Method for robot measurement system calibration and its uncertainty evaluation

Abstract

This invention discloses a method for calibrating and evaluating the uncertainty of a robot measurement system. First, a robot motion error model is established to clarify the error propagation path. After building the theoretical framework, N sets of end effector pose data are measured, and geometric parameter errors are calculated, while non-geometric parameter errors caused by external loads are empirically approximated. Next, the discrete probability distributions of relevant parameters are estimated, and a continuous probability density function and its characteristics are obtained through approximate fitting. Finally, confidence probabilities are set and substituted into the error model for large-scale pseudo-random simulation to obtain the end effector error probability distribution. The evaluation is completed by combining the measurement mean and standard uncertainty. This method pinpoints the core source of uncertainty, clarifies the parameter influence path, fully utilizes limited sample information, and avoids distribution representation bias and distortion problems, providing a precise theoretical foundation and reliable data support for uncertainty evaluation of high-dimensional parameter systems.

Description

Technical Field

[0001] This invention relates to the field of robot control technology, and in particular to a method for calibrating a robot measurement system and evaluating its uncertainty. Background Technology

[0002] Unlike traditional single-parameter linear calibration, robot internal parameter calibration is essentially a nonlinear optimization problem involving multiple parameters. Therefore, even small measurement errors in the position and orientation of the robot's end effector can lead to ill-posedness in the optimization model, resulting in internal parameter matrix calibration failure and increased calibration uncertainty.

[0003] For robots performing automated drilling, precision assembly, trajectory tracking, and other industrial applications, on-site calibration of internal parameters is crucial. However, on-site robot internal parameter calibration models often suffer from ill-posedness; even minute measurement errors in position and orientation can lead to calibration failure, resulting in significant calibration uncertainty. These uncertainties are difficult to assess solely based on positioning results provided by laser trackers.

[0004] The performance of a robot largely depends on the accuracy of its calibration, with geometric parameter deviations accounting for approximately 90% of the end effector's posture error. To minimize the modeling error of the calibration model, methods such as least squares and its improved variants, swarm intelligence algorithms, and neural network methods have been used for optimization. For example, previous researchers introduced regularization techniques to address this limitation. As an extension of least squares, the Levenberg-Marquardt (LM) algorithm improves the stability of the original algorithm to some extent. However, the standard LM algorithm is prone to getting trapped in local optima. To address this issue, Li and his colleagues proposed a variable-step-size LM algorithm, effectively overcoming this deficiency and improving calibration performance. Luo's team further incorporated the concept of differential evolution (DE) into the LM algorithm. The powerful global search capability of the DE algorithm effectively compensates for the limitations of the LM algorithm in global optimization. However, in high-dimensional systems, when a large number of motion parameters need to be identified, the related computational process becomes extremely complex.

[0005] Numerous errors are unavoidable during robot calibration, increasing measurement uncertainty. The coupling and propagation of parameter uncertainties can cause robot posture to deviate from acceptable ranges, or even render the task impossible to complete. Therefore, assessing the uncertainty of robot calibration is crucial.

[0006] Traditional calibration methods often require configuration changes to the robot, thus interfering with its normal operation. Field calibration methods avoid such interference, maintaining the robot's original working state and external settings. The calibration model of a field robot is a multi-parameter, nonlinear numerical system, making direct evaluation difficult. To address these issues, saddle point approximation and first-order reliability methods can be used to quantify the uncertainties of complex systems. However, first-order reliability methods are not accurate enough for robot systems; while saddle point approximation methods are more accurate than first-order reliability methods, they require numerous function calls and involve a large computational load. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of the prior art by providing a method for calibrating a robot measurement system and evaluating its uncertainty.

[0008] The objective of this invention is achieved through the following technical solution: a method for calibrating a robot measurement system and evaluating its uncertainty, the specific method of which is as follows:

[0009] Step 1: Establish the robot's motion error model and determine the error propagation path;

[0010] Step 2: Establishing the theoretical framework: The error of the robot's end effector includes geometric parameter errors caused by internal parameters and non-geometric parameter errors caused by changes in external load;

[0011] Step 3: Measure and obtain N sets of position and attitude data of the end effector, and calculate the geometric parameter error under the corresponding configuration; at the same time, make an empirical approximation of the non-geometric parameter error caused by external load changes based on the observation data;

[0012] Step 5: Estimate the discrete probability distributions of internal parameters and external load variation parameters, and use an approximate fitting method to obtain the continuous probability density function and its characteristics for each parameter;

[0013] Step 6: Set the confidence probability, substitute the continuous probability density function of each parameter into the kinematic error model, and perform a large-scale pseudo-random simulation to simulate the probability distribution of the end effector error; based on the simulated end effector error probability distribution, and combined with the average value and standard uncertainty of the measurement results, complete the evaluation of the calibration uncertainty of the robot measurement system.

[0014] As a preferred option, the specific method for establishing the motion error model in step one is as follows:

[0015] S1: Based on the geometric relationship between adjacent links of the robot, construct the differential transformation matrix of adjacent links. The differential operators of adjacent nodes in the differential transformation matrix represent geometric parameter errors. The geometric parameter errors include link length deviation, link torsion angle deviation, shaft offset deviation, and shaft rotation angle deviation.

[0016] S2: By solving the partial derivatives of the differential transformation matrix, the error coefficient matrix is ​​obtained, and at the same time, the mapping relationship between the measurement error and the geometric parameter error of adjacent joints is established.

[0017] S3: Based on the characteristics of the robot's serial structure, the calculation formula for the position and orientation measurement error of the end effector is obtained by accumulating the deviation matrix of each joint. This calculation formula reveals the source of small deviations in the robot's kinematic parameters.

[0018] As a preferred approach, when solving for geometric parameter errors, a ridge regression regularization strategy is used to solve the overdetermined nonlinear equations, thereby reducing the sensitivity of the solution to measurement noise.

[0019] Preferably, the equation corresponding to the ridge regression regularization strategy is:

[0020] ;

[0021] In the formula, It is a regularization parameter. It is the identity matrix. This is the measured position of the end effector; This is the transpose of the error coefficient matrix. This is the error coefficient matrix.

[0022] As a preferred option, the theoretical end effector value The measured end effector position The relationship between them is as follows:

[0023] ;

[0024] in, For the robot's end effector error, It is the measured position of the end effector. For the theoretical end effector position, For the end effector along x Shaft position error, For the end effector along y Shaft position error, For the end effector along z Shaft position error, For the end effector x Axis attitude error, For the end effectory Axis attitude error; For the end effector z The attitude error of the axis.

[0025] Preferably, in step six, the number of simulations in the large-scale pseudo-random simulation satisfies the following condition:

[0026] ;

[0027] in, is the confidence probability.

[0028] Preferably, in step five, the continuous probability density function of each parameter adopts any one of the following distributions: uniform distribution, exponential distribution, normal distribution, chi-square distribution, and beta distribution.

[0029] As a preferred method, in-situ calibration is used, which maintains the robot in normal working condition during the calibration process and does not change the robot's original configuration and external settings.

[0030] Preferably, in step two, the end effector error of the robot is the sum of geometric parameter error and non-geometric parameter error, and the input distribution of non-geometric parameter error is constructed based on observation data and empirical methods.

[0031] The beneficial effects of this invention are:

[0032] This invention establishes an error model by analyzing the error propagation and accumulation patterns of 25 intrinsic parameters of a robot within a kinematic model. Compared to traditional, general modeling methods that do not distinguish the contribution of parameters, this directly identifies the core source of uncertainty in robot in-situ calibration. This modeling approach clarifies the influence path of each intrinsic parameter on the end effector's posture error, avoiding model distortion caused by ambiguity in the error source, and laying a precise theoretical foundation for subsequent uncertainty assessment. Secondly, considering the high-dimensionality of the intrinsic parameters, this invention starts with a limited set of N sets of end effector pose data, first estimating the discrete probability density function of each parameter, and then obtaining the continuous probability density function and its characteristics through an approximate fitting method. The advantages of this approach are twofold: firstly, it fully utilizes the effective information from the limited sample data, avoiding parameter distribution representation bias caused by insufficient sample size; secondly, the fitting process of the continuous probability density function avoids the distortion problem caused by overestimation of the discrete PDF, significantly improving the representation accuracy of the intrinsic parameter probability distribution and providing reliable data support for uncertainty assessment of high-dimensional parameter systems. Attached Figure Description

[0033] Figure 1 This is a diagram showing the structural parameters of the robot.

[0034] Figure 2 This is a distribution propagation diagram for a large-scale pseudo-random simulation. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention are within the scope of protection of the present invention.

[0036] Those skilled in the art should understand that, in the disclosure of this invention, the terms "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the above terms should not be construed as limiting this invention.

[0037] It is understood that the term "a" should be understood as "at least one" or "one or more", that is, in one embodiment, the number of an element can be one, while in another embodiment, the number of the element can be multiple, and the term "a" should not be understood as a limitation on the number.

[0038] like Figures 1 to 2 As shown, the calibration and uncertainty evaluation method for the robot measurement system is as follows:

[0039] Step 1: Establish the robot's motion error model and determine the error propagation path;

[0040] Step 2: Establishing the theoretical framework: The error of the robot's end effector includes geometric parameter errors caused by internal parameters and non-geometric parameter errors caused by changes in external load;

[0041] Step 3: Measure and obtain N sets of position and attitude data of the end effector, and calculate the geometric parameter error under the corresponding configuration; at the same time, make an empirical approximation of the non-geometric parameter error caused by external load changes based on the observation data;

[0042] Step 5: Estimate the discrete probability distributions of internal parameters and external load variation parameters, and use an approximate fitting method to obtain the continuous probability density function and its characteristics for each parameter;

[0043] Step 6: Set the confidence probability, substitute the continuous probability density function of each parameter into the kinematic error model, and perform a large-scale pseudo-random simulation to simulate the probability distribution of the end effector error; based on the simulated end effector error probability distribution, and combined with the average value and standard uncertainty of the measurement results, complete the evaluation of the calibration uncertainty of the robot measurement system.

[0044] Specifically, in step one, the method for establishing the motion error model is as follows:

[0045] S1: Based on the geometric relationship between adjacent links of the robot, construct the differential transformation matrix of adjacent links. The differential operators of adjacent nodes in the differential transformation matrix represent geometric parameter errors. The geometric parameter errors include link length deviation, link torsion angle deviation, shaft offset deviation, and shaft rotation angle deviation.

[0046] S2: By solving the partial derivatives of the differential transformation matrix, the error coefficient matrix is ​​obtained, and at the same time, the mapping relationship between the measurement error and the geometric parameter error of adjacent joints is established.

[0047] S3: Based on the characteristics of the robot's serial structure, the calculation formula for the position and orientation measurement error of the end effector is obtained by accumulating the deviation matrix of each joint. This calculation formula reveals the source of small deviations in the robot's kinematic parameters.

[0048] For an n-degree-of-freedom robot, the position and orientation of its end effector and its structural parameters The relationship between them can be expressed as:

[0049] (1);

[0050] in Tr (·) denotes a translation matrix. Rot (·) denotes a rotation matrix. It is the angle of the i-th joint, which controls the change in the robot's pose. d i , , These are all structural parameters of the robot, and their detailed meanings are as follows: d i It is an axis x i 1 to axis x i exist z i Offset in direction Indicates axis z i 1 to axis z iexist x i 1. Rotation angle in the direction of rotation. It is about y The rotation angle of the axis.

[0051] See Figure 1 , Figure 1 The diagram shows the structural parameters of the robot. In the diagram, {B} is the base coordinate system (BCS) and {F} is the flange coordinate system (FCS).

[0052] Due to manufacturing errors and assembly deviations, geometric parameter errors are unavoidable in industrial robots, which negatively impact positioning accuracy. Therefore, robot kinematic parameter identification aims to determine these geometric errors based on the measured posture (position and orientation) of the end effector.

[0053] Based on the kinematic model in equation (1), the differential transformation matrix of each pair of adjacent links i-1 and i is... for:

[0054] (2);

[0055] Among them, the differential operators of adjacent nodes This represents the geometric parameter error. .in, This refers to geometric parameter errors.

[0056] From formula (2), we can see that, It can also be expressed as:

[0057] (3);

[0058] in, It is the error coefficient.

[0059] Among them, error coefficient The calculation formula is as follows:

[0060] (4);

[0061] In the formula, It is a matrix The partial derivatives of the structural deviation a i-1 is the independent variable.

[0062] Error coefficient The calculation formula is as follows:

[0063] (5);

[0064] In the formula, It is a matrix The partial derivatives of the structural deviation is the independent variable.

[0065] Error coefficient The calculation formula is as follows:

[0066] (6);

[0067] In the formula, It is a matrix The partial derivatives of the structural deviation d i is the independent variable.

[0068] Error coefficient The calculation formula is as follows:

[0069] (7);

[0070] In the formula, It is a matrix The partial derivatives of the structural deviation is the independent variable.

[0071] Error coefficient The calculation formula is as follows:

[0072] (8);

[0073] In the formula, It is a matrix The partial derivatives of the structural deviation is the independent variable. , .

[0074] in, Includes translation part and rotating part Translation section It can be represented as:

[0075] (9);

[0076] in .

[0077] Rotating part It can be represented as:

[0078] (10).

[0079] The measurement error (including position and orientation) of two adjacent joints is related to the geometric parameter error of the link. This mapping relationship can be derived by combining equations (9) and (10).

[0080] Based on the serial structure of a six-degree-of-freedom robot (n=6), the error of the end effector can be obtained by accumulating the deviation matrix of each joint, as follows:

[0081] (11);

[0082] in, This represents the measurement error of the position and orientation at the end effector. Based on the structural characteristics of the robot and the error between adjacent coordinate systems in equation (3), the measurement error of the end effector can be derived. for:

[0083] (12).

[0084] Among them, the above formula (12) reveals the main sources of small deviations in the robot's kinematic parameters, including .in, Indicates from X i 1 to X i Around the axis Z i The rotation angle deviation, in physical terms, is the rotation error of the base around the first axis. The base is fixed on the platform, therefore... It is simplified to zero. Because... Defined in the zero-position state between two parallel axes (obtainable by translation between the two coordinate systems), around y The rotation angle of the shaft (introducing the twist angle parameter) Solve the singularity problem of kinematic model when the front and rear joints of a robot are parallel or nearly parallel. for (the error value), therefore this includes... and Measurement error and geometric parameter deviation The relationship between them can be represented as:

[0085] (13).

[0086] in and Let represent the error coefficient matrix. The end effector error can be decoupled from the contribution of each joint structural parameter, as shown in equation (14):

[0087] (14).

[0088] In equation (14), the calculation method for parameter F is shown in equation (12).

[0089] in addition, and This can be further formalized as:

[0090] (15);

[0091] in, , , , , .

[0092] (16);

[0093] Where N is the number of measurement data sets.

[0094] According to equation (8), the geometric parameter error The solution is determined by solving a set of overdetermined nonlinear equations. However, due to the ill-posed nature of this inverse problem, the solution is highly sensitive to measurement noise. To address this issue, a ridge regression regularization strategy is introduced.

[0095] When solving for geometric parameter errors, a ridge regression regularization strategy is used to solve overdetermined nonlinear equations, reducing the sensitivity of the solution to measurement noise.

[0096] The equation corresponding to the ridge regression regularization strategy is:

[0097] (17);

[0098] In the formula, It is a regularization parameter. It is the identity matrix. This is the measured position of the end effector; This is the transpose of the error coefficient matrix. This is the error coefficient matrix.

[0099] Theoretical end effector value The measured end effector position The relationship between them is as follows: (18);

[0100] in, For the robot's end effector error; r This is the allowable error tolerance; This is the measured position of the end effector. ; For the theoretical end effector position, ; For the end effector along x Shaft position error, For the end effector along y Shaft position error, For the end effector along z Shaft position error, For the end effector x Axis attitude error, For the end effector y Axis attitude error; For the end effector z The attitude error of the axis.

[0101] The definitions of each element are as follows:

[0102] (19);

[0103] in, , The functional relationship between them is expressed as a function . P m =[ x m ,y m ,z m ] T This represents the measured position vector.

[0104] In step two, the robot's end effector error is the sum of geometric parameter error and non-geometric parameter error. The input distribution of non-geometric parameter error is based on observation data and constructed through empirical methods.

[0105] Specifically, the error of the robot's end effector mainly consists of geometric parameter errors and non-geometric parameter errors, which can be expressed as:

[0106] (20);

[0107] in D n This represents the error component caused by non-geometric factors (such as load variations). This represents the error component caused by geometric parameters.

[0108] This theoretical framework analyzes the uncertainties caused by the robot's 25 intrinsic parameters and 1 external load variation parameter by estimating their discrete probability distributions. Furthermore, an approximate fitting method is used to estimate the continuous probability density function and its characteristics for each parameter, which reduces evaluation errors caused by overestimating the probability density function. Incorporating the continuous probability density functions of the intrinsic parameters into the motion error model and performing large-scale pseudo-random simulations allows for the estimation of uncertainties in field calibration. Non-geometric factors, such as the external load variation parameter, do not have a definite functional relationship with the robot's end effector position and attitude errors. Therefore, the input distribution is constructed empirically based on observational data.

[0109] In step five, the continuous probability density function of each parameter can be any one of the following distributions: uniform distribution, exponential distribution, normal distribution, chi-square distribution, and beta distribution.

[0110] Specifically, uniformly distributed as The expression is as follows:

[0111] ;

[0112] Exponential distribution The expression is as follows:

[0113] ;

[0114] normal distribution The expression is as follows:

[0115] .

[0116] In the above expression, [a,b] represents the range of values ​​for the variable.

[0117] (twenty one);

[0118] in, g k express Gamma The function is used to normalize the chi-square distribution, while g d This represents the degree of freedom.

[0119] beta distribution is The expression is as follows:

[0120] ;

[0121] in Let represent the beta function. The mean of the beta distribution is . Its variance is If the interval [a,b] exceeds the range [0,1], the dataset...N B Through mapping functions The dataset is mapped to the specified interval [0,1], thus obtaining a dataset that follows the same beta distribution and is within the range [a,b]. N b .

[0122] In this invention, by adjusting the joint angles of the robot... Treating the observed values ​​as observations and substituting the observed samples into equation (19), we can obtain the following about... The probability density function, This set of data represents the position of the end effector along the x, y, and z axes and its orientation around the x, y, and z axes of the end effector.

[0123] Its distribution and propagation process is as follows Figure 2 As shown. Based on the average value of the measurement results. The robot system is evaluated using standard uncertainty. The specific evaluation method is described in formula (23):

[0124] (twenty three);

[0125] By substituting the simulation results into equation (23), the average end-effector pose can be estimated. The corresponding standard deviation can be obtained through the formula get.

[0126] In the model of the robot kinematic parameter recognition system, the 25 input quantities can be represented as follows: Assuming the confidence probability has been determined. The number of simulations in a large-scale pseudo-random simulation satisfies the following condition:

[0127] ;

[0128] in, This represents the confidence probability. Subsequently, numerous pseudo-random simulation experiments were conducted to accurately capture the overall distribution of the input variables during model execution.

[0129] For a symmetric probability density function interval, the expanded uncertainty U is given by the following formula:

[0130] (twenty four)

[0131] At a confidence level of Given 25 degrees of freedom, the t-distribution table shows the coverage coefficient k. For the asymmetric probability density function, determine whether it satisfies... Shortest coverage area To calculate its expanded uncertainty.

[0132] This invention employs an in-situ calibration method, which maintains the robot's normal operating state during the calibration process without altering the robot's original configuration or external settings.

[0133] The present invention has the following effects:

[0134] This invention evaluates the in-situ calibration uncertainty of robot kinematic parameters and proposes an enhanced Monte Carlo method based on the probability density functions of 25 intrinsic parameters of the robot. First, the invention establishes a kinematic error model of the robot by analyzing the error propagation and accumulation of each intrinsic parameter within its kinematic model. Second, to address the main sources of uncertainty caused by the 25 identified intrinsic parameters, the discrete probability density function (PDF) of each parameter is estimated from a finite sample (N sets of end effector position and attitude data). Furthermore, an approximate fitting method is used to obtain the continuous PDF and its characteristics for each parameter, thereby avoiding evaluation errors caused by overestimation of the PDF. Third, by substituting the continuous probability density functions of the intrinsic parameters into the kinematic error model and performing large-scale pseudo-random simulations, the uncertainty of in-situ calibration can be evaluated.

[0135] This invention establishes an error model by analyzing the error propagation and accumulation patterns of 25 intrinsic parameters of a robot within a kinematic model. Compared to traditional, general modeling methods that do not distinguish the contribution of parameters, this directly identifies the core source of uncertainty in robot in-situ calibration. This modeling approach clarifies the influence path of each intrinsic parameter on the end effector's posture error, avoiding model distortion caused by ambiguity in the error source, and laying a precise theoretical foundation for subsequent uncertainty assessment. Secondly, considering the high-dimensionality of the intrinsic parameters, this invention starts with a limited set of N sets of end effector pose data, first estimating the discrete probability density function of each parameter, and then obtaining the continuous probability density function and its characteristics through an approximate fitting method. The advantages of this approach are twofold: firstly, it fully utilizes the effective information from the limited sample data, avoiding parameter distribution representation bias caused by insufficient sample size; secondly, the fitting process of the continuous probability density function avoids the distortion problem caused by overestimation of the discrete PDF, significantly improving the representation accuracy of the intrinsic parameter probability distribution and providing reliable data support for uncertainty assessment of high-dimensional parameter systems.

[0136] This invention substitutes the continuous PDF of internal parameters into the kinematic error model and achieves the assessment of in-situ calibration uncertainty through large-scale pseudo-random simulation. By simulating the probability distribution propagation process of parameters through extensive random sampling, it can accurately capture the evolution law of uncertainty under the coupling effect of 25 internal parameters, effectively solving the technical problem of accurately assessing the uncertainty of high-dimensional parameter systems. Furthermore, this method requires no additional configuration changes to the robot, is fully adaptable to in-situ calibration application scenarios, and ensures the continuity of the production process.

[0137] This invention assesses calibration uncertainty entirely based on the robot's in-situ working state, without interfering with its normal production operation, thus meeting the on-site calibration needs of industrial scenarios such as automated drilling and precision assembly. By accurately assessing calibration uncertainty, it provides a quantitative basis for optimizing and adjusting the robot's kinematic parameters, effectively suppressing end-effector posture deviations caused by the coupling propagation of parameter uncertainties, and significantly improving the robot's motion accuracy and task completion quality.

[0138] This invention is not limited to the preferred embodiments described above. Anyone can derive other products in various forms under the guidance of this invention. However, regardless of any changes in shape or structure, any technical solution that is the same as or similar to this application falls within the protection scope of this invention.

Claims

1. A method for calibrating and evaluating the uncertainty of a robot measurement system, characterized in that, The specific method is as follows: Step 1: Establish the robot's motion error model and determine the error propagation path; the specific method for establishing the motion error model is as follows: S1: Based on the geometric relationship between adjacent links of the robot, construct the differential transformation matrix of adjacent links. The differential operators of adjacent nodes in the differential transformation matrix represent geometric parameter errors. The geometric parameter errors include link length deviation, link torsion angle deviation, shaft offset deviation, and shaft rotation angle deviation. S2: By solving the partial derivatives of the differential transformation matrix, the error coefficient matrix is ​​obtained, and at the same time, the mapping relationship between the measurement error and the geometric parameter error of adjacent joints is established. S3: Based on the characteristics of the robot's serial structure, the calculation formula for the position and orientation measurement error of the end effector is obtained by accumulating the deviation matrix of each joint. This calculation formula reveals the source of small deviations in the robot's kinematic parameters. Step 2: Establishing the theoretical framework: The error of the robot's end effector includes geometric parameter errors caused by internal parameters and non-geometric parameter errors caused by changes in external load; Step 3: Measure and obtain N sets of position and attitude data of the end effector, and calculate the geometric parameter error under the corresponding configuration; at the same time, make an empirical approximation of the non-geometric parameter error caused by external load changes based on the observation data; Step 5: Estimate the discrete probability distributions of internal parameters and external load variation parameters, and use an approximate fitting method to obtain the continuous probability density function and its characteristics for each parameter; Step 6: Set the confidence probability, substitute the continuous probability density function of each parameter into the kinematic error model, and perform a large-scale pseudo-random simulation to simulate the probability distribution of the end effector error; based on the simulated end effector error probability distribution, and combined with the average value and standard uncertainty of the measurement results, complete the evaluation of the calibration uncertainty of the robot measurement system.

2. The calibration and uncertainty evaluation method for the robot measurement system according to claim 1, characterized in that, When solving for geometric parameter errors, a ridge regression regularization strategy is used to solve overdetermined nonlinear equations, reducing the sensitivity of the solution to measurement noise.

3. The calibration and uncertainty evaluation method for the robot measurement system according to claim 2, characterized in that, The equation corresponding to the ridge regression regularization strategy is: ； In the formula, It is a regularization parameter. It is the identity matrix. This is the measured position of the end effector; This is the transpose of the error coefficient matrix. This is the error coefficient matrix.

4. The calibration and uncertainty evaluation method for the robot measurement system according to claim 1, characterized in that, Theoretical end effector value The measured end effector position The relationship between them is as follows: ； in, For the robot's end effector error, It is the measured position of the end effector. For the theoretical end effector position, For the end effector along x Shaft position error, For the end effector along y Shaft position error, For the end effector along z Shaft position error, For the end effector x Axis attitude error, For the end effector y Axis attitude error; For the end effector z The attitude error of the axis.

5. The calibration and uncertainty evaluation method for the robot measurement system according to claim 1, characterized in that, In step six, the number of simulations in the large-scale pseudo-random simulation satisfies the following condition: ； in, is the confidence probability.

6. The calibration and uncertainty evaluation method for the robot measurement system according to claim 1, characterized in that, In step five, the continuous probability density function of each parameter can be any one of the following distributions: uniform distribution, exponential distribution, normal distribution, chi-square distribution, and beta distribution.

7. The calibration and uncertainty evaluation method for the robot measurement system according to claim 1, characterized in that, The in-situ calibration method is adopted, which maintains the robot in normal working condition during the calibration process and does not change the robot's original configuration and external settings.

8. The calibration and uncertainty evaluation method for the robot measurement system according to claim 1, characterized in that, In step two, the robot's end effector error is the sum of geometric parameter error and non-geometric parameter error. The input distribution of non-geometric parameter error is based on observation data and constructed through empirical methods.

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