A pose measurement device and parameter identification method applied to robot calibration

Abstract

This invention discloses a pose measurement device and parameter identification method for robot calibration. The pose measurement device includes an adapter plate, a target ball base, a target ball, and a two-axis tilt sensor. The method includes: measuring the pose data of a parallel robot using a laser tracker and the pose measurement device; collecting link length observation data of the parallel robot using an encoder; estimating the posterior value of the actual link length using a particle filter algorithm; constructing an expectation function containing the geometric parameters of the parallel robot; substituting the pose data, link length observation data, and the posterior value of the actual link length into the expectation function; maximizing the expectation function value using an expectation maximization algorithm; identifying the geometric parameters of the parallel robot; and writing the parameters into the parallel robot controller to control the movement of the parallel robot. The device of this invention can continuously measure pose, improving the efficiency of error measurement during robot calibration. The parameter identification method considers both input and output data errors, enabling more accurate parameter identification.

Description

Technical Field

[0001] This invention relates to the field of robot calibration and control technology, specifically to a pose measurement device and parameter identification method for robot calibration. Background Technology

[0002] With the rapid development of robotics technology, robots are frequently used in various fields such as machining and component assembly. Stewart parallel robots (or six-DOF parallel mechanisms), with their high rigidity, high load capacity, and excellent motion accuracy, are widely used in the aerospace industry for the docking and assembly of large components. However, due to limitations in machining tolerances, assembly errors, and mechanical wear after prolonged operation, the actual geometric parameters of Stewart parallel robots (such as hinge coordinates and link length zero-position offset) often deviate from their nominal design values. This deviation leads to a significant decrease in the pose accuracy of the robot's end effector, failing to meet the requirements of high-precision operations. Therefore, high-precision kinematic calibration of the robot—that is, accurately obtaining its actual geometric parameters and compensating for them through identification algorithms—is a crucial step in ensuring its performance.

[0003] Robot calibration technology generally consists of four basic steps: modeling, measurement, identification, and compensation. Studies have shown that pose models offer better identification results than position and attitude models, but require measurement of the robot's position and attitude data. Currently, laser trackers are commonly used for measurement, but laser trackers for pose measurement are relatively expensive and require specialized target devices. Pose measurement can also be achieved using multiple target balls, but continuous pose measurement is not possible, and the measurement efficiency is relatively low.

[0004] In the identification step, the geometric parameters of the Stewart parallel robot are identified using input and output data. Measurement errors are typically introduced due to resolution limitations and random noise inherent in the measuring equipment itself. However, because the encoder accuracy of the Stewart parallel robot is limited, the input data also contains errors, a problem often overlooked. In the calibration model of the Stewart robot, the length of the link is usually used as the input variable. Existing mainstream calibration algorithms (such as the standard least squares method and the Levenberg-Marquardt algorithm) generally adopt the classic regression model assumption, assuming that the input data (the link length fed back by the servo encoder) is accurate and attributing the error only to the pose measurement at the output end. However, in actual physical systems, the measured value of the link length also contains errors, such as encoder error, lead screw backlash, and return error, resulting in readings that do not fully represent the actual link length. Existing research shows that ignoring input data errors and directly applying traditional estimation processes (such as the least squares method) will lead to significant bias in the established model parameters, and may even render the identification results invalid. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a pose measurement device and parameter identification method for robot calibration. This device enables continuous pose measurement, improves error measurement efficiency, and the parameter identification method simultaneously considers the errors of both input and output data, achieving more accurate parameter identification.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A pose measurement device for robot calibration, specifically a parallel robot, including a fixed platform and a moving platform, the pose measurement device including a transition plate, a target ball base, a target ball and a two-axis tilt sensor; It is installed on the moving platform of the parallel robot via an adapter plate; The position of the parallel robot is measured using a target ball; The attitude of the parallel robot is measured using a two-axis tilt sensor.

[0008] The present invention also proposes a parameter identification method using the pose measurement device described above, comprising the following steps: The pose data of the parallel robot, including position and orientation, is measured using a laser tracker and pose measurement device. The link length observation data of the parallel robot is collected using an encoder; The posterior value of the true link length is estimated using a particle filter algorithm; Construct an expectation function containing the geometric parameters of the parallel robot to be identified; The pose data, link length observation data, and posterior values ​​of the actual link length are substituted into the expectation function, and the expectation function value is maximized through the expectation maximization algorithm to identify the geometric parameters of the parallel robot. Geometric parameters are written into the parallel robot controller to control the movement of the parallel robot.

[0009] To optimize the above technical solution, the specific measures also include: Furthermore, the specific steps of measuring the pose data of the parallel robot using a laser tracker and pose measurement device are as follows: Determine the transformation relationship between the laser tracker's measurement coordinate system and the parallel robot's control coordinate system; Determine the transformation relationship between the coordinate system of the pose measurement device and the measurement coordinate system of the laser tracker; The position of the target ball is measured using a laser tracker, which serves as the position data for the pose points of the parallel robot; The attitude data of a parallel robot is measured using a two-axis tilt sensor; By utilizing the transformation relationship between the coordinate system of the laser tracker and the control coordinate system of the parallel robot, and the transformation relationship between the coordinate system of the pose measurement device and the coordinate system of the laser tracker, position data and attitude data are unified into the control coordinate system of the parallel robot. Position data and attitude data together constitute the pose data of a parallel robot.

[0010] Furthermore, the specific steps for estimating the posterior value of the true link length using the particle filter algorithm are as follows: For a given pose point k, generate N particles. Let represent the observed link length of the j-th particle at the measured pose point k, where j = 1, ..., N, used to approximate the distribution of link lengths:

[0011] in, This represents the probability of the true link length at the measured pose point k given the observed link length of the j-th particle at the measured pose point k-1. Indicates the increment of the variable. The mean is variance is The normal distribution; The weight of each particle is calculated using the following formula:

[0012] in, It is the weight of the j-th particle at pose point k. It is the weight of the j-th particle at pose point k-1. This represents the probability of measuring the link length based on the observed link length of the j-th particle at the measurement pose point k. The link length is the measurement pose point k fed back by the encoder. Let represent the probability of measuring the pose of the j-th particle at the measured pose point k, given the observed link length. For measuring the pose data of the parallel robot, This represents the probability of the link length observation of the j-th particle at the measurement pose point k under the link length observation value of the j-th particle at the measurement pose point k-1. The posterior value of the true link length is obtained by weighted averaging. :

[0013] in, This represents the normalized particle weights.

[0014] Furthermore, the specific method for constructing the expectation function containing the geometric parameters of the parallel robot to be identified is as follows:

[0015] In the formula, Indicates the first h Step-by-step iterative geometric structure parameters Geometric parameters under conditions The expected function, Indicates the first h Step-by-step iterative geometric structure parameters and observation dataset Hidden variable set under the condition Expectations Represents geometric structure parameters Hidden variable set under the condition and observation dataset The likelihood function; Represents all observed datasets. , This represents the dataset of link length observations fed back by all encoders. This represents the entire pose dataset. Indicates the set of hidden variables. , This is the actual link length.

[0016] Furthermore, the step of maximizing the expected function value using the expected maximization algorithm to identify the geometric parameters of the parallel robot specifically involves: Maximizing the expected value of the function is equivalent to minimizing the posterior value with respect to the true link length. To calculate the prediction error, the following optimization objective function is constructed:

[0017] in, This is the prediction error, where M is the number of measurement pose points. For measuring the pose data of the parallel robot, Represents the posterior value of the current actual link length. and the positive kinematic function under the geometric structure parameter η; The particle swarm optimization algorithm is adopted, with each measurement pose point corresponding to a particle. M particles are initialized, and the fitness value of each particle is calculated according to the optimization objective function. At the same time, the particle update position is determined according to the individual optimal value of the particle and the global optimal value of the particle swarm. The position and fitness value of individual particles are continuously calculated iteratively. When the maximum number of iterations is reached or the fitness value converges, the optimal particle in the particle swarm is used as the final geometric structure parameter of the parallel robot.

[0018] Furthermore, the specific steps for determining the transformation relationship between the laser tracker measurement coordinate system and the parallel robot control coordinate system are as follows: A target ball is placed sequentially into the four positioning holes on the moving plane of the parallel robot. The three-dimensional coordinates of the four positioning holes, Q1, Q2, Q3, and Q4, are used to fit a spatial plane. The normal to the spatial plane is taken as the Z-axis direction vector of the parallel robot's control coordinate system. Based on the positional relationship between the positioning holes and the control coordinate system of the parallel robot, the direction vectors of Q1 and Q2 are determined as the direction vectors of the X-axis. Determine the direction vector of the Y-axis according to the right-hand coordinate system rule. By fitting the center of a spatial sphere using a positioning hole, the center of the spatial sphere is determined as the origin Q of the parallel robot control coordinate system, and the coordinates of the origin are... Thus, the expression matrix of the parallel robot control coordinate system between the laser tracker measurement coordinate system is determined as follows:

[0019] In the formula, It is the expression matrix of the parallel robot control coordinate system between the laser tracker measurement coordinate system.

[0020] Furthermore, the transformation relationship between the coordinate system of the pose measurement device and the measurement coordinate system of the laser tracker is specifically as follows: The output data of the biaxial tilt sensor are the X-axis tilt angle α and the Y-axis tilt angle β. The pitch angle is calculated based on the output definition of the biaxial tilt sensor and the definition of the rotation matrix. and roll angle :

[0021] According to pitch angle and roll angle Calculate the rotation matrix as follows:

[0022] When controlling a parallel robot to a certain pose, the pose is calculated using the three-dimensional coordinates of three target spheres from a laser tracker. The calculation steps are as follows: A spatial plane is fitted using the three-dimensional coordinates q1, q2, and q3 of the three target spheres, and the normal to the spatial plane is used as the Z-axis direction vector of the pose measurement device's coordinate system. Based on the positional relationship between the target ball and the coordinate system of the pose measurement device, the direction vectors of q1 and q2 are determined as the direction vectors of the X-axis. Determine the direction vector of the Y-axis according to the right-hand coordinate system rule. Let q2 be defined as the origin p of the coordinate system of the pose measurement device. m This allows us to determine the representation matrix of the pose measurement device coordinate system within the laser tracker measurement coordinate system. as follows:

[0023] The attitude matrix of the pose measurement device is: , and The conversion relationship between them is as follows:

[0024] in, R Representing the rotation matrix and attitude matrix The transformation matrix.

[0025] Furthermore, the step of determining the particle update position based on the individual optimal value of the particle and the global optimal value of the particle swarm specifically involves: Update the position using the following formula:

[0026] In the formula, where, yes t +1 iterations of the first iteration k Particle velocity, yes t +1 iterations of the first iteration k Particle positions, x b It is the optimal position for an individual. x g It is the optimal position for all. r 1, r Both 2 are random numbers between [0,1]. c 1,c 2, c 3 are all fixed learning factors. K It is a contractile factor. ,in C = c 1+ c 2.

[0027] The beneficial effects of this invention are: First, this measuring device can achieve continuous pose measurement, improving the efficiency of error measurement in the robot calibration process. Second, the parameter identification method can simultaneously consider the errors of input and output data, achieving more accurate parameter identification and effectively improving the positioning accuracy of parallel robots. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the parallel robot calibration system of the present invention; Figure 2 This is a schematic diagram of the pose measurement device of the present invention installed on a parallel robot; Figure 3 This is a schematic diagram of the posture measurement device of the present invention. Detailed Implementation

[0029] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0030] Example 1 This invention proposes a pose measurement device for robot calibration, specifically a parallel robot, including a fixed platform and a moving platform. The pose measurement device 3 includes a transition plate 301, a target ball base, a target ball, and a two-axis tilt sensor 305. It is installed on the moving platform of the parallel robot via adapter plate 301; The position of the parallel robot is measured using a target ball; The attitude of the parallel robot is measured using a two-axis tilt sensor 305.

[0031] The overall parallel robot calibration system is as follows: Figure 1 As shown, the system includes a laser tracker 1, a parallel robot 2, and a pose measurement device 3.

[0032] Laser tracker 1 is placed on one side of the parallel robot 2. Laser tracker 1 is capable of measuring the three-dimensional spatial coordinates of the target sphere. See also Figure 2The pose measurement device 3 is installed on the moving platform of the parallel robot 2 to realize the pose measurement of the parallel robot 1.

[0033] See Figure 3 As shown, the measuring device 3 includes an adapter plate 301, three target ball bases 302, 303, and 304, three target balls 306, 307, and 308, and a two-axis tilt sensor 305. The two-axis tilt sensor 305 has a measurement accuracy better than 0.01 degrees and a resolution better than 0.001 degrees. During installation, the X and Y axes of the two-axis tilt sensor 305 should be kept parallel to the X and Y axes of the control coordinate system of the parallel robot 2. The adapter plate 301 requires high flatness to ensure that the three target ball bases 302, 303, and 304 are on the same plane. The measuring device 3 of this invention achieves position measurement through a single target ball and attitude measurement through the two-axis tilt sensor 305, measuring only the pitch angle θ and roll angle Φ. Research literature indicates that even with some attitude errors included in the error model, the calibration effect of a full pose error model can still be achieved.

[0034] Example 2 This invention proposes a parameter identification method using the pose measurement device of Embodiment 1, comprising the following steps: The pose data of the parallel robot, including position and orientation, is measured using a laser tracker 1 and a pose measurement device 3; specifically: Determine the transformation relationship between the laser tracker's measurement coordinate system and the parallel robot's control coordinate system; specifically: A target ball is placed sequentially into the four positioning holes on the moving plane of the parallel robot. The three-dimensional coordinates of the four positioning holes, Q1, Q2, Q3, and Q4, are used to fit a spatial plane. The normal to the spatial plane is taken as the Z-axis direction vector of the parallel robot's control coordinate system. Based on the positional relationship between the positioning holes and the control coordinate system of the parallel robot, the direction vectors of Q1 and Q2 are determined as the direction vectors of the X-axis. Determine the direction vector of the Y-axis according to the right-hand coordinate system rule. By fitting the center of a spatial sphere using a positioning hole, the center of the spatial sphere is determined as the origin Q of the parallel robot control coordinate system, and the coordinates of the origin are... Thus, the expression matrix of the parallel robot control coordinate system between the laser tracker measurement coordinate system is determined as follows:

[0035] In the formula, It is the expression matrix of the parallel robot control coordinate system between the laser tracker measurement coordinate system.

[0036] Determine the transformation relationship between the coordinate system of the pose measurement device and the measurement coordinate system of the laser tracker; specifically: The output data of the biaxial tilt sensor 305 are the X-axis tilt angle α and the Y-axis tilt angle β. The pitch angle is calculated based on the output definition of the biaxial tilt sensor and the definition of the rotation matrix. and roll angle :

[0037] According to pitch angle and roll angle Calculate the rotation matrix as follows:

[0038] When controlling a parallel robot to a certain pose, the pose is calculated using the three-dimensional coordinates of three target spheres from a laser tracker. The calculation steps are as follows: A spatial plane is fitted using the three-dimensional coordinates q1, q2, and q3 of the three target spheres, and the normal to the spatial plane is used as the Z-axis direction vector of the pose measurement device's coordinate system. Based on the positional relationship between the target ball and the coordinate system of the pose measurement device, the direction vectors of q1 and q2 are determined as the direction vectors of the X-axis. Determine the direction vector of the Y-axis according to the right-hand coordinate system rule. Let q2 be defined as the origin p of the coordinate system of the pose measurement device. m This allows us to determine the representation matrix of the pose measurement device coordinate system within the laser tracker measurement coordinate system. as follows:

[0039] The attitude matrix of the pose measurement device is: , and The conversion relationship between them is as follows:

[0040] in, R Representing the rotation matrix and attitude matrix The transformation matrix.

[0041] The position of the target ball is measured using laser tracker 1, and used as the position data of the pose point of the parallel robot; The attitude data of the parallel robot was measured using a two-axis tilt sensor 305. By utilizing the transformation relationship between the coordinate system of the laser tracker and the control coordinate system of the parallel robot, and the transformation relationship between the coordinate system of the pose measurement device and the coordinate system of the laser tracker, position data and attitude data are unified into the control coordinate system of the parallel robot. Position data and attitude data together constitute the pose data of a parallel robot.

[0042] Because parallel robots have many geometric parameters, at least 50 pose points generally need to be measured. During the measurement process, the laser tracker continuously tracks the target ball q2, and the two-axis tilt sensor realizes the attitude measurement. The system can measure 3 positional quantities and 2 attitude quantities for each pose point.

[0043] The link length observation data of the parallel robot is collected using an encoder; The state-space representation of a parallel robot considering input and output data noise is as follows: Input generating equation: , in Let be the link length vector at the k-th measurement pose point. Let be a function of the dynamic change in the length of the link. w k This is process noise.

[0044] Input observation equation: , in The length of the linkage fed back by the encoder. Measure the noise of the encoder.

[0045] Output observation equation:

[0046] in The pose measured by the laser tracker. For the forward kinematics equations of the parallel robot, Measurement noise for laser trackers and biaxial tilt sensors. η The geometric parameters to be identified include the coordinates of the hinge points of the static platform, the coordinates of the hinge points of the dynamic platform, and the zero-point deviation of the rod length.

[0047] Due to the nonlinearity of the system, the actual link length can be directly solved. Posterior estimation is difficult, so the particle filter algorithm is used to approximate the true link length. The posterior. The particle filter algorithm is used to estimate the posterior value of the true link length as follows: For a given pose point k, generate N particles. Let represent the observed link length of the j-th particle at the measured pose point k, where j = 1, ..., N, used to approximate the distribution of link lengths:

[0048] in, This represents the probability of the true link length at the measured pose point k given the observed link length of the j-th particle at the measured pose point k-1. Indicates the increment of the variable. The mean is variance is The normal distribution; The weight of each particle is calculated using the following formula:

[0049] in, It is the weight of the j-th particle at pose point k. It is the weight of the j-th particle at pose point k-1. This represents the probability of measuring the link length based on the observed link length of the j-th particle at the measurement pose point k. The link length is the measurement pose point k fed back by the encoder. Let represent the probability of measuring the pose of the j-th particle at the measured pose point k, given the observed link length. For measuring the pose data of the parallel robot, This represents the probability of the link length observation of the j-th particle at the measurement pose point k under the link length observation value of the j-th particle at the measurement pose point k-1. The posterior value of the true link length is obtained by weighted averaging. :

[0050] in, This represents the normalized particle weights.

[0051] Construct an expectation function containing the geometric parameters of the parallel robot to be identified; specifically:

[0052] In the formula, Indicates the first h Step-by-step iterative geometric structure parameters Geometric parameters under conditions The expected function, Indicates the first h Step-by-step iterative geometric structure parameters and observation dataset Hidden variable set under the condition Expectations Represents geometric structure parameters Hidden variable set under the condition and observation dataset The likelihood function; Represents all observed datasets. , This represents the dataset of link length observations fed back by all encoders. This represents the entire pose dataset. Indicates the set of hidden variables. , This is the actual link length.

[0053] By substituting pose data, observed link length data, and the posterior value of the actual link length into the expectation function, and maximizing the expectation function value using the expectation-maximization (EM) algorithm, the geometric parameters of the parallel robot are identified; specifically: Maximizing the expected value of the function is equivalent to minimizing the posterior value with respect to the true link length. To calculate the prediction error, the following optimization objective function is constructed:

[0054] in, This is the prediction error, where M is the number of measurement pose points. For measuring the pose data of the parallel robot, Represents the posterior value of the current actual link length. and the positive kinematic function under the geometric structure parameter η; Since the measuring device of the present invention cannot measure the Z-axis attitude angle, the Z-axis attitude error is removed in the optimization objective function, and only the five-degree-of-freedom position calculation is considered.

[0055] To solve the above nonlinear objective function, this embodiment employs a particle swarm optimization algorithm. Each measured pose point corresponds to one particle. M particles are initialized, and the fitness value of each particle is calculated according to the optimization objective function. Simultaneously, the particle update position is determined based on the individual optimal value of the particle and the global optimal value of the particle swarm. The position is updated using the following formula:

[0056] In the formula, where, yes t +1 iterations of the first iteration k Particle velocity, yes t +1 iterations of the first iteration k Particle positions, x b It is the optimal position for an individual. x g It is the optimal position for all. r 1, r Both 2 are random numbers between [0,1]. c 1, c 2, c 3 are all fixed learning factors. K It is a contractile factor. ,in C =c 1+ c 2.

[0057] The position and fitness value of individual particles are continuously calculated iteratively. When the maximum number of iterations is reached or the fitness value converges, the optimal particle in the particle swarm is used as the final geometric structure parameter of the parallel robot.

[0058] Geometric parameters are written into the parallel robot controller to control the movement of the parallel robot.

[0059] The above measurement methods can be applied to the calibration of serial robots to improve their accuracy.

[0060] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0061] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A pose measurement device for robot calibration, wherein the robot is specifically a parallel robot, comprising a fixed platform and a moving platform, characterized in that: The pose measurement device (3) includes an adapter plate (301), a target ball base, a target ball, and a two-axis tilt sensor (305). It is installed on the moving platform of the parallel robot via an adapter plate (301); The position of the parallel robot is measured using a target ball; The attitude of the parallel robot was measured using a two-axis tilt sensor (305).

2. A parameter identification method using the pose measurement device of claim 1, characterized in that, Includes the following steps: The pose data of the parallel robot, including position and orientation, are measured using a laser tracker (1) and a pose measurement device (3); The link length observation data of the parallel robot is collected using an encoder; The posterior value of the true link length is estimated using a particle filter algorithm; Construct an expectation function containing the geometric parameters of the parallel robot to be identified; The pose data, link length observation data, and posterior values ​​of the actual link length are substituted into the expectation function, and the expectation function value is maximized through the expectation maximization algorithm to identify the geometric parameters of the parallel robot. Geometric parameters are written into the parallel robot controller to control the movement of the parallel robot.

3. The parameter identification method as described in claim 2, characterized in that, The specific steps for measuring the pose data of the parallel robot using a laser tracker (1) and a pose measurement device (3) are as follows: Determine the transformation relationship between the laser tracker's measurement coordinate system and the parallel robot's control coordinate system; Determine the transformation relationship between the coordinate system of the pose measurement device and the measurement coordinate system of the laser tracker; The position of the target ball is measured using a laser tracker (1) and used as the position data of the pose point of the parallel robot; The attitude data of the parallel robot were measured using a two-axis tilt sensor (305); By utilizing the transformation relationship between the coordinate system of the laser tracker and the control coordinate system of the parallel robot, and the transformation relationship between the coordinate system of the pose measurement device and the coordinate system of the laser tracker, position data and attitude data are unified into the control coordinate system of the parallel robot. Position data and attitude data together constitute the pose data of a parallel robot.

4. The parameter identification method as described in claim 2, characterized in that, The specific method for estimating the posterior value of the true link length using the particle filter algorithm is as follows: For a given pose point k, generate N particles. Let represent the observed link length of the j-th particle at the measured pose point k, where j = 1, ..., N, used to approximate the distribution of link lengths: in, This represents the probability of the true link length at the measured pose point k given the observed link length of the j-th particle at the measured pose point k-1. Indicates the increment of the variable. The mean is variance is The normal distribution; The weight of each particle is calculated using the following formula: in, It is the weight of the j-th particle at pose point k. It is the weight of the j-th particle at pose point k-1. This represents the probability of measuring the link length based on the observed link length of the j-th particle at the measurement pose point k. The link length is the measurement pose point k fed back by the encoder. Let represent the probability of measuring the pose of the j-th particle at the measured pose point k, given the observed link length. For measuring the pose data of the parallel robot, This represents the probability of the link length observation of the j-th particle at the measurement pose point k under the link length observation value of the j-th particle at the measurement pose point k-1. The posterior value of the true link length is obtained by weighted averaging. : in, This represents the normalized particle weights.

5. The parameter identification method as described in claim 2, characterized in that, The specific method for constructing the expectation function containing the geometric parameters of the parallel robot to be identified is as follows: In the formula, Indicates the first h Step-by-step iterative geometric structure parameters Geometric parameters under conditions The expected function, Indicates the first h Step-by-step iterative geometric structure parameters and observation dataset Hidden variable set under the condition Expectations Represents geometric structure parameters Hidden variable set under the condition and observation dataset The likelihood function; Represents all observed datasets. , This represents the dataset of link length observations fed back by all encoders. Represents the entire pose dataset. Indicates the set of hidden variables. , This is the actual length of the connecting rod.

6. The parameter identification method as described in claim 2, characterized in that, The specific steps for identifying the geometric parameters of the parallel robot by maximizing the expected function value using the expected maximization algorithm are as follows: Maximizing the expected value of the function is equivalent to minimizing the posterior value with respect to the true link length. To calculate the prediction error, the following optimization objective function is constructed: in, This is the prediction error, where M is the number of measurement pose points. For measuring the pose data of the parallel robot, Represents the posterior value of the current actual link length. and the positive kinematic function under the geometric structure parameter η; The particle swarm optimization algorithm is adopted, with each measurement pose point corresponding to a particle. M particles are initialized, and the fitness value of each particle is calculated according to the optimization objective function. At the same time, the particle update position is determined according to the individual optimal value of the particle and the global optimal value of the particle swarm. The position and fitness value of individual particles are continuously calculated iteratively. When the maximum number of iterations is reached or the fitness value converges, the optimal particle in the particle swarm is used as the final geometric structure parameter of the parallel robot.

7. The parameter identification method as described in claim 3, characterized in that, The specific steps for determining the transformation relationship between the laser tracker measurement coordinate system and the parallel robot control coordinate system are as follows: A target ball is placed sequentially into the four positioning holes on the moving plane of the parallel robot. The three-dimensional coordinates of the four positioning holes, Q1, Q2, Q3, and Q4, are used to fit a spatial plane. The normal to the spatial plane is taken as the Z-axis direction vector of the parallel robot's control coordinate system. Based on the positional relationship between the positioning holes and the control coordinate system of the parallel robot, the direction vectors of Q1 and Q2 are determined as the direction vectors of the X-axis. Determine the direction vector of the Y-axis according to the right-hand coordinate system rule. By fitting the center of a spatial sphere using a positioning hole, the center of the spatial sphere is determined as the origin Q of the parallel robot control coordinate system, and the coordinates of the origin are... Thus, the expression matrix of the parallel robot control coordinate system between the laser tracker measurement coordinate system is determined as follows: In the formula, It is the expression matrix of the parallel robot control coordinate system between the laser tracker measurement coordinate system.

8. The parameter identification method as described in claim 3, characterized in that, The specific transformation relationship between the coordinate system of the pose measurement device and the coordinate system of the laser tracker is as follows: The output data of the biaxial tilt sensor (305) are the X-axis tilt angle α and the Y-axis tilt angle β. The pitch angle is calculated according to the output definition of the biaxial tilt sensor and the definition of the rotation matrix. and roll angle : According to pitch angle and roll angle Calculate the rotation matrix as follows: When controlling a parallel robot to a certain pose, the pose is calculated using the three-dimensional coordinates of three target spheres from a laser tracker. The calculation steps are as follows: A spatial plane is fitted using the three-dimensional coordinates q1, q2, and q3 of the three target spheres, and the normal to the spatial plane is used as the Z-axis direction vector of the pose measurement device's coordinate system. Based on the positional relationship between the target ball and the coordinate system of the pose measurement device, the direction vectors of q1 and q2 are determined as the direction vectors of the X-axis. Determine the direction vector of the Y-axis according to the right-hand coordinate system rule. Let q2 be defined as the origin p of the coordinate system of the pose measurement device. m This allows us to determine the representation matrix of the pose measurement device coordinate system within the laser tracker measurement coordinate system. as follows: The attitude matrix of the pose measurement device is: , and The conversion relationship between them is as follows: in, R Representing the rotation matrix and attitude matrix The transformation matrix.

9. The parameter identification method as described in claim 6, characterized in that, The process of determining the particle update position based on the individual optimal value of the particle and the global optimal value of the particle swarm is as follows: Update the position using the following formula: In the formula, where, yes t +1 iterations of the first iteration k Particle velocity, yes t +1 iterations of the first iteration k Particle positions, x b It is the optimal position for an individual. x g It is the optimal position for all. r 1, r Both 2 are random numbers between [0,1]. c 1, c 2, c 3 are all fixed learning factors. K It is a contractile factor. ,in C = c 1+ c 2.

Images