Error self-calibration method, device, equipment, system and medium for multi-joint mechanical arm

Abstract

The invention relates to a multi-joint mechanical arm error self-calibration method, a multi-joint mechanical arm error self-calibration device, multi-joint mechanical arm error self-calibration equipment, a multi-joint mechanical arm error self-calibration system and a medium, in particular to the technical field of error self-calibration. And establishing a target function for error self-calibration of the multi-joint mechanical arm, performing iterative calculation by utilizing the target function according to the set iterative data set in combination with the target Jacobian matrix and the target iterative step length, and obtaining a positioning precision value of the multi-joint mechanical arm, and when the positioning precision value is smaller than a preset value, performing error self-calibration of the multi-joint mechanical arm. And iteration is ended, and error self-calibration operation of the multi-joint mechanical arm is completed, so that the error self-calibration operation of the multi-joint mechanical arm can be directly performed during use, the error self-calibration operation of the multi-joint mechanical arm can be realized without distance constraint or plane constraint, the calibration difficulty is simplified, and the operation convenience is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of error self-calibration, and in particular to a multi-joint mechanical arm error self-calibration method, device, equipment, system and medium. Background Art

[0002] With the continuous advancement of science and technology, multi-joint robotic arm technology has become an important part of the field of industrial automation. In many industrial applications, multi-joint robotic arms are widely used to perform precise operations and tasks. However, due to the limitations of the multi-joint robotic arm's own assembly accuracy, parts wear, and external influences during use, there is a deviation between the theoretical posture and the actual posture of the multi-joint robotic arm's end device, which directly affects the positioning accuracy of the multi-joint robotic arm. In order to solve this problem, the multi-joint robotic arm error self-calibration technology came into being, aiming to improve the operating accuracy and reliability of the multi-joint robotic arm by measuring and compensating these errors.

[0003] At present, the error self-calibration technology of multi-joint manipulators has made certain progress. The main technical methods include calibration technologies based on distance constraints, plane constraints and point constraints. These methods restrict the end device of the multi-joint manipulator to a specific point, surface or distance, use known physical constraints to establish equations, compare the theoretical posture and actual posture of the multi-joint manipulator, and thus identify the error parameters. For example, CN 115741706 A proposed a calibration method based on distance constraints, using a calibration ball plate to measure the difference in ball center distance for calibration; CN 113459094 A proposed a tool coordinate system and zero point self-calibration method, which calculates the error value by aligning spatial points multiple times; CN 117226840 A proposed a calibration method based on three spatial plane constraints, which completes the error calibration by touching the plane. These technologies have improved the positioning accuracy of multi-joint manipulators to a certain extent, but there are still some limitations in practical applications.

[0004] Although the existing multi-joint robot arm error self-calibration technology has achieved certain results, there are still some shortcomings. The calibration devices based on distance constraints and plane constraints are often bulky and difficult to carry, and the calibration process is complicated, which increases the difficulty of actual operation. Summary of the invention

[0005] The main purpose of the present invention is to propose a multi-joint robotic arm error self-calibration method, device, equipment, system and medium, aiming to solve the technical problems in the related art that the calibration devices based on distance constraints and plane constraints are often bulky and difficult to carry, and the calibration process is complicated, which increases the difficulty of actual operation.

[0006] To achieve the above object, the present invention proposes a multi-joint robotic arm error self-calibration method, wherein the multi-joint robotic arm has multiple joints, and the two ends of the multi-joint robotic arm are a mounting end and a free end, respectively, and the free end is detachably mounted with an end device, and the multi-joint robotic arm error self-calibration method comprises the following steps:

[0007] According to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm respectively established, an objective function for self-calibration of the multi-joint robotic arm error is established; wherein the objective function is expressed by formula 1, which is:

[0008]

[0009] is the augmented matrix of the error pose transformation matrix of the end of the multi-joint robot, are all parameters to be identified, p i is the coordinate of the i-th point in three-dimensional space, and R is the radius of the calibration sphere;

[0010] According to the set iteration data set, combined with the target Jacobian matrix and the target iteration step, the objective function is used to perform iterative calculation and obtain the positioning accuracy value of the multi-joint robotic arm; wherein the iteration data set includes an iteration initial value;

[0011] When the positioning accuracy value is less than a preset value, the iteration is terminated and the error self-calibration operation of the multi-joint robotic arm is completed.

[0012] In one embodiment, before the step of establishing an objective function for error self-calibration of the multi-joint robotic arm according to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm respectively established, the step further includes:

[0013] The DH method is used to establish the kinematic model of the multi-joint robotic arm; wherein the kinematic model is expressed by Formula 2, which is:

[0014]

[0015] is the homogeneous transformation matrix, a i Indicates the length of the robot arm, d i Represents the joint offset value, θ i Represents the arm length and torsion angle of the robot arm, α i represents the joint rotation angle, β i Indicates the y-axis rotation angle;

[0016] A geometric error model of the multi-joint robotic arm is established; wherein the geometric error model is expressed using Formula 3, which is:

[0017] Δ base =J G ·X G

[0018] J G is the geometric error transfer Jacobian matrix, which is a 6×24-order matrix and is a known parameter after determining the position and posture of the multi-joint manipulator; X G =[X 1 T X 2 T … X 6 T ] T , including all geometric errors of the arm lengths of two adjacent robotic arms of the multi-joint robotic arm, is a 24×1-order vector and is a parameter that needs to be identified;

[0019] Establish an end device error model of the multi-joint robotic arm; wherein the end device error model is expressed using Formula 4, which is:

[0020]

[0021] F is the end load value of the cantilever beam of the terminal device, y t is the end deflection value of the cantilever beam, θ t is the rotation angle of the terminal device, l is the length of the beam, E is the elastic modulus, I is the cross-sectional inertia moment, c 1 and c 2 are the deflection coefficient and the bending moment coefficient, respectively, which are the parameters that need to be identified.

[0022] In one embodiment, the step of establishing an objective function for self-calibration of the multi-joint robotic arm error according to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm respectively established comprises:

[0023] According to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm that are respectively established, a nonlinear least squares method is used to establish an objective function for self-calibration of the multi-joint robotic arm errors.

[0024] In one embodiment, the step of establishing a geometric error model of the multi-joint robotic arm comprises:

[0025] Establishing a first coordinate system sequence of the multi-joint robotic arm and a corresponding second coordinate system sequence of the terminal device respectively;

[0026] Acquire a deviation sequence between the first coordinate system sequence and the corresponding second coordinate system sequence;

[0027] A homogeneous transformation matrix is ​​used to perform total differential processing on each deviation in the deviation sequence, so as to transform the first coordinate system sequence and the second coordinate system sequence into a base coordinate system to obtain a geometric error model of the multi-joint robotic arm.

[0028] In one embodiment, the step of using a homogeneous transformation matrix to perform full differential processing on each deviation in the deviation sequence to convert both the first coordinate system sequence and the second coordinate system sequence to a base coordinate system to obtain a geometric error model of the multi-joint robotic arm includes:

[0029] For each deviation in the deviation sequence, the homogeneous transformation matrix is ​​used to perform full differential processing on the deviation to obtain a current total differential equation, so as to transform the corresponding first coordinate system and the second coordinate system into the base coordinate system, and obtain a geometric error model of the multi-joint robotic arm; wherein the current total differential equation is expressed by Formula 5, which is:

[0030]

[0031] dT i For deviation.

[0032] In one embodiment, when the positioning accuracy value is less than a preset value, the step of ending iteration and completing the error self-calibration operation of the multi-joint robotic arm includes:

[0033] When the positioning accuracy value is less than 0.1 mm, the iteration is terminated and the error self-calibration operation of the multi-joint robotic arm is completed.

[0034] Based on the same technical concept, in a second aspect, the present invention further proposes a multi-joint mechanical arm error self-calibration device, wherein the multi-joint mechanical arm has a plurality of joints, and the two ends of the multi-joint mechanical arm are respectively a mounting end and a free end, and the free end is detachably mounted with an end device, and the multi-joint mechanical arm error self-calibration device comprises:

[0035] The objective function establishment module is used to establish an objective function for the error self-calibration of the multi-joint robotic arm according to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm respectively established; wherein the objective function is expressed by formula 1, which is:

[0036]

[0037] is the augmented matrix of the error pose transformation matrix of the end of the multi-joint robot, are all parameters to be identified, p i is the coordinate of the i-th point in three-dimensional space, and R is the radius of the calibration sphere;

[0038] A calculation module, used to perform iterative calculations using the objective function according to a set iterative data set, in combination with a target Jacobian matrix and a target iterative step length, and obtain a positioning accuracy value of the multi-joint robotic arm; wherein the iterative data set includes an iterative initial value;

[0039] The calibration module is used to end the iteration and complete the error self-calibration operation of the multi-joint robotic arm when the positioning accuracy value is less than a preset value.

[0040] Based on the same technical concept, in the third aspect, the present invention also proposes a multi-joint robotic arm error self-calibration device, the multi-joint robotic arm error self-calibration device comprises a processor and a memory, the memory stores a multi-joint robotic arm error self-calibration program, and when the multi-joint robotic arm error self-calibration program is executed by the processor, the multi-joint robotic arm error self-calibration method described in the first aspect is implemented.

[0041] Based on the same technical concept, in a fourth aspect, the present invention further proposes a multi-joint robot arm error self-calibration system, comprising:

[0042] The multi-joint robot arm error self-calibration device according to the third aspect; and

[0043] A multi-joint robotic arm, wherein the multi-joint robotic arm is communicatively connected to the multi-joint robotic arm error self-calibration device, and the multi-joint robotic arm error self-calibration device can control the multi-joint robotic arm to perform self-calibration operations.

[0044] Based on the same technical concept, in the fifth aspect, the present invention also proposes a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by one or more processors, the multi-joint robot arm error self-calibration method described in the first aspect is implemented.

[0045] The technical solution of the present invention establishes an objective function for self-calibration of the errors of the multi-joint robotic arm according to the kinematic model, geometric error model and deformation error model of the terminal device of the multi-joint robotic arm that are respectively established. According to the set iterative data set, in combination with the target Jacobian matrix and the target iteration step, the objective function is used to perform iterative calculation and obtain the positioning accuracy value of the multi-joint robotic arm. When the positioning accuracy value is less than a preset value, the iteration is terminated and the error self-calibration operation of the multi-joint robotic arm is completed. Therefore, the present invention can directly perform self-calibration operation on the errors of the multi-joint robotic arm when in use, and the error self-calibration operation of the multi-joint robotic arm can be realized without distance constraints or plane constraints, which simplifies the calibration difficulty and increases the convenience of operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0047] Figure 1 A flow chart of the multi-joint robotic arm error self-calibration method provided by the present invention;

[0048] Figure 2 Flowcharts of some exemplary embodiments of the present invention;

[0049] Figure 3 This is a flowchart of step S500 of the present invention;

[0050] Figure 4 A schematic diagram of a coordinate system of a multi-joint robotic arm according to an example of the present invention;

[0051] Figure 5 A schematic diagram of positioning error and number of iterations of a multi-joint robotic arm according to an example of the present invention;

[0052] Figure 6 This is a schematic diagram of the terminal device position before and after compensation according to an example of the present invention;

[0053] Figure 7 This is a schematic diagram of the positioning accuracy of an example of the present invention.

[0054] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0055] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] It should be noted that if the embodiments of the present invention involve directional indications (such as up, down, left, right, front, back, etc.), the directional indications are only used to explain the relative position relationship, movement status, etc. between the components in a certain specific posture. If the specific posture changes, the directional indication will also change accordingly.

[0057] In addition, if there are descriptions involving "first", "second", etc. in the embodiments of the present invention, the descriptions of "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of technical features indicated. Therefore, the features limited to "first" and "second" may explicitly or implicitly include at least one of the features. In addition, if "and / or" or "and / or" appears in the full text, its meaning includes three parallel solutions. Taking "A and / or B" as an example, it includes solution A, solution B, or solutions that satisfy both A and B. In addition, the technical solutions between the various embodiments can be combined with each other, but it must be based on the ability of ordinary technicians in this field to implement. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0058] The invention provides a multi-joint mechanical arm error self-calibration method.

[0059] See also Figures 1 to 7 In one embodiment of the present invention, a multi-joint robot arm error self-calibration method is provided, wherein the multi-joint robot arm has a plurality of joints, and the two ends of the multi-joint robot arm are a mounting end and a free end, respectively, and the free end is detachably mounted with an end device, and the multi-joint robot arm error self-calibration method comprises the following steps:

[0060] S100, establishing an objective function for error self-calibration of the multi-joint robotic arm according to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm respectively established; wherein the objective function is expressed by formula 1, which is:

[0061]

[0062] is the augmented matrix of the error pose transformation matrix of the end of the multi-joint robot, are all parameters to be identified, p i is the coordinate of the i-th point in three-dimensional space, and R is the radius of the calibration sphere;

[0063] S200, according to the set iteration data set, combined with the target Jacobian matrix and the target iteration step, using the objective function to perform iterative calculation and obtain the positioning accuracy value of the multi-joint robotic arm; wherein the iteration data set includes an iteration initial value;

[0064] S300: When the positioning accuracy value is less than a preset value, the iteration is terminated and the error self-calibration operation of the multi-joint robotic arm is completed.

[0065] It should be particularly and clearly stated that the preset value used in this embodiment is 0.1 mm.

[0066] In this embodiment, according to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm that are respectively established, an objective function for self-calibration of the multi-joint robotic arm errors is established, and according to the set iterative data set, combined with the target Jacobian matrix and the target iteration step, the objective function is used to perform iterative calculations and obtain the positioning accuracy value of the multi-joint robotic arm. When the positioning accuracy value is less than a preset value, the iteration is terminated and the error self-calibration operation of the multi-joint robotic arm is completed. This allows the present invention to directly perform self-calibration operations on the errors of the multi-joint robotic arm when in use, and the error self-calibration operation of the multi-joint robotic arm can be achieved without distance constraints or plane constraints, which simplifies the calibration difficulty and increases the convenience of operation.

[0067] In one embodiment, before step S100, the method further includes:

[0068] S400, using the DH method to establish a kinematic model of the multi-joint robotic arm; wherein the kinematic model is expressed using Formula 2, which is:

[0069]

[0070] is the homogeneous transformation matrix, a i Indicates the length of the robot arm, d i Represents the joint offset value, θ i Represents the arm length and torsion angle of the robot arm, α i represents the joint rotation angle, β i Indicates the y-axis rotation angle;

[0071] S500, establishing a geometric error model of the multi-joint robotic arm; wherein the geometric error model is expressed using Formula 3, which is:

[0072] Δbase =J G ·X G

[0073] J G is the geometric error transfer Jacobian matrix, which is a 6×24-order matrix and is a known parameter after determining the position and posture of the multi-joint manipulator; X G =[X 1 T X 2 T … X 6 T ] T , including all geometric errors of the arm lengths of two adjacent robotic arms of the multi-joint robotic arm, is a 24×1-order vector and is a parameter that needs to be identified;

[0074] S600, establishing an end device error model of the multi-joint robotic arm; wherein the end device error model is expressed using Formula 4, which is:

[0075]

[0076] F is the end load value of the cantilever beam of the terminal device, y t is the end deflection value of the cantilever beam, θ t is the rotation angle of the terminal device, l is the length of the beam, E is the elastic modulus, I is the cross-sectional inertia moment, c 1 and c 2 are the deflection coefficient and the bending moment coefficient, respectively, which are the parameters that need to be identified.

[0077] In one embodiment, step S100 includes:

[0078] According to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm that are respectively established, a nonlinear least squares method is used to establish an objective function for self-calibration of the multi-joint robotic arm errors.

[0079] In one embodiment, step S500 includes:

[0080] S510, respectively establishing a first coordinate system sequence of the multi-joint robotic arm and a corresponding second coordinate system sequence of the terminal device;

[0081] S520, obtaining a deviation sequence between the first coordinate system sequence and the corresponding second coordinate system sequence;

[0082] S530, using a homogeneous transformation matrix to perform total differential processing on each deviation in the deviation sequence, so as to transform both the first coordinate system sequence and the second coordinate system sequence into a base coordinate system to obtain a geometric error model of the multi-joint robotic arm.

[0083] In one embodiment, the step of using a homogeneous transformation matrix to perform full differential processing on each deviation in the deviation sequence to convert both the first coordinate system sequence and the second coordinate system sequence to a base coordinate system to obtain a geometric error model of the multi-joint robotic arm includes:

[0084] For each deviation in the deviation sequence, the homogeneous transformation matrix is ​​used to perform full differential processing on the deviation to obtain a current total differential equation, so as to transform the corresponding first coordinate system and the second coordinate system into the base coordinate system, and obtain a geometric error model of the multi-joint robotic arm; wherein the current total differential equation is expressed by Formula 5, which is:

[0085]

[0086] dT i For deviation.

[0087] In one embodiment, when the positioning accuracy value is less than a preset value, the step of ending iteration and completing the error self-calibration operation of the multi-joint robotic arm includes:

[0088] When the positioning accuracy value is less than 0.1 mm, the iteration is terminated and the error self-calibration operation of the multi-joint robotic arm is completed.

[0089] In some exemplary embodiments, the multi-joint robot arm error self-calibration method of the present invention is implemented in the following manner:

[0090] Step 1: Establish a kinematic model of a multi-joint robotic arm, and use the DH model to define the link length, joint offset, link torsion angle, joint rotation angle, and y-axis rotation angle to represent the posture relationship of adjacent coordinate systems;

[0091] Step 2: Establish the geometric error model of the multi-joint robot and the deformation error model of the end device;

[0092] Step 3: Use the nonlinear least squares method to establish the optimization objective function and set the initial value of the iteration according to the actual situation;

[0093] In this embodiment, for example, the initial value of the calibration method proposed in the present invention is selected. The geometric error of the multi-joint robot arm is small, and the initial value can be set to 0; the initial value of the deformation error parameter of the terminal device can be estimated according to its physical meaning; the coordinates p of the center of the calibration ball c =[xc ,y c ,z c ] T The actual position measured by the terminal device can be obtained by fitting using the least squares method.

[0094] Step 4: Calculate the error Jacobian matrix based on the joint angles of the multi-joint robot;

[0095] Step 5: Use the incremental equation to calculate the iteration step size and update the objective function;

[0096] Step 6: Calculate the error. If it is less than a given value, the iteration ends. The given value is the end positioning accuracy allowed by the multi-joint robot arm. In this embodiment, it is set to 0.1 mm. The obtained value is the error of the multi-joint robot arm. If it is greater than the given value, return to step 4 and repeat the iteration.

[0097] The kinematic model of the multi-joint robot arm is established according to the DH method. The pose transformation between two adjacent coordinate systems can be expressed using the homogeneous transformation matrix express.

[0098]

[0099] In the formula, a i Indicates the connecting rod length, d i represents the joint offset, θ i represents the connecting rod torsion angle, α i represents the joint rotation angle, β i Indicates the y-axis rotation angle.

[0100] It should be noted that the above explanation of the method embodiment is also applicable to devices of similar embodiments, and is not limited to 6-DOF serial multi-joint robotic arms, but is also applicable to other types of serial multi-joint robotic arms.

[0101] Preferably, the transformation matrix is ​​obtained by continuously multiplying the transformation matrices between adjacent links. The pose of the multi-joint manipulator end device coordinate system relative to the base coordinate system can be expressed as:

[0102]

[0103] The method for constructing the geometric error model of the multi-joint robot and the deformation error model of the end device is as follows:

[0104] For example, there is a deviation dT between the theoretical transformation matrix and the actual transformation matrix of two adjacent coordinate systems. i . Assume that the theoretical homogeneous transformation matrix is Then the actual homogeneous transformation matrix is

[0105]

[0106] Furthermore, for dT i Performing total differentiation yields

[0107]

[0108] Convert the differential operator to a column vector, then

[0109]

[0110] In the formula, Δ i represents the error of the i-th coordinate system relative to the i-1-th coordinate system, G i is the geometric error transfer matrix, X i is the geometric error vector.

[0111] For example, in practical applications, it is necessary to convert the errors of all coordinate systems into the base coordinate system.

[0112]

[0113] Among them, K i represents the coordinate system error transfer matrix, K i n, o, a, p in the equation are the homogeneous transformation matrices of the i coordinate system relative to the base coordinate system. n,o,a,p in.

[0114] For a general industrial multi-joint robot, the deformation of its connecting rods and joints is small. In a small range, the coordinate system differential transformation can be linearly superimposed. Therefore, the errors of all coordinate systems are superimposed on the base coordinate system to obtain

[0115]

[0116] K i is the coordinate system error transfer matrix, K 1 is the unit matrix. Combining equations (6) and (7), we get

[0117]

[0118] J G is the geometric error transfer Jacobian matrix, which is a 6×24-order matrix and is a known parameter after the multi-joint robot arm posture is determined. G =[X 1 T X 2 T …X 6 T ] T , which includes all geometric errors of two adjacent links of the multi-joint robot arm, is a 24×1-order vector and is a parameter that needs to be identified.

[0119] Furthermore, the deformation error of the end device of the multi-joint robotic arm is constructed.

[0120] The end deflection of a cantilever beam with a load of magnitude F at the end is y t and the rotation angle θ t It can be expressed by the following formula:

[0121]

[0122] Where I is the length of the beam, E is the elastic modulus, I is the moment of inertia of the cross section, and c 1 and c 2 are the deflection coefficient and the bending moment coefficient, respectively, which are the parameters that need to be identified.

[0123] Furthermore, according to the DH model established above, the z-axis of the tool coordinate system of the multi-joint robot arm represents the tool extension direction. Therefore, the effective length of the end link is

[0124]

[0125] l t is the length of the end link, so

[0126]

[0127] The same can be said

[0128]

[0129] Express the above formula in the form of differential operator column vector, that is

[0130]

[0131] The deformation error of the end device is relative to the base coordinate system, so its error differential operator can be directly linearly superimposed with the geometric error differential operator. Finally, the total error of the end of the multi-joint robot tool relative to the base coordinate system is

[0132] Δ total =J·X

[0133] Among them, Δ total Represents the total error differential operator vector, representing the small translation and rotation of the multi-joint robot end device coordinate system along the base coordinate system x, y, z axis. The total error transfer Jacobian matrix J = [J G J t ], which is a 6×26 matrix. is the 26×1 order error parameter vector to be determined.

[0134] Furthermore, an error parameter identification model of a multi-joint robotic arm is derived.

[0135] For a general 6-DOF serial multi-joint robot, due to the existence of errors, the homogeneous transformation matrix of its end device coordinate system relative to the base coordinate system is

[0136]

[0137] The self-calibration method proposed in this invention establishes constraint equations based on spherical constraints, which only requires the position information of the terminal device coordinate system but not the attitude information. The position of the actual terminal working coordinate system can be expressed as

[0138]

[0139] Substituting into

[0140] p R =A·X+p N

[0141] Among them, A is the error posture transformation matrix of the end of the multi-joint robot arm, which is a 3×26-order matrix. During the calibration process, a calibration ball with high processing accuracy and known diameter is required. When the end device of the multi-joint robot arm touches the surface of the calibration ball, its actual position coordinates should have the following constraint equations:

[0142]

[0143] Among them, x c ,y c ,z c is the coordinate of the calibration ball in the base coordinate system, which is an unknown condition; R is the radius of the calibration ball, which is a known condition. c ,y c ,z c As the parameter to be identified, it is moved to the parameter vector to be determined.

[0144]

[0145] where p c =[x c ,y c ,z c ] T , It is the augmented matrix of the error posture transformation matrix of the multi-joint manipulator end. According to the spherical constraint equation, it can be obtained

[0146]

[0147] Furthermore, it is necessary to identify the error parameters of the multi-joint robot.

[0148] The end device of the multi-joint robot collects position information by touching the surface of the calibration ball. Its theoretical position is a standard ball. However, due to the influence of errors, its actual position in three-dimensional space is not a standard ball. Therefore, the parameter identification method is to establish appropriate error parameters so that the actual position of the end device of the multi-joint robot is fitted into a three-dimensional standard ball after superimposing the error. Consider the following optimization objective function:

[0149]

[0150] For the calibration method proposed in the present invention, it is necessary to collect n points on the calibration sphere and perform fitting, and the multi-joint robot arm has different postures at different points.

[0151]

[0152] For the i-th point

[0153]

[0154] in, is the augmented matrix of the error pose transformation matrix of the end of the multi-joint robot, are all parameters to be identified, p i is the coordinate of the i-th point in three-dimensional space, and R is the radius of the calibration sphere.

[0155] Further, in Performing a first-order Taylor expansion on the function f(x) and ignoring higher-order terms yields

[0156]

[0157] and

[0158]

[0159] therefore

[0160]

[0161] The incremental equation is solved using the LM algorithm:

[0162]

[0163] λ is an adjustable coefficient greater than 0.

[0164] Generally, for nonlinear least squares problems, the selection of initial values ​​is very important. If the initial values ​​are not chosen properly, it may lead to slow convergence or fall into a local optimal solution.

[0165] For example, for the initial value selection of the calibration method proposed in the present invention, the geometric error of the multi-joint robot arm is small, and the initial value can be set to 0; the initial value of the deformation error parameter of the terminal device can be estimated according to its physical meaning; the coordinates p of the center of the calibration ball c =[x c ,y c ,z c ] T The actual position measured by the terminal device can be used to obtain the fitting result using the least squares method. After obtaining the initial value, proceed to step 4 to calculate the error Jacobian matrix based on the joint angles of the multi-joint robot arm, and then proceed to step 5 to use Calculation step length The parameters are continuously updated iteratively so that the objective function gradually approaches the minimum value. In step 6, the iteration is stopped when the error is less than the given value, otherwise it returns to step 4 for further iteration.

[0166] The present invention is used to identify the error parameters of the multi-joint robot arm. After setting the initial value, the iterative process is as follows: Figure 5 As shown in Figure 2. After 50 iterations, the data converges and the iteration ends.

[0167] In particular, the error after calibration by the present invention is compensated to the multi-joint robot arm, and compared with the position of the end device of the multi-joint robot arm without compensation, such as Figure 6 As shown in the figure, the sphere is the actual calibration sphere, the blue dot is the position of the multi-joint robot arm end device when the error is not compensated, and it is far away from the calibration sphere surface. The red dot is the position of the multi-joint robot arm end device after error compensation, which is basically attached to the calibration sphere surface, and it restores the original touch position well.

[0168] Compare the positioning accuracy of the multi-joint mechanical arm before and after error compensation of the present invention. Figure 7 After calibration and error compensation, the maximum error value of the end position of the multi-joint robot arm is reduced from the original 5.559mm to 1.104mm, and the accuracy is improved by 80.1%; the average error value is reduced from the original 3.657mm to 0.665mm, and the accuracy is improved by 81.8%, thus verifying the effectiveness of the self-calibration method proposed in this invention.

[0169] Through the above method, the present invention has the following effects when used specifically:

[0170] A multi-joint robotic arm error self-calibration method using spherical constraints is provided, which can improve the calibration efficiency while meeting the requirements of the positioning accuracy of the end of the multi-joint robotic arm, and solve the problems of the existing multi-joint robotic arm calibration method having cumbersome procedures and low efficiency;

[0171] The self-calibration method proposed in the present invention only requires a high-precision calibration ball with a known diameter. The calibration device is easy to carry and has low cost. The error model established in the present invention is applicable to general serial multi-joint robotic arms, has strong versatility, and has great advantages in practical applications.

[0172] The self-calibration method proposed in the present invention takes into account the errors of the multi-joint robot arm itself and the end device of the multi-joint robot arm at the same time, and can obtain higher end positioning accuracy after error identification and compensation.

[0173] Based on the same technical concept, in a second aspect, the present invention further proposes a multi-joint mechanical arm error self-calibration device, wherein the multi-joint mechanical arm has a plurality of joints, and the two ends of the multi-joint mechanical arm are respectively a mounting end and a free end, and the free end is detachably mounted with an end device, and the multi-joint mechanical arm error self-calibration device comprises:

[0174] The objective function establishment module is used to establish an objective function for the error self-calibration of the multi-joint robotic arm according to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm respectively established; wherein the objective function is expressed by formula 1, which is:

[0175]

[0176] is the augmented matrix of the error pose transformation matrix of the end of the multi-joint robot, are all parameters to be identified, p i is the coordinate of the i-th point in three-dimensional space, and R is the radius of the calibration sphere;

[0177] A calculation module, used to perform iterative calculations using the objective function according to a set iterative data set, in combination with a target Jacobian matrix and a target iterative step length, and obtain a positioning accuracy value of the multi-joint robotic arm; wherein the iterative data set includes an iterative initial value;

[0178] The calibration module is used to end the iteration and complete the error self-calibration operation of the multi-joint robotic arm when the positioning accuracy value is less than a preset value.

[0179] The multi-joint mechanical arm error self-calibration device provided in the embodiment of the present application adopts the multi-joint mechanical arm error self-calibration method in the above embodiment, which can solve the technical problem that the calibration device based on distance constraint and plane constraint is often bulky and not easy to carry, and the calibration process is complicated, which increases the difficulty of actual operation. Compared with the prior art, the beneficial effects of the multi-joint mechanical arm error self-calibration device provided in the embodiment of the present application are the same as the beneficial effects of the multi-joint mechanical arm error self-calibration method provided in the above embodiment, and other technical features in the multi-joint mechanical arm error self-calibration device are the same as the features disclosed in the above embodiment method, which will not be repeated here.

[0180] Based on the same technical concept, in the third aspect, the present invention also proposes a multi-joint robotic arm error self-calibration device, the multi-joint robotic arm error self-calibration device comprises a processor and a memory, the memory stores a multi-joint robotic arm error self-calibration program, and when the multi-joint robotic arm error self-calibration program is executed by the processor, the multi-joint robotic arm error self-calibration method described in the first aspect is implemented.

[0181] The multi-joint robotic arm error self-calibration device in the embodiment of the present application may include but is not limited to mobile terminals such as mobile phones, laptop computers, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Descriptions), PMPs (Portable Media Players), vehicle-mounted terminals (such as vehicle-mounted control terminals), etc., as well as fixed terminals such as digital TVs, desktop computers, etc.

[0182] The multi-joint robot arm error self-calibration device may include a processing device 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM: Read Only Memory) 1002 or a program loaded from a storage device 1003 to a random access memory (RAM: Random Access Memory) 1004. In RAM1004, various programs and data required for the operation of the multi-joint robot arm error self-calibration device are also stored. The processing device 1001, ROM1002, and RAM1004 are connected to each other via a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to the I / O interface 1006: input devices 1007 including, for example, a touch screen, a touchpad, a keyboard, a mouse, an image sensor, a microphone, an accelerometer, a gyroscope, etc.; output devices 1008 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; storage devices 1003 including, for example, a magnetic tape, a hard disk, etc.; and communication devices 1009. The communication device 1009 can allow the multi-joint robot arm error self-calibration device to communicate wirelessly or wired with other devices to exchange data. Although the multi-joint robot arm error self-calibration device with various systems is shown in the figure, it should be understood that it is not required to implement or have all the systems shown. More or fewer systems may be implemented or have alternatively.

[0183] In particular, according to the embodiments disclosed in the present application, the process described above with reference to the flowchart can be implemented as a computer software program. For example, the embodiments disclosed in the present application include a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through a communication device, or installed from a storage device 1003, or installed from a ROM 1002. When the computer program is executed by the processing device 1001, the above-mentioned functions defined in the method of the embodiment disclosed in the present application are executed.

[0184] The multi-joint mechanical arm error self-calibration device provided by the present application adopts the multi-joint mechanical arm error self-calibration method in the above embodiment, which can solve the technical problem that the calibration device based on distance constraint and plane constraint is often bulky and not easy to carry, and the calibration process is complicated, which increases the difficulty of actual operation. Compared with the prior art, the beneficial effects of the multi-joint mechanical arm error self-calibration device provided by the present application are the same as the beneficial effects of the multi-joint mechanical arm error self-calibration method provided by the above embodiment, and other technical features in the multi-joint mechanical arm error self-calibration device are the same as the features disclosed in the method of the previous embodiment, which will not be repeated here.

[0185] It should be understood that the various parts disclosed in this application can be implemented by hardware, software, firmware or a combination thereof. In the description of the above embodiments, specific features, structures, materials or characteristics can be combined in any one or more embodiments or examples in a suitable manner.

[0186] In addition, the multi-joint mechanical arm error self-calibration device provided in the embodiment of the present application can solve the technical problem that the calibration device based on distance constraints and plane constraints is often bulky, not easy to carry, and the calibration process is complicated, which increases the difficulty of actual operation. Compared with the prior art, the beneficial effects of the multi-joint mechanical arm error self-calibration device provided in the embodiment of the present application are the same as the beneficial effects of the multi-joint mechanical arm error self-calibration method provided in the above embodiment, and other technical features in the multi-joint mechanical arm error self-calibration device are the same as the features disclosed in the above embodiment method, which will not be repeated here.

[0187] Based on the same technical concept, in a fourth aspect, the present invention further proposes a multi-joint robot arm error self-calibration system, comprising:

[0188] The multi-joint robot arm error self-calibration device according to the third aspect; and

[0189] A multi-joint robotic arm, wherein the multi-joint robotic arm is communicatively connected to the multi-joint robotic arm error self-calibration device, and the multi-joint robotic arm error self-calibration device can control the multi-joint robotic arm to perform self-calibration operations.

[0190] In addition, the multi-joint mechanical arm error self-calibration system provided in the embodiment of the present application can solve the technical problem that the calibration devices based on distance constraints and plane constraints are often bulky and difficult to carry, and the calibration process is complicated, which increases the difficulty of actual operation. Compared with the prior art, the beneficial effects of the multi-joint mechanical arm error self-calibration system provided in the embodiment of the present application are the same as the beneficial effects of the multi-joint mechanical arm error self-calibration method provided in the above embodiment, and other technical features in the multi-joint mechanical arm error self-calibration system are the same as the features disclosed in the above embodiment method, which will not be repeated here.

[0191] Based on the same technical concept, in the fifth aspect, the present invention also proposes a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by one or more processors, the multi-joint robot arm error self-calibration method described in the first aspect is implemented.

[0192] The computer-readable storage medium provided in the present application may be, for example, a USB flash drive, but is not limited to electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, systems or devices, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, system or device. The program code contained on the computer-readable storage medium may be transmitted using any appropriate medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination of the above.

[0193] The computer-readable storage medium may be included in the multi-joint robot arm error self-calibration device; or may exist independently without being assembled into the multi-joint robot arm error self-calibration device.

[0194] The above-mentioned computer-readable storage medium carries one or more programs. When the above-mentioned one or more programs are executed by the multi-joint robotic arm error self-calibration device, the multi-joint robotic arm error self-calibration device can implement the multi-joint robotic arm error self-calibration method described above.

[0195] Computer program code for performing the operations of the present application may be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, C++, and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0196] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present application. In this regard, each square box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, the program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0197] The modules involved in the embodiments described in this application may be implemented by software or hardware, wherein the name of the module does not constitute a limitation on the unit itself in some cases.

[0198] The readable storage medium provided by the present application is a computer-readable storage medium, which stores computer-readable program instructions (i.e., computer programs) for executing the above-mentioned multi-joint robot arm error self-calibration method, and can solve the technical problems that the calibration devices based on distance constraints and plane constraints are often bulky and difficult to carry, and the calibration process is complicated, which increases the difficulty of actual operation. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided by the present application are the same as the beneficial effects of the multi-joint robot arm error self-calibration method provided by the above-mentioned embodiment, and will not be repeated here.

[0199] The above description is only an exemplary embodiment of the present invention, and does not limit the patent scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the technical concept of the present invention, or directly / indirectly applied in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. A multi-joint robot arm error self-calibration method, characterized in that: The multi-joint mechanical arm has a plurality of joints, and the two ends of the multi-joint mechanical arm are a mounting end and a free end respectively, and the free end is detachably mounted with an end device. The multi-joint mechanical arm error self-calibration method comprises the following steps: According to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm respectively established, an objective function for self-calibration of the multi-joint robotic arm error is established; wherein the objective function is expressed by formula 1, which is: is the augmented matrix of the error pose transformation matrix of the end of the multi-joint robot, are all parameters to be identified, p i is the coordinate of the i-th point in three-dimensional space, and R is the radius of the calibration sphere; According to the set iteration data set, combined with the target Jacobian matrix and the target iteration step, the objective function is used to perform iterative calculation and obtain the positioning accuracy value of the multi-joint robotic arm; wherein the iteration data set includes an iteration initial value; When the positioning accuracy value is less than a preset value, the iteration is terminated and the error self-calibration operation of the multi-joint robotic arm is completed.

2. The multi-joint robot arm error self-calibration method according to claim 1, characterized in that: Before the step of establishing an objective function for self-calibration of the multi-joint robotic arm error according to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm respectively established, the step further includes: The DH method is used to establish the kinematic model of the multi-joint robotic arm; wherein the kinematic model is expressed by Formula 2, which is: is the homogeneous transformation matrix, a i Indicates the length of the robot arm, d i Represents the joint offset value, θ i Represents the arm length and torsion angle of the robot arm, α i represents the joint rotation angle, β i Indicates the y-axis rotation angle; A geometric error model of the multi-joint robotic arm is established; wherein the geometric error model is expressed using Formula 3, which is: D base =J G ·X G J G is the geometric error transfer Jacobian matrix, which is a 6×24-order matrix and is a known parameter after determining the position and posture of the multi-joint manipulator; X G =[X1 T X2 T … X6 T ] T , including all geometric errors of the arm lengths of two adjacent robotic arms of the multi-joint robotic arm, is a 24×1-order vector and is a parameter that needs to be identified; Establish an end device error model of the multi-joint robotic arm; wherein the end device error model is expressed using Formula 4, which is: F is the end load value of the cantilever beam of the terminal device, y t is the end deflection value of the cantilever beam, θ t is the rotation angle value of the terminal device, l is the length of the beam, E is the elastic modulus, I is the cross-sectional inertia moment, c1 and c2 are the deflection coefficient and bending moment coefficient respectively, which are the parameters that need to be identified.

3. The multi-joint robot arm error self-calibration method according to claim 2, characterized in that: The step of establishing an objective function for self-calibration of the multi-joint robotic arm error according to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm respectively established comprises: According to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm that are respectively established, a nonlinear least squares method is used to establish an objective function for self-calibration of the multi-joint robotic arm errors.

4. The multi-joint robot arm error self-calibration method according to claim 3, characterized in that: The step of establishing a geometric error model of the multi-joint robotic arm comprises: Establishing a first coordinate system sequence of the multi-joint robotic arm and a corresponding second coordinate system sequence of the terminal device respectively; Acquire a deviation sequence between the first coordinate system sequence and the corresponding second coordinate system sequence; A homogeneous transformation matrix is ​​used to perform total differential processing on each deviation in the deviation sequence, so as to transform the first coordinate system sequence and the second coordinate system sequence into a base coordinate system to obtain a geometric error model of the multi-joint robotic arm.

5. The multi-joint robot arm error self-calibration method according to claim 4, characterized in that: The step of using a homogeneous transformation matrix to perform full differential processing on each deviation in the deviation sequence to transform both the first coordinate system sequence and the second coordinate system sequence into a base coordinate system to obtain a geometric error model of the multi-joint robotic arm comprises: For each deviation in the deviation sequence, the homogeneous transformation matrix is ​​used to perform full differential processing on the deviation to obtain a current total differential equation, so as to transform the corresponding first coordinate system and the second coordinate system into the base coordinate system, and obtain a geometric error model of the multi-joint robotic arm; wherein the current total differential equation is expressed by Formula 5, which is: dT i For deviation.

6. The multi-joint robot arm error self-calibration method according to any one of claims 1 to 5, characterized in that: When the positioning accuracy value is less than a preset value, the step of ending the iteration and completing the error self-calibration operation of the multi-joint robotic arm comprises: When the positioning accuracy value is less than 0.1 mm, the iteration is terminated and the error self-calibration operation of the multi-joint robotic arm is completed.

7. A multi-joint robot arm error self-calibration device, characterized in that: The multi-joint mechanical arm has a plurality of joints, and the two ends of the multi-joint mechanical arm are respectively a mounting end and a free end, and the free end is detachably mounted with an end device, and the multi-joint mechanical arm error self-calibration device comprises: The objective function establishment module is used to establish an objective function for the error self-calibration of the multi-joint robotic arm according to the kinematic model, geometric error model and terminal device deformation error model of the multi-joint robotic arm respectively established; wherein the objective function is expressed by formula 1, which is: is the augmented matrix of the error pose transformation matrix of the end of the multi-joint robot, are all parameters to be identified, p i is the coordinate of the i-th point in three-dimensional space, and R is the radius of the calibration sphere; A calculation module, used to perform iterative calculations using the objective function according to a set iterative data set, in combination with a target Jacobian matrix and a target iterative step length, and obtain a positioning accuracy value of the multi-joint robotic arm; wherein the iterative data set includes an iterative initial value; The calibration module is used to end the iteration and complete the error self-calibration operation of the multi-joint robotic arm when the positioning accuracy value is less than a preset value.

8. A multi-joint robot arm error self-calibration device, characterized in that: The multi-joint robotic arm error self-calibration device includes a processor and a memory, wherein a multi-joint robotic arm error self-calibration program is stored in the memory, and when the multi-joint robotic arm error self-calibration program is executed by the processor, the multi-joint robotic arm error self-calibration method as described in any one of claims 1 to 6 is implemented.

9. A multi-joint robot arm error self-calibration system, characterized in that: include: The multi-joint robot arm error self-calibration device as claimed in claim 8; and A multi-joint robotic arm, wherein the multi-joint robotic arm is communicatively connected to the multi-joint robotic arm error self-calibration device, and the multi-joint robotic arm error self-calibration device can control the multi-joint robotic arm to perform self-calibration operations.

10. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by one or more processors, the multi-joint robot arm error self-calibration method according to any one of claims 1 to 6 is implemented.

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