Robot redundancy measurement system high-precision calibration method based on sphere center invariance

Abstract

The invention provides a high-precision calibration method for a robot redundancy measurement system based on sphere center invariance, and aims to accurately solve a robot-camera hand-eye relationship, a relationship between a robot base and a world coordinate system, and a rotation center shaft of an external turntable at the same time. According to the method, a six-axis robot equipped with a three-dimensional vision sensor and a rotary table with a calibration ball support are utilized, the robot is controlled to move to a plurality of remarkably different poses when the rotary table is in a zero position (and a specific rotation pose), and point cloud data of a calibration ball are collected. The center coordinate of the calibration ball in a fixed coordinate system is calculated based on the visual observation and recorded robot tail end pose. All related calibration parameters are integrated and solved by establishing a unified nonlinear optimization model for minimizing a sphere center position error. In the optimization process, a differential operator and speed adjoint method is adopted to improve the solving precision. Error accumulation of traditional step-by-step calibration is avoided, efficient and high-precision system parameter calibration is achieved, and reliable guarantee is provided for high-precision robot operation and simulation application.

Description

Technical Field

[0001] This invention belongs to the field of fine calibration of multi-degree-of-freedom industrial robotic arms, specifically involving a high-precision calibration method for a robot redundancy measurement system based on the invariance of the sphere's center. Background Technology

[0002] Robotic arms, as the most widely used devices in the field of industrial robots, have the ability to replace humans in performing a large number of repetitive and dangerous tasks, thereby improving production efficiency and workplace safety. Currently, the main methods for robotic arm calibration include traditional geometric parameter calibration, vision-guided calibration, and object-to-object calibration. In vision-guided calibration, eye-in-hand calibration is widely used. Eye-in-hand calibration obtains the camera-end-effector pose relationship by collecting multiple sets of pose data corresponding to the camera and the robotic arm, and solving the AX=XB equation. However, for complex working scenarios, such as those containing a seventh axis (turntable), the calibration requires not only the eye-in-hand matrix but also the solution of multiple unknowns, such as the transformation matrix between the base and the turntable and the solution of the turntable's central axis. Therefore, addressing the step-by-step calibration problem in current vision-guided calibration, inventing a high-precision calibration method for a robot redundant measurement system based on sphere center invariance is of great significance for improving the calibration efficiency and accuracy of industrial robots. Summary of the Invention

[0003] The purpose of this invention is to provide a high-precision calibration method for a robot redundant measurement system based on the invariance of the sphere center. The method uses a depth camera to acquire point cloud information of the calibration sphere on the measurement support on the turntable, calculates the corresponding robot joint angles, and finally proposes an integrated calibration method that combines hand-eye calibration, base-turntable calibration, and turntable rotation axis calibration to complete the calibration in a unified manner.

[0004] This method is applicable to industrial scenarios involving a seventh axis—a turntable—and aims to address the difficulties and low efficiency of existing step-by-step calibration methods in complex scenarios. Building upon existing calibration methods, it employs differential operators and velocity adjoint methods to construct equations with error compensation. Solving these equations yields compensation values, which are then used to compensate for initial calibration errors, resulting in higher-precision integrated calibration. This improves both calibration efficiency and accuracy. The technical solution adopted is as follows:

[0005] A high-precision calibration method for a robot redundant measurement system based on sphere center invariance includes the following steps:

[0006] Point cloud data of the calibration ball on the measuring bracket at the zero position and after being rotated by a known angle were acquired using a depth camera. The point cloud data were then filtered and preprocessed to remove noise and highlight the relevant features of the calibration ball.

[0007] The filtered point cloud is processed by a spherical fitting algorithm to extract the three-dimensional center coordinates of the calibration sphere.

[0008] Synchronously collect the angle data of each joint of the robot at the corresponding moment to provide basic data for subsequent calibration calculations;

[0009] Based on the extracted center position of the sphere and the corresponding joint angles, a nonlinear least squares optimization problem is constructed. The calibration parameters to be determined, the hand-eye pose, the robot-workpiece coordinate system pose, the rotation Euler angles of the turntable center pose, and the translation operator are used as optimization variables. The calibration objective function is constructed by utilizing the position invariance of the calibration sphere center before and after rotation. The Levenberg-Marquardt (LM) algorithm or Gauss-Newton iteration method is used to solve the hand-eye pose, robot-workpiece coordinate system pose, and turntable center pose simultaneously.

[0010] To further improve the system calibration accuracy, this invention extracts the geometric pose error parameters affecting the robot measurement system and constructs the pose error parameter identification equation of the measurement system based on the invariance of the sphere's center position. The parametric equation is transformed into the form AX = b using the velocity adjoint matrix, and the pose parameters are accurately identified based on algorithms such as least squares and LM.

[0011] Preferably, the filter preprocessing specifically includes the following steps:

[0012] Point cloud filtering of the calibration sphere is achieved by segmenting the RANSAC plane and constraining the radius of the calibration sphere. Then, a fitting algorithm is used to acquire the point cloud of the calibration sphere.

[0013] Preferably, the synchronous calibration and geometric pose parameters specifically include the following steps:

[0014] By utilizing the invariance of the ball center position before and after the turntable rotation, a synchronous calibration and geometric pose parameter error identification algorithm is constructed. The equation in the form AX = b is constructed using the velocity adjoint matrix and Kronecker product to solve the equation.

[0015] Preferably, the method for calibrating the geometric parameters of the measurement system specifically includes the following steps:

[0016] The Levenberg-Marquardt algorithm or the Gauss-Newton iterative method is used to iteratively solve the constructed nonlinear objective function. By calculating the Jacobian matrix and residual function, the unknown calibration parameters are optimized. The nonlinear least squares problem is transformed into a system of linear equations through Taylor expansion. The parameter update amounts are calculated, and the parameter values ​​are iteratively updated until the set convergence conditions are met.

[0017] Specifically, a high-precision calibration method for a robot redundant measurement system based on sphere center invariance includes the following steps:

[0018] A high-precision calibration method for a robot redundant measurement system based on sphere center invariance includes the following steps:

[0019] S1. System configuration: Configure a six-axis robot with a three-dimensional vision sensor installed at the end of its manipulator; configure a turntable with a support, on which a calibration ball for calibration is fixed;

[0020] S2. Data Acquisition: Control the turntable to at least two different rotation angles, including an initial zero position and at least one preset non-zero position; for each rotation angle of the turntable, control the robot's end effector to move to multiple different spatial poses, and use the 3D vision sensor to acquire the point cloud data of the calibration sphere; simultaneously record the homogeneous transformation matrix from the corresponding robotic arm end effector coordinate system to the robot base coordinate system.

[0021] S3. Calculation of sphere center coordinates: Based on the point cloud data collected each time and the corresponding robot end-effector transformation matrix, calculate the position of the center point of the calibration sphere in the world coordinate system;

[0022] S4. Parameter Integration and Solution: Using all transformation matrices recorded in step S2 for different turntable rotation angles and the three-dimensional coordinates of all calibration ball center points calculated in step S3, a nonlinear optimization model based on the consistency of the calibration ball center point positions is constructed; taking minimizing the objective function of the ball center rotation pose consistency model as the criterion, all the following parameters are solved simultaneously through a nonlinear optimization algorithm:

[0023] (a) The pose transformation relationship between the three-dimensional vision sensor coordinate system and the coordinate system of the robotic arm end effector, i.e., the hand-eye calibration parameters;

[0024] (b) The pose transformation relationship between the robot's base coordinate system and the world coordinate system;

[0025] (c) The coordinates of the center point of the rotation center axis of the turntable in the world coordinate system.

[0026] Preferably, in step S1, the calibration ball is a standard sphere of known diameter that is rigidly fixed to the bracket, and its center point is known relative to the mounting position of the bracket.

[0027] Preferably, the calculation of the sphere center coordinates in step S3 includes:

[0028] The point cloud data of the collected calibration sphere is denoised and filtered to extract the effective point cloud; the three-dimensional coordinates of the center point of the calibration sphere are solved based on the least squares spherical fitting algorithm; the set of sphere center coordinates is calculated before and after the turntable rotation. s P1}、{ s P2}

[0029] Preferably, the objective function of the nonlinear optimization model in step S4 is:

[0030] min∑‖ w PZ k ·Y·A k ·X· s P k || 2 k = 1, 2;

[0031] Among them, Z k This represents the rotation model of the turntable at the k-th rotation angle;

[0032] s P k This represents the set of fitted sphere centers at the k-th rotation angle;

[0033] Y represents the rigid body transformation matrix between the robot's base coordinate system and the world coordinate system;

[0034] X represents the rigid body transformation matrix from the 3D sensor coordinate system to the coordinate system of the robotic arm's end effector;

[0035] A k This represents the rigid body transformation matrix from the robot arm end-effector coordinate system to the robot arm base coordinate system at the k-th rotation angle.

[0036] The parameter vector to be optimized is [X,Y,Z] k It contains 14 degrees of freedom.

[0037] Preferably, after step S4, the method further includes constructing a geometric error model of the robot measurement system and a pose error compensation method using the velocity adjoint matrix;

[0038] Assuming a turntable transformation error ΔZ, a base-world transformation error ΔY, a robot kinematic error ΔA, and a hand-eye transformation error ΔX, establish the true kinematic chain equations for the robot measurement system:

[0039]

[0040] Preferably, by ignoring second-order and higher-order error terms, and simplifying the pose error model of the robot measurement system using first-order differential approximation and velocity adjoint transformation, we obtain:

[0041] ΔP i =M1·D Z +M2·D Y +M3·D A +M4·D X

[0042] in:

[0043] D i =[D Z D Y D A D X ] T For each error term, there is a differential operator.

[0044] M i =[M1,M2,M3,M4] T This represents the Jacobian mapping matrix.

[0045] Preferably, the measurement system error equation is constructed as a nonlinear least squares problem to identify the pose error parameters of the measurement system:

[0046]

[0047] Where i represents the error type number.

[0048] Compared with the prior art, the advantages of the present invention are:

[0049] This invention acquires 3D point cloud data using a depth camera, combines it with robot joint angle information, and employs a unified nonlinear least squares solution framework. It integrates error compensation and adaptive iterative algorithms to achieve integrated calibration of hand-eye calibration, base-turntable calibration, and turntable rotation axis calibration. This method effectively overcomes the shortcomings of traditional step-by-step calibration methods, such as complexity, inefficiency, and low accuracy, significantly improving calibration efficiency and accuracy. It is particularly suitable for complex industrial robot systems containing a seventh-axis turntable, meeting the high-precision and high-efficiency requirements of industrial automation. Attached Figure Description

[0050] Figure 1 This is a flowchart of a robot integration calibration method based on 3D machine vision.

[0051] Figure 2 This is a schematic diagram of a robot vision measurement system with a turntable.

[0052] Figure 3 This is a diagram showing the actual physical coordinates of the sphere's center.

[0053] Figure 4 A graph showing the parameter error after accurate compensation.

[0054] Figure 5 This is the effect image after registering several calibration balls by rotating them at a fixed angle. Detailed Implementation

[0055] The high-precision calibration method for the robot redundancy measurement system based on sphere center invariance of the present invention will be described in more detail below with reference to the schematic diagram.

[0056] like Figures 1-3 A high-precision calibration method for a robot redundant measurement system based on sphere center invariance includes the following steps:

[0057] Step 1: Define the coordinate system and parameters, clearly define the spatial relationships, and establish the foundation for the mathematical model.

[0058] Definition of coordinate systems: Robotic arm base coordinate system B, robot end effector coordinate system E, turntable fixed base coordinate system T, turntable rotation coordinate system R(θ), 3D vision sensor coordinate system S, world coordinate system W.

[0059] Among them, 3D vision sensor, i.e. 3D camera.

[0060] 3D vision sensor coordinate system, i.e., three-dimensional vision sensor coordinate system.

[0061] Parameters to be optimized: H = [R_H|t_H] represents the rigid body transformation matrix from the sensor to the end effector of the robotic arm. right The parameters are vectorized to form the parameter vector to be optimized, h_vec = [h_x, h_y, h_z, γ_z, β_y, α_x].

[0062] B = [R_B|t_B] represents the rigid body transformation matrix from the robot arm base to the turntable base. right The parameters are vectorized to form the parameter vector to be optimized, b_vec = [b_x,b_y,b_z,γ_z,β_y,α_x].

[0063] Where R is the rotational degree of freedom (rotation operator) and t is the translational degree of freedom (translation operator).

[0064] Based on existing technology, the rotary table rotation model is as follows:

[0065]

[0066] The parameter vector to be optimized is: [X0,Y0] (XY coordinates of the turntable rotation center in the T-frame).

[0067] Where the rotation operator Given the translation operator unknown;

[0068] As shown above, the parameter vector to be optimized contains a total of n parameters to be optimized.

[0069] The n parameters to be optimized include: h_x, h_y, h_z, γ_z, β_y, α_x, b_x, b_y, b_z, γ_z, β_y, α_x, X0, Y0.

[0070] Homogeneous transformation matrix A detailed explanation of parameter vectorization:

[0071] The homogeneous transformation matrix described above consists of a 3×3 rotation matrix and a 3×1 translation matrix. The specific meaning of forming the parameter vector to be optimized is to solve the rotation matrix part of the homogeneous transformation matrix to obtain three Euler angles. These three Euler angles correspond to γ_z, β_y, and α_x in the parameter vector h_vec = [h_x, h_y, h_z, γ_z, β_y, α_x]. The translation matrix directly corresponds to h_x, h_y, and h_z in the parameter vector h_vec = [h_x, h_y, h_z, γ_z, β_y, α_x].

[0072] Similarly, the meaning of the six parameters in b_vec = [b_x,b_y,b_z,γ_z,β_y,α_x] is also the same.

[0073] Detailed inverse solution method (existing technology): Let the elements in row i and column j of the rotation matrix be r. ij Based on the expression of the rotation matrix, the values ​​of Euler angles can be derived using trigonometric functions.

[0074] γ_z=θ z =atan2(r 21 r 11 ),

[0075]

[0076] α_x=θ x =atan2(r 32 r 33 ).

[0077] The "Robot Redundancy Measurement System" includes: Figure 2 Robots and turntables in the middle.

[0078] Step 2: Obtain the centers of n fitted spheres in the sensor coordinate system. s P j .

[0079] j = 1..n. j - the number of the fitted sphere center.

[0080] Multi-pose data acquisition uses a turntable to create geometric constraints, reducing parameter coupling.

[0081] There are N calibration balls on the support, where n / 2≤N.

[0082] The "calibration ball" is a standard spherical object, and its setting method is as follows:

[0083] A support is provided on the rotary table, and the relative position between the rotary table and the support is known, secured by locating pins. The support has built-in calibration balls. If the number of built-in calibration balls is insufficient, or if more calibration balls are desired to improve solution accuracy, standard spheres can be manually placed on the support as manually added calibration balls. The number of calibration balls should be at least half the number of parameters to be determined; for example, if there are 14 parameters, at least 7 calibration balls are required.

[0084] Step 2A: After rotating the turntable around the Z-axis by an angle θ, obtain n / 2 fitted sphere center coordinates.

[0085] The center of the ball, that is, the center of the ball.

[0086] The control turntable is brought to its zero position, and the robotic arm is activated to different poses. The 3D camera captures images of n / 2 calibration spheres. Then, feature extraction and point cloud segmentation algorithms are used to obtain the fitted sphere center coordinates.

[0087] Specifically: Start the robotic arm to a pose and collect data from one of the n / 2 calibration balls;

[0088] Then, the robotic arm is activated to another pose to collect data from one of the n / 2 calibration balls that has not yet been collected.

[0089] By analogy, the images of n / 2 calibration spheres are captured to obtain n / 2 fitted sphere centers.

[0090] like Figure 2 As shown, data was collected from 7 (n / 2 = 7) of the N = 10 calibration balls.

[0091] The robotic arm is in different positions when collecting blue and green calibration balls.

[0092] There are no special requirements for the robotic arm pose used when collecting data from the remaining 5 calibration balls, as long as the robotic arm's accessibility is met.

[0093] For each pose, a calibration ball is collected.

[0094] In this embodiment, the number of robotic arm poses used in step 2A is 7.

[0095] Step 2B: After rotating the turntable around the Z-axis by an angle θ, obtain the remaining n / 2 fitted sphere center coordinates.

[0096] After controlling the turntable to rotate around the Z-axis by an angle θ, the robotic arm is activated to different poses, and the 3D camera captures images of the n / 2 calibration spheres from step 2A. Then, feature extraction and point cloud segmentation algorithms are used to obtain the coordinates of the fitted sphere centers.

[0097] The 3D camera captures the robot arm's pose when fitting the center of the sphere; this is also a single pose, captured for one calibration sphere. Therefore, the number of robot arm poses used in step 2B is 7.

[0098] The calibration balls collected in steps 2B and 2A are from the same batch of calibration balls.

[0099] θ can be 0°, 45°, 90°, etc.

[0100] Step 3: Obtain the stiffness transformation matrix A from the robot arm end effector coordinate system E to the robot arm base coordinate system B. k .

[0101] Step 3A: Based on each shooting in Step 2, read the joint angle vector q_p at each acquisition time P = 1..p using the robot teach pendant;

[0102] Different robot models have their own DH parameters, and the joint angle vectors mentioned here are directly read from the robot teach pendant.

[0103] Step 3B: Call the forward kinematics function: A_p = FK(q_p), and output the homogeneous transformation matrix from the robot arm base coordinate system B to the robot arm end effector coordinate system E.

[0104] The output of step 3B will be used as the input to the geometric constraints in step 4. That is, the fitted spherical coordinates obtained at the zero position of the turntable and the fitted spherical coordinates obtained after the turntable rotates around the Z-axis by an angle θ will be used as known quantities and substituted into step 4 respectively.

[0105] Step 4: Establish a framework for fitting the center of the sphere. s P j kinematics model transferred to world coordinate system w P′.

[0106] According to kinematic analysis, the point cloud acquired by the 3D camera can be obtained through a kinematic chain: 3D sensor coordinate system {S} → robotic arm end effector coordinate system {E} → robotic arm base {B} → world coordinate system {W}. This allows the point cloud to be positioned within the part coordinate system (world coordinate system).

[0107]

[0108] That is, the kinematic chain model w P′ applies to the value obtained in step 2. s P j This includes the fitted spherical coordinates obtained at the zero position of the turntable and the fitted spherical coordinates obtained after the turntable rotates around the Z-axis by an angle θ.

[0109] in, -Stiffness transformation matrix from the 3D sensor coordinate system to the robotic arm end effector coordinate system E;

[0110] -Stiffness transformation matrix from robot arm base coordinate system B to world coordinate system W;

[0111] Step 5: Construct a position that makes the ideal center of the sphere. w P and the fitted center of the sphere s P j The objective function that minimizes the difference between them.

[0112] Based on the invariance of the ball center pose in space before and after the turntable rotation, the following objective function is constructed:

[0113]

[0114] Specifically:

[0115]

[0116]

[0117] When the fitted sphere center obtained at the zero position of the turntable is substituted, Z k =Z1=R(0),A k =A1

[0118] When the fitted sphere center is obtained by rotating the turntable around the Z-axis by an angle θ, Z k =Z2=R(θ), A k =A2.

[0119] The objective function mentioned above contains rotation matrix multiplication, so its nonlinear output will be input into step 6, thereby achieving synchronous calibration of hand-eye pose, robot-turntable pose, and turntable rotation axis (rotation center).

[0120] w P represents the calibration sphere, and the actual physical center coordinates of the sphere in the world coordinate system, where the actual physical center coordinates are known, such as... Figure 3 The image shows the actual physical coordinates of the spheres, displaying the coordinates of 10 calibration spheres.

[0121] In step 5, the unknowns include:

[0122] The known quantities include: w P, s P j ,

[0123] Invariance of the center of the sphere: For the same set of calibration spheres, the position of the center of the sphere on the entire turntable in space is A before rotation and A′ after rotation. Through the corresponding inverse operation, it can be seen that the position of the center of the sphere remains unchanged before and after rotation.

[0124] Figure 5 This is an image showing the effect of registering the corresponding reference spheres (calibration spheres) before and after rotation, based on the invariance of the sphere center. The blue sphere represents the reference sphere acquired when the turntable is at zero position, and the red sphere represents the reference sphere after the turntable has rotated 90°. The current image shows the effect of registering the corresponding calibration spheres before and after rotation by using the characteristic of the invariance of the sphere center through inverse operation. This process solves for the parameters that need to be calculated.

[0125] The positions of the ball's center substituted in steps 4, 5, and 6 utilize the method of ball center invariance.

[0126] Step 6: Use the Levenberg-Marquardt (LM) or Gauss-Newton iterative method to perform preliminary solutions for the unknown parameters in Step 5, obtain initial values, and achieve accurate estimation of system parameters.

[0127] An improved Gauss-Newton algorithm is used for iterative optimization, and an adaptive step size control strategy is introduced to effectively overcome the overshoot divergence problem of traditional methods.

[0128] Let the average registration error of the current iteration be avg, and the error of the previous iteration be avg0. When avg > avg0 is detected, the following correction operation is performed:

[0129] 1) Gradient direction correction: Reverse the current parameter update amount to counteract the overshoot effect by reversing the gradient direction.

[0130] 2) Adaptive step size adjustment: The step size is adjusted using an exponential shrinkage strategy to ensure fine adjustment when approaching the optimal solution.

[0131] 3) Double threshold termination criterion: The iteration stops when either the error change converges or the step size reaches the threshold.

[0132] The results from step 6 and step 3 will be used as inputs for step 7 to establish the error compensation model.

[0133] Step 7: Establish an error compensation model.

[0134] Error modeling and disturbance analysis: Quantifying the unmodeled errors in the system yields the following actual transformation model:

[0135]

[0136] In step 7: ΔZ represents the turntable transformation error; ΔY represents the base-world transformation error; ΔA represents the robot kinematics error; and ΔX represents the hand-eye transformation error.

[0137] Rigid body transformation matrix from the X-3D sensor coordinate system to the robot end effector coordinate system

[0138] Rigid body transformation matrix from Y-axis robot base coordinate system B to world coordinate system W

[0139] Z-turntable rotation model [Rt;0 0], where R is a known quantity, and X0 and Y0 in t are obtained in step 6. Z refers to Z1 or Z2.

[0140] A - Rigid body transformation matrix from the robot arm end-effector coordinate system E to the robot arm base coordinate system B The robot's joint angles are obtained through forward kinematics. A refers to either A1 or A2.

[0141] If Z adopts Z1, then A adopts A1; similarly, if Z adopts Z2, then A adopts A2.

[0142] In step 7, the unknowns include: ΔX, ΔY, ΔZ, and ΔA.

[0143] The known quantities include: X, Y, Z, and A. These are determined in step 6.

[0144]

[0145] θ is the known rotation angle of the turntable;

[0146] X0 and Y0 are the results obtained in step 6;

[0147] Instead of step 4, the turntable transformation is introduced into step 7. Reason:

[0148] In step 4, the turntable transformation is not known and contains unknowns. After solving for the unknowns in step 6, the turntable model is determined. Then, in the fine-tuning and error compensation section, the XY values ​​in the turntable model are further compensated for errors to find a solution with smaller errors.

[0149] ΔZ represents the introduced error in X0 and Y0, namely ΔX0 and ΔY0.

[0150] Step 8: Based on the error compensation model in Step 7, construct the pose error model ΔP. i .

[0151] First-order error propagation modeling, ignoring second-order and higher-order error terms, simplifies the robot measurement system pose error model through first-order differential approximation and velocity adjoint transformation, thus constructing a linear model:

[0152] ΔP i =M i ·D i =M1·D Z +M2·D Y +M3·D A +M4·D X

[0153] in:

[0154] D i =[D Z D Y D A D X ] T For each error term, there is a differential operator.

[0155] M i =[M1,M2,M3,M4] T This represents the Jacobian mapping matrix.

[0156] The Jacobian mapping matrix is ​​a mathematical description of the error propagation relationship. It is constructed through the adjoint transformation of the kinematic chain to realize the linear mapping from the 24-dimensional error space (D) to the pose residual space (ΔP), providing a theoretical basis for error source decomposition and compensation calculation. Its physical essence is the partial derivative matrix of the pose residual with respect to the error parameters.

[0157] Based on the error compensation model in step 7, construct the pose error model ΔP. i The process:

[0158] w P=(Z+ΔZ)(Y+ΔY)(A+ΔA)(X+ΔX)· s P j This formula can be simplified to:

[0159] w P = Z * Y * A * X * s P j +ΔZ*Y*A*X* s P j +Z*ΔY*A*X* s P j +Z*Y*ΔA*X* s P j +Z*Y*A*ΔX* s P j ,

[0160] The simplification here involves expanding the product chain. After expansion, we find that Z*Y*A*X* s P j This part is the chain equation from step 4, which has already been solved in step 6; it is essentially the known part.

[0161] The above only retains the error matrix of the first-order terms, which is the aforementioned ΔZ*Y*A*X*. s P j As for other error matrices containing two errors, we omit them because in error analysis, ΔX, ΔY, ΔZ, and ΔA are all "small quantities," and the product of two errors would be an even smaller quantity. Therefore, we omit them here for ease of calculation.

[0162] Where Z*Y*A*X* s P j It is a known quantity containing error (already calculated in step 6 above).

[0163] make w PZ*Y*A*X* s P j =ΔP is the positional residual;

[0164] Y*A*X* s P j =YP

[0165] A*X* s P j =AP

[0166] X* s P j =XP

[0167] Z*Y*A=W;

[0168] Further simplification yields ΔP = ΔZ*YP + Z*ΔY*AP + Z*Y*ΔA*XP + W*ΔX* s P j ,

[0169] Using differential operators and the velocity adjoint method, it can ultimately be simplified to:

[0170] ΔP=M1D Z +M2·D Y +M3·D A +M4·D X .

[0171] The Jacobian matrix is ​​unknown and usually does not have an explicit, simple expression.

[0172] In the velocity adjoint method, we don't need to explicitly write out or compute this huge Jacobian matrix at all. This is precisely the greatest advantage of the adjoint method.

[0173] We can assume that M i The matrices are the components of the decomposed and rearranged Jacobian matrices. They are obtained by differentiating, discretizing, and integrating the original physical equations. D i It is unknown, D Z D Y D A D X These velocity adjoint vectors are the core unknowns of the entire linear system. The entire calculation process involves first defining and constructing M. i (Through mathematical derivation) and then reassemble D i A linear system with unknowns is called M i ·D i In this form, the final numerical solution for D is obtained. i Differential operators and velocity adjoint methods are existing mathematical approaches.

[0174] Where M1 corresponds to ΔZ*YP; where ΔZ*YP=M1·D Z And so on.

[0175] M2 corresponds to Z*ΔY*AP;

[0176] M3 corresponds to Z*Y*ΔA*XP;

[0177] M4 corresponds to W*ΔX* s P j .

[0178] The true meaning of "correspondence" here is:

[0179] In the final system of linear equations, the change in the objective function ΔP caused by parameter perturbations (ΔX, ΔY, ΔZ, ΔA) can be expressed as a set of known matrices (M1, M2, M3, M4) and the corresponding unknown velocity adjoint vector (D). Z D Y D A D X The sum of the products of ).

[0180] More precisely, ΔZ*YP is the contribution term of the perturbation ΔZ to ΔP. In the derivation process, through mathematical operations such as differential operators and velocity adjoint methods, we successfully rewrote this term as M1·D Z .

[0181] D Z The velocity adjoint vector of ΔZ (ΔZ*YP=M1·D) ZD Y The velocity adjoint vector of ΔY, D A Let ΔA be the velocity adjoint vector, and D be the velocity adjoint vector. X The velocity adjoint vector of ΔX;

[0182] The velocity adjoint vector is a 6-dimensional vector (containing linear and angular velocity components), and each M can be made possible using differential operators and the velocity adjoint method. i ·D i Capture the contribution of the corresponding differential transformation to the position error.

[0183] Step 9: Precise compensation optimization. The measurement system error equation is constructed as a nonlinear least squares problem, and the pose error parameters of the measurement system are identified.

[0184]

[0185] Where V represents the number of error types, in this embodiment V = 4.

[0186] i - The number of the error type.

[0187] In step 9, the unknown quantity is D. i .

[0188] The solution method for the least squares problem constructed above is an existing method. There is sufficient data, and it can be directly solved by fitting using common methods.

[0189] For the aforementioned nonlinear optimization problem, approximate convex optimization and heuristic algorithms (such as genetic algorithms, LM algorithms, etc.) can be used to iteratively solve for the pose error geometric parameters D.

[0190] For the obtained pose error geometric parameters D, the geometric error matrices ΔX, ΔY, ΔZ, and ΔA are solved by reverse engineering.

[0191] The specific inverse solution steps are as follows: Decompose D from D. Z D Y D A D X D Z D Y D A D X Consider the corresponding Lie algebra se(3) element ξ, convert the corresponding Lie algebra vector into matrix form [ξ], and finally apply the exponential mapping to inversely obtain the geometric error matrix ΔX, ΔY, ΔZ, Δa.

[0192] The compensated data is, for example... Figure 4 As shown. Figure 4 The data for 12 calibration balls is displayed in the image.

[0193] For the aforementioned nonlinear optimization problem, approximate convex optimization and heuristic algorithms (such as genetic algorithms, LM algorithms, etc.) can be used to iteratively solve for the pose error geometric parameters D.

[0194] Step 10: Based on the pose error geometric parameters D obtained in Step 9, the deviation can be reduced by compensating for the pose error. The compensated chain equation can be written as:

[0195]

[0196] in To compensate for the pose error, the position of the center of the calibration ball is collected, and the error between the calculated position and the actual position is minimized.

[0197] Z is the turntable transformation obtained in step 6, and ΔZ is the geometric error matrix obtained in step 9. Adding the two together gives the turntable transformation after accurate compensation, which means that the unknowns X0 and Y0 in the turntable transformation are accurately determined.

[0198] Similarly, Y represents the matrix obtained in step 6. A represents the matrix obtained in step 6. X represents the matrix obtained in step 6. ΔY, ΔA, and ΔX are the error compensation matrices obtained in step 9.

[0199] Step 10 yields a chain equation after precise compensation. The output shows that the error between the point cloud position obtained from the error acquisition and the actual nominal position is very small. All parameters that need to be calibrated are obtained in step 6, and the parameters to be compensated are obtained in step 9. Step 10 simply integrates all the solutions into the chain equation for use.

[0200] The output is the final calibration result, and the effect after registration is shown in the figure below. Figure 5 As shown, it can be directly used for high-precision vision guidance.

[0201] The purpose of step 10 is to compensate and optimize the initial values ​​obtained in step 6, and the optimized parameter values ​​are used as the final calibration results.

[0202] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. A high-precision calibration method for a robot redundant measurement system based on sphere center invariance, characterized in that, Includes the following steps: S1. System configuration: Configure a six-axis robot with a three-dimensional vision sensor installed at the end of its manipulator; configure a turntable with a support, on which a calibration ball for calibration is fixed; S2. Data Acquisition: Control the turntable to at least two different rotation angles, including an initial zero position and at least one preset non-zero position; for each rotation angle of the turntable, control the robot's end effector to move to multiple different spatial poses, and use the 3D vision sensor to acquire the point cloud data of the calibration sphere; simultaneously record the homogeneous transformation matrix from the corresponding robotic arm end effector coordinate system to the robot base coordinate system. S3. Calculation of sphere center coordinates: Based on the point cloud data collected each time and the corresponding robot end-effector transformation matrix, calculate the position of the center point of the calibration sphere in the world coordinate system; S4. Parameter Integration and Solution: Using all transformation matrices recorded in step S2 for different turntable rotation angles and the three-dimensional coordinates of all calibration ball center points calculated in step S3, a nonlinear optimization model based on the consistency of the calibration ball center point positions is constructed; taking minimizing the objective function of the ball center rotation pose consistency model as the criterion, all the following parameters are solved simultaneously through a nonlinear optimization algorithm: (a) The pose transformation relationship between the three-dimensional vision sensor coordinate system and the coordinate system of the robotic arm end effector, i.e., the hand-eye calibration parameters; (b) The pose transformation relationship between the robot's base coordinate system and the world coordinate system; (c) The coordinates of the center point of the rotation center axis of the turntable in the world coordinate system.

2. The high-precision calibration method for a robot redundancy measurement system based on sphere center invariance according to claim 1, characterized in that, In step S1, the calibration ball is a standard sphere of known diameter that is rigidly fixed to the bracket, and the installation position of its center point relative to the bracket is known.

3. The high-precision calibration method for a robot redundancy measurement system based on sphere center invariance according to claim 1 or 2, characterized in that, Step S3, calculating the coordinates of the sphere's center, includes: The point cloud data of the collected calibration sphere is denoised and filtered to extract the effective point cloud; the three-dimensional coordinates of the center point of the calibration sphere are solved based on the least squares spherical fitting algorithm; the set of sphere center coordinates is calculated before and after the turntable rotation. s P1}、{ s P2} 4. The high-precision calibration method for a robot redundancy measurement system based on sphere center invariance according to claim 3, characterized in that, The objective function of the nonlinear optimization model described in step S4 is: min∑‖ w P-Z k ·Y·A k ·X· s P k ‖ 2 ,k=1,2; Among them, Z k This represents the rotation model of the turntable at the k-th rotation angle; sP k This represents the set of fitted sphere centers at the k-th rotation angle; Y represents the rigid body transformation matrix between the robot's base coordinate system and the world coordinate system; X represents the rigid body transformation matrix from the 3D sensor coordinate system to the coordinate system of the robotic arm's end effector; A k This represents the rigid body transformation matrix from the robot arm end-effector coordinate system to the robot arm base coordinate system at the k-th rotation angle. The parameter vector to be optimized is [X,Y,Z] k It contains 14 degrees of freedom.

5. The high-precision calibration method for a robot redundancy measurement system based on sphere center invariance according to claim 4, characterized in that, Step S4 is followed by constructing a geometric error model of the robot measurement system and a pose error compensation method using the velocity adjoint matrix; Assuming a turntable transformation error ΔZ, a base-world transformation error ΔY, a robot kinematic error ΔA, and a hand-eye transformation error ΔX, establish the true kinematic chain equations for the robot measurement system:

6. The high-precision calibration method for a robot redundancy measurement system based on sphere center invariance according to claim 5, characterized in that, Ignoring second-order and higher-order error terms, the pose error model of the robot measurement system is simplified using first-order differential approximation and velocity adjoint transformation, resulting in: ΔP i =M1·D Z +M2·D Y +M3·D A +M4·D X in: D i =[D Z D Y D A D X ] T For each error term, there is a differential operator. M i =[M1,M2,M3,M4] T This represents the Jacobian mapping matrix.

7. The high-precision calibration method for a robot redundancy measurement system based on sphere center invariance according to claim 6, characterized in that, The measurement system error equation is constructed as a nonlinear least squares problem to identify the pose error parameters of the measurement system. Where i represents the error type number.

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