Mechanical arm rigidity modeling and identifying method and device for nuclear power operation and maintenance

Abstract

The invention belongs to the technical field of nuclear power operation and maintenance, aims to solve the problem of precision compensation after a mechanical arm generates elastic deformation under the action of a large load, and discloses a mechanical arm rigidity modeling and identification method and device for nuclear power operation and maintenance. Carrying out coordinate system definition on all joints in the virtual joint group, fitting the arm lever deflection between any two joints, carrying out kinematics modeling on the robot comprising the virtual joint group and the real joint to obtain a Jacobian matrix representing the relation between the end speed of the robot and the joint speed of the robot, and establishing a rigidity model of the robot; rigidity parameters of the rigidity model are optimized, and the rigidity parameters are identified through a weighted least square method; the device comprises a mechanical arm, a laser tracker, a force sensor and a target mounting seat. The invention provides a mechanical arm virtual stiffness modeling method aiming at the situation that a large-load low-stiffness mechanical arm is prone to deflection errors.

Description

Technical Field

[0001] The present application belongs to the field of nuclear power operation and maintenance technology, and in particular relates to a method and device for modeling and identifying stiffness of a robotic arm used for nuclear power operation and maintenance. Background Art

[0002] The robotic arms used in nuclear power plant operation and maintenance scenarios differ from standardized industrial robots. To adapt to specific scenarios, they must be compact, lightweight, and capable of handling large loads. This can cause deformation of the arms due to heavy loads and low rigidity, leading to significant errors in the operational trajectory. Industrial-grade or collaborative robots, due to their inherently high structural rigidity or low load capacity, experience errors due to external loads and structural flexibility that are far lower than system parameter errors caused by machining and assembly errors. Therefore, the primary calibration process for industrial robots involves calibrating system parameter errors such as link length, base coordinate system, and zero position.

[0003] The main methods for stiffness identification of robotic arms include the finite element method (FEA), the matrix analysis method (MSA), and the virtual joint method (VJM). Among them, the most accurate is the technology based on finite element analysis (FEA), which takes into account the actual shape and size of the robot components. However, due to the high computational cost, this method is usually applied to the final design stage. The matrix analysis method combines the main ideas of finite element analysis and uses a simplified unit - a three-dimensional flexible beam, which obviously reduces the amount of calculation but cannot eliminate the shortcomings of finite element analysis. The virtual joint method describes the elastic deformation of the links, joints, and actuators by adding virtual joints (localized springs) on the basis of the traditional rigid model. This method provides a reasonable trade-off between model accuracy and computational complexity.

[0004] After the stiffness modeling of the manipulator is complete, the stiffness parameters need to be identified and calculated. Existing methods, due to the influence of measurement noise, easily produce non-positive stiffness parameters, which is inconsistent with physical properties. The large difference in the magnitude of the stiffness parameters also affects identification accuracy. A complete elastostatic model of the manipulator contains a large number of stiffness parameters, and the influence of measurement noise makes identification extremely difficult. Summary of the Invention

[0005] The purpose of this application is to provide a method and device for modeling and identifying the stiffness of a robotic arm for nuclear power operation and maintenance, so as to solve the problem of precision compensation after the robotic arm undergoes elastic deformation under a large load.

[0006] In order to achieve the above objectives, this application provides the following technical solutions:

[0007] In a first aspect, the present application provides a method for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance, comprising:

[0008] Step 1: The one-dimensional joint group for arm deflection fitting is used as the virtual joint group of a single arm. The coordinate system of all joints in the virtual joint group is defined based on the real joints to fit the arm deflection between any two joints.

[0009] Step 2: Based on the coordinate system definition, the robot including the virtual joint group and real joints is kinematically modeled to obtain the Jacobian matrix that represents the relationship between the robot end velocity and the robot joint velocity, which is used to establish the robot stiffness model;

[0010] Step 3: Based on the combination of algebraic and statistical methods, the stiffness parameters of the stiffness model established in step 2 are optimized and the stiffness parameters are identified by weighted least squares method.

[0011] As a feasible approach, the arm is equivalent to a cantilever beam, and the springs fitting the arm deflection are regarded as six one-dimensional joints fitted by six links with a length of 0, including three moving joints and three rotating joints. The real joints of the robot are simplified to one-dimensional springs, and the stiffness matrix of the entire arm and joint combination is expressed as a 7×7 stiffness matrix.

[0012] As an implementable approach, the coordinate system definition rules are adopted in step 1, including:

[0013] According to the coordinate system definition of the real joint, determine the initial coordinate system of the virtual joint of the previous link connected to it;

[0014] The coordinate systems of the last two rotational degrees of freedom are obtained by rotating 360 degrees around X and 360 degrees around Y respectively;

[0015] The first translational degree of freedom has the same coordinate system as the last rotational degree of freedom;

[0016] The coordinate systems for the last two translational degrees of freedom are obtained by rotating -360 degrees around Y and -360 degrees around X, respectively.

[0017] As an implementable manner, the real joint coordinate system posture in the arm and joint combination is consistent with the last joint coordinate system posture of the arm virtual joint group.

[0018] As an implementable approach, the entire 3R3T1R open-chain joint group is modeled to obtain the Jacobian matrix J(θ) that characterizes the relationship between the robot end velocity and the robot joint velocity;

[0019] The stiffness matrix of all joints of the robot is expressed as K θ , according to the kinematics of the manipulator and the relationship between the couples, the relationship between the external torque and the end displacement deviation caused by it is obtained:

[0020]

[0021] Where, Represents the flexibility of all virtual joint groups and real joints, which is the stiffness K θ The reciprocal of J ξ is the Jacobian matrix of the Cartesian space of the end of the robot relative to the joint space, τ is the generalized torque of all joints of the robot, F f represents the external load force vector at the end of the robot, ξ X Indicates the motion posture deviation of the robot arm before and after the end is loaded;

[0022] Assume that the observation matrix b i =ξ X , solve the flexibility matrix by the least square method to obtain the stiffness K θ :

[0023]

[0024] Where N represents the N configurations of the robot arm motion, and A is obtained by solving the joint angles, end forces and end posture deviations of the N configurations. i and b i .

[0025] As an implementable approach, step 3 includes:

[0026] Step 3.1: Perform singular value decomposition on the observation matrix and group the parameters according to the decomposition results;

[0027] Step 3.2: Perform a secondary decomposition of the parameter submatrix to be determined, extract the key principal component columns through QR decomposition and add them to the identifiable group;

[0028] Step 3.3: Calculate the current parameter residuals, construct a weight matrix based on the residual heterogeneity, and repeatedly update the parameters through weighted least squares until the residuals converge;

[0029] Step 3.4: Calculate the standard deviation of the parameters and normalize them, eliminate the parameters whose magnitude is less than the threshold, and repeat step 3.3 for the retained parameters to obtain the final stiffness parameters.

[0030] As an implementable approach, in step 3.1, the stiffness parameters are optimized by algebraic methods:

[0031] Perform SVD decomposition on the observation matrix to obtain an orthogonal matrix:

[0032] V=[V1 V2 ... V r V r+1 ... V m ]

[0033] Where r corresponds to the number of non-zero elements on the diagonal of the S matrix, and m is the original number of stiffness parameters;

[0034] According to the grouping of the orthogonal matrix V, the parameters in the stiffness vector are divided into three groups:

[0035] Group C1: V submatrix [V r+1 ... V m ] The parameter number corresponding to the number of columns whose row vectors are equal to zero;

[0036] C2 group: V submatrix [V1 ... V r ] The parameter number corresponding to the number of columns whose row vectors are equal to zero;

[0037] Group C3: Remaining parameters.

[0038] As an implementable method, for the remaining stiffness parameter numbers of group C3, select the observation matrix columns corresponding to the numbers to form a matrix, perform SVD decomposition on the matrix again, and use the obtained orthogonal matrix V to calculate the following matrix L:

[0039]

[0040] Where m′ represents the number of parameters in group C3, [V1 V2 ... V m ′] * To extract the relevant rows of the V matrix, ensure full rank;

[0041] Perform QR decomposition on the L matrix:

[0042] AP=QR(L)

[0043] The first n non-repeated row indices of the permutation matrix P represent linearly independent pivot columns in the matrix space of the matrix L, and the corresponding parameters are found according to the indices.

[0044] As an implementable method, in step 3.3, the C obtained by least squares θ , and find the residual E:

[0045]

[0046] Calculate the covariance matrix of the residual E and calculate the weight matrix η:

[0047]

[0048] Modify the weight matrix and obtain the new flexibility parameters through weighted least squares:

[0049]

[0050] Repeat the above iterative process, use the new flexibility parameter to solve the residual again, and obtain a new weight until the residual is less than a certain value.

[0051] As an implementable approach, in step 3.4, the covariance matrix of the parameters is obtained by the following formula:

[0052]

[0053] Extract the diagonal parameters and estimate their standard deviation σ j , for the parameter vector C θ Each element C in i Divide by its standard deviation to obtain the normalization parameter v i :

[0054]

[0055] Using the normalization parameter v i , perform parameter optimization, eliminate parameters whose normalized parameter magnitude is less than the threshold, and perform step 3.3 again for the retained parameters to calculate the flexibility parameters of the manipulator and obtain the final stiffness parameters.

[0056] In the second aspect, the present application provides a robotic arm stiffness modeling and identification device for nuclear power operation and maintenance, which implements the above-mentioned method. The device includes a robotic arm, a laser tracker, and a force sensor and a target mounting seat installed at the end of the robotic arm, and the target mounting seat is installed with an end posture target; the end posture of the robotic arm when it is not loaded is measured by the laser tracker, and an end load is installed at the end of the robotic arm, and the end posture after the load is added is measured by the laser tracker.

[0057] Compared with the existing technology, the robot arm stiffness modeling and identification method and device for nuclear power operation and maintenance provided by this application have the following beneficial effects:

[0058] This application addresses the problem of deflection errors that are common in high-load, low-rigidity robotic arms. This application develops a virtual stiffness modeling method for robotic arms. Based on the established robotic arm stiffness model, a stiffness parameter simplification and identification method is proposed. This application ensures the reversibility of the observation matrix during the identification process, eliminates redundant parameters and parameters with negligible impact, and forms a flexible and implementable stiffness identification experimental device.

[0059] Furthermore, this application proposes a modeling method for virtual joints of robotic arms, expanding the original modeling method that only considers the joints of robotic arms to a modeling method that considers the stiffness of connecting rods. This method is universal for robotic arms with different configurations, and the modeling method has high computational efficiency.

[0060] Furthermore, the present application takes into account the situation where parameters in the stiffness model are difficult to identify, and instantiates a method that combines algebra and probability statistics to eliminate and optimize the parameters, thereby avoiding low identification accuracy caused by measurement noise.

[0061] In addition, based on the stiffness modeling and identification method, an experimental device was designed. This experimental device does not require additional loading equipment, can flexibly adjust the measurement configuration of the robotic arm, and quickly obtain the end position and force measurement data before and after load loading. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] In order to more clearly illustrate the technical solution of this application, the following is a brief introduction to the drawings required for the technical description.

[0063] Figure 1 Flowchart of the stiffness modeling and identification method of the manipulator arm for nuclear power operation and maintenance provided in this application;

[0064] Figure 2 Schematic diagram of the method for defining virtual joints of a robotic arm provided in this application;

[0065] Figure 3 This is a schematic diagram of the structure of the robotic arm stiffness modeling and identification device for nuclear power operation and maintenance provided in this application;

[0066] Figure 4 Schematic diagram of the robotic arm stiffness measurement experiment process provided in this application.

[0067] Description of reference numerals:

[0068] 1. Robotic arm; 2. Force sensor; 3. End load; 4. Target mount; 5. Laser tracker. DETAILED DESCRIPTION

[0069] The following is further explained in detail through specific implementation methods.

[0070] like Figure 1 As shown, the present application provides a method for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance, including:

[0071] Step 1: The one-dimensional joint group for arm deflection fitting is used as the virtual joint group of a single arm. The coordinate system of all joints in the virtual joint group is defined based on the real joints to fit the arm deflection between any two joints.

[0072] Step 2: Based on the coordinate system definition, the robot including the virtual joint group and real joints is kinematically modeled to obtain the Jacobian matrix that represents the relationship between the robot end velocity and the robot joint velocity, which is used to establish the robot stiffness model;

[0073] Step 3: Optimize the stiffness parameters of the stiffness model based on a combination of algebraic and statistical methods, and identify the stiffness parameters using the weighted least squares method.

[0074] In this application, since the virtual joint is fitted as a six-dimensional spring, the six-dimensional spring can essentially be regarded as a one-dimensional joint in the direction of six degrees of freedom, so the six-dimensional spring is split into six one-dimensional springs.

[0075] The robot's linkage model can be roughly thought of as a cantilever beam. According to EB beam theory, the stiffness matrix of a cantilever beam is a 6×6 matrix, where the six degrees of freedom correspond to three translational and three rotational stiffnesses. The deformation angles of these stiffnesses are mainly generated around the following six axes:

[0076] Translational degrees of freedom:

[0077] The translational stiffness along the X-axis corresponds to the translational deformation of the beam in the transverse X-direction;

[0078] The translational stiffness along the Y axis corresponds to the translational deformation of the beam in the vertical Y direction;

[0079] The translational stiffness along the Z axis corresponds to the translational deformation of the beam in the longitudinal Z direction (along the axis of the beam).

[0080] Rotational degrees of freedom:

[0081] The rotational stiffness about the X-axis corresponds to the torsional deformation of the beam about the transverse axis and is usually related to the torsional stiffness of the beam;

[0082] The rotational stiffness around the Y axis corresponds to the bending deformation of the beam around the vertical axis and mainly affects the lateral bending of the beam;

[0083] The rotational stiffness about the Z axis corresponds to the bending deformation of the beam about the longitudinal axis, affecting the bending of the beam in the up-down direction.

[0084] The six-dimensional virtual spring at the motor has a much smaller stiffness in the motor's rotational direction than in other directions, so it can be considered a one-dimensional spring. The spring used for arm deflection fitting can be considered as six one-dimensional joints formed by six zero-length links, including three translational joints and three rotational joints.

[0085] The one-dimensional joint group for arm deflection fitting is defined as the virtual joint group of a single arm. For the deflection of a single robot arm, a coordinate system transformation definition for the virtual joint group is proposed to fit the arm deflection between any two joints. The details are as follows:

[0086] Determine the initial coordinate system of the virtual joint of the previous link connected to it according to the coordinate system definition of the real joint;

[0087] The coordinate systems of the last two rotational degrees of freedom are obtained by rotating 360 degrees around X and 360 degrees around Y respectively;

[0088] The first translational degree of freedom has the same coordinate system as the last rotational degree of freedom;

[0089] The coordinate systems for the last two translational degrees of freedom are obtained by rotating -360 degrees around Y and -360 degrees around X, respectively.

[0090] The order of the transformation can be changed, but the real joint coordinate system posture must be consistent with the last joint coordinate system posture of the virtual joint group. The coordinate system definition rule can be expressed as follows: Figure 2 As shown in the figure, the green arrow represents the Y-axis direction of each joint coordinate system, the red arrow represents the X-axis direction of each joint coordinate system, and the blue arrow represents the Z-axis direction of each joint coordinate system. The figure shows the coordinate system definition of a group of arm combinations. The real joint is the basis for the coordinate system definition of the arm virtual joint group. The definition of virtual joint 1 is consistent with that of the real joint. The coordinate system definitions of virtual joints 2 to 6 are obtained through coordinate system transformation. The definition of virtual joint 6 is consistent with that of the real joint. In particular, the base is the first arm to start virtualizing the joint.

[0091] The entire 3R3T1R open chain joint group is modeled to obtain the Jacobian matrix J(θ) that represents the relationship between the robot end velocity and the robot joint velocity;

[0092] The stiffness matrix of all joints of the robot is expressed as K θ , according to the kinematics of the manipulator and the relationship between the couples, the relationship between the external torque and the end displacement deviation caused by it is obtained:

[0093]

[0094] Where, Represents the flexibility of all virtual joint groups and real joints, which is the stiffness K θ The reciprocal of J ξ is the Jacobian matrix of the Cartesian space of the end of the robot relative to the joint space, τ is the generalized torque of all joints of the robot, F f represents the external load force vector at the end of the robot, ξ X Indicates the motion posture deviation of the robot arm before and after the end is loaded;

[0095] Assume that the observation matrix b i =ξ X , the flexibility matrix is ​​solved by the least square method to obtain the stiffness:

[0096]

[0097] Where N represents the N configurations of the robot arm motion, and A is obtained by solving the joint angles, end forces and end posture deviations of the N configurations. i and b i .

[0098] For the stiffness model established above, there are a large number of stiffness parameters. Taking the six-axis robot arm as an example, there are at least 42 stiffness parameters. Moreover, under the premise of simplification, the calculated stiffness parameters may be non-positive. There are also parameters with relatively small absolute values. The measurement noise leads to low recognition accuracy, and the deformation caused by it has a very small impact on the entire robot arm and can be ignored. Parameter optimization should be performed to eliminate them.

[0099] The following is an example process of parameter optimization and identification:

[0100] Step 3.1: Optimize stiffness parameters by algebraic methods.

[0101] Perform SVD decomposition on the observation matrix to obtain an orthogonal matrix:

[0102] V=[V1 V2 ... V r V r+1 ... V m ]

[0103] Where r corresponds to the number of non-zero elements on the diagonal of the S matrix, and m is the original number of stiffness parameters.

[0104] According to the grouping of the orthogonal matrix V, the parameters in the stiffness vector can be divided into three groups:

[0105] The first group C1, V submatrix [V r+1 ... V m ] The parameter number corresponding to the column number where the row vector is equal to zero is the identifiable parameter;

[0106] The second group C2, V submatrices [V1 ... V r ] The parameter numbers corresponding to the columns whose row vectors are equal to zero are unrecognizable parameters and are eliminated;

[0107] The remaining parameters of the third group C3 need to be further determined.

[0108] Step 3.2: Parameter optimization based on QR decomposition.

[0109] For the remaining stiffness parameter numbers of group C3, select the observation matrix columns corresponding to the numbers to form a matrix, perform SVD decomposition on the matrix again, and use the obtained orthogonal matrix V to calculate the following matrix L:

[0110]

[0111] Where m′ represents the number of parameters in group C3, [V1 V2 ... V m ′] * To extract the relevant rows of the V matrix, full rank is guaranteed.

[0112] Perform QR decomposition on the L matrix:

[0113] AP=QR(L)

[0114] The first n non-repeating row indices of the permutation matrix P represent the linearly independent main element columns in the matrix space of the matrix L. The corresponding parameters are found according to the indices. After adding the C1 group, the rank of the observation matrix is ​​correspondingly improved, which can avoid the phenomenon that the noise disturbance will be amplified when the matrix is ​​not full rank.

[0115] Step 3.3: Parameter optimization based on dimensional balance.

[0116] C obtained by least squares θ , and find the residual E:

[0117]

[0118] Calculate the covariance matrix of the residual E, diagonalize the covariance matrix and take the square root, and take the inverse matrix of the matrix, which is the weight matrix η:

[0119]

[0120] Modify the weight matrix and obtain the new flexibility parameters through weighted least squares:

[0121]

[0122] Repeat the above iterative process, use the new flexibility parameter to solve the residual again, and obtain a new weight until the residual is less than a certain value.

[0123] Step 3.4: Parameter identification strategy based on probabilistic statistical methods.

[0124] The flexibility parameters obtained at this stage may have large differences in magnitude. The covariance matrix of the parameters is obtained by the following formula, and the diagonal parameters are extracted to estimate their standard deviation σ j , for the parameter vector C θ Each element C in i Divide by its standard deviation to obtain the normalized parameter.

[0125]

[0126] Using the normalization parameter v i, we can identify which parameters are unidentifiable and which are identifiable. Larger parameters indicate higher recognition accuracy, indicating that the robotic arm has significant flexibility at that joint. Remove the corresponding flexibility parameters with smaller normalized parameters. The remaining parameters are identifiable. Repeat step 3.3 for these parameters to calculate the flexibility parameters of the robotic arm, and thus the stiffness parameters.

[0127] In view of the above-mentioned method for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance, this application provides a device (experimental device) for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance, such as Figure 3 As shown, the device includes a robotic arm 1, a force sensor 2, an end load 3, a target mount 4, an end position target, a laser tracker 5, and a workstation. The end position target is used in conjunction with the tracker to obtain the end position. The end load 3 is a component that applies an arbitrary load. The end position target is mounted on the target mount 4. The workstation is in communication with the force sensor 2 and the laser tracker 5. Signal cables from the force sensor 2 and the laser tracker 5 are connected to the workstation to collect data from the force sensor 2 and the laser tracker 5.

[0128] The force sensor 2 and the end load 3 are installed at the end of the robot arm 1, and the target mounting base 4 is installed at the end of the robot arm 1. The installation order is: first install the force sensor 2, then install the target mounting base 4, and finally install the end load 3. The advantage of this is that whether the end load 3 is installed or not will not affect the installation relationship between the target mounting base 4 and the robot arm, that is, the target mounting base 4 does not need to be removed because of installing or unloading the end load 3.

[0129] The laser tracker 5 is the main posture data measuring instrument, which is used to measure the end posture change of the robot arm 1 before and after the end load 3 is applied to the end. The end posture target is installed at the end of the robot arm and has a fixed relative relationship with the end of the robot arm. It cooperates with the laser tracker 5 to reflect the end posture change. The force sensor 2 is installed at the end of the robot arm to measure the force condition of the end load. The end load 3 is also installed at the end of the robot arm. The load can be conveniently increased step by step through screws and other connection methods. The workstation is used to receive the measurement data of the force sensor 2 and the laser tracker 5, and use the method described above to identify the stiffness parameters. The device does not require additional loading equipment, can flexibly adjust the measurement posture of the robot arm 1, and quickly obtain the end posture and force measurement data before and after load loading.

[0130] like Figure 4 As shown, the main process of using the device is as follows:

[0131] (1) Install and deploy all measuring instruments without any end load;

[0132] (2) Obtain the transformation relationship between the end pose target and the end flange of the manipulator, and the transformation relationship between the base coordinate system of the manipulator 1 and the measurement coordinate system of the laser tracker 5 through the manipulator hand-eye calibration method;

[0133] (3) Calibrate the force sensor 2 at the end of the robotic arm;

[0134] (4) Plan the measurement configuration of the manipulator 1 and use the laser tracker 5 to measure and record the end position of the manipulator 1 when it is unloaded, and check whether the value of the strength sensor 2 is zero;

[0135] (5) The robot arm installs the end load 3;

[0136] (6) The robot arm 1 moves to all measurement positions, and the end position of the robot arm 1 after the load is added is measured and recorded by the laser tracker 5;

[0137] (7) Obtain the stiffness parameters of the robotic arm through stiffness modeling and identification methods.

[0138] The above description is only a specific implementation method of the present application, but the scope of protection of the present application is not limited thereto. Any changes or replacements that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed in this application should be covered by the scope of protection of the present application.

Claims

1. A method for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance, characterized in that: include: Step 1: The one-dimensional joint group for arm deflection fitting is used as the virtual joint group of a single arm. The coordinate system of all joints in the virtual joint group is defined based on the real joints to fit the arm deflection between any two joints. Step 2: Based on the coordinate system definition, the robot including the virtual joint group and real joints is kinematically modeled to obtain the Jacobian matrix that represents the relationship between the robot end velocity and the robot joint velocity, which is used to establish the robot stiffness model; Step 3: Optimize the stiffness parameters of the stiffness model based on a combination of algebraic and statistical methods, and identify the stiffness parameters using the weighted least squares method.

2. The method for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance according to claim 1 is characterized in that: The arm is equivalent to a cantilever beam, and the springs fitting the arm deflection are regarded as six one-dimensional joints fitted by six links with a length of 0, including three moving joints and three rotating joints. The real joints of the robot are simplified to one-dimensional springs, and the stiffness matrix of the entire arm and joint combination is expressed as a 7×7 stiffness matrix.

3. The method for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance according to claim 1 is characterized in that: In step 1, the coordinate system definition rules are used, including: According to the coordinate system definition of the real joint, determine the initial coordinate system of the virtual joint of the previous link connected to it; The coordinate systems of the last two rotational degrees of freedom are obtained by rotating 360 degrees around X and 360 degrees around Y respectively; The first translational degree of freedom has the same coordinate system as the last rotational degree of freedom; The coordinate systems for the last two translational degrees of freedom are obtained by rotating -360 degrees around Y and -360 degrees around X, respectively.

4. The method for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance according to claim 1 is characterized in that: The entire 3R3T1R open chain joint group is modeled to obtain the Jacobian matrix J(θ) that represents the relationship between the robot end velocity and the robot joint velocity; The stiffness matrix of all joints of the robot is expressed as K θ , according to the kinematics of the manipulator and the relationship between the couples, the relationship between the external torque and the end displacement deviation caused by it is obtained: Where, Represents the flexibility of all virtual joint groups and real joints, which is the stiffness K θ The reciprocal of J ξ is the Jacobian matrix of the Cartesian space of the end of the robot relative to the joint space, τ is the generalized torque of all joints of the robot, F f represents the external load force vector at the end of the robot, ξ X Indicates the motion posture deviation of the robot arm before and after the end is loaded; Assume that the observation matrix b i =ξ X , the flexibility matrix is ​​solved by the least square method to obtain the stiffness: Where N represents the N configurations of the robot arm motion, and A is obtained by solving the joint angles, end forces and end posture deviations of the N configurations. i and b i .

5. The method for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance according to claim 1 is characterized in that: Step 3 includes: Step 3.1: Perform singular value decomposition on the observation matrix and group the parameters according to the decomposition results; Step 3.2: Perform a secondary decomposition of the parameter submatrix to be determined, extract the key principal component columns through QR decomposition and add them to the identifiable group; Step 3.3: Calculate the current parameter residuals, construct a weight matrix based on the residual heterogeneity, and repeatedly update the parameters through weighted least squares until the residuals converge; Step 3.4: Calculate the standard deviation of the parameters and normalize them, eliminate the parameters whose magnitude is less than the threshold, and repeat step 3.3 for the retained parameters to obtain the final stiffness parameters.

6. The method for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance according to claim 5 is characterized in that: In step 3.1, the stiffness parameters are optimized by algebraic methods: Perform SVD decomposition on the observation matrix to obtain an orthogonal matrix: V=[V1 V2 ... V r V r+1 ... V m ] Where r corresponds to the number of non-zero elements on the diagonal of the S matrix, and m is the original number of stiffness parameters; According to the grouping of the orthogonal matrix V, the parameters in the stiffness vector are divided into three groups: Group C1: V submatrix [V r+1 ... V m ] The parameter number corresponding to the number of columns whose row vectors are equal to zero; C2 group: V submatrix [V1 ... V r ] The parameter number corresponding to the number of columns whose row vectors are equal to zero; Group C3: Remaining parameters.

7. The method for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance according to claim 6 is characterized in that: For the remaining stiffness parameter numbers of group C3, select the observation matrix columns corresponding to the numbers to form a matrix, perform SVD decomposition on the matrix again, and use the obtained orthogonal matrix V to calculate the following matrix L: Where m′ represents the number of parameters in group C3, [V1 V2 ... V m ′] * To extract the relevant rows of the V matrix, ensure full rank; Perform QR decomposition on the L matrix: AP=QR(L) The first n non-repeated row indices of the permutation matrix P represent linearly independent pivot columns in the matrix space of the matrix L, and the corresponding parameters are found according to the indices.

8. The method for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance according to claim 5 is characterized in that: In step 3.3, C is obtained by least squares θ , and find the residual E: Calculate the covariance matrix of the residual E and calculate the weight matrix η: Modify the weight matrix and obtain the new flexibility parameters through weighted least squares: Repeat the above iterative process, use the new flexibility parameter to solve the residual again, and obtain a new weight until the residual is less than a certain value.

9. The method for modeling and identifying stiffness of a manipulator arm for nuclear power operation and maintenance according to claim 5, characterized in that: In step 3.4, the covariance matrix of the parameters is obtained by the following formula: Extract the diagonal parameters and estimate their standard deviation σ j , for the parameter vector C θ Each element C in i Divide by its standard deviation to obtain the normalization parameter v i : Using the normalization parameter v i , perform parameter optimization, eliminate parameters whose normalized parameter magnitude is less than the threshold, and perform step 3.3 again for the retained parameters to calculate the flexibility parameters of the manipulator and obtain the final stiffness parameters.

10. A robot arm stiffness modeling and identification device for nuclear power operation and maintenance, characterized in that: Based on the method according to any one of claims 1 to 9, the device comprises a robotic arm (1), a laser tracker (5), a force sensor (2) and a target mounting seat (4) mounted at the end of the robotic arm (1), wherein an end position target is mounted on the target mounting seat (4); the end position of the robotic arm (1) when no load is applied is measured by the laser tracker (5), an end load (3) is mounted at the end of the robotic arm (1), and the end position after the load is applied is measured by the laser tracker (5).

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