constant, and the first external force always points to the preset first fixed point; The second special force condition is specifically: the force-bearing point of the robot coincides with the end point of the robot, the magnitude of the second external force is constant, and the second external force always points to the preset second fixed point; The third special force condition is specifically: the force point of the robot coincides with the end point of the robot, the magnitude of the third external force is constant, and the third external force always points to a preset fixed direction.

7. The deformation error compensation method based on error superposition according to claim 5, characterized in that: The measurement methods of the first true deformation error, the second true deformation error and the third true deformation error all include: measuring the first position of the end point of the robot in the absence of external force load; measuring the second position of the end point of the robot under special force conditions; calculating the true deformation error based on the first position and the second position; the true deformation error is a vector with the first position as the starting point and the second position as the end point.

8. A deformation error compensation device based on error superposition, characterized in that: include: Data acquisition module, used to obtain robot joint angles and external force vectors; The deformation error prediction fusion model is used to predict the deformation error based on the robot joint angle and external force vector to obtain the predicted deformation error; a compensation module, configured to compensate the robot motion control algorithm according to the predicted deformation error; The deformation error prediction fusion model includes: an external force vector decomposition unit, configured to decompose the external force vector according to the robot joint angles through the robot forward kinematics to obtain force weights in the directions of the first external force, the second external force, and the third external force; A first deformation error prediction sub-model, configured to predict a first deformation error caused by a first external force based on a joint angle of the robot; A second deformation error prediction sub-model, configured to predict a second deformation error caused by a second external force based on the robot joint angle; a third deformation error prediction sub-model, configured to predict a third deformation error caused by a third external force according to the robot joint angle; an error superposition unit, configured to perform error superposition on the first deformation error, the second deformation error, and the third deformation error according to the force weight to obtain a final predicted deformation error; The directions of the first external force, the second external force and the third external force depend on the joint angle of the robot and the special force conditions used to train the first deformation error prediction sub-model, the second deformation error prediction sub-model and the third deformation error prediction sub-model; the special force conditions are the force conditions in which the external force acting on the robot is determined by the joint angle of the robot; the first external force, the second external force and the third external force are linearly independent.

9. The deformation error compensation device based on error superposition according to claim 8, characterized in that: The training method of the first deformation error prediction sub-model includes: STA1, obtaining the robot joint angle under a preset first special force condition and measuring a first true deformation error corresponding to the robot joint angle; the first special force condition is: the robot is subjected to a first external force determined by the robot joint angle; STA2, inputting the robot joint angle into the first deformation error prediction sub-model to be trained; the first deformation error prediction sub-model outputs the predicted first deformation error; STA3, updating the parameters of the first deformation error prediction sub-model corresponding to the current robot joint angle by comparing the difference between the first deformation error and the first true deformation error; STA4, change the robot joint angle, keep the first special force condition unchanged, repeat steps STA1-STA3, and thus update the parameters of the first deformation error prediction sub-model corresponding to the new robot joint angle, until all robot joint angles within the preset range are traversed to obtain the trained first deformation error prediction sub-model.

10. An electronic device, characterized in that: include: processor; a memory for storing a computer program executed by the processor; Wherein, when the processor executes the computer program, it implements the deformation error compensation method based on error superposition as described in any one of claims 1 to 7.

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