Spherical surface and plane combined constraint multi-beam three-dimensional laser scanner calibration method

Abstract

The invention relates to a spherical surface and plane combined constraint multi-beam three-dimensional laser scanner calibration method, which comprises the following steps of: establishing a multi-beam three-dimensional laser scanner imaging model based on an observation principle of a multi-beam three-dimensional laser scanner, and defining a system error; establishing a spherical equation of the spherical target plate and a plane equation of the planar target plate based on the geometrical characteristics of the planar target plate and the spherical target plate, and obtaining a spherical-plane combined constraint equation; calculating an initial exterior element of the multi-beam three-dimensional laser scanner by utilizing spatial similarity transformation; calculating a system error based on the spherical surface-plane combined constraint equation and the initial exterior element; and substituting the system error into a multi-beam three-dimensional laser scanner imaging model, correcting the point cloud coordinate, and evaluating the calibration effect according to the flatness of the point cloud before and after correction. Compared with the prior art, the three-dimensional laser scanner has the advantages that the detection capability of calibration on angle errors is improved, and the observation precision of the three-dimensional laser scanner in a three-dimensional space is improved.

Description

Technical Field

[0001] This invention relates to the field of surveying and mapping science and technology, and in particular to a calibration method for a multi-beam three-dimensional laser scanner with combined spherical and planar constraints. Background Technology

[0002] In the field of modern surveying and 3D reconstruction, multi-beam 3D laser scanners have become indispensable key equipment due to their ability to efficiently acquire large-area 3D point cloud data. Compared with single-point lidar, multi-beam lidar can detect multiple laser points simultaneously, quickly acquiring more discrete 3D points within the field of view, greatly improving operational efficiency. It has been widely used in many fields such as topographic mapping, architectural modeling, industrial inspection, and cultural heritage protection.

[0003] However, due to various factors such as instrument structural defects, limitations in industrial manufacturing capabilities, and complex measurement environments, multi-beam 3D laser scanners generate significant data uncertainty during observation and data processing. Deviations in the scanner's internal mechanical structure, instability of electronic components, and interference during laser emission and reception all contribute to systematic errors. These systematic errors not only significantly affect observation accuracy but also have a cumulative effect during data processing, severely reducing the reliability and accuracy of the final measurement results.

[0004] Therefore, self-calibration of multi-beam 3D laser scanners has become a key method to ensure the accuracy of measurement data. Its core lies in achieving quantitative compensation for systematic errors through geometric constraints. Self-calibration methods typically rely on target devices with specific geometric features. By establishing a mathematical relationship between the instrument's observation coordinate system and the reference coordinate system, precise calibration of systematic errors such as ranging and angle measurement can be achieved. For example, Chinese patent CN104820217B discloses a calibration method for a multi-normal-plane multi-element linear array detection imaging lidar, which performs calibration by acquiring high-precision observation data from multiple planar target plates in different orientations.

[0005] The geometric design of the calibration target directly determines the dimension and strength of the constraints, and different shapes of calibration targets each have their own advantages and disadvantages. Traditional planar targets are widely used due to their simple structure and low cost, but they can only provide two-dimensional planar distance constraints, resulting in limited ability to separate systematic errors and difficulty in effectively detecting angular measurement errors. Spherical targets construct three-dimensional spatial constraints through a sphere center reference point, which can simultaneously achieve joint calibration of distance measurement errors and angular measurement errors. However, their high precision manufacturing tolerances and high cost, coupled with the easy attenuation of reflected signals from the spherical edge, make data acquisition difficult, limiting their widespread application.

[0006] In summary, existing calibration methods for multi-beam 3D laser scanners have limitations in terms of accuracy, cost, and ease of operation, making it difficult to meet the growing demand for high-precision and high-efficiency measurements. Therefore, a new calibration method is needed that comprehensively considers various constraints to improve calibration accuracy and efficiency, which has significant practical implications and application value. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the existing technology by providing a multi-beam three-dimensional laser scanner calibration method with joint constraints of spherical and planar surfaces, which can achieve high-precision calculation of calibration parameters and improve the absolute accuracy of calibration parameters.

[0008] The objective of this invention can be achieved through the following technical solutions:

[0009] A method for calibrating a multi-beam 3D laser scanner with joint constraints of spherical and planar surfaces, wherein the calibration equipment includes a planar target plate and a spherical target plate, and the multi-beam 3D laser scanner simultaneously scans the planar target plate and the spherical target plate to obtain point cloud coordinates for calibration, the method comprising:

[0010] Based on the observation principle of a multi-beam 3D laser scanner, an imaging model of the multi-beam 3D laser scanner is established, and systematic errors are defined.

[0011] Based on the geometric features of planar and spherical target plates, the spherical equation of the spherical target plate and the planar equation of the planar target plate are established, and the joint constraint equation of spherical-planar is obtained.

[0012] The initial exterior elements of a multi-beam 3D laser scanner are solved using spatial similarity transformation;

[0013] The system error is calculated based on the spherical-plane joint constraint equation and the initial exterior elements;

[0014] The system error is substituted into the imaging model of the multi-beam 3D laser scanner to correct the point cloud coordinates, and the calibration effect is evaluated based on the flatness of the point cloud before and after correction.

[0015] Furthermore, the expression for the multi-beam three-dimensional laser scanner imaging model is as follows:

[0016]

[0017] Where, x′ 0_scanner y′ 0_scanner and z′ 0_scanner L' represents the coordinates of the origin point where the laser beam is emitted. k This is the ranging value, where n is the laser emission direction vector;

[0018]

[0019] θ k =(22.49-0.642·(i-1))×0.001,i=1,2,...64

[0020] Where, n x n y and n z Let θ be the components of the direction vector n in the three directions of the coordinate axes. k θ′ is the angle between the k-th laser beam, the light source, and the first galvanometer mirror. x This represents the corrected horizontal angle observation, θ′. y This represents the corrected vertical angle observation value, where i is the number of distance measuring units.

[0021] Furthermore, the systematic errors include exterior element errors, angle measurement errors, and distance measurement errors;

[0022] The expression for the angle measurement error is:

[0023] θ x '=θ x -c-c1·θ x

[0024] θ y '=θ y -ξ-ξ1·θ y

[0025] Where c and ξ are the fixed systematic error terms for angle measurement, c1 and ξ1 are the proportional systematic error coefficients, and θ′ x This represents the corrected horizontal angle observation, θ′. y θ represents the corrected vertical angle observation. x θ represents the observed horizontal angle. y Represents the observed value of the vertical angle;

[0026] The expression for the ranging error is:

[0027] L' k =L k -l k

[0028] Among them, L' k This is the corrected distance measurement value, L. k This is the original distance measurement value, l k This represents the error term of the fixed distance measurement system.

[0029] Furthermore, the process of establishing the spherical equation of the spherical target plate and the planar equation of the planar target plate, and obtaining the spherical-planar joint constraint equation includes: using a total station and a ground laser scanner to measure the three-dimensional coordinates of feature points on the surface of the planar target plate and the spherical target plate, and using the least squares method to fit the spherical equation and the planar equation respectively, obtaining the planar parameters of the planar equation and the spherical parameters of the spherical equation, and combining the planar equation and the spherical equation to obtain the spherical-planar joint constraint equation.

[0030] Furthermore, the process of fitting the plane equation includes:

[0031] The three-dimensional coordinates of at least three non-collinear measurement points on a planar target plate are obtained using a total station and a ground laser scanner.

[0032] An error function is constructed based on the plane equation of the target plate. The distance from each measurement point to the target plate is taken as the error term, and the sum of the squares of the distances from all measurement points to the target plate is minimized. The optimal parameters are obtained as plane parameters using the Lagrange multiplier method.

[0033] Furthermore, the process of fitting the equation of the sphere includes:

[0034] Using a total station and a ground laser scanner, the surface points of the spherical target plate were measured from multiple angles to obtain the three-dimensional coordinates of at least four non-coplanar measurement points;

[0035] An error function is constructed based on the spherical equation of the spherical target plate. The distance from each measurement point to the spherical target plate is taken as the error term, and the sum of the squares of the distances from all measurement points to the spherical target plate is minimized. The optimal parameters are obtained as spherical parameters according to the Lagrange multiplier method. The spherical parameters include the coordinates of the center of the spherical target plate and the radius of the spherical target plate.

[0036] Furthermore, the plane equation of the planar target plate is expressed as follows:

[0037] AX+BY+CZ+D=0

[0038] Where A, B, C, and D are planar parameters, and X, Y, and Z are coordinate variables of points on the target plate;

[0039] The expression for the spherical equation of the spherical target plate is:

[0040] (XX s ) 2 +(YY s ) 2 +(ZZ s ) 2 -R 2 =0

[0041] Among them, X S YS and Z S Let R be the coordinates of the center of the spherical target plate, and R be the radius of the spherical target plate.

[0042] The expression for the joint constraint equation of the sphere and the plane is:

[0043]

[0044] Furthermore, the initial exoscopic elements include the coordinates and attitude information of the mechanical optical center origin of the multi-beam 3D laser scanner in the external coordinate system;

[0045] The process of solving the initial exponent elements includes:

[0046] Obtain the preset coordinates of the mechanical structure points from the multi-beam 3D laser scanner and the external reference coordinates of the corresponding structure points measured by the total station;

[0047] The preset coordinates of the mechanical structure points are matched one-to-one with the external reference coordinates to form point pairs, and error equations are constructed based on the point pairs;

[0048] Based on the error equation, the optimal rotation matrix parameters are obtained using the Lagrange multiplier method, and the translation parameters are determined based on the Euler angles.

[0049] Based on the optimal rotation matrix parameters and translation parameters, the spatial similarity transformation relationship between the coordinate system of the mechanical structure points of the multi-beam 3D laser scanner and the external coordinate system is determined. The spatial similarity transformation relationship includes translation, rotation, and scaling transformation.

[0050] Based on the spatial similarity transformation relationship, the mechanical structure points of the multi-beam 3D laser scanner are transformed into the external coordinate system to obtain the coordinates and attitude information of the mechanical optical center origin of the multi-beam 3D laser scanner in the external coordinate system.

[0051] Furthermore, the process of calculating the systematic error includes:

[0052] Based on the spherical-planar joint constraint equation, and considering measurement errors, the point cloud is constrained to the planar target plate and the spherical target plate to establish a parametric mathematical model.

[0053] The parametric mathematical model is linearized, and the linearized parametric mathematical model is iteratively solved to obtain the system error.

[0054] Furthermore, the expression for the parameter mathematical model is:

[0055] f(L,X)=0

[0056] L=(θx,θy,r1,r2,…,r i )

[0057]

[0058] Where L is the set of observations, and θ x θ represents the observed horizontal angle. y Represents the vertical angle observation value, r i Let X represent the distance observation value, and X be the set of calibration parameters, where... ω, κ, ΔX, ΔY, and ΔZ are the exterior element error correction parameters, α0 is the horizontal angle measurement error parameter, θ0 is the vertical angle measurement error parameter, and ρ... channels This refers to the ranging error parameter.

[0059] Compared with the prior art, the beneficial effects of the present invention include:

[0060] 1. This invention incorporates a partial spherical target plate into a planar target plate, maintaining the low-cost advantage of the planar target plate while integrating the three-dimensional angular constraint capability of the spherical target plate. This improves the detection capability of the calibration in terms of angular errors and enhances the observation accuracy of the 3D laser scanner in three-dimensional space. It achieves an optimal balance between accuracy, cost, robustness, and practicality, providing an efficient and reliable solution for high-precision self-calibration of multi-beam 3D laser scanners. While retaining the simple structure, low manufacturing cost, and ease of popularization of the planar target plate, this invention only requires the introduction of a partial spherical target plate to achieve three-dimensional constraints, eliminating the need to rely on global surface target calibration. Compared to pure spherical target plate calibration solutions, this significantly reduces precision manufacturing and maintenance costs, while avoiding the data acquisition difficulties caused by signal attenuation at the edge of the sphere. It balances calibration accuracy and engineering practicality, making it easier to promote and apply in real-world scenarios.

[0061] 2. This invention combines the low-cost advantage of planar target plates with the three-dimensional spatial constraint capability of spherical target plates by using spherical and planar constraints to construct a complete model covering ranging error, angle measurement error and exterior orientation element error, and completes the self-calibration of a high-precision multi-beam three-dimensional laser scanner.

[0062] 3. This invention employs a spatial similarity transformation method to calculate the initial exterior orientation elements based on the preset mechanical coordinates of the mechanical structure points of the scanner and the external reference coordinates measured by the total station. The coordinates of the mechanical structure points have rigidity and high precision characteristics. Compared with the commonly used point cloud matching to achieve coordinate system transformation, the accuracy is higher, the stability and reliability of the initial pose parameters are better, and it is less affected by the quality of the point cloud.

[0063] 4. This invention establishes a joint constraint equation for the sphere and the plane, combines it with high-precision observation data, and uses the least squares method to fit the plane and sphere parameters, providing a stable geometric benchmark for error calculation. During parameter estimation, conditional adjustment with parameters and iterative calculations ensure more stable results for the system error parameters and pose parameters. Experimental verification shows that the calibration parameters exhibit consistent trends under different working conditions, proving the method's strong robustness and adaptability to complex measurement environments.

[0064] 5. This invention clarifies the complete process from imaging model establishment, constraint equation construction, and initial exterior orientation element calculation to parameter iterative estimation and accuracy evaluation; it calculates the initial exterior orientation elements through spatial similarity transformation, providing reliable initial values ​​for parameter optimization; it uses mature mathematical methods such as the Lagrange multiplier method and the least squares method to fit the target equation and calculate the transformation parameters, ensuring process standardization; and it uses point cloud flatness as an intuitive evaluation index, which can quantify the calibration effect and facilitate operation and repeated verification.

[0065] 6. Multibeam 3D laser scanners primarily output sparse point clouds, and traditional point target calibration requires a large amount of dense point data, limiting its applicability. This invention, through geometric constraints on planes and spheres, can construct stable constraints even in sparse point cloud scenarios by fitting equations of feature points on the target surface. This enables accurate calibration of the system errors of multiple ranging units and multiple laser beams in multibeam scanners, and is suitable for various high-precision 3D measurement scenarios such as topographic mapping, architectural modeling, and industrial inspection. Attached Figure Description

[0066] Figure 1 This is a flowchart of the method of the present invention;

[0067] Figure 2 This is a comparison of calibration parameters under different working conditions in the embodiments of the present invention;

[0068] Figure 3 This is a comparison chart of relative accuracy under the GK1 working condition in this embodiment of the invention;

[0069] Figure 4 This is a comparison chart of relative accuracy under the GK2 working condition in this embodiment of the invention;

[0070] Figure 5 This is a comparison chart of relative accuracy under the GK3 working condition in this embodiment of the invention;

[0071] Figure 6 This is a comparison chart of relative accuracy under the GK4 working condition in this embodiment of the invention;

[0072] Figure 7 This is a comparison chart of absolute accuracy under the GK1 working condition in this embodiment of the invention;

[0073] Figure 8This is a comparison chart of absolute accuracy under the GK2 working condition in this embodiment of the invention;

[0074] Figure 9 This is a comparison chart of absolute accuracy under the GK3 working condition in this embodiment of the invention;

[0075] Figure 10 This is a comparison chart of absolute accuracy under the GK4 operating condition in an embodiment of the present invention. Detailed Implementation

[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0077] Example 1

[0078] This invention relates to a multi-beam 3D laser scanner, specifically a multi-beam sparse 3D laser scanner, which is a type of 3D laser scanning device. Its key feature is the simultaneous scanning using multiple laser beams (multiple ranging units), enabling efficient acquisition of 3D point cloud data of the target. It is primarily used for the rapid acquisition of 3D spatial information. Self-calibration of the multi-beam 3D laser scanner is a crucial method for ensuring the accuracy of measurement data; its core lies in achieving quantitative compensation for systematic errors through geometric constraints.

[0079] The target plate devices used in the self-calibration method include planar target plates and spherical target plates. Traditional planar target plates are widely used due to their simple structure and low cost, but they can only provide two-dimensional planar distance constraints, which limits the ability to separate system errors and makes it difficult to effectively detect angle measurement errors. Spherical target plates construct three-dimensional spatial constraints through the sphere's center reference point, which can simultaneously achieve joint calibration of distance measurement errors and angle measurement errors. However, their spherical precision manufacturing tolerances are high and the cost is expensive. Furthermore, the reflection signal from the spherical edge is easily attenuated, making data acquisition difficult and limiting their widespread application.

[0080] This embodiment discloses a calibration method for a multi-beam 3D laser scanner with joint constraints of spherical and planar surfaces. The calibration equipment includes a planar target plate and a spherical target plate. The multi-beam 3D laser scanner simultaneously scans the planar target plate and the spherical target plate to obtain point cloud coordinates. The specific steps of this method are as follows: Figure 1 As shown, steps S1-S5 are included, and the specific content of each step is as follows:

[0081] Step S1: Based on the observation principle of the multi-beam 3D laser scanner, establish the imaging model of the multi-beam 3D laser scanner and define the systematic error.

[0082] The expression for the imaging model of a multi-beam 3D laser scanner is:

[0083]

[0084] Where, x′ 0_scanner y′ 0_scanner and z′ 0_scanner L' represents the coordinates of the origin point where the laser beam is emitted. k This is the ranging value, where n is the laser emission direction vector;

[0085]

[0086] θ k =(22.49-0.642·(i-1))×0.001,i=1,2,...64

[0087] Where, n x n y and n z Let θ be the components of the direction vector n in the three directions of the coordinate axes. k θ′ is the angle between the k-th laser beam, the light source, and the first galvanometer mirror. x This represents the corrected horizontal angle observation, θ′. y This represents the corrected vertical angle observation value, where i is the number of distance measuring units.

[0088] This imaging model is a mathematical framework that describes how scanner observations are transformed into the three-dimensional coordinates of the target. It defines the ideal observation process of the scanner. By establishing the model, the scanner's original observation data—horizontal angle, vertical angle, and the distance measurement values ​​of each distance measuring unit—can be correlated with the coordinates of the target point in three-dimensional space.

[0089] Systematic error refers to the error between the observation system composed of a multi-beam 3D laser scanner and the ideal state, including exterior element error, angle measurement error and distance measurement error;

[0090] The mathematical expression for angular measurement error is:

[0091] θ x '=θ x -c-c1·θ x

[0092] θ y '=θ y -ξ-ξ1·θ y

[0093] Where c and ξ are the fixed systematic error terms for angle measurement, which are constant errors that do not change with the angle magnitude, such as instrument installation eccentricity and mechanical zero-position deviation; c1 and ξ1 are the proportional systematic error coefficients, which are errors proportional to the angle itself, such as the angle magnification / reduction error caused by shaft tilt, and the magnitude of the error changes linearly with the angle; θ′ x This represents the corrected horizontal angle observation, θ′. y θ represents the corrected vertical angle observation. x θ represents the observed horizontal angle. y Represents the observed value of the vertical angle;

[0094] The mathematical expression for ranging error is:

[0095] L' k =L k -l k

[0096] Among them, L' k This is the corrected distance measurement value, L. k This is the original distance measurement value, l k This represents the fixed systematic error term in distance measurement, which is a constant error that does not change with the distance.

[0097] Step S2: Based on the geometric features of the planar target plate and the spherical target plate, establish the spherical equation of the spherical target plate and the planar equation of the planar target plate, and obtain the spherical-planar joint constraint equation.

[0098] The process of establishing the spherical equations of the spherical target plate and the planar equations of the planar target plate, and obtaining the joint spherical-planar constraint equations includes:

[0099] The total station and a ground laser scanner were used to measure the three-dimensional coordinates of feature points on the surface of planar and spherical target plates; the total station obtained the three-dimensional coordinates of multiple feature points on the target plate through its own angle and distance measurement functions.

[0100] The least squares method is used to fit the equations of the sphere and the plane respectively, and the plane parameters of the plane equation and the spherical parameters of the sphere equation are obtained.

[0101] By combining the plane equation and the sphere equation, we obtain the sphere-plane joint constraint equation.

[0102] The process of fitting the plane equation includes:

[0103] The three-dimensional coordinates of at least three non-collinear measurement points on a planar target plate are obtained using a total station and a ground laser scanner. In practical applications, more points, such as 16 or 20 points, are measured to improve the fitting accuracy.

[0104] An error function is constructed based on the plane equation of the target plate. The distance from each measurement point to the target plate is taken as the error term, and the sum of the squares of the distances from all measurement points to the target plate is minimized.

[0105] The optimal parameters are obtained using the Lagrange multiplier method and used as plane parameters.

[0106] The process of fitting the equation of a sphere includes:

[0107] Using a total station and a ground laser scanner, the surface points of the spherical target plate are measured from multiple angles to obtain the three-dimensional coordinates of at least four non-coplanar measurement points; in practical applications, 10 to 20 points are usually measured to improve accuracy.

[0108] An error function is constructed based on the spherical equation of the spherical target plate. The distance from each measurement point to the spherical target plate is taken as the error term, and the sum of the squares of the distances from all measurement points to the spherical target plate is minimized.

[0109] The optimal parameters are obtained using the Lagrange multiplier method and are used as spherical parameters, which include the coordinates of the center of the spherical target and the radius of the spherical target.

[0110] The expression for the plane equation of the planar target plate is:

[0111] AX+BY+CZ+D=0

[0112] Where A, B, C, and D are planar parameters, and X, Y, and Z are coordinate variables of points on the target plate;

[0113] The expression for the spherical equation of the spherical target plate is:

[0114] (XX s ) 2 +(YY s ) 2 +(ZZ s ) 2 -R 2 =0

[0115] Among them, X S Y S and Z S Let R be the coordinates of the center of the spherical target plate, and R be the radius of the spherical target plate.

[0116] The expression for the joint constraint equations of the sphere and the plane is:

[0117]

[0118] Step S3: Solve the initial exterior elements of the multibeam 3D laser scanner using spatial similarity transformation.

[0119] The initial exoplanar elements include the coordinates and attitude information of the mechanical optical center origin of the multibeam 3D laser scanner in the external coordinate system;

[0120] The process of solving for the initial exponent elements includes:

[0121] Obtain the preset coordinates of the mechanical structure points from the multi-beam 3D laser scanner and the external reference coordinates of the corresponding structure points measured by the total station;

[0122] The preset coordinates of the mechanical structure points are matched one-to-one with the external reference coordinates to form point pairs, and error equations are constructed based on the point pairs;

[0123] Based on the error equation, the optimal rotation matrix parameters are obtained using the Lagrange multiplier method, and the translation parameters are determined based on the Euler angles.

[0124] Based on the optimal parameters of the rotation matrix and translation, the spatial similarity transformation relationship between the coordinate system of the mechanical structure point of the multi-beam 3D laser scanner and the external coordinate system is determined. The spatial similarity transformation relationship includes translation, rotation and scaling transformation.

[0125] Based on the spatial similarity transformation relationship, the mechanical structure points of the multi-beam 3D laser scanner are transformed into the external coordinate system to obtain the coordinates and attitude information of the mechanical optical center origin of the multi-beam 3D laser scanner in the external coordinate system.

[0126] Step S4: Calculate the system error based on the spherical-plane joint constraint equations and the initial exterior elements.

[0127] The process of calculating systematic error includes:

[0128] Based on the spherical-planar joint constraint equation, and considering measurement errors, the point cloud is constrained to both the planar target plate and the spherical target plate to establish a parametric mathematical model.

[0129] The linearized parameter mathematical model is then iteratively solved to obtain the system error.

[0130] The process of calculating systematic errors is actually to perform adjustment using planes and spheres as constraints with attached parameters, constraining the point cloud to the plane and the sphere, and establishing a mathematical model related to the target parameters.

[0131] The expression for the parametric mathematical model is:

[0132] f(L,X)=0

[0133] L=(θx,θy,r1,r2,…,r i )

[0134]

[0135] Where L is the set of observations, and θ x θ represents the observed horizontal angle. y Represents the vertical angle observation value, r i Let X represent the distance observation value, and X be the set of calibration parameters, where... ω, κ, ΔX, ΔY, and ΔZ are the exterior element error correction parameters, α0 is the horizontal angle measurement error parameter, θ0 is the vertical angle measurement error parameter, and ρ... channels This refers to the ranging error parameter.

[0136] X represents the parameters that need to be solved. To transform this model into a solvable form, the parametric mathematical model is further linearized. The specific expression after linearization is as follows:

[0137]

[0138] Where L0 and X0 are the initial values ​​of the observations and parameters, m is the number of observations L, and n is the number of parameters X. Let X be the correction for the i-th observation. j Let X and L represent the j-th parameter. i Let L represent the i-th observation.

[0139] From the solution form of conditional adjustment with parameters, we can obtain the expression for the solution as follows:

[0140]

[0141] in, N AA =AQA T .

[0142] Step S5: Substitute the system error into the imaging model of the multi-beam 3D laser scanner, correct the point cloud coordinates, and evaluate the calibration effect based on the flatness of the point cloud before and after correction.

[0143] Example 2

[0144] This embodiment, based on Embodiment 1 above, discloses the actual comparative experimental process and results of a multi-beam three-dimensional laser scanner calibration method with joint constraints of sphere and plane, in order to verify the effectiveness and robustness of the self-verification method proposed in Embodiment 1 above.

[0145] (1) Robustness verification

[0146] Experimental data under four working conditions (GK1-GK4) were used to compare the calibration results. The differences in calibration parameters under different working conditions were compared to verify the robustness of the calibration parameters obtained by the proposed spherical and planar joint constraint calibration method. Figure 2As shown, the overall trend of calibration parameters is consistent across different operating conditions.

[0147] (2) Validity verification

[0148] To verify the effectiveness of the proposed joint calibration method, it was compared with the calibration method using only a planar target plate. The relative accuracy (the flatness of the point cloud after calibration with calibration constraints) and absolute accuracy (the flatness of the point cloud after calibration without constraints) were used for evaluation.

[0149] like Figures 3-6 As shown, Figures 3-6 The results show the relative accuracy comparison for GK1, GK2, GK3, and GK4 data, with target plate numbers ranging from 1 to 13 and sphere numbers from 14 to 25. It can be seen that the flatness of the planar target plate is higher than that of the spherical surface. Overall, the point cloud flatness obtained by the combined calibration method is comparable to that obtained using only the planar calibration method.

[0150] As shown in Table 1, the relative accuracy improvement of the proposed joint calibration method is all above 87%.

[0151] Table 1 Relative Accuracy Table

[0152]

[0153] like Figures 7-10 As shown, Figures 7-10 This is the absolute accuracy evaluation result. Specifically, using balls 1-7 as verification data, the collected ball point cloud data were corrected using calibration parameters obtained from the proposed joint calibration method and the planar calibration method alone. Based on the comparison of point cloud flatness after correction, the proposed joint calibration method shows that the overall flatness of the point cloud after ball correction is better than the planar calibration method.

[0154] The specific flatness data are shown in Table 2. The flatness of the point cloud was calculated based on the GK1-GK4 data respectively. Compared with the plane-based calibration method, the proposed joint calibration method improved the absolute accuracy by using RMSE as the flatness measurement index. The average improvement was 0.88 cm, which shows that the proposed method is effective in improving the absolute accuracy of the point cloud after calibration.

[0155] Table 2 Absolute Precision Table

[0156]

[0157] In summary, the method proposed in Example 1, based on the traditional planar calibration method, introduces the three-dimensional spatial constraint of the spherical target plate. By constructing a systematic error parameter model that includes ranging error and angle measurement error, it achieves high-precision calculation of calibration parameters and improves the absolute accuracy of calibration parameters.

[0158] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for calibrating a multi-beam 3D laser scanner with combined spherical and planar constraints, wherein the calibration equipment includes a planar target plate and a spherical target plate, and the multi-beam 3D laser scanner simultaneously scans the planar target plate and the spherical target plate to obtain point cloud coordinates for calibration, characterized in that, The method includes: Based on the observation principle of a multi-beam 3D laser scanner, an imaging model of the multi-beam 3D laser scanner is established, and systematic errors are defined. Based on the geometric features of planar and spherical target plates, the spherical equation of the spherical target plate and the planar equation of the planar target plate are established, and the joint constraint equation of spherical-planar is obtained. The initial exterior elements of a multi-beam 3D laser scanner are solved using spatial similarity transformation; The system error is calculated based on the spherical-plane joint constraint equation and the initial exterior elements; The system error is substituted into the imaging model of the multi-beam 3D laser scanner to correct the point cloud coordinates, and the calibration effect is evaluated based on the flatness of the point cloud before and after correction.

2. The method for calibrating a multi-beam three-dimensional laser scanner with combined spherical and planar constraints according to claim 1, characterized in that, The expression for the multi-beam 3D laser scanner imaging model is: Where, x′ 0_scanner y′ 0_scanner and z′ 0_scanner L' represents the coordinates of the origin point where the laser beam is emitted. k This is the corrected ranging value, where n is the laser emission direction vector; θ k =(22.49-0.642·(i-1))×0.001,i=1,2,...64 Where, n x n y and n z Let θ be the components of the direction vector n in the three directions of the coordinate axes. k θ is the angle between the k-th laser beam, the light source, and the first galvanometer mirror. x ′ represents the corrected horizontal angle observation value, θ y ′ represents the corrected vertical angle observation value, and i is the number of distance measuring units.

3. The calibration method for a multi-beam three-dimensional laser scanner with combined spherical and planar constraints according to claim 1, characterized in that, The systematic errors include exterior element errors, angle measurement errors, and distance measurement errors; The expression for the angle measurement error is: i x '=θ x -c-c1·θ x i y '=θ y -ξ-ξ1·θ y Where c and ξ are the fixed systematic error terms for angle measurement, c1 and ξ1 are the proportional systematic error coefficients, and θ x ′ represents the corrected horizontal angle observation value, θ y ′ represents the corrected vertical angle observation value, θ x θ represents the observed horizontal angle. y Represents the observed value of the vertical angle; The expression for the ranging error is: L' k =L k -L k Among them, L' k This is the corrected distance measurement value, L. k This is the original distance measurement value, l k This represents the error term of the fixed distance measurement system.

4. The calibration method for a multi-beam three-dimensional laser scanner with combined spherical and planar constraints according to claim 1, characterized in that, The process of establishing the spherical equation of the spherical target plate and the planar equation of the planar target plate, and obtaining the spherical-planar joint constraint equation includes: measuring the three-dimensional coordinates of feature points on the surface of the planar target plate and the spherical target plate using a total station and a ground laser scanner, fitting the spherical equation and the planar equation respectively using the least squares method, obtaining the planar parameters of the planar equation and the spherical parameters of the spherical equation, and combining the planar equation and the spherical equation to obtain the spherical-planar joint constraint equation.

5. The method for calibrating a multi-beam three-dimensional laser scanner with combined spherical and planar constraints according to claim 4, characterized in that, The process of fitting the plane equation includes: The three-dimensional coordinates of at least three non-collinear measurement points on a planar target plate are obtained using a total station and a ground laser scanner. An error function is constructed based on the plane equation of the target plate. The distance from each measurement point to the target plate is taken as the error term, and the sum of the squares of the distances from all measurement points to the target plate is minimized. The optimal parameters are obtained as plane parameters using the Lagrange multiplier method.

6. The method for calibrating a multi-beam three-dimensional laser scanner with combined spherical and planar constraints according to claim 4, characterized in that, The process of fitting the equation of the sphere includes: Using a total station and a ground laser scanner, the surface points of the spherical target plate were measured from multiple angles to obtain the three-dimensional coordinates of at least four non-coplanar measurement points; An error function is constructed based on the spherical equation of the spherical target plate. The distance from each measurement point to the spherical target plate is taken as the error term, and the sum of the squares of the distances from all measurement points to the spherical target plate is minimized. The optimal parameters are obtained as spherical parameters according to the Lagrange multiplier method. The spherical parameters include the coordinates of the center of the spherical target plate and the radius of the spherical target plate.

7. The method for calibrating a multi-beam three-dimensional laser scanner with combined spherical and planar constraints according to claim 1, characterized in that, The plane equation of the planar target plate is expressed as follows: AX+BY+CZ+D=0 Where A, B, C, and D are planar parameters, and X, Y, and Z are coordinate variables of points on the target plate; The expression for the spherical equation of the spherical target plate is: (X-X s ) 2 +(Y-Y s ) 2 +(Z-Z s ) 2 -R 2 =0 Among them, X S Y S and Z S Let R be the coordinates of the center of the spherical target plate, and R be the radius of the spherical target plate. The expression for the joint constraint equation of the sphere and the plane is:

8. The method for calibrating a multi-beam three-dimensional laser scanner with combined spherical and planar constraints according to claim 1, characterized in that, The initial exoscopic elements include the coordinates and attitude information of the mechanical optical center origin of the multibeam 3D laser scanner in the external coordinate system; The process of solving the initial exponent elements includes: Obtain the preset coordinates of the mechanical structure points from the multi-beam 3D laser scanner and the external reference coordinates of the corresponding structure points measured by the total station; The preset coordinates of the mechanical structure points are matched one-to-one with the external reference coordinates to form point pairs, and error equations are constructed based on the point pairs; Based on the error equation, the optimal rotation matrix parameters are obtained using the Lagrange multiplier method, and the translation parameters are determined based on the Euler angles. Based on the optimal rotation matrix parameters and translation parameters, the spatial similarity transformation relationship between the coordinate system of the mechanical structure points of the multi-beam 3D laser scanner and the external coordinate system is determined. The spatial similarity transformation relationship includes translation, rotation, and scaling transformation. Based on the spatial similarity transformation relationship, the mechanical structure points of the multi-beam 3D laser scanner are transformed into the external coordinate system to obtain the coordinates and attitude information of the mechanical optical center origin of the multi-beam 3D laser scanner in the external coordinate system.

9. The calibration method for a multi-beam three-dimensional laser scanner with combined spherical and planar constraints according to claim 1, characterized in that, The process of calculating the systematic error includes: Based on the spherical-planar joint constraint equation, and considering measurement errors, the point cloud is constrained to the planar target plate and the spherical target plate to establish a parametric mathematical model. The parametric mathematical model is linearized, and the linearized parametric mathematical model is iteratively solved to obtain the system error.

10. The method for calibrating a multi-beam three-dimensional laser scanner with combined spherical and planar constraints according to claim 9, characterized in that, The expression for the mathematical model of the parameters is: f(L,X)=0 L=(θx,θy,r1,r2,…,r i ) Where L is the set of observations, and θ x θ represents the observed horizontal angle. y Represents the vertical angle observation value, r i Let X represent the distance observation value, and X be the set of calibration parameters, where... ω, κ, ΔX, ΔY, and ΔZ are the exterior element error correction parameters, α0 is the horizontal angle measurement error parameter, θ0 is the vertical angle measurement error parameter, and ρ... channels This refers to the ranging error parameter.

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