A double-layer nonlinear optimization monocular vision hand-eye calibration method based on outlier sample screening

Abstract

The application discloses a double-layer nonlinear optimization monocular vision hand-eye calibration method based on outlying sample screening. h2e An Euler angle transformation is carried out to ensure the orthogonality of the rotation matrix R; an optimization model H1 of the hand-eye matrix is constructed, and a traditional LM nonlinear optimization method is used to perform first optimization on the initial value of the hand-eye matrix to obtain a hand-eye matrix after the first optimization; the optimization model H1 of the hand-eye matrix is modified to obtain a second optimization model H2, and then an LM nonlinear optimization method with the outlying sample screening method is used to perform second optimization on the hand-eye matrix after the first optimization to obtain a hand-eye matrix after the second optimization; and the method can reduce the influence of random errors existing in the monocular vision system of the robot and improve the calibration precision of the hand-eye matrix of the robot.

Description

Technical Field

[0001] This invention belongs to the fields of computer vision and robotics, specifically relating to a two-layer nonlinear optimized monocular vision hand-eye calibration method based on outlier sample screening. Background Technology

[0002] With the development of industrial intelligence, cases of combining vision technology with industrial robots are emerging one after another. The method of mounting a vision system on the end effector of a robot is called "eye-on-hand," which benefits from the robot's flexibility. It has a wider operating range than vision sensors fixed in one position. Currently, it is widely used in various robot manufacturing systems, typically in robotic welding, grinding, assembly, aerospace, and automotive fields. However, for vision robots, the accuracy of hand-eye calibration directly affects the final positioning accuracy of the robot's end effector; therefore, the stability and accuracy of hand-eye calibration are particularly important.

[0003] Currently, there are three main methods for hand-eye calibration: Tsai's calibration method, the Dual-Quaternion calibration method, and Zhang Zhengyou's calibration method. Tsai's calibration method obtains the calibration matrix by performing nonlinear least-squares solutions on multiple known relationships between the robot's end effector and the camera. The Dual-Quaternion calibration method represents the motion relationship between the robot's end effector and the camera as a dual quaternion, and then obtains the calibration matrix by solving the parameters of the dual quaternion through nonlinear optimization. Zhang Zhengyou's calibration method is a hand-eye calibration method based on camera intrinsic and extrinsic parameters. This method calibrates the camera's intrinsic and extrinsic parameters and obtains the calibration matrix through optimized matching between camera measurements and the robot's motion trajectory.

[0004] Current methods for solving hand-eye calibration, such as the "Layered Hand-Eye Calibration Robot Motion Pose Automatic Generation Method, System, Device, and Medium" disclosed in Chinese Invention Patent No. CN115781698A, disclose a specific hand-eye calibration process: controlling the robot to move to the target point and taking a picture of the calibration board; detecting the corner points of the chessboard and ensuring the reprojection error is less than a preset value; if within the preset range, the hand-eye calibration task is executed; otherwise, the preset parameters are adjusted, the robot's position data is recalculated, and the motion-photograph-verification task is re-executed; and the hand-eye calibration solution is performed based on the recorded robot pose and camera-calibration board pose. However, the hand-eye matrix obtained by this method is not optimized, which can lead to errors that cause inaccurate hand-eye calibration, and also affect the accuracy and robustness of the robot system. Summary of the Invention

[0005] To address the aforementioned problems, this invention designs a two-layer nonlinear optimization method based on the principle of nonlinear optimization and outlier sample screening, with initial values ​​for the hand-eye matrix... After initial optimization using the traditional LM method, a secondary optimization method incorporating outlier sample screening is used. This method can complete the calibration without the need for a special target, reducing random errors in the robot vision system. The accuracy of the proposed calibration method meets the working requirements of vision robots in the industrial field.

[0006] To achieve the above objectives, the main technical solution of the present invention is as follows:

[0007] First, a checkerboard calibration board is selected and its position is fixed. The position and posture of the robot's end effector are then changed to ensure that the checkerboard calibration board is fully visible within the monocular camera's field of view. Next, the expression for feature point P on the checkerboard calibration board within the field of view is solved in the robot's base coordinate system (1-1), and the initial values ​​of the hand-eye matrix are obtained. Finally, the initial values ​​of the hand-eye matrix are optimized using LM nonlinear optimization. The initial optimization yields the hand-eye matrix after the first optimization. Then, a second nonlinear optimization is performed based on sample selection to obtain the hand-eye matrix after the second optimization. During the iteration process, points with large random errors are removed from the sample point set to obtain the hand-eye matrix after the second optimization. This can be used as the final result of hand-eye alignment, and specifically includes the following steps:

[0008] Step 1: Create three coordinate systems in the robot system: camera coordinate system OX. C Y C Z C (1-3), the robot's end effector TCP coordinate system OX E Y E Z E (1-2) and robot base coordinate system OX B Y B Z B (1-1);

[0009] Step 2: Solve for the coordinate expression of feature point P in the robot base coordinate system 1-1, which includes at least the following two steps:

[0010] Step 2-1: Mark the coordinates of the first corner point, i.e., feature point P, on the checkerboard calibration board in camera coordinate system 1-3. C P is marked with coordinates P in the robot's base coordinate system 1-1. B The PNP algorithm is used to solve for the coordinates of feature point P in camera coordinate system 1-3. C ;

[0011] Step 2-2: According to Figure 1 The coordinate transformation relationship shown can be expressed by equation (1).

[0012]

[0013] Obtain the coordinates P of the feature point in the robot base coordinate system 1-1. B ;

[0014] Step 3: Initial values ​​of the hand-eye matrix The determination of [the value] includes at least the following three steps:

[0015] Step 3-1: First, change the pose of the robot's end effector so that the monocular camera takes pictures of feature point P in different poses, collecting n (n≥4) pictures. The coordinates of feature point P in the world coordinate system under different poses can be solved by equation (2). B :

[0016]

[0017] The feature points in the n images are P1, P2, ..., Pn. n Its position in the robot's base coordinate system 1-1 remains unchanged, therefore Equation (2) can then be rewritten as:

[0018]

[0019] Step 3-2: In equation (3), and Let i and j represent the transformation matrices from the robot end-effector TCP coordinate system 1-2 to the robot base coordinate system 1-1 in the i-th and j-th samples, respectively (i = 1, 2, ..., n-1, j = i+1, i+2, ..., n).

[0020] Will and Rewritten as equation (4):

[0021]

[0022] The matrix equation is obtained from equations (3) and (4), as shown in equation (5):

[0023]

[0024] Step 3-3: Let A be the left-hand coefficient matrix, X be the unknown quantity of the hand-eye matrix, and b be the right-hand coefficient matrix; given that A and b are known, the problem of solving X is transformed into the problem of solving the matrix equation; since the number of collected images is redundant for solving the above matrix equation, in order to minimize the final error, the least squares method is used to solve the matrix equation, and the least squares solution of the matrix equation is shown in equation (6):

[0025] X = (A T A) -1 A T b (6)

[0026] After solving for the initial hand-eye matrix X, that is, the initial value of the hand-eye matrix... Hand-eye matrix rotational component R h2e Peaceful movement h2e The components are shown in equation (7):

[0027]

[0028] Step 4, Initial LM Nonlinear Optimization, which includes at least the following five steps:

[0029] Step 4-1: Initialize the hand-eye matrix obtained in Step 3. It is represented as shown in equation (8):

[0030]

[0031] Step 4-2: Hand-eye matrix The rotational component R in h2e Perform Euler angle transformation to determine the transformation angle θ between the x, y, and z axes of the camera coordinate system 1-3 and the x, y, and z axes of the robot's end effector TCP coordinate system 1-2 during the rotation process. x θ y θ z As shown in equation (9):

[0032]

[0033] Step 4-3: Use the inverse Euler angle transformation to find the rotation matrix R, as shown in equation (10):

[0034]

[0035] Therefore, the initial value of the hand-eye matrix As shown in equation (11):

[0036]

[0037] Step 4-4: Constructing the error function W1 and loss function L1: Since the coordinates of feature point P are constant in the world coordinate system, an initial optimization model H1 is established. The error function W1 of the initial optimization model H1 is shown in equation (12):

[0038]

[0039] The loss function L1 of the initial optimization model H1 is shown in equation (13):

[0040]

[0041] Step 4-5: Using the error function W1 and loss function L1 from equations (12) and (13), the LM algorithm is used to initialize the hand-eye matrix. The first optimization is performed, resulting in the optimized hand-eye matrix. The Euler angles are represented as shown in equation (14):

[0042] [θ x θ y θ z t x t y t z ] T (14)

[0043] Step 5, combining sample selection with quadratic nonlinear optimization, includes at least the following six steps:

[0044] Step 5-1: Optimize the hand-eye matrix after the first step. The Euler angle representation is converted into a matrix representation, as shown in equation (15):

[0045]

[0046] Step 5-2: Use the method of calculating the mean to obtain the standard point P. S The coordinates of the in the robot base coordinate system 1-1 are shown in equation (16):

[0047]

[0048] Step 5-3: Correct the initial optimization model H1 and substitute the standard point P. S The coordinates; the corrected error function W2 is shown in equation (17):

[0049]

[0050] The corrected loss function L2 is shown in equation (18):

[0051]

[0052] Step 5-4: Initialize the iteration-related parameters for the second optimization and substitute them into the hand-eye matrix after the first optimization. These are the initial values ​​for the second optimization iteration;

[0053] Step 5-5: Determine if the iteration count m and error e meet the stopping requirements. If the error e is less than the set error threshold e′, stop the iteration; otherwise, obtain the step size Δh for this iteration. If the step size Δh is less than the set step size threshold Δh′, stop the iteration; otherwise, update the hand-eye matrix. Parameters related to the iteration of the LM algorithm;

[0054] Step 5-6: Mark outliers for sample points in each iteration; obtain the number of iterations m that have not been filtered; if the number reaches s, filter the sample points; the filtering step refers to traversing all samples to determine the number of times the samples are marked in the above s iterations, and consider sample points with a number of markings exceeding 0.5*s as sample points with large errors, and remove all sample points with large errors from the sample point set.

[0055] The features and beneficial effects of this invention are:

[0056] 1. The present invention provides a two-layer nonlinear optimization monocular vision hand-eye calibration method based on outlier sample screening. Compared with the hand-eye matrix calibration method of traditional methods, the two-layer nonlinear optimization monocular vision hand-eye calibration method based on outlier sample screening can improve the stability of the robot vision system and meet industrial requirements in terms of accuracy.

[0057] 2. This algorithm introduces a two-layer optimization method with outlier detection. During the optimization process, Euler angle transformation is used to ensure the orthogonality of the hand-eye matrix, which can accurately calibrate the hand-eye matrix of the visual robot, reduce the influence of random errors in the system, and improve the robustness of hand-eye calibration. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of coordinate system transformation.

[0059] Figure 2 Flowchart of the overall process for a two-layer nonlinear optimized hand-eye calibration method for outlier screening;

[0060] Figure 3 The flowchart for the first nonlinear optimization of the hand-eye matrix;

[0061] Figure 4 The flowchart shows the LM algorithm with sample selection.

[0062] In the attached diagram, 1-1 represents the robot's base coordinate system OX. BY B Z B ; 1-2 represents the TCP coordinate system OX of the robot's end effector. E Y E Z E ; 1-3 is the camera coordinate system OX C Y C Z C . Detailed Implementation

[0063] The present invention will be further described below with reference to the accompanying drawings.

[0064] Appendix Figure 1 The construction methods of the robot base coordinate system 1-1, camera coordinate system 1-3, and robot end effector TCP coordinate system 1-2, and the transformation relationships among them are explained; see attached. Figure 3 As shown, the hand-eye matrix equation is first established, and the initial values ​​of the hand-eye matrix are solved using the linear least squares method. Secondly, the initial values ​​of the hand-eye matrix The rotational component R in h2e Euler angle transformation is performed to ensure the orthogonality of the rotation matrix R; then, an initial optimization model H1 for the hand-eye matrix is ​​constructed, and the initial values ​​of the hand-eye matrix are determined using the traditional LM nonlinear optimization method. Perform the first optimization; as shown in the attached document. Figure 4 As shown, the initial optimization model H1 of the hand-eye matrix is ​​finally corrected to obtain the secondary optimization model H2. Then, the LM nonlinear optimization method with the addition of a sample selection method is used to optimize the hand-eye matrix after the first optimization. A second optimization is performed to obtain the optimized hand-eye matrix. The aforementioned two-layer nonlinear optimized monocular vision hand-eye calibration method based on outlier sample screening includes the following steps:

[0065] Step 1: Use the PNP algorithm to solve for the coordinates of feature point P in camera coordinate system 1-3. C Solve for the coordinate expression of feature point P in robot base coordinate system 1-1. B The PNP algorithm includes at least the following three steps:

[0066] Step 1-1: Set the world coordinates of the corner points of the chessboard calibration board to [X...]. W Y W Z W 1] T The corner point [uv 1] in the pixel coordinate system. T Given the coordinates of the world coordinates, the relationship between the world coordinates and the pixel coordinates is shown in equation (19):

[0067]

[0068] Step 1-2: Where M is the camera intrinsic parameter generated by camera calibration, and R... C and T C These are the rotation and translation components in the extrinsic parameter matrix, Z. C It is the depth of the 3D point in the camera coordinate system; finally, the extrinsic parameter matrix can be optimized by minimizing the reprojection error.

[0069] Step 1-3: Based on the coordinate transformation relationship (19), the coordinates of point P in the base coordinate system can be calculated using formula (20). B The coordinates of point P in the camera coordinate system can be represented as P C ;

[0070]

[0071] Step 2: Use the least squares method to solve for the initial values ​​of the hand-eye matrix.

[0072] Step 3: Orthogonalize the hand-eye matrix using inverse Euler angle transformation;

[0073] Step 4: Construct the error function W1 and the loss function L1: Since the coordinates of feature point P in the robot base coordinate system 1-1 remain unchanged, establish the initial optimization model H1;

[0074] Step 5: LM Optimization Solution: Based on the error function W1 and the loss function L1, the LM algorithm is used for the first optimization to obtain the hand-eye matrix after the first optimization. Euler angles representation;

[0075] Step 6: Initialize the iteration-related parameters for the second optimization and substitute them into the hand-eye matrix after the first optimization. These are the initial values ​​for the second optimization iteration;

[0076] Step 7: Determine if the iteration count m and error e meet the stopping condition. If the error e is less than the set error threshold e′, stop the iteration; otherwise, obtain the step size Δh for this iteration. If the step size Δh is less than the set step size threshold Δh′, stop the iteration; otherwise, update the hand-eye matrix. Parameters related to the iteration of the LM algorithm;

[0077] Step 8: Based on the density of the sample points, calculate the k-th local outlier factor for each sample point and mark the outliers. This step includes at least the following four steps:

[0078] Step 8-1: Calculate P for each sample point L The k-th distance neighborhood O L The k-th reachable distance reach_dist k (OL ,P L As shown in equation (21):

[0079] reach_dist k (O L ,P L )=max{d k (O L ),d(O L ,P L )} (twenty one)

[0080] Where, d k (O L ) represents the neighborhood point O L The k-th distance, i.e., the sample point O L The distance to the k-th nearest neighbor, d(O L ,P L ) represents the neighborhood point O L Point P L The distance;

[0081] Step 8-2: Calculate P for each sample point L Locally achievable density lrd k (P L As shown in equation (22):

[0082]

[0083] Where, N k (P L ) is P L The set of all points in the k-th distance neighborhood;

[0084] Step 8-3: Calculate the Local Outlier Factor (LOF) for each point. k (P L As shown in equation (23):

[0085]

[0086] Step 8-4: Mark the sample points with the largest local outlier factor in the first t% and consider them as outliers in the current iteration. When the local outlier factor of all sample points is less than σ, the sample points are considered to have a low degree of abnormality and no outliers are marked in the current iteration.

[0087] Step 9: Mark outliers for sample points in each iteration; obtain the number of iterations m that have not been filtered. If the number reaches s, filter the sample points. The filtering step refers to traversing all samples to determine the number of times the samples have been marked in the above s iterations. Sample points with a number of markings exceeding 0.5*s are considered as sample points with large errors, and all sample points with large errors are removed from the sample point set.

[0088] The above are merely specific application examples of the present invention and do not constitute any limitation on the scope of protection of the present invention. In addition to the above embodiments, the present invention may have other implementation methods. All technical solutions formed by equivalent substitution or equivalent transformation fall within the scope of protection claimed by the present invention.

Claims

1. A two-layer nonlinear optimization monocular vision hand-eye calibration method based on outlier sample screening, comprising at least one monocular camera, a checkerboard calibration board, and an industrial robot, wherein the position of the checkerboard calibration board remains fixed during the calibration process; the method places the checkerboard calibration board within the field of view of the monocular camera and calibrates the hand-eye matrix by acquiring images from the monocular camera, characterized in that, The monocular vision hand-eye calibration method uses a two-layer nonlinear optimization algorithm based on outlier sample screening, which includes at least the following five steps: Step 1: Acquire images of the checkerboard calibration board taken by a monocular camera: Adjust the robot's end effector pose and acquire images of the checkerboard calibration board taken by a monocular camera. Acquire a total of n (n≥4) images, and ensure that the checkerboard calibration board is fully displayed in the monocular camera's field of view; the position of the checkerboard calibration board remains unchanged relative to the robot's base coordinate system 1-1 during the image acquisition process. Step 2: Calculate the coordinates of feature point P in robot base coordinate system 1-1. B The PNP algorithm is used to solve for the coordinates of feature point P in camera coordinate system 1-3. C Then, according to equation (1): Calculate coordinates P C The coordinate expression P in robot base coordinate system 1-1 B The feature point P refers to a fixed corner point on the chessboard calibration board; It is calculated from the robot's motion parameters. Let the initial values ​​of the hand-eye matrix be those to be determined. Step 3: Solve for the initial values ​​of the hand-eye matrix. It contains a rotational component R h2e Translation component t h2e Establish the hand-eye matrix equation, as shown in equation (2): In the formula For the sample acquired in the i-th photo, the homogeneous form of the coordinates of feature point P in the camera coordinate system 1-3; The initial values ​​of the hand-eye matrix are solved using the linear least squares method. and the initial hand-eye matrix The rotational component R in h2e Perform Euler angle transformation to obtain the rotation matrix R, ensuring the orthogonality of the rotation matrix R; Step 4: Initialize the hand-eye matrix First optimization: Construct an initial optimization model H1 for the hand-eye matrix, and use the LM nonlinear optimization method to initialize the hand-eye matrix. The first optimization is performed, resulting in the optimized hand-eye matrix. The initial optimization model H1 includes the error function W1 and loss function L1 from the first LM optimization; Step 5: Optimize the hand-eye matrix based on the outlier screening method after the first optimization. A second optimization is performed: the initial optimization model H1 of the hand-eye matrix is ​​modified to obtain the secondary optimization model H2, and then the LM nonlinear optimization method with the inclusion of a sample selection method is used to optimize the hand-eye matrix after the first optimization. A second optimization is performed to obtain the optimized hand-eye matrix. The outlier screening mentioned above refers to outlier detection of sample points and removal of abnormal values ​​from the samples; the LM nonlinear optimization method with outlier screening added is based on the LM algorithm, with an outlier screening method added to the iterative part; the correction of model H1 refers to optimizing the error function W1 and the loss function L1 to obtain the quadratic optimization model H2; the quadratic optimization model H2 includes the corrected error function W2 and the corrected loss function L2 from the second LM optimization with the sample screening method.

2. The method for bilayer nonlinear optimization monocular vision hand-eye calibration based on outlier sample screening according to claim 1, characterized in that: In step 1, the robot end-effector pose is adjusted and the chessboard calibration board image is captured by a monocular camera. The corner points of the chessboard calibration board are distributed as 4 corner points in the horizontal direction and 3 corner points in the vertical direction. Adjusting the robot end-effector pose means that the position and posture of the robot end-effector are required to change during the shooting process.

3. The method for bilayer nonlinear optimization monocular vision hand-eye calibration based on outlier sample screening according to claim 1, characterized in that: In step 2, the coordinates P of feature point P in robot base coordinate system 1-1 are calculated. B The coordinate P B The calculation process is as follows: The PNP algorithm is used to solve for the coordinates of feature point P in camera coordinate system 1-3. C According to equation (1), the coordinates of feature point P in robot base coordinate system 1-1 can be obtained. B .

4. The method for bilayer nonlinear optimization monocular vision hand-eye calibration based on outlier sample screening according to claim 1, characterized in that: In step 3, the initial value of the hand-eye matrix is ​​solved using the linear least squares method. and the initial hand-eye matrix rotational component R h2e Perform Euler angle transformation to ensure the orthogonality of the rotation matrix R; this involves at least the following five steps: Step 4-1: For each shooting posture, the feature points in the n images are: P1, P2, ..., P n Its position in the robot's base coordinate system 1-1 remains unchanged, therefore Equation (1) can be written as equation (3): in, and These are the transformation matrices from the robot's end-effector TCP coordinate system 1-2 to the robot's base coordinate system 1-1 in the i-th and j-th image samples, respectively. ; Step 4-2: ... and Rewritten as equation (4): Among them, R i and t i These are the pose matrices of the robot's end effector in TCP coordinate system 1-2 relative to the robot's base coordinate system 1-1 for the i-th image. The rotation matrix and translation vector; R j and t j These are the pose matrices of the robot's end effector in TCP coordinate system 1-2 relative to the robot's base coordinate system 1-1 for the j-th image. The rotation matrix and translation vector; the matrix equation is obtained from equations (3) and (4), as shown in equation (5): Where, x i , y i , z i Let r1, r2, and r3 be the three-dimensional coordinate components of the same feature point P in the i-th image in camera coordinate system 1-3, and let r1, r2, and r3 be the rotation matrix R to be determined. h2e Let A be the three column vectors; let A be the left coefficient matrix, X be the unknowns of the hand-eye matrix, and b be the right coefficient matrix; Step 4-3: Solve the matrix equation using the least squares method. The least squares solution of the matrix equation is shown in equation (6): After solving for the initial hand-eye matrix X, that is, the initial value of the hand-eye matrix... Hand-eye matrix rotational component R h2e Translation component t h2e As shown in equation (7): Rotational component R h2e It is derived from equation (6), which does not meet the requirement that the rotation matrix R must be an orthogonal matrix, and orthogonalization is required; Step 4-4: Initialize the hand-eye matrix It is represented as shown in equation (8): Hand-eye matrix The rotational component R in h2e Perform Euler angle transformation to determine the transformation angles of the x, y, and z axes of the camera coordinate system 1-3 around the x, y, and z axes of the robot's end effector TCP coordinate system 1-2 during the rotation. As shown in equation (9): Step 4-5: Use the inverse Euler angle transformation to find the rotation matrix R, as shown in equation (10): Therefore, the initial value of the hand-eye matrix As shown in equation (11):

5. The method for bilayer nonlinear optimization monocular vision hand-eye calibration based on outlier sample screening according to claim 1, characterized in that: Construct an optimization model H for the hand-eye matrix, and use the LM nonlinear optimization method to initialize the hand-eye matrix. The first optimization is performed, resulting in the optimized hand-eye matrix. It includes at least the following two steps: Step 5-1: Based on the fact that the coordinates of feature point P in world coordinate system 1-1 remain unchanged, establish an initial optimization model H1. The initial optimization model H1 includes the error function W1 and loss function L1 of LM optimization. The error function W1 is shown in equation (12): in, These are the rotation angle optimization variables around the x-axis, y-axis, and z-axis, respectively; t x , t y , t z Let x, y, and z be the optimization variables of the translation vector, respectively. The loss function L1 of the initial optimization model H1 is shown in equation (13): Step 5-2: Using the error function W1 and loss function L1 from equations (12) and (13), the LM algorithm is used to initialize the hand-eye matrix. The first optimization is performed, resulting in the optimized hand-eye matrix. The Euler angles are represented as shown in equation (14):

6. The method for bilayer nonlinear optimization monocular vision hand-eye calibration based on outlier sample screening according to claim 1, characterized in that: The initial optimization model H1 of the hand-eye matrix is ​​modified to obtain the secondary optimization model H2. Then, the LM nonlinear optimization method with the inclusion of a sample selection method is used to optimize the hand-eye matrix after the first optimization. A second optimization is performed to obtain the optimized hand-eye matrix. It includes at least the following six steps: Step 6-1: Optimize the hand-eye matrix after the first step. The Euler angle representation is converted into a matrix representation, as shown in equation (15): Step 6-2: Use the method of calculating the mean to obtain the standard point P. S The coordinate values ​​in the robot's base coordinate system 1-1 are shown in equation (16): Where, x s , y s , z s These are the standard point P. S The x, y, and z coordinate components in the robot's base coordinate system 1-1; Step 6-3: Correct the initial optimization model H1 and substitute the standard point P. S The corrected error function W2 is shown in equation (17): The corrected loss function L2 is shown in equation (18): in, Let be the error function of the i-th sample under the modified model; Step 6-4: Initialize the iteration-related parameters for the second optimization and substitute them into the hand-eye matrix after the first optimization. These are the initial values ​​for the second optimization iteration; Step 6-5: Determine if the iteration count m and error e meet the stopping requirements. If the error e is less than the set error threshold e', stop the iteration; otherwise, obtain the step size Δh for this iteration. If the step size Δh is less than the set step size threshold Δh', stop the iteration; otherwise, update the hand-eye matrix. Parameters related to the iteration of the LM algorithm; Step 6-6: Mark outliers for sample points in each iteration; obtain the number of iterations m that have not been filtered; if the number reaches s, filter the sample points; the filtering step refers to traversing all samples to determine the number of times the samples have been marked in the above s iterations, and considering sample points with a number of markings exceeding 0.5*s as sample points with large errors, and removing all sample points with large errors from the sample point set.

7. The method for bilayer nonlinear optimization monocular vision hand-eye calibration based on outlier sample screening according to claim 6, characterized in that: The outlier labeling method in Step 6-6 calculates the k-th local outlier factor for each sample point based on the sample point density and labels the outliers. It includes at least the following four steps: Step 7-1: Calculate P for each sample point L reach_dist, the k-th reachable distance in the k-th distance neighborhood k (O L , P L As shown in equation (19): Where, d k (O L ) represents the neighborhood point O L The k-th distance, i.e., the sample point O L The distance to the k-th nearest neighbor, d(O L , P L ) represents the neighborhood point O L Point P L The distance; Step 7-2: Calculate P for each sample point L Locally achievable density lrd k (P L As shown in equation (20): Where, N k (P L ) is P L The set of all points in the k-th distance neighborhood; Step 7-3: Calculate the Local Outlier Factor (LOF) for each point. k (P L As shown in equation (21): Step 7-4: Mark the sample points with the largest local outlier factor in the first t% and consider them as outliers in the current iteration. When the local outlier factor of all sample points is less than σ, the sample points are considered to have a low degree of abnormality and no outliers are marked in the current iteration.

Images