A hand-eye calibration method based on the registration of planar polygon contour point sets

Abstract

This invention discloses a hand-eye calibration method based on the registration of a planar polygonal contour point set. The steps are as follows: S1, design a calibration reference object with a polygonal contour; S2, use a line laser contour sensor on the end flange of a robot to perform multi-point scanning on each edge contour at different poses to collect multiple point cloud contour data; S3, set the ideal target position of the calibration reference object, construct a target vertex set, and initialize the hand-eye calibration parameters; S4, construct a fitting vertex set of the polygonal contour based on the point cloud contour data, and perform coarse registration with the target vertex set; S5, construct a coarse registration contour feature point set and a coarse registration projection feature point set based on the ideal target position, and obtain the optimal solution for the hand-eye calibration parameters by minimizing the distance difference between the matching point pairs of the two; S6, design a hand-eye calibration performance evaluation index to evaluate and select the optimal solution for the hand-eye calibration parameters. This method has high registration efficiency and accuracy, low cost, and good stability.

Description

Technical Field

[0001] This invention relates to the field of robot hand-eye calibration technology based on line laser contour sensors, and particularly to a hand-eye calibration method based on the registration of planar polygon contour point sets. Background Technology

[0002] With the continuous improvement of intelligent manufacturing levels in industry and the increasing demands for production efficiency and product quality, robot-driven intelligent vision measurement, guidance, and positioning technologies are being widely applied and have become an important part of future intelligent manufacturing. Among them, robot hand-eye calibration methods are a key technology for realizing intelligent manufacturing and have significant practical value for achieving high-precision manufacturing.

[0003] The shape and machining accuracy of the calibration reference are key factors affecting the accuracy of robot hand-eye calibration. Commonly used calibration references include spheres, cylinders, local planes, and straight edges. Among them, the standard sphere has good spatial symmetry, making it easy to construct calibration models, so there is a lot of research on it. However, its machining and maintenance costs are high, and subtle errors in the spherical contour can introduce nonlinear disturbances into the calibration system, thereby reducing calibration accuracy and robustness. Using cylindrical features, single-plane features, and straight-edge features establishes geometric constraint equations by studying the contour features and spatial distribution characteristics of the calibration reference, and then constructs and solves a nonlinear optimization model. Although this calibration method is more flexible and reduces the machining difficulty of the reference, it still has some drawbacks.

[0004] The published patent WO2021012124A1 uses a camera to capture the projection of a laser onto a calibration board and records the coordinates of the projection in the camera coordinate system. The calibration transformation matrix is ​​calculated based on at least three projection coordinates and the pose coordinates of the robot arm's end effector. The system components are relatively complex, and the calibration accuracy is closely related to the accuracy of the camera, laser, and calibration board. The published patent CN119359775A proposes a robot-based line laser calibration method and device. This technology uses a line laser sensor to scan a calibration board containing solid circles of different radii and extract two-dimensional image information. The hand-eye calibration matrix is ​​solved by jointly calculating the coordinates of the center of the solid circles in the robot coordinate system and the line laser sensor coordinate system. Its calibration accuracy is closely related to the contour processing accuracy and consistency of multiple solid circles on the calibration board. The published patent CN115371564A proposes a method and system for calibrating the relative pose of a line laser sensor and a robot flange. The calibration block of this technology contains at least four sets of semi-cylinders arranged radially on the upper surface. Without moving the industrial robot, the line laser sensor only needs to measure the calibration block once. At the same time, the optical dynamic tracking system and the matching light pen are used to complete the measurement of the pose of the calibration block. The calibration solution is based on matrix equation operation, without the need for optimal solution calculation. The method is simple and the result is highly accurate. However, it requires a high-precision optical dynamic tracking system, so the calibration cost is relatively high.

[0005] Publicly available patent CN112549018A proposes a rapid hand-eye calibration method for robots using line lasers. This method uses a thimble with a pointed tip as the calibration reference. The thimble is illuminated by repeatedly changing the orientation of the line laser camera, and the three axial components of the calibration transformation matrix are recorded. A calibration-correction-calibration method is used to obtain the hand-eye transformation matrix. However, since the center beam of the line laser must coincide with the tip of the thimble each time it is illuminated, deviations caused by human factors inevitably exist, thus reducing calibration accuracy. Publicly available patent CN111986268A proposes a hand-eye calibration method for 3D line laser scanning cameras. This method uses a regular triangular pyramid as the calibration reference. The robot uses a 3D line scanning camera to collect and record the coordinates of the pyramid's vertices in both the line laser coordinate system and the base coordinate system. An equivalent equation is established based on these vertices to derive the calibration matrix. This method has a high processing cost for the calibration object, and the acquisition of vertex coordinates introduces systemic bias, reducing calibration accuracy.

[0006] Therefore, it is necessary to design a hand-eye calibration method that has an easy-to-manufacture calibration reference structure, can guarantee the accuracy of the machining contour, and can obtain high-precision calibration results. Summary of the Invention

[0007] The purpose of this invention is to provide a hand-eye calibration method based on planar polygon contour point set registration to solve the above-mentioned technical problems.

[0008] Therefore, the technical solution of the present invention is as follows:

[0009] A hand-eye calibration method based on the registration of planar polygon contour point sets, comprising the following steps:

[0010] S1. Design a calibration reference object, which is a platform with a polygonal outline on the top surface. The polygonal outline has closure, asymmetry and boundedness. The top surface of the platform and its bottom surface are connected by a slope.

[0011] S2. Fix the calibration reference object within the robot's workspace and control the line laser profile sensor fixed on the robot's end flange to scan the feature points of each side profile on the polygonal profile multiple times in different poses to collect multiple point cloud profile data; the feature points are multiple points evenly distributed at equal intervals on each side profile.

[0012] S3. In the robot's base coordinate system, set the ideal target position of the calibration reference object, calculate the ideal position coordinates of each vertex of its polygonal contour, and construct the target vertex set; initialize the hand-eye calibration parameters;

[0013] S4. Extract the coordinates of contour feature points from multiple point cloud contour data, and calculate the fitted position coordinates of each vertex of the polygon contour on the calibration reference in the base coordinate system based on the initialized hand-eye calibration parameters, so as to construct a fitted vertex set; perform coarse registration between the fitted vertex set and the target vertex set to obtain the coarse registration transformation matrix.

[0014] S5. Using the coarse registration transformation matrix, the coordinates of the contour feature points in the base coordinate system are transformed into the coordinates of the coarse registration contour feature points, and a coarse registration contour feature point set is constructed. Based on the target vertex set, the straight line equation of each side contour on the polygon contour is determined, and the coarse registration contour feature points are projected onto the straight line equation of the corresponding side contour to obtain the coordinates of the coarse registration projected feature points, and a coarse registration projected feature point set is constructed. The objective function is set with the goal of minimizing the distance difference between each matching point pair in the coarse registration contour feature point set and the coarse registration projected feature point set, and fine registration is carried out from the coarse registration contour feature point set to the coarse registration projected feature point set to obtain the optimal solution of the hand-eye calibration parameters.

[0015] S6. Design hand-eye calibration performance evaluation indicators to evaluate and screen hand-eye calibration parameters.

[0016] Furthermore, in step S1, the calibration reference is designed as a platform with an asymmetrical right-angled triangular outline on the top surface, and the top surface of the platform and its bottom surface are connected by a ramp, with the angle between the ramp and the bottom surface of the platform being 40°~60°.

[0017] Furthermore, in step S2, the spacing between adjacent scanned feature points on each edge contour is 2mm to 3mm.

[0018] Furthermore, in step S2, the collected point cloud contour data are filtered and outlier removal is performed; wherein, the filtering process uses the mean filtering method or the Gaussian filtering method; and the outlier removal process uses the clustering method or the distance threshold method.

[0019] Further, in step S3, the hand-eye calibration parameters include: a homogeneous transformation matrix between the end flange coordinate system and the base coordinate system, which is a fixed matrix and is obtained based on the robot pose parameters; and a homogeneous transformation matrix between the sensor coordinate system and the end flange coordinate system, which is a matrix to be optimized, with initial estimates obtained through on-site direct measurement or 3D software mapping. Among these, the end flange coordinate system is a coordinate system constructed based on the robot end flange, and the sensor coordinate system is a coordinate system constructed based on the line laser profile sensor.

[0020] In the hand-eye calibration parameters of step S3, the homogeneous transformation matrix between the end flange coordinate system and the base coordinate system is obtained based on the robot pose parameters; the initial estimate of the homogeneous transformation matrix between the sensor coordinate system and the end flange coordinate system is obtained by direct on-site measurement or 3D software mapping.

[0021] Furthermore, the specific implementation steps of step S4 are as follows:

[0022] S401. Extract the coordinates of the contour feature points and the coordinates of other points coplanar with the polygon contour from each point cloud contour data. After coordinate system transformation, obtain the coordinates of the contour feature points and the coordinates of other points coplanar with the polygon contour in the base coordinate system. The two are used to construct the fitting point set in the base coordinate system.

[0023] S402. Based on the set of fitted points constructed in step S401, a fitted plane is obtained by fitting.

[0024] S403. Extract the coordinates of the contour feature points on each side contour from the coordinates of the contour feature points in the entire base coordinate system, and project them onto the fitting plane to construct the projection feature point set of each side contour.

[0025] S404. Based on the projection feature point set of each side contour, perform straight line fitting on each side contour, and obtain the coordinates of the intersection points between the fitted straight lines to obtain the coordinates of each fitted vertex of the polygon contour, and construct the fitted vertex set.

[0026] S405. The Kabsch algorithm is used to perform coarse registration between the fitted vertex set and the target vertex set to obtain the coarse registration transformation matrix.

[0027] Furthermore, the specific implementation steps of step S5 are as follows:

[0028] S501. Using the coarse registration transformation matrix, transform the coordinates of the contour feature points in the base coordinate system to obtain the coordinates of the coarse registration contour feature points, and construct the coarse registration contour feature point set.

[0029] S502. Based on the target vertex set, determine the equation of the straight line of each side profile on the polygonal contour;

[0030] S503. Extract the coordinates of the coarse registration contour feature points on each side contour and project them onto the straight line equation of the corresponding side contour to obtain the coordinates of the coarse registration projection feature points and construct the coarse registration projection feature point set.

[0031] S504. Construct an objective function and iteratively implement the Kabsch algorithm to achieve fine registration from the coarse registration feature point set to the coarse registration projection feature point set, so as to obtain the optimal solution of the homogeneous transformation matrix between the sensor coordinate system and the end flange coordinate system in the hand-eye calibration parameters; objective function The expression is:

[0032] ,

[0033] In the formula, Let m be the fine registration transformation matrix for the l-th iteration, and m be the number of contour feature points. and Let the coordinates of the coarse registration contour feature points and their corresponding coarse registration projection feature points be obtained in the l-th iteration. j The feature point number is the outline feature point number. Let be the set of rotation and translation matrices for the l-th iteration.

[0034] Furthermore, in step S504, the fine registration process from the coarse registration feature point set to the coarse registration projection feature point set is implemented as follows:

[0035] 1) Generate a set of candidate rotation matrices using an adaptive evolution strategy based on the covariance matrix. Translation matrix To constitute the current iteration process That is, the first l The homogeneous transformation matrix between the sensor coordinate system and the end flange coordinate system in the next iteration;

[0036] 2) Based on the current iteration process First, the coordinates of the contour feature points extracted from the point cloud contour data are... Coordinates of other points coplanar with the polygon outline Transformed into the coordinates of the contour feature points in the base coordinate system of the l-th iteration. The coordinates of other points coplanar with the polygon contour in the base coordinate system of the l-th iteration. To construct the set of fitted points for the l-th iteration; and to obtain the fitted plane for the l-th iteration using the set of fitted points for the l-th iteration. And the coordinates of the contour feature points in the base coordinate system for all l-th iterations. The coordinates of the contour feature points on each edge contour are extracted and then projected sequentially onto the fitting plane of the l-th iteration. The projected feature points on each edge contour are obtained, and a set of projected feature points for each edge contour in the base coordinate system in the l-th iteration is constructed. For each edge contour, a straight line is fitted. By calculating the coordinates of the intersection points between the fitted lines, the set of fitted vertices for the l-th iteration is constructed. Finally, the Kabsch algorithm is used to fit the vertex set in the l-th iteration. With the target vertex set Perform coarse registration to obtain the coarse registration transformation matrix of the l-th iteration. ;

[0037] 3) Using the coarse registration transformation matrix of the l-th iteration For the coordinates of the contour feature points in the base coordinate system of the l-th iteration The transformation is performed to obtain the coordinates of the coarse registration contour feature points in the l-th iteration. And construct the coarse registration contour feature point set for the l-th iteration. ;

[0038] 4) Coordinates of the coarse registration contour feature points in all l-th iterations The coordinates of coarse registration contour feature points on each edge contour are extracted and projected onto the target vertex set. The equation of the straight line corresponding to the edge profile is obtained. The coordinates of the coarse registration projection feature points in the l-th iteration are obtained above. And construct the coarse registration projection feature point set for the l-th iteration. ;

[0039] 5) The coarse registration transformation matrix of the l-th iteration Considered as the fine registration transformation matrix of the current l-th iteration And it is matched with the coarse registration contour feature point set of the l-th iteration. and the coarse registration projection feature point set of the l-th iteration Substitute the values ​​into the objective function to calculate the objective function value for the current l-th iteration;

[0040] 6) Repeat steps 1) through 5) until the objective function value converges to its minimum value. The iteration ends at this point. The corresponding rotation matrix during the iteration process is... Translation matrix The optimal solution for the homogeneous transformation matrix between the sensor coordinate system and the end flange coordinate system.

[0041] Furthermore, the performance evaluation index for hand-eye calibration consists of side length loss error and contour loss error.

[0042] Furthermore, the specific implementation steps of step S6 are as follows:

[0043] S601. Based on the optimal solution of hand-eye calibration parameters obtained in step S5, the polygonal contour is reconstructed to obtain the reconstructed vertex set, and the length of each edge contour is calculated based on the reconstructed vertex set.

[0044] S602. Based on the target vertex set and the reconstructed vertex set, calculate the side length loss error LE for each edge of the polygonal contour. K And the contour loss error PLE of the polygonal contour, the calculation expression of which is:

[0045] ,

[0046] In the formula, Let K be the length of the contour of the Kth edge calculated based on the reconstructed vertex set. Let n be the length of the Kth edge contour calculated based on the target vertex set, and n be the number of edge contours.

[0047] S603, Set the side length loss error threshold and the contour loss error threshold, and when the side length loss error of each side contour on the polygon contour is LE K When all values ​​are below the side length loss error threshold and the contour loss error PLE is below the contour loss error threshold, the optimal solution of the hand-eye calibration parameters is determined to meet the registration requirements.

[0048] Compared with existing technologies, the beneficial effects of this hand-eye calibration method based on planar polygon contour point set registration include: 1) The calibration reference designed by this method meets the registration requirements while having a simple structure, easily guaranteed contour accuracy, and low processing and registration application costs; 2) In the specific registration process of this method, the coarse registration method uses planar polygon fitting vertices to form registration point pairs with target vertices, and the fine registration method uses contour line projection to generate target contour line feature points that correspond one-to-one with the current contour line feature points, and uses projection constraints to establish a reliable correspondence between point pairs, eliminating the need for point-to-point search to find nearest neighbors in traditional registration methods, effectively improving registration efficiency and accuracy; 3) This method is also equipped with a side length loss error LE design. K The hand-eye calibration performance evaluation index, along with contour loss error (PLE), can quantify and filter the registration accuracy of hand-eye calibration parameters. Through a complete calibration-evaluation-screening process, it ensures the accuracy and stability of hand-eye calibration result points. Attached Figure Description

[0049] Figure 1 This is a flowchart of the hand-eye calibration method based on planar polygon contour point set registration according to the present invention;

[0050] Figure 2 This is a top view of the calibration reference object in an embodiment of the present invention;

[0051] Figure 3 This is a schematic diagram showing the positional arrangement of the robot, the line laser profile sensor, and the calibration reference in an embodiment of the present invention;

[0052] Figure 4 This is a schematic diagram of the laser lines used by a linear laser profile sensor to scan multiple feature points on each edge profile of a calibration reference object from three different directions using three different postures.

[0053] Figure 5 This is a schematic diagram of the process of coarsely registering the fitted position coordinates of each vertex of the polygonal contour on the calibration reference with the ideal target position of each vertex of the polygonal contour in step S4 of the present invention.

[0054] Figure 6 This is a schematic diagram showing the comparison between a line laser beam emitted by the line laser profile sensor and the line laser sampling profile curve drawn from the corresponding collected point cloud profile data in step S4 of this embodiment of the invention.

[0055] Figure 7 This is a schematic diagram illustrating the change of the contour feature point set obtained after the fine registration operation in step S5 in an embodiment of the present invention relative to the coarse registration contour feature point set in the initial step S4. Detailed Implementation

[0056] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention.

[0057] See Figures 1-7 The specific implementation steps of the hand-eye calibration method based on the registration of planar polygon contour point sets are described below.

[0058] S1. Design a calibration reference object, which is a platform with a polygonal outline on its top surface. The polygonal outline is closed, asymmetrical, and bounded. The top surface of the platform and its bottom surface are connected by a slope. The angle between the slope and the bottom surface of the platform is generally 40° to 60°.

[0059] In the design of the calibration reference in step S1, the purpose of its polygonal contour being asymmetric and closed is to ensure effective registration and the existence of a unique solution; while the purpose of the polygonal contour being bounded is to ensure that the calibration reference is located within the robot's workspace.

[0060] like Figure 2 As shown, the calibration reference in this embodiment is designed as a frustum with an asymmetrical right-angled triangular profile on its top surface. The top surface of the frustum and its bottom surface are connected by a ramp, and the angle between the ramp and the bottom surface of the frustum is 60°. In this asymmetrical right-angled triangular profile, the right-angle vertex is designated as A1, and the other two vertices are designated as A2 and A3, respectively. Correspondingly, the two right-angled sides are designated as A1A2 and A1A3, and the hypotenuse is designated as A2A3.

[0061] Compared with other types of polygonal contours, the asymmetric right-angled triangle contour of this embodiment is the simplest polygon that satisfies the bounded plane and has a closed contour. It is formed by only three closed lines, which makes it very easy to achieve high-precision processing and relatively low cost.

[0062] In practical applications, such as Figure 3 As shown, the calibration reference is preferably fixed horizontally on a substrate. Through holes are provided at the four corners of the substrate so that the calibration reference can be horizontally fixed at a designated position through the substrate.

[0063] S2. Fix the calibration reference designed in step S1 within the robot's workspace, and control the line laser profile sensor fixed on the robot's end flange to scan the feature points of each side profile of the polygonal profile multiple times (≥2 times) in different poses to collect multiple point cloud profile data. Each side profile of the polygonal profile has multiple scan feature points, which are evenly distributed at equal intervals on the side profile, with a spacing of 2mm to 3mm between adjacent scan feature points.

[0064] For robots, the end effector is the robot's hand, and the line laser profile sensor is the robot's eye. Only through precise hand-eye calibration can the robot obtain the contour data of the target object based on the line laser profile sensor (eye) and accurately drive the end effector to perform precise trajectory movements.

[0065] To achieve the above objectives, such as Figure 3 As shown, the calibration reference object is placed horizontally and fixed within the robot's workspace; in the figure, B represents the robot base, and F... B This corresponds to the base coordinate system; E represents the robot end effector flange, F E This corresponds to the end flange coordinate system; S represents the line laser profile sensor, which is fixed on the robot's end flange, and F... S This corresponds to the sensor coordinate system; C represents the calibration reference, which is fixed to the robot's adjacent side via a horizontal base plate.

[0066] In this embodiment, each side of the asymmetrical right-angled triangle contour has at least 10 scanning feature points, and these feature points are evenly distributed at equal intervals along the contour. The spacing between adjacent scanning feature points on each side is set to 2mm to 3mm. Therefore, when the line laser contour sensor scans each side of the asymmetrical right-angled triangle contour, it acquires several point cloud contour data lines passing through the scanning feature points.

[0067] In step S2, different poses specifically refer to the line laser profile sensor sequentially scanning multiple feature points on each edge profile from different directions under various different poses. For example... Figure 4 The diagram illustrates a laser line sensor scanning multiple feature points on each side profile of a calibration reference object using three distinct postures and from three different directions. Based on the shape characteristics of the asymmetrical right-angled triangle profile and the arrangement of the scanning feature points in this embodiment, each scan can simultaneously pass through the scanning feature points on two adjacent side profiles, resulting in high calibration efficiency. This is another advantage of the structural design of the calibration reference object with an asymmetrical right-angled triangle profile on its top surface in this embodiment.

[0068] During each scan, the line laser from the line laser contour sensor typically intersects with two side contours on the polygonal contour. Therefore, two points located on different side contours can be extracted simultaneously from each point cloud contour data point; these points are also called side contour feature points. Since the side contour feature points extracted from the same point cloud contour data point are mutually constrained in the data, this method of obtaining side contour feature points is more conducive to achieving accurate registration in the subsequent process.

[0069] As a preferred technical solution in this embodiment, the multiple point cloud contour data collected in step S2 are filtered and outlier removal processes are performed to remove noisy and abnormal data points from each point cloud contour data before proceeding to step S3, thereby improving the data processing quality. Specifically, the filtering process uses mean filtering or Gaussian filtering; the outlier removal process uses clustering or distance thresholding methods.

[0070] S3. In the base coordinate system, set the ideal target position of the calibration reference object and calculate the ideal position coordinates of each vertex of its polygonal contour to construct the target vertex set; initialize the hand-eye calibration parameters used for registration.

[0071] The specific implementation steps of step S3 are described below.

[0072] S301. Set the ideal target position of the calibration reference object; the ideal target position can be located at any position within the robot's workspace, in order to generate a set of reference data for subsequent registration.

[0073] In this embodiment, see Figure 5 For ease of calculation, the ideal target position of the calibration reference is set as: the right-angled vertex of the asymmetric right-angled triangle profile. A 1. Coordinate system with base F B The origin O B When they overlap, their two side profiles, i.e., the side profiles, are considered to be overlapping. A 1 A 2 and edge contour A 1 A 3. Relative to the base coordinate system F B of X B shaft and Y B Axis coincidence.

[0074] S302. Based on the ideal target position set in step S301, calculate the coordinates of each vertex on the polygon contour in the base coordinate system F. B The ideal target position coordinates, that is, the target vertex coordinates, are used to construct the target vertex set.

[0075] In this embodiment, the three vertices of the asymmetric right-angled triangle profile are in the base coordinate system F B The ideal target position coordinates are as follows: , Let represent the target vertex, where i is the vertex index, i = 1, 2, 3; correspondingly, the target vertex set is constructed from the ideal target position coordinates of these three vertices, which is represented as: .

[0076] S303. Initialize the hand-eye calibration parameters used for registration, including the end flange coordinate system F. E With base coordinate system F B Homogeneous transformation matrix between and sensor coordinate system F S coordinate system F of the end flange E Homogeneous transformation matrix between ;in, The transformation matrix is ​​fixed and can be specifically obtained from the robot's pose parameters; The initial estimate of the transformation matrix to be optimized can be obtained through, but is not limited to, direct on-site measurement or 3D software mapping.

[0077] S4, see also Figure 5Based on the multiple point cloud contour data collected in step S2, the coordinates of contour feature points are extracted. Based on the hand-eye calibration parameters initialized in step S3, the fitted position coordinates of each vertex of the polygon contour on the calibration reference object in the base coordinate system are calculated, and a fitted vertex set is constructed. The fitted vertex set and the target vertex set are coarsely registered to obtain the coarse registration transformation matrix.

[0078] In this embodiment, the specific implementation process of step S4 is described as follows.

[0079] S401. Based on the angular variation between the asymmetric right-angled triangle contour and the adjacent slope on the calibration reference, extract the coordinates of contour feature points corresponding to the side contour from each point cloud contour data. After coordinate system transformation, the coordinates of the contour feature points in the base coordinate system are obtained. j is the sequence number of the contour feature point; based on the coordinates of the contour feature points in each point cloud contour data. Extract the coordinates of other points coplanar with the asymmetric right-angled triangle contour from each point cloud contour data. After coordinate system transformation, the coordinates of other points coplanar with the asymmetric right-angled triangle outline are obtained in the base coordinate system. k represents the index of other points coplanar with the asymmetric right-angled triangle contour; furthermore, the coordinates of the contour feature points in the base coordinate system... Coordinates of other points coplanar with the contour of the asymmetric right triangle in the base coordinate system Together, we construct the set of fitted points in the base coordinate system.

[0080] like Figure 6 The diagram shows a comparison between a line laser beam emitted by a line laser profile sensor and the line laser sampling profile curve plotted from the corresponding collected point cloud profile data. In the figure, the line laser beam emitted by the line laser sampling contour curve is shown as the light blue line on the left side of the figure, and the line laser sampling contour curve drawn from the point cloud contour data is shown as the blue curve on the right side of the figure. Among them, on the line laser beam shown on the left side of the figure, points a and b are the intersection points of the laser beam with the side contours A1A2 and A2A3, respectively, which are contour feature points. Points c and d are the intersection points of the line laser beam with the outer contour of the bottom surface of the platform. Furthermore, based on the angle change between the asymmetric right-angled triangle contour and the adjacent slope on the calibration reference, the positions of the two contour feature points a and b can be determined and their coordinates extracted on the line laser sampling contour curve shown on the right side of the figure according to the change of the Z-axis coordinate. Then, based on the coordinates of these two contour feature points a and b, the coordinates of all points coplanar with the asymmetric right-angled triangle contour can be filtered from the point cloud contour data, that is, the coordinates of all laser points corresponding to the line segment ab in the line laser sampling contour curve.

[0081] The coordinates of the laser point extracted from the line laser sampling contour curve are in the sensor coordinate system F. S The coordinates of the laser point below are obtained by directly reading the X and Z axes from the linear laser sampling contour curve, with the Y axis coordinate being 0. This is to construct the base coordinate system F. B To fit the point set, the sensor coordinate system F needs to be extracted from each point cloud contour data. S Coordinates of lower contour feature points and sensor coordinate system F S Coordinates of other laser points coplanar with the asymmetric right-angled triangle profile And perform coordinate system transformation, the expression of which is:

[0082] ;

[0083] In the coordinate system transformation of step S401, Substitute the initial estimate determined in step S3.

[0084] S402. In the set of fitted points constructed in step S401, due to the instability of measurement, the coordinates of all laser points are not completely on the same plane; therefore, it is first necessary to use principal component analysis to fit the fitted plane Σ based on the set of fitted points.

[0085] S403. Coordinates of contour feature points in all base coordinate systems In the process, the coordinates of the contour feature points on each side contour are extracted and projected sequentially onto the fitting plane Σ to obtain the projected feature points on each side contour. A set of projected feature points for each side contour in the base coordinate system is then constructed. K is the outline number, and j is the outline feature point number.

[0086] S404, Based on the projection feature point set of each edge contour in the base coordinate system The least squares method is used to fit a straight line to each side profile, resulting in a fitted straight line for each side profile. The coordinates of the intersection points between the fitted straight lines are then obtained, which gives the fitted vertex coordinates of the three vertices of the asymmetric right-angled triangle profile on the calibration reference at the actual setting position. , Let i = 1, 2, 3 represent the fitted vertices; based on the coordinates of these three fitted vertices, a set of fitted vertices is constructed. .

[0087] S405. Using the Kabsch algorithm, fit the vertex set. With the target vertex set Perform coarse registration to obtain the coarse registration transformation matrix. .

[0088] Specifically, this step first obtains the target vertex set. Fitting vertex set The centroids of the two vertex sets are used to align the centroids of the two vertex sets, resulting in a decentralized target vertex set. and decentralized fitting vertex set Then, the covariance matrix H between the two decentralized vertex sets is calculated, and the coarse registration transformation matrix between the two vertex sets is obtained by using the SVD decomposition method. .

[0089] Among them, the coarse registration transformation matrix The expression is:

[0090] ,

[0091] In the formula, For coarse registration rotation matrix, This is the coarse registration translation matrix. The first set of points is specifically substituted into the target set of points. ; This is the second set of points, specifically substituted into the decentralized target vertex set. , The third set of points is specifically substituted into the fitted vertex set. , The fourth point set is specifically substituted into the decentralized fitting vertex set. Both U and V are orthogonal matrices.

[0092] Compared to traditional coarse registration methods that rely on iterative optimization, the method of this invention designs a calibration reference with a polygonal profile and calculates the fitted vertex set of the polygonal profile. With the target vertex set This invention enables coarse registration of three vertices based on the analytical properties of matrix operations, avoiding the time-consuming process of multiple iterations and significantly improving efficiency while ensuring registration accuracy. In summary, the method of this invention can quickly establish a coarse correspondence in the global scope.

[0093] S5, see also Figure 7Using a coarse registration transformation matrix, the coordinates of contour feature points in the base coordinate system are transformed into coarse registration contour feature point coordinates to construct a coarse registration contour feature point set. Based on the target vertex set, the straight line equation of each side contour on the polygon contour is determined, and the coarse registration contour feature points are projected onto the straight line equation of the corresponding side contour to obtain the coordinates of the coarse registration projected feature points to construct a coarse registration projected feature point set. The objective function is set to minimize the distance difference between each matching point pair in the coarse registration contour feature point set and the coarse registration projected feature point set, and fine registration is performed from the coarse registration contour feature point set to the coarse registration projected feature point set to obtain the optimal solution of hand-eye calibration parameters.

[0094] In this embodiment, the specific implementation process of step S5 is described as follows.

[0095] S501. Using the coarse registration transformation matrix obtained in step S4 For the base coordinate system F B Coordinates of lower contour feature points After transformation, the base coordinate system F is obtained. B Coarse registration contour feature point coordinates And a coarse registration contour feature point set is constructed. Its transformation expression is:

[0096] .

[0097] S502, Based on the target vertex set Determine the equation of the straight line on each side of the contour of an asymmetric right triangle. K is the edge contour number, K=1, 2, 3.

[0098] S503, Coordinates of all coarse registration contour feature points The coordinates of coarse registration contour feature points on each edge contour are extracted and projected onto the corresponding straight line equation of the edge contour. The coordinates of the coarse registration projection feature points are obtained. And construct the coarse registration projection feature point set. Among them, due to the coarse registration projection feature points Coordinates of feature points of the coarse registration contour All are derived from the coordinates of the contour feature points in the base coordinate system. The transformation yields a correspondence between the two; based on the number of contour feature points being m, the coarse registration contour feature point set and the coarse registration projection feature point set can also form m sets of registration point pairs.

[0099] The method of this invention adopts a strategy of projecting the coordinates of coarse registration contour feature points onto the straight line equation of the corresponding edge contour to obtain the coordinates of the corresponding coarse registration projected feature points, thereby forming a coarse registration projected feature point set. In essence, the corresponding coarse registration projected feature points are used as the nearest neighbors of fine registration to determine the reliable correspondence between point pairs. This operation method changes the paradigm of relying on point pairs to search for nearest neighbors in the traditional fine registration process, effectively improving the registration efficiency.

[0100] S504. Constructing the objective function Based on the Kabsch algorithm, iterative registration of the coarse registration feature point set to the coarse registration projection feature point set is achieved to obtain the sensor coordinate system F in the hand-eye calibration parameters. S coordinate system F of the end flange E Homogeneous transformation matrix between The optimal solution.

[0101] Among them, the objective function is based on minimizing the distance difference between each matching point pair in the coarse registration contour feature point set and the coarse registration projection feature point set. The expression is defined as:

[0102] ,

[0103] In the formula, l represents the number of iterations. Let m be the fine registration transformation matrix for the l-th iteration, and m be the number of contour feature points. and Let the coordinates of the coarse registration contour feature points and their corresponding coarse registration projection feature points be obtained in the l-th iteration. Let be the set of rotation and translation matrices for the l-th iteration.

[0104] The specific implementation steps of step S504 are as follows:

[0105] 1) Generate a set of candidate rotation matrices using an adaptive evolution strategy based on the covariance matrix. Translation matrix To constitute the current iteration process That is, the homogeneous transformation matrix between the sensor coordinate system and the end flange coordinate system in the l-th iteration; where, in the first iteration (i.e., l=1), The initial estimate determined in step S3 is used. The coarse registration transformation matrix obtained in step S4 is used. , and Substitute them into the coarse registration contour feature point set obtained in step S501 respectively. The coarse registration projection feature point set is obtained from step S503. ;

[0106] 2) Based on the current iteration process Using the same processing method as in step S4, the coordinates of the contour feature points extracted from the point cloud contour data are first... Coordinates of other points coplanar with the contour of the asymmetric right triangle Transformed into the coordinates of the contour feature points in the base coordinate system of the l-th iteration. The coordinates of other points coplanar with the asymmetric right-angled triangle profile in the base coordinate system of the l-th iteration. To construct the set of fitted points for the l-th iteration; and to obtain the fitted plane for the l-th iteration using the set of fitted points for the l-th iteration. And the coordinates of the contour feature points in the base coordinate system for all l-th iterations. The coordinates of the contour feature points on each edge contour are extracted and then projected sequentially onto the fitting plane of the l-th iteration. The projected feature points on each edge contour are obtained, and a set of projected feature points for each edge contour in the base coordinate system in the l-th iteration is constructed. For each edge contour, a straight line is fitted. By calculating the coordinates of the intersection points between the fitted lines, the set of fitted vertices for the l-th iteration is constructed. Finally, the Kabsch algorithm is used to fit the vertex set in the l-th iteration. With the target vertex set Perform coarse registration to obtain the coarse registration transformation matrix of the l-th iteration. ;

[0107] 3) Using the coarse registration transformation matrix of the l-th iteration For the coordinates of the contour feature points in the base coordinate system of the l-th iteration The transformation is performed to obtain the coordinates of the coarse registration contour feature points in the l-th iteration. And construct the coarse registration contour feature point set for the l-th iteration. ;

[0108] In step 3), the transformation expression is specifically as follows:

[0109] ,

[0110] In the formula, This is the homogeneous transformation matrix between the end flange coordinate system and the base coordinate system. For the first l The homogeneous transformation matrix between the sensor coordinate system and the end flange coordinate system in the next iteration;

[0111] 4) Coordinates of the coarse registration contour feature points in all l-th iterations The coordinates of coarse registration contour feature points on each edge contour are extracted and projected onto the target vertex set. The equation of the straight line corresponding to the edge profile is obtained. The coordinates of the coarse registration projection feature points in the l-th iteration are obtained above. And construct the coarse registration projection feature point set for the l-th iteration. ;

[0112] 5) The coarse registration transformation matrix of the l-th iteration Considered as the fine registration transformation matrix of the current l-th iteration And it is matched with the coarse registration contour feature point set of the l-th iteration. and the coarse registration projection feature point set of the l-th iteration Substitute into the objective function In the process, calculate the objective function value for the current l-th iteration;

[0113] 6) Repeat steps 1) through 5) until the objective function value converges to its minimum value. The iteration ends at this point. The corresponding rotation matrix during the iteration process is... Translation matrix The optimal solution of the homogeneous transformation matrix between the sensor coordinate system and the end flange coordinate system, together with the homogeneous transformation matrix between the end flange coordinate system and the base coordinate system, constitutes the optimal solution of the hand-eye calibration parameters.

[0114] In step 1) above, if the calculation result of the objective function does not meet the iteration convergence condition after the current iteration process ends, the calculation results of the objective function up to the current time are sorted from smallest to largest, and the hand-eye calibration parameters corresponding to the first 50% of the objective function calculation results are taken as the parent population to be retained and used in the next iteration calculation.

[0115] In practical applications, rotation matrix Alternatively, the RPY angle can be used to represent the angle, depending on the actual situation.

[0116] like Figure 7 The image shows the set of contour feature points obtained after the fine registration operation in step S5. Compared to the coarse registration contour feature point set in the initial step S4 The change is specifically manifested in that the projection point on the ideal contour line is closer, and thus the asymmetric right-angled triangle contour reconstructed from it has a higher degree of alignment with the asymmetric right-angled triangle contour of the reference object at the ideal target position.

[0117] S6. Design a performance evaluation index for hand-eye calibration, which consists of side length loss error and contour loss error, to quantify the relative optimization accuracy of hand-eye calibration parameters and realize the evaluation and selection of hand-eye calibration parameters.

[0118] In this embodiment, the specific implementation steps of step S6 are as follows:

[0119] S601. Based on step S5, obtain the sensor coordinate system F. S coordinate system F of the end flange E The optimal solution of the homogeneous transformation matrix between the two is used to reconstruct the contour of the asymmetric right triangle in the same way as in step S4, in order to obtain the reconstructed vertex set. Based on reconstructing vertex sets Calculate the lengths of the three sides of the profile;

[0120] S602. Calculate the side length loss error (LE) for each side of an asymmetric right-angled triangle profile. K And the contour loss error PLE of the asymmetric right-angled triangle contour, the calculation expressions for both are as follows:

[0121] ,

[0122] In the formula, Let K be the length of the contour of the Kth edge calculated based on the reconstructed vertex set. The length of the Kth edge contour is calculated based on the target vertex set, and n is the number of edge contours. In this embodiment, n=3.

[0123] S603. Set the side length loss error threshold (0.15 in this embodiment) and the contour loss error threshold (0.1 in this embodiment), and when the side length loss error LE of each contour calculated in step S602 is... K When all values ​​are below the side length loss error threshold, and the contour loss error PLE is below the contour loss error threshold, the optimal solution for the current hand-eye calibration parameters (i.e., the sensor coordinate system F) is determined. S coordinate system F of the end flange E The optimal solution of the homogeneous transformation matrix between them satisfies the calibration accuracy requirements; otherwise, the current hand-eye calibration result should be discarded, and the calibration experiment should be carried out again considering the nonlinear error based on the hand-eye calibration system, and / or, considering the insufficient amount of point cloud contour data and the instability of data acquisition in the experiment, the setting of the scanning pose and the number of scanning feature points of the line laser contour sensor in step S2 should be changed until the hand-eye calibration result meets the judgment requirements of S603.

[0124] To demonstrate the advantages of the method of the present invention in actual hand-eye calibration operations, the method of this embodiment was applied to actual robot hand-eye calibration to test its practical application effect.

[0125] In practical application testing, such as Figure 2As shown, the calibration reference has an asymmetrical right-angled triangular profile, where the length of side profile A1A3 is 25mm and the length of side profile A1A2 is 50mm; in the base coordinate system F B The target vertex coordinates are set as A1(0,0,0), A2(-50,0,0) and A3(0,25,0) respectively.

[0126] The surface contour of a calibration reference object was acquired using a robot and a line laser contour sensor, resulting in five sets of contour data. Each set of data was scanned using three distinct robot poses in three different directions, with ten line laser sampling contour curves scanned under each pose. The robot poses used in each set of contour data were ensured to be different from each other. The five sets of feature data were combined; selecting k sets yielded a total of 3k robot poses. When k = 1, 2, 3, 4, the corresponding number of poses were 3, 6, 9, and 12, respectively. Subsequently, the side length loss error LE was used... K The contour loss error (PLE) is used to quantify and evaluate the calibration results under different pose numbers.

[0127] Table 1 below shows a comparison of the evaluation indicators of the calibration results calibrated by combining the poses of three robots.

[0128] Table 1:

[0129]

[0130] Table 2 below shows a comparison of the evaluation indicators of the calibration results for the calibration of the 12 robot combination postures.

[0131] Table 2:

[0132]

[0133] The comparison of the evaluation indicators in Tables 1 and 2 shows that as the number of calibration attitudes increases, the side length loss error LE... K The PLE (Potential Loss Error) value is continuously decreasing, indicating that acquiring sufficient robot heterogeneous poses to collect point cloud contour data can continuously improve the accuracy and performance of hand-eye calibration. Furthermore, compared to Table 1, Table 2 shows that when a sufficient amount of robot heterogeneous poses and point cloud contour data is acquired, even the presence of data with significant errors in the point cloud contour data (see combination index 1 and combination indexes (1,2,3,4)) does not affect the final accurate registration, demonstrating a certain degree of error tolerance. In addition, although the calibration and registration methods of this invention are simple, the designed complete calibration-evaluation-screening process effectively provides feedback on different loss error results, guiding the rapid selection of the most accurate hand-eye calibration parameters to ensure the accuracy of the hand-eye calibration result points, and exhibits good stability.

[0134] Furthermore, from the perspective of reconstructing a standard sphere with a diameter of 38.1 mm, the differences in calibration accuracy between the method of this invention and the traditional single-step method based on the standard sphere are compared and analyzed.

[0135] Specifically, the hand-eye calibration parameters obtained under 12 robot pose combinations using the method of this invention are used to reconstruct the standard sphere, and the reconstruction diameter deviation and spherical projection error are calculated. The specific calculation results are shown in Table 3 below. Correspondingly, 10 sets of hand-eye calibration parameters are obtained based on the single-step method of the standard sphere, and these calibration results are used to reconstruct the contour of the standard sphere. Similarly, the reconstruction diameter deviation and spherical projection error are calculated, and the specific calculation results are shown in Table 4 below. Among them, the spherical projection error refers to the absolute value of the difference between the distance from the spherical contour measurement data point to the center of the reconstructed sphere and the reconstruction radius. This index is used to reflect the distribution of each spherical contour measurement point on the reconstructed sphere.

[0136] Table 3:

[0137]

[0138] Table 4:

[0139]

[0140] Comparing Tables 3 and 4, it can be seen that the average diameter deviation of the standard sphere reconstructed using the method of the present invention is 0.0185 mm, which is significantly smaller than the average diameter deviation of 0.0555 mm of the standard sphere reconstructed using the traditional single-step method based on the standard sphere. Similarly, the spherical projection error of the standard sphere reconstructed using the method of the present invention, both in terms of maximum value and average value, is lower than the corresponding spherical projection error of the standard sphere reconstructed using the single-step method based on the standard sphere. This proves that the method of the present invention has better stability and reliability than the traditional single-step method based on the standard sphere.

[0141] In summary, the advantages of the hand-eye calibration method based on planar polygon contour point set registration in this invention are as follows: First, the calibration reference object designed by this method has a simple structure and does not require processing complex curved surfaces, resulting in low processing costs and easy assurance of contour accuracy. Second, the coarse registration method and fine registration method designed by this method can automatically establish a reliable correspondence between registration point pairs, eliminating the need to use the point-to-point search method to find the nearest neighbor in traditional registration methods, thus improving registration efficiency. Third, in the fine registration method, the corresponding coarse registration contour feature point coordinates are obtained by projecting them onto the straight line equation of the corresponding side contour. The coordinates of the quasi-projected feature points are used to form a coarse registration projection feature point set, that is, the corresponding projection points are used as the nearest neighbors for fine registration, thus establishing a reliable correspondence between point pairs. This changes the paradigm of relying on point pairs to search for nearest neighbors in the traditional fine registration process and improves registration efficiency. Finally, this method only uses a line laser contour sensor in the calibration process, and can complete the calibration without the need for other expensive detection equipment. It also designs a calibration-evaluation-screening system to quantify the relative accuracy of hand-eye calibration parameters in order to screen out the best hand-eye calibration results. It has strong universality and good prospects for industrial application and promotion.

[0142] In summary, the above-disclosed embodiments are merely illustrative of the present invention. The embodiments do not describe all details in detail, nor do they limit the invention to the specific implementations described. Any modifications and substitutions made by those skilled in the art within the scope of this invention should be included within the protection scope of this invention.

Claims

1. A hand-eye calibration method based on the registration of planar polygon contour point sets, characterized in that, The steps are as follows: S1. Design a calibration reference object, which is a platform with a polygonal outline on the top surface. The polygonal outline has closure, asymmetry and boundedness. The top surface of the platform and its bottom surface are connected by a slope. S2. Fix the calibration reference object within the robot's workspace and control the line laser profile sensor fixed on the robot's end flange to scan the feature points of each side profile on the polygonal profile multiple times in different poses to collect multiple point cloud profile data; the feature points are multiple points evenly distributed at equal intervals on each side profile. S3. In the robot's base coordinate system, set the ideal target position of the calibration reference object, calculate the ideal position coordinates of each vertex of its polygonal contour, and construct the target vertex set; initialize the hand-eye calibration parameters; S4. Extract the coordinates of contour feature points from multiple point cloud contour data, and based on the initialized hand-eye calibration parameters, calculate the fitted position coordinates of each vertex of the polygon contour on the calibration reference in the base coordinate system, and construct the fitted vertex set; perform coarse registration between the fitted vertex set and the target vertex set to obtain the coarse registration transformation matrix. S5. Using the coarse registration transformation matrix, transform the coordinates of the contour feature points in the base coordinate system into the coordinates of the coarse registration contour feature points, and construct the coarse registration contour feature point set. Based on the target vertex set, the equation of the straight line of each edge contour on the polygonal contour is determined. The coarse registration contour feature points are projected onto the straight line equation of the corresponding edge contour to obtain the coordinates of the coarse registration projection feature points and construct the coarse registration projection feature point set. The objective function is set with the goal of minimizing the distance difference between each matching point pair in the coarse registration contour feature point set and the coarse registration projection feature point set. Fine registration is then performed from the coarse registration contour feature point set to the coarse registration projection feature point set to obtain the optimal solution of the hand-eye calibration parameters. S6. Design hand-eye calibration performance evaluation indicators to evaluate and select the optimal solution for hand-eye calibration parameters.

2. The hand-eye calibration method based on planar polygon contour point set registration according to claim 1, characterized in that, In step S1, the calibration reference is designed as a platform with an asymmetrical right-angled triangular outline on the top surface, and the top surface of the platform and its bottom surface are connected by a ramp, with the angle between the ramp and the bottom surface of the platform being 40°~60°.

3. The hand-eye calibration method based on planar polygon contour point set registration according to claim 1, characterized in that, In step S2, the spacing between adjacent scanned feature points on each edge contour is 2mm to 3mm.

4. The hand-eye calibration method based on planar polygon contour point set registration according to claim 1, characterized in that, In step S2, the collected point cloud contour data are filtered and outlier removal is performed; the filtering process uses the mean filtering method or the Gaussian filtering method; the outlier removal process uses the clustering method or the distance threshold method.

5. The hand-eye calibration method based on planar polygon contour point set registration according to claim 1, characterized in that, In step S3, the hand-eye calibration parameters include: a homogeneous transformation matrix between the end flange coordinate system and the base coordinate system constructed based on the robot end flange, which is obtained from the robot pose parameters; and a homogeneous transformation matrix between the sensor coordinate system and the end flange coordinate system constructed based on the line laser profile sensor, the initial estimated value of which is obtained by direct on-site measurement or 3D software mapping.

6. The hand-eye calibration method based on planar polygon contour point set registration according to claim 1, characterized in that, The specific implementation steps of step S4 are as follows: S401. Extract the coordinates of the contour feature points and the coordinates of other points coplanar with the polygon contour from each point cloud contour data. After coordinate system transformation, obtain the coordinates of the contour feature points and the coordinates of other points coplanar with the polygon contour in the base coordinate system. The two are used to construct the fitting point set in the base coordinate system. S402. Based on the set of fitted points constructed in step S401, a fitted plane is obtained by fitting. S403. Extract the coordinates of the contour feature points on each side contour from the coordinates of the contour feature points in the entire base coordinate system, and project them onto the fitting plane to construct the projection feature point set of each side contour. S404. Based on the projection feature point set of each side contour, perform straight line fitting on each side contour, and obtain the coordinates of the intersection points between the fitted straight lines to obtain the coordinates of each fitted vertex of the polygon contour, and construct the fitted vertex set. S405. The Kabsch algorithm is used to perform coarse registration between the fitted vertex set and the target vertex set to obtain the coarse registration transformation matrix.

7. The hand-eye calibration method based on planar polygon contour point set registration according to claim 6, characterized in that, The specific implementation steps of step S5 are as follows: S501. Using the coarse registration transformation matrix, transform the coordinates of the contour feature points in the base coordinate system to obtain the coordinates of the coarse registration contour feature points, and construct the coarse registration contour feature point set. S502. Based on the target vertex set, determine the equation of the straight line of each side profile on the polygonal contour; S503. Extract the coordinates of the coarse registration contour feature points on each edge contour and project them onto the straight line equation of the corresponding edge contour to obtain the coordinates of the coarse registration projection feature points and construct the coarse registration projection feature point set. S504. Construct the objective function and iteratively implement the fine registration from the coarse registration feature point set to the coarse registration projection feature point set based on the Kabsch algorithm, so as to obtain the optimal solution of the homogeneous transformation matrix between the sensor coordinate system and the end flange coordinate system in the hand-eye calibration parameters. objective function The expression is: ， In the formula, Let m be the fine registration transformation matrix for the l-th iteration, and m be the number of contour feature points. and Let the coordinates of the coarse registration contour feature points and their corresponding coarse registration projection feature points be obtained in the l-th iteration. j The feature point number is the outline feature point number. Let be the set of rotation and translation matrices for the l-th iteration.

8. The hand-eye calibration method based on planar polygon contour point set registration according to claim 7, characterized in that, In step S504, the fine registration process from the coarse registration feature point set to the coarse registration projection feature point set is implemented as follows: 1) Generate a set of candidate rotation matrices using an adaptive evolution strategy based on the covariance matrix. Translation matrix To constitute the current iteration process That is, the first l The homogeneous transformation matrix between the sensor coordinate system and the end flange coordinate system in the next iteration; 2) Based on the current iteration process First, the coordinates of the contour feature points extracted from the point cloud contour data are... Coordinates of other points coplanar with the polygon outline Transformed into the coordinates of the contour feature points in the base coordinate system of the l-th iteration. The coordinates of other points coplanar with the polygon contour in the base coordinate system of the l-th iteration. To construct the set of fitted points for the l-th iteration; and to obtain the fitted plane for the l-th iteration using the set of fitted points for the l-th iteration. And the coordinates of the contour feature points in the base coordinate system for all l-th iterations. The coordinates of the contour feature points on each edge contour are extracted and then projected sequentially onto the fitting plane of the l-th iteration. The projected feature points on each edge contour are obtained, and a set of projected feature points for each edge contour in the base coordinate system in the l-th iteration is constructed. For each edge contour, a straight line is fitted. By calculating the coordinates of the intersection points between the fitted lines, the set of fitted vertices for the l-th iteration is constructed. Finally, the Kabsch algorithm is used to fit the vertex set in the l-th iteration. With the target vertex set Perform coarse registration to obtain the coarse registration transformation matrix of the l-th iteration. ; 3) Using the coarse registration transformation matrix of the l-th iteration For the coordinates of the contour feature points in the base coordinate system of the l-th iteration The transformation is performed to obtain the coordinates of the coarse registration contour feature points in the l-th iteration. And construct the coarse registration contour feature point set for the l-th iteration. ; 4) Coordinates of the coarse registration contour feature points in all l-th iterations The coordinates of coarse registration contour feature points on each edge contour are extracted and projected onto the target vertex set. The equation of the straight line of the corresponding side profile is obtained. The coordinates of the coarse registration projection feature points in the l-th iteration are obtained above. And construct the coarse registration projection feature point set for the l-th iteration. ; 5) The coarse registration transformation matrix of the l-th iteration Considered as the fine registration transformation matrix of the current l-th iteration And it is matched with the coarse registration contour feature point set of the l-th iteration. and the coarse registration projection feature point set of the l-th iteration Substitute the values ​​into the objective function to calculate the objective function value for the current l-th iteration; 6) Repeat steps 1) through 5) until the objective function value converges to its minimum value. The iteration ends at this point. The corresponding rotation matrix during the iteration process is... Translation matrix The optimal solution for the homogeneous transformation matrix between the sensor coordinate system and the end flange coordinate system.

9. The hand-eye calibration method based on planar polygon contour point set registration according to claim 1, characterized in that, The performance evaluation index for hand-eye calibration consists of side length loss error and contour loss error.

10. The hand-eye calibration method based on planar polygon contour point set registration according to claim 9, characterized in that, The specific implementation steps of step S6 are as follows: S601. Based on the optimal solution of hand-eye calibration parameters obtained in step S5, the polygonal contour is reconstructed to obtain the reconstructed vertex set, and the length of each edge contour is calculated based on the reconstructed vertex set. S602. Based on the target vertex set and the reconstructed vertex set, calculate the side length loss error LE for each edge of the polygonal contour. K And the contour loss error PLE of the polygonal contour, the calculation expression of which is: ， In the formula, Let K be the length of the contour of the Kth edge calculated based on the reconstructed vertex set. Let n be the length of the Kth edge contour calculated based on the target vertex set, and n be the number of edge contours. S603. Set the side length loss error threshold and the contour loss error threshold. When the side length loss error of each side contour on the polygon contour is lower than the side length loss error threshold and the contour loss error is lower than the contour loss error threshold, determine that the optimal solution of the hand-eye calibration parameters meets the registration requirements.

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