A calibration method for dual robot collaboration errors based on kinematic model

Abstract

The present invention discloses a calibration method for the collaborative error of dual robots based on a kinematic model. The collaborative error definition is given according to the transformation matrix of the master robot relative to the base coordinate system, the transformation matrix of the slave robot relative to the base coordinate system, the transformation matrix of the base coordinate system relative to the world coordinate system, and the actual relationship of the dual robots relative to the world coordinate system; the dual robot tool coordinate system fitting error model is constructed based on the conversion relationship between the master robot link coordinate system and its tool coordinate system; the dual robot base coordinate system fitting error model is constructed based on the base coordinate system modeling error; the dual robot link parameter error model is constructed; based on the given definition and the constructed model, the dual robot collaborative positioning error is parameter identified and calibrated. The present invention can improve the collaborative accuracy of dual robots, reduce the fluctuation of collaborative errors, identify parameter errors under a smaller random sampling scale, and significantly improve the robot collaborative error after compensation and the effect is stable.

Description

Technical Field

[0001] The invention belongs to the technical field of industrial robot calibration, and in particular relates to a calibration method for dual-robot collaborative errors based on a kinematic model. Background Art

[0002] Industrial robots are widely used in handling, welding, assembly and other fields, but most of the current scenarios are based on single-robot applications. Even if there are many robots on a production line, each robot is mostly performing its own duties at its own workstation, without much coordination and communication between them, and there are few applications of dual-robot or multi-robot coordination technology. In order to adapt to the complexity of tasks, the convenience of operation and the flexibility of the system, it is necessary to expand the traditional single-robot mode to dual-robot coordinated operation, that is, the two robots cooperate with each other through certain coordination strategies to complete the expected tasks.

[0003] Taking the robot automated handling and assembly of large wing parts as an example, the usual practice is to install multiple pairs of suction cups at the end of the robot for adsorption, but it is difficult to overcome the shaking problem caused by the large size of the parts, which must be solved for aircraft assembly. Another example is the bidirectional electromagnetic riveting in aviation operations, which requires precise guarantee of close coordination of the movements of the two robot ends. The above examples involve typical occasions for multi-robot collaborative operations, which can be summarized as: handling and precision assembly of large-sized, weakly rigid or objects that exceed the load of a single robot, and work that must be completed through robot collaboration, such as electromagnetic riveting, cold forming and ultrasonic testing. In addition, collaboration to improve efficiency, such as simultaneous welding, is also a common application scenario. And to coordinate the postures on the ends of multiple robots, the collaborative accuracy is our focus: poor collaborative accuracy will lead to mission failure, damage to the workpiece or robot, and other consequences. Therefore, the collaborative positioning accuracy of dual robots and even multi-robot systems is one of the key technologies that need to be solved urgently for the promotion and application of robots.

[0004] Research on robot precision calibration is relatively mature. It is divided into online and offline calibration according to whether the error is compensated in real time. The latter can be divided into kinematic model-based calibration and non-kinematic model-based calibration. The kinematic model-based calibration method generally calibrates the kinematic parameters and base coordinate system parameters; non-kinematic model calibration generally refers to calibration using neural network model technology.

[0005] The existing technology uses non-motion model calibration in the offline calibration method. By measuring the posture of the dual robots and using the joint angle as training data, two ANN models are trained to compensate for the absolute accuracy and relative accuracy respectively, so that the accuracy of the master and slave robots is significantly improved. This method regards the dual robot system as a "black box" and ignores the differences between various error sources to a certain extent. However, the physical meaning of the parameters of the ANN model is not clear, and it is not helpful to reveal the internal mechanism of robot accuracy compensation. At the same time, this method requires a large amount of training data and has a high time cost. 800 pairs of posture data were measured in this paper.

[0006] In the calibration based on motion models, the focus is currently on the research of base coordinate system calibration strategies. Some researchers installed reflective paper at the ends of the dual robots, used a binocular vision system to measure four points on the ends of the robots that were not in the same plane, established and solved its homogeneous equations to obtain the relative position relationship of the dual robot base coordinate system. Generally speaking, methods that rely on customized tools require manual operation and judgment during the calibration process, which restricts the efficiency and accuracy of the calibration. Summary of the invention

[0007] The technical problem to be solved by the present invention is to address the deficiencies of the above-mentioned prior art and to provide a calibration method for the collaborative error of dual robots based on a kinematic model. The method takes into account the coupled kinematic parameter errors, robot base coordinate system errors, and tool coordinate system errors that affect the collaborative accuracy of multiple robots, and uniformly models the kinematic parameter errors of the DH model, the base coordinate system establishment errors, and the tool coordinate system establishment errors. The method is successfully applied to the calibration of dual robots, which significantly improves the collaborative accuracy of dual robots and reduces the fluctuation of collaborative errors.

[0008] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0009] A calibration method for dual robot collaborative error based on kinematic model, comprising:

[0010] Step S1: According to the transformation matrix of the master robot relative to the base coordinate system, the transformation matrix of the slave robot relative to the base coordinate system, the transformation matrix of the base coordinate system relative to the world coordinate system, and the actual relationship between the dual robots and the world coordinate system, a definition of the dual robot coordination error is given;

[0011] Step S2: constructing a fitting error model of the dual robot tool coordinate system based on the conversion relationship between the main robot link coordinate system and its tool coordinate system;

[0012] Step S3: constructing a dual-robot base coordinate system fitting error model based on the base coordinate system modeling error;

[0013] Step S4: constructing a dual robot link parameter error model based on the kinematic parameter error of the DH model;

[0014] Step S5: Based on the definition of step S1 and the model constructed in steps S2-S4, the LM algorithm is used to identify and calibrate the parameter errors of the dual robots with the goal of minimizing the collaborative error.

[0015] To optimize the above technical solutions, the specific measures taken also include:

[0016] The collaborative error of the dual robots constructed in the above step S1 is expressed according to the following formula:

[0017] ; (7)

[0018] in, and They represent the transformation matrices of the master robot tool coordinate system relative to the master robot base coordinate system and the slave robot tool coordinate system relative to the slave robot base coordinate system respectively;

[0019] and Respectively represent the transformation matrices of the master robot base coordinate system and the slave robot base coordinate system relative to the world coordinate system;

[0020] and They respectively represent the actual relationship between the master robot tool coordinate system and the slave robot tool coordinate system relative to the world coordinate system;

[0021] By analyzing the geometric relationship of the dual robots, the collaborative error in the above equation is expressed as:

[0022] ;

[0023] in , , They are the error caused by the fitting error of the robot tool coordinate system, the error caused by the fitting error of the base coordinate system and the error caused by the parameter error of the dual robot link.

[0024] The above step S2 constructs a dual robot tool coordinate system fitting error model based on the following formula:

[0025] ;

[0026] ;

[0027] In the formula, The conversion relationship between the main robot's No. 6 link coordinate system and the main robot's tool coordinate system is: The coordinate system of the main robot No. 6 link is about the main robot tool coordinate system according to z - y - x The angle of rotation using the Euler angle method, They are respectively the coordinate system of the main robot No. 6 link relative to the main robot tool coordinate system x , y , z The translation distance of the axis, , and so on. express OK The zero vector of the column, and They are the position error vector and attitude error vector of the main robot's No. 6 link coordinate system relative to the main robot's tool coordinate system, and are the position error vector and attitude error vector of the robot tool coordinate system relative to the robot No. 12 link coordinate system, represents the error of the corresponding parameter, They are respectively from the robot tool coordinate system around the robot No. 12 link coordinate system according to z - y - x The angle of rotation using the Euler angle method, They are respectively from the robot tool coordinate system relative to the robot No. 12 link coordinate system x , y , z The translation distance of the axis;

[0028] The constructed dual robot tool coordinate system fitting error model is: ; (9)

[0029] In the formula,

[0030] ;

[0031] The first three represent the rotation vectors of the homogeneous transformation matrix of the slave robot's tool coordinate system relative to the master robot's No. 6 link coordinate system, and the last one is the translation vector, and so on.

[0032] The above step S3 constructs the dual robot base coordinate system fitting error model according to the following formula:

[0033] ;

[0034] ;

[0035] ;

[0036] ;

[0037] ;

[0038] The constructed dual-robot base coordinate system fitting error model is: ; (13)

[0039] In the formula,

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] ;

[0045] The base coordinate system of the slave robot revolves around the base coordinate system of the master robot according to z- y - x The angle value of the Euler angle rotation method, The origin of the robot base coordinate system is relative to the main robot base coordinate system. x , y , z The distance between the axes, The first three represent the rotation vectors of the homogeneous transformation matrix from the robot tool coordinate system to the robot base coordinate system, and the last one is the translation vector.

[0046] The dual robot link parameter error model constructed in the above step S4 is:

[0047] ; (27)

[0048] In the formula,

[0049] ; (28)

[0050] is a 3×6 matrix, each Matrix The expression for a column vector is:

[0051] ;

[0052] ;

[0053] ;

[0054] is a 3×6 matrix, each Matrix The expression for a column vector is:

[0055] ;

[0056] .

[0057] In the above step S5, the dual robot collaborative error is established based on steps S2-S4. Mathematical matrix model between various parameter errors to identify parameter errors and then compensate for coordination errors , calibrate the robot, and the collaborative error matrix of the dual robots is:

[0058] ; (29)

[0059] In the formula, is the Jacobian matrix of the robot considering multiple sources of error, is the column vector of all errors;

[0060] Taking the minimum error matrix shown in formula (29) as the goal, the LM algorithm is used to identify the corresponding , the specific calculation formula is:

[0061] ; (30)

[0062] In the formula, represents the damping factor, is the identity matrix.

[0063] The above identification The process is:

[0064] (1) Calculate the k Jacobian matrix of the robot considering multi-source errors at the iteration;

[0065] (2) Calculate the first k The parameter error corresponding to the iteration;

[0066] (3) Based on k The parameter error calculation corresponding to the iteration k The ratio of the actual drop to the estimated drop at the iteration ;

[0067] (4) Based on ratio Update Robot parameter errors and optimization factors at the iteration;

[0068] (5) When the set conditions are met, the loop ends. The parameter error obtained at this time is the optimal parameter error, and the robot calibration is completed.

[0069] The present invention has the following beneficial effects:

[0070] In order to improve the collaborative accuracy of dual robots working together, the present invention proposes a definition and representation method of the collaborative error of dual robots, establishes an extended kinematic error model of coupled kinematic parameter error, robot base coordinate system error and tool coordinate system error, and proposes a kinematic calibration method for a dual robot collaborative system taking these three error sources into consideration. The DH model kinematic parameter error, base coordinate system establishment error and tool coordinate system establishment error are uniformly modeled and successfully applied to the calibration of dual robots. The present invention can significantly improve the collaborative accuracy of dual robots and reduce the fluctuation of collaborative error. It can identify parameter errors under a smaller random sampling scale, and the robot collaborative error is significantly improved after compensation and the effect is stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 It is a coordinate system diagram of the dual robot connecting rod of the present invention;

[0072] Figure 2 It is a flow chart of collaborative error parameter identification of the present invention. DETAILED DESCRIPTION

[0073] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0074] Although the steps in the present invention are arranged with numbers, they are not used to limit the order of the steps. Unless the order of the steps is clearly stated or the execution of a certain step requires other steps as a basis, the relative order of the steps can be adjusted. It is understood that the term "and / or" used in this article involves and covers any and all possible combinations of one or more of the associated listed items.

[0075] The present invention provides a calibration method for the dual robot collaborative error based on a kinematic model, which takes into account the coupled kinematic parameter errors, robot base coordinate system errors, and tool coordinate system errors that affect the collaborative accuracy of multiple robots, and unifies the DH model kinematic parameter errors, base coordinate system establishment errors, and tool coordinate system establishment errors. It is successfully applied to the calibration of dual robots, significantly improving the collaborative accuracy of dual robots and reducing the fluctuation of collaborative errors. The method is specifically as follows:

[0076] Step S1: According to the transformation matrix of the master robot relative to the base coordinate system, the transformation matrix of the slave robot relative to the base coordinate system, the transformation matrix of the base coordinate system relative to the world coordinate system, and the actual relationship between the dual robots and the world coordinate system, the definition and expression of the dual robot coordination error are given;

[0077] Step S2: constructing a fitting error model of the dual robot tool coordinate system based on the conversion relationship between the main robot link coordinate system and its tool coordinate system;

[0078] Step S3: constructing a dual-robot base coordinate system fitting error model based on the base coordinate system modeling error;

[0079] Step S4: constructing a dual robot link parameter error model;

[0080] Step S5: Based on the definition of step S1 and the error model constructed in steps S2-S4, the LM algorithm is used to identify and calibrate the parameter errors of the dual robots with the goal of minimizing the collaborative error. The dual robots are used as the object, and the points of their end effectors are planned. They are divided into a parameter identification sample group and a test group, and the collaborative errors before and after calibration are studied.

[0081] In the embodiment, step S1 obtains the error of the transformation matrix between the end effectors of the dual robots, and the error matrix represents the collaborative error of the dual robots. The collaborative positioning error is modeled under the premise of only considering the geometric error of the robots. Specifically, it is as follows:

[0082] Using the homogeneous transformation matrix and They represent the position transformation relationship of the tool coordinate system of the master robot and the tool coordinate system of the slave robot relative to the world coordinate system. In the collaborative working state, theoretically, the tool coordinate systems of the master robot and the slave robot should reach and The homogeneous transformation matrix between the master robot tool coordinate system and the slave robot tool coordinate system is , then:

[0083] ; (1)

[0084] In theory, to obtain the relationship between the robot tool coordinate system and the world coordinate system, it must be transferred through the base coordinate system, so:

[0085] ; (2)

[0086] ; (3)

[0087] In the formula, and They represent the transformation matrices of the master robot tool coordinate system relative to the master robot base coordinate system and the slave robot tool coordinate system relative to the slave robot base coordinate system, respectively, and can be directly set during task planning; and They represent the transformation matrices of the master robot base coordinate system and the slave robot base coordinate system relative to the world coordinate system. Substituting equations (2) and (3) into equation (1), we can obtain the theoretical pose transformation of the master robot tool coordinate system relative to the slave robot tool coordinate system at any time: .

[0088] However, in the actual working process, due to the error factor, the actual relationship between the main robot tool coordinate system and the main robot base coordinate system relative to the world coordinate system is and , these two transformation matrices can be actually measured. The transformation matrices of the two are , there is the following relationship:

[0089] ; (4)

[0090] There is a relationship between theoretical and practical homogeneous transformation matrices:

[0091] ; (5)

[0092] Solving equation (5) yields:

[0093] ; (6)

[0094] Combining equations (1) to (6), the dual robot collaborative error expression can be obtained as:

[0095] ; (7)

[0096] The links between the base coordinate system and the tool coordinate system of the main robot are link 1 to link 6 in order, and the coordinate system is defined as ( i = 1, 2, …, 6) system, the connecting rod from the robot from the base coordinate system to the tool coordinate system is defined in order of the coordinate system ( j = 7, 8, …, 12). The robot's error can be divided into geometric error and non-geometric error, and only geometric error is considered. Figure 2 Considering the geometric relationship of the dual robots, it can be seen that the collaborative error consists of three parts: (1) the error caused by the robot tool coordinate system fitting error ; (2) Error caused by base coordinate system fitting error ; (3) Errors caused by dual robot link parameter errors .Right now: ;

[0097] In the embodiment, step S2 establishes a dual robot tool coordinate system fitting error model, which is specifically as follows:

[0098] The conversion relationship between the main robot's No. 6 link coordinate system and the main robot's tool coordinate system is:

[0099] ; (8)

[0100] In the formula, The coordinate system of the main robot No. 6 link is about the main robot tool coordinate system according to z - y - x The angle of rotation using the Euler angle method, They are the coordinate system of the main robot No. 6 link relative to the main robot tool coordinate system. x , y , z The translation distance of the axis, The coordinate system of the dual robot link of the present invention is as follows: Figure 1 shown.

[0101] The partial differentials of the six parameters of the tool coordinate system are calculated to obtain the tool coordinate system error vector of the master robot and the tool coordinate system error vector of the robot. Finally, the error caused by the tool coordinate system fitting is obtained as follows:

[0102] ; (9)

[0103] In the formula,

[0104] (10);

[0105] in, Represents the rotation vector and translation vector of the homogeneous transformation matrix of the slave robot tool coordinate system relative to the master robot's No. 6 link coordinate system, , and so on.

[0106] In the embodiment, step S3 establishes a dual-robot base coordinate system fitting error model, which is specifically as follows:

[0107] The modeling error of the base coordinate system is:

[0108] ; (11)

[0109] In the formula, The base coordinate system of the slave robot revolves around the base coordinate system of the master robot according to z - y - x The angle value of the Euler angle rotation method, The origin of the robot base coordinate system is relative to the main robot base coordinate system. x , y , z The distance between the axes,

[0110] ; (12)

[0111] The error caused by the basic coordinate system fitting is:

[0112] ; (13)

[0113] In the formula,

[0114] ; (14)

[0115] In the embodiment, step S4 establishes a dual robot link parameter error model, which is specifically as follows:

[0116] Using the M-DH model, the transformation matrix of two adjacent joints is:

[0117] ; (15)

[0118] In the formula, They are joint angle, link offset, link length, link torsion angle and Connecting rod z Shaft winding y Small rotation angles of the axis are possible only when the theoretical axes of adjacent joints are parallel. .

[0119] When there is an error in the actual DH parameters of the robot, there are:

[0120] ; (16)

[0121] In the formula, For the The coordinate system of the connecting rod No. The linear error transformation matrix between the link coordinate systems is: and Separate Connecting rod No. The real and theoretical coordinate transformation relationship between the connecting rod coordinate systems.

[0122] Since the linkage error is essentially a coordinate transformation, the error can also be expressed by superimposing small translation and rotation changes, that is:

[0123] ; (17)

[0124] In the formula, represents the translation transformation, Indicates press z - y - x Coordinate system rotation transformation performed by Euler angles, Respectively x, y, z The translation error in the direction, Respectively represent the z, y, x The rotation error of the axis, the rotation mode is z - y - x Euler angles.

[0125] For the main robot, the multiplication of the homogeneous transformation matrix of its link when solving the collaborative error is a process from the end to the base. When only the link coordinate system error caused by the DH parameter is considered, It can be obtained by taking partial differential of the formula, namely:

[0126] ; (18)

[0127] In the formula, For connecting rod Substituting equation (18) into equation (17) yields the following DH parameter error:

[0128] ; (19)

[0129] The solution is:

[0130] ; (20)

[0131] Combining equation (19) and equation (20), we can get:

[0132] ;(twenty one)

[0133] In the formula,

[0134] ;(twenty two)

[0135] The coordinate system error of the connecting rod of the main robot can be obtained as:

[0136] ;(twenty three)

[0137] In the formula, for Composition dimensional column vector, and so on. is a 3×6 matrix, each Matrix The expression for a column vector is:

[0138] ;(twenty four)

[0139] For the slave robot, similar to the master robot, the link coordinate system error of the slave robot is:

[0140] ; (25)

[0141] is a 3×6 matrix, each Matrix The expression for a column vector is:

[0142] ; (26)

[0143] Combining equations (23) and (25), the error caused by the parameter error of the dual robot link is: ; (27)

[0144] In the formula,

[0145] ; (28)

[0146] In the embodiment, step S5 performs parameter identification for the dual-robot collaborative positioning error, specifically as follows:

[0147] According to equations (9), (13) and (27), the collaborative error of the dual robots can be written as:

[0148] ; (29)

[0149] In the formula, is the Jacobian matrix of the robot considering multiple sources of error, is the column vector of all errors;

[0150] For dual robots, a series of sampling points are measured in the actual calibration to identify Make Minimum.

[0151] The damped least squares method (also known as the Levenberg-Marquardt algorithm, abbreviated as the LM algorithm) is used. This method can effectively avoid the singularity problem of the identification matrix. The calculation formula is:

[0152] ; (30)

[0153] In the formula, represents the damping factor, is the identity matrix.

[0154] Figure 2 The present invention uses the LM algorithm to identify the formula (29) The process includes:

[0155] (1) Calculate the k The matrix at the iteration ;

[0156] (2) Calculate the k The parameter error corresponding to the iteration:

[0157] ; (31)

[0158] In the formula, Indicatesk The change in parameter error at the iteration, Indicates k The parameter error at the iteration, Indicates k The robot collaborative error matrix at the iteration is: Indicates k The damping factor at the iteration is adjusted by the following formula during the iteration process: ; (32)

[0159] In the formula, represents the two-norm of a vector, is called the optimization factor.

[0160] (3) Calculate the k The actual decrease in the iteration The estimated decrease Ratio ;

[0161] ; (33)

[0162] ; (34)

[0163] ; (35)

[0164] in, Used to decide whether to accept a trial step And adjust the iteration parameters The size of the factor. Generally speaking The larger the value, the more the objective function decreases, so we accept , looking forward to the next trial step Longer, so smaller ;on the contrary, The smaller the value, the more likely it is to be rejected. , increase ;

[0165] (4) Update k +1 robot parameter error and optimization factor at iteration ;

[0166] ; (36)

[0167] ; (37)

[0168] In the formula, represents the two-norm of the vector; and , , is a given constant, which is The lower bound of , which prevents numerical difficulties caused by too large trial steps when the sequence of iteration points is close to the solution of the system of equations;

[0169] Indicates k The change in parameter error at the iteration, Indicates k The parameter error at the iteration, Indicates k The robot collaborative error matrix at the iteration is: Indicates k The damping factor at the iteration, It is called the optimization factor;

[0170] (5) When ( The loop ends when the maximum number of iterations is reached (the residual error norm expected at convergence). , the parameter error obtained at this time is the optimal parameter error, and the robot calibration is completed.

[0171] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0172] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A calibration method for dual robot collaborative error based on kinematic model, characterized in that: include: Step S1: According to the transformation matrix of the master robot tool coordinate system relative to the master robot base coordinate system, the transformation matrix of the slave robot tool coordinate system relative to the slave robot base coordinate system, the transformation matrix of the master robot base coordinate system and the slave robot base coordinate system relative to the world coordinate system, and the actual relationship between the master robot tool coordinate system and the slave robot tool coordinate system and the world coordinate system, a definition of dual robot collaborative error is given; Step S2: constructing a fitting error model of the dual robot tool coordinate system based on the conversion relationship between the main robot link coordinate system and its tool coordinate system; Step S3: constructing a dual-robot base coordinate system fitting error model based on the base coordinate system modeling error; Step S4: constructing a dual robot link parameter error model based on the DH model kinematic parameter error; Step S5: Based on the definition in step S1 and the model constructed in steps S2 to S4, the LM algorithm is used to identify and calibrate the parameter errors of the dual robots with the goal of minimizing the collaborative error; The collaborative error of the dual robots constructed in step S1 is expressed according to the following formula: ；（7） in, and They represent the transformation matrices of the master robot tool coordinate system relative to the master robot base coordinate system and the slave robot tool coordinate system relative to the slave robot base coordinate system respectively; and Respectively represent the transformation matrices of the master robot base coordinate system and the slave robot base coordinate system relative to the world coordinate system; and They respectively represent the actual relationship between the master robot tool coordinate system and the slave robot tool coordinate system relative to the world coordinate system; By analyzing the geometric relationship of the dual robots, the collaborative error in the above equation is expressed as: ； in , , They are the error caused by the robot tool coordinate system fitting error, the error caused by the base coordinate system fitting error and the error caused by the dual robot link parameter error; The step S2 constructs a dual robot tool coordinate system fitting error model based on the following formula: ； ； In the formula, The conversion relationship between the main robot's No. 6 link coordinate system and the main robot's tool coordinate system is: The coordinate system of the main robot No. 6 link is about the main robot tool coordinate system according to zyx The angle of rotation using the Euler angle method, They are respectively the coordinate system of the main robot No. 6 link relative to the main robot tool coordinate system x , y , z The translation distance of the axis, , and so on. express OK The zero vector of the column, and They are the position error vector and attitude error vector of the main robot's No. 6 link coordinate system relative to the main robot's tool coordinate system, and are the position error vector and attitude error vector of the robot tool coordinate system relative to the robot No. 12 link coordinate system, represents the error of the corresponding parameter, They are respectively from the robot tool coordinate system around the robot No. 12 link coordinate system according to zyx The angle of rotation using the Euler angle method, They are respectively from the robot tool coordinate system relative to the robot No. 12 link coordinate system x , y , z The translation distance of the axis; The constructed dual robot tool coordinate system fitting error model is: ; (9) In the formula, ； The first three represent the rotation vectors of the homogeneous transformation matrix of the slave robot's tool coordinate system relative to the master robot's No. 6 link coordinate system, and the last one is the translation vector, and so on.

2. The calibration method of dual robot collaborative error based on kinematic model according to claim 1 is characterized in that: The step S3 constructs a dual-robot base coordinate system fitting error model according to the following formula: ； ； ； ； ； The constructed dual-robot base coordinate system fitting error model is: ; (13) In the formula, ； ； ； ； ； The robot base coordinate system revolves around the main robot base coordinate system according to zyx The angle value of the rotation using the Euler angle method, The origin of the robot base coordinate system is relative to the main robot base coordinate system. x , y , z The distance between the axes, The first three represent the rotation vectors of the homogeneous transformation matrix of the robot tool coordinate system relative to the robot base coordinate system, and the last one is the translation vector.

3. The calibration method of dual robot collaborative error based on kinematic model according to claim 1 is characterized in that: The dual robot link parameter error model constructed in step S4 is: ；（27） In the formula, ；（28） is a 3×6 matrix, each Matrix The expression for a column vector is: ； ； ； is a 3×6 matrix, each Matrix The expression for a column vector is: ； 。 4. The calibration method of dual robot collaborative error based on kinematic model according to claim 1 is characterized in that: In step S5, the dual robot collaborative error is established based on steps S2 to S4. Mathematical matrix model between various parameter errors to identify parameter errors and then compensate for coordination errors , calibrate the robot, and the collaborative error matrix of the dual robots is: ；（29） In the formula, is the Jacobian matrix of the robot considering multiple sources of error, is the column vector of all errors; Taking the minimum error matrix shown in formula (29) as the goal, the LM algorithm is used to identify the corresponding , the specific calculation formula is: ；（30） In the formula, represents the damping factor, is the identity matrix.

5. The calibration method of dual robot collaborative error based on kinematic model according to claim 4 is characterized in that: Identification The process is: (1) Calculate the k Jacobian matrix of the robot considering multi-source errors at the iteration; (2) Calculate the first k The parameter error corresponding to the iteration; (3) Based on k The parameter error calculation corresponding to the iteration k The ratio of the actual drop to the estimated drop at the iteration ; (4) Based on ratio Update Robot parameter errors and optimization factors at the iteration; (5) When the set conditions are met, the loop ends. The parameter error obtained at this time is the optimal parameter error, and the robot calibration is completed.

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