An adaptive calibration method for the revolution ball of a rotary scanning system

Abstract

The present application relates to the field of precision measurement, and specifically relates to a kind of revolution ball adaptive calibration method of rotary scanning system, comprising: acquisition original point cloud dataset;Encoder angle reading is normalized, based on the angle reading after normalization, calculate angle mapping coefficient;Establish the sensor installation pose model based on ZYX Euler angle rotation matrix, based on the sensor installation pose model, sensor ranging data is mapped as the correction component parallel to each axis of world coordinate system;The correction component parallel to x axis is used to calculate angle offset increment, and the normalized angle reading, angle mapping coefficient and angle offset increment are used to calculate the synthetic rotation angle trajectory under world coordinate system;Establish target function, based on target function, using variable parameter regularization optimization strategy iteration to solve calibration parameter set, obtain optimal calibration parameter.The present application effectively overcomes the restriction of calibration ball size on geometric configuration, and improves the convergence of high-dimensional parameter solving.

Description

Technical Field

[0001] This invention relates to the field of precision measurement technology, and more specifically to an adaptive calibration method for a revolution sphere in a rotating scanning system. Background Technology

[0002] Rotary scanning measurement systems are core equipment in the field of precision inspection, widely used for the morphological measurement of complex rotating parts (such as triple-eccentric butterfly valves, precision shafts, and aspherical lenses). Their core working principle involves a high-precision rotary stage driving the workpiece to rotate circumferentially, while a laser displacement sensor or confocal microscope sensor performs a linear scan along the axial direction. By synchronously acquiring encoder angle data, sensor ranging data, and stage position data, the system can reconstruct a high-density three-dimensional point cloud of the workpiece surface. Although this system boasts high measurement efficiency, its final measurement accuracy is highly dependent on the accurate calibration of sensor geometric parameters, attitude parameters, and system revolution parameters.

[0003] Existing technologies typically rely on "center alignment" calibration logic, requiring the calibration sphere's center to be strictly aligned with its rotation axis. This means the calibration sphere undergoes pure rotation within the measurement system. However, in reality, the sphere's rotation axis may not pass through its own center; its motion is actually a coupled motion of rotation and revolution. Traditional calibration methods lack a methodology for multi-parameter joint identification using the "revolutionary trajectory" generated by the standard sphere's rotation around its axis. Due to this lack of a revolution-based sphere calibration method, the system cannot effectively utilize the geometric constraint information generated by the standard sphere in an eccentric state. This results in the sensor often only observing local arc segments of the sphere during scanning, failing to obtain continuous spherical surface data across the entire circumference. This leads to nonlinear coupling between revolution parameters and sensor attitude parameters, resulting in extremely poor identifiability of key geometric parameters such as pitch angle. When dealing with high-dimensional nonlinear optimization problems, regularization terms are typically introduced to constrain attitude angle parameters during iteration, preventing physical divergence during iteration. However, existing calibration attempts often employ fixed regularization penalty coefficients, failing to dynamically adjust them based on the signal-to-noise ratio, spatial distribution density, or geometric configuration characteristics of the actual point cloud. Excessive regularization strength restricts the parameter optimization space, leading to systematic biases; conversely, insufficient strength fails to suppress outlier interference, resulting in poor convergence or extreme instability in the solution space. The calibration process, particularly in high-dimensional solution spaces, involves at least nine nonlinear parameters, including sensor reference, three-axis attitude, and revolution dynamics. Lacking dedicated optimization paths designed for the revolution trajectory, traditional Levenberg-Marquardt (LM) algorithms or Gauss-Newton methods are prone to getting trapped in local minima in high-dimensional solution spaces without high-precision initial value guidance. This not only results in low calibration success rates but may also produce logically consistent but physically flawed pseudo-solutions, introducing imperceptible systematic errors into subsequent measurements. Patent CN202310970995.3A describes a calibration method for 3D reconstruction based on bundle adjustment using calibration ball rotation. However, to reduce computational complexity, it simplifies the sensor attitude to a one-dimensional or two-dimensional tilt model, neglecting the fundamental impact of roll, pitch, and yaw three-axis coupling on the rotation angle mapping. In fact, the tangential displacement caused by the yaw angle directly leads to a shift in the geometric correspondence between the encoder angle reading and the actual sensor scanning point. Ignoring this three-axis coupling correction directly limits the system's application accuracy in sub-micron precision measurement scenarios. Summary of the Invention

[0004] To address the aforementioned technical problems, such as poor sensor attitude parameter discernibility, inability to adaptively adjust regularization coefficients, susceptibility to local optima in high-dimensional optimization, and neglect of three-axis attitude coupling effects, this invention provides an adaptive calibration method for a revolution sphere in a rotating scanning system. This invention overcomes the limitations of the calibration sphere radius on geometric configuration, establishes a complete three-axis rotation correction mathematical model, and solves the convergence problem of high-dimensional parameter solutions through a two-stage optimization strategy based on variable parameter regularization constraints, thereby achieving robust calibration under complex operating conditions.

[0005] The technical means employed in this invention are as follows:

[0006] An adaptive calibration method for the orbital sphere of a rotating scanning system includes the following steps: The calibration ball is installed in the rotary table fixture, and the rotary table is controlled to rotate at a constant angular velocity to collect the original point cloud dataset, which includes sensor axial displacement, encoder angle reading and sensor ranging data. The encoder angle readings are normalized, and the angle mapping coefficient is calculated based on the normalized angle readings. A sensor mounting pose model based on the ZYX Euler angle rotation matrix is ​​established, and the sensor ranging data is mapped into correction components parallel to each axis of the world coordinate system based on the sensor mounting pose model. The angle offset increment is calculated using the correction component parallel to the x-axis, and the composite rotation angle trajectory in the world coordinate system is calculated using the normalized angle reading, the angle mapping coefficient, and the angle offset increment. An objective function is established, and based on the objective function, a variable parameter regularization optimization strategy is used to iteratively solve the calibration parameter set to obtain the optimal calibration parameters. The objective function is established based on the sum of squared residuals between the Euclidean distance from the measurement point to the center of the calibration sphere and the radius of the calibration sphere.

[0007] Furthermore, the formula for calculating the ZYX Euler angle rotation matrix is ​​as follows:

[0008] in, Let ZYX be the Euler angle rotation matrix. The pitch angle, This is the roll angle. Yaw angle This is the fundamental rotation operator about the z-axis of the world coordinate system. For the fundamental rotation operator about the y-axis of the world coordinate system, This is the fundamental rotation operator about the x-axis of the world coordinate system. The formula for calculating the fundamental rotation operator about the x-axis of the world coordinate system is: , The formula for calculating the fundamental rotation operator about the y-axis of the world coordinate system is: , The formula for calculating the fundamental rotation operator about the z-axis of the world coordinate system is: .

[0009] Furthermore, the formula for calculating the gap ratio is:

[0010] in, ρ The gap ratio, g i The angle offset increment is calculated as the difference in encoder values ​​between two adjacent samples, using the following formula:

[0011] in, This is the increment of the angle offset. The correction component is parallel to the x-axis. r Let be the radius of rotation. The formula for calculating the synthetic rotation angle trajectory is:

[0012] in, k For angle mapping coefficients, To synthesize the rotation angle trajectory, This is the normalized angle reading. The formula for calculating the radius of rotation is:

[0013] in, Let be the radius of rotation. The correction component is parallel to the y-axis. For the sensor measurement center in the world coordinate system Horizontal offset in the axial direction For the sensor measurement center in the world coordinate system Radial offset in the axial direction, For the sensor in the world coordinate system The reference value for distance measurement along the axial direction.

[0014] Furthermore, the variable parameter regularization optimization strategy includes: The first phase performs global coarse localization, employing high regularization strength. A hierarchical sampling multi-starting-point strategy is introduced to lock the parameter magnitude; The second phase involves local fine-tuning, reducing the regularization strength based on the first phase. The outlier removal mechanism is used to perform iterative solutions and output the optimal calibration parameters.

[0015] Furthermore, it also includes filtering the original data point set, the filtering comprising: iterative elimination based on the absolute deviation of the median and spatial consistency checks based on K-nearest neighbors. The iterative elimination based on the absolute deviation of the median includes: Construct a spatial circle model, calculate the residuals from each observation point to the circumference, calculate the MAD value, and mark the points whose absolute residual value is greater than M×MAD as outliers. Repeat this process multiple times until the original point cloud dataset is stable, where M is an empirical coefficient. The K-nearest neighbor-based spatial consistency check includes: Calculate the average k-nearest neighbor distance for each data point and remove isolated noise points with abnormal density.

[0016] Furthermore, the formula for calculating the angle mapping coefficient is as follows:

[0017] in, k est For angle mapping coefficients, This is the normalized angle reading.

[0018] Furthermore, the formula for calculating the objective function is as follows:

[0019] in, Let be the objective function. The x-axis coordinate component of the i-th measurement point after being mapped to the world coordinate system by the synthesized rotation angle. The y-axis coordinate component of the i-th measurement point after being mapped to the world coordinate system by the synthesized rotation angle. The z-axis coordinate component of the i-th measurement point after being mapped to the world coordinate system by the synthesized rotation angle. C x To calibrate the x-axis coordinate components of the sphere's center in the world coordinate system, C y To calibrate the y-axis coordinate components of the sphere's center in the world coordinate system, C z To calibrate the z-axis coordinate components of the sphere's center in the world coordinate system, The total number of measurement points. These are the regularization weight coefficients. Install pose vectors on the three axes of the sensor. Let be the prior expectation vector. To calibrate the radius of the sphere, the formulas for calculating the coordinate components of the x, y, and z axes of the measurement point after mapping to the world coordinate system via a composite rotation angle are as follows:

[0020] in, The x-axis coordinate components of the measurement point after being mapped to the world coordinate system by the synthesized rotation angle. The y-axis coordinate component of the measurement point after being mapped to the world coordinate system by the synthesized rotation angle. The z-axis coordinate component of the measurement point after being mapped to the world coordinate system by the synthesized rotation angle. To synthesize the rotation angle trajectory, The correction component is parallel to the y-axis. For the sensor measurement center in the world coordinate system Horizontal offset in the axial direction For the sensor measurement center in the world coordinate system Radial offset in the axial direction, For the sensor in the world coordinate system Distance reference value in the axial direction, The correction component is parallel to the x-axis. The correction component is parallel to the z-axis. This represents the axial height of the laser line.

[0021] Furthermore, the adjustment step of the regularization weight coefficient includes: The gap ratio of the encoder is calculated. When the gap ratio is less than a preset threshold, the data is determined to have circumferential continuity, and the regularization weight coefficient in the objective function is reduced. When the gap ratio is greater than or equal to the preset threshold, the data is determined to have circumferential discontinuity, and the regularization weight coefficient is increased.

[0022] Furthermore, the calibration parameter set includes: radial depth offset, horizontal offset, pitch angle, roll angle, yaw angle, calibration sphere orbital radius, initial phase, angle mapping coefficient, and fitted sphere center height. Furthermore, the method also includes: Establish a world coordinate system with the rotation center as the origin and the rotation axis as the axis; use a preset transformation matrix to align the original point cloud of the side-mounted sensor in attitude, so that the direction of the aligned sensor coordinate axis is consistent with the world coordinate system, and the main axis of the sensor coordinate axis points to the axis direction of the world coordinate system.

[0023] Compared with the prior art, the present invention has the following advantages: 1. This invention supports two scenarios: the orbital radius is smaller than the calibrated sphere radius and the orbital radius is larger than the calibrated sphere radius, adapting to various actual situations in real production processes; 2. When the orbital radius is smaller than the radius of the calibration sphere, observation data covering a complete 360° angle can be obtained, which greatly improves the identifiability of parameters and calibration accuracy.

[0024] 3. This invention introduces a complete three-axis rotation correction operator and uses the tangential component for angle correction, effectively eliminating the interference of sensor pitch, roll, and yaw errors on angle mapping parameters.

[0025] 4. Through adaptive regularization strategy and two-stage annealing optimization, the system can automatically adjust the constraint strength according to the continuity characteristics of point cloud data, effectively solving the problem that the 9-parameter high-dimensional space is prone to getting trapped in local optima.

[0026] 5. The calibration method collects point cloud data of a standard calibration sphere under coupled rotation and revolution motion. It automatically identifies the geometric configuration type as either "large sphere case / envelope configuration" or "small sphere case / standard configuration" using the angular displacement gap ratio of the normalized encoder data. The method establishes a complete three-axis rotation correction model conforming to the right-hand coordinate system, extracts the tangential offset component caused by attitude error, and compensates it into the rotation angle mapping equation to eliminate the nonlinear coupling between attitude and revolution parameters. Furthermore, this invention employs a two-stage annealing optimization strategy combining high and low regularization. Through the first stage of global coarse positioning and the second stage of local refinement, robust convergence in a 9-parameter high-dimensional solution space is achieved. This invention overcomes the strict limitations of traditional calibration on the radius and center alignment of the calibration sphere, exhibiting strong self-centering capability and environmental adaptability. Experiments show that this invention significantly improves the discriminability of geometric parameters such as pitch angle, achieving a calibration residual RMSE of 0.032 mm and a success rate exceeding 95%. This invention is applicable to submicron-level non-contact measurement of complex rotating bodies such as triple eccentric butterfly valves and precision shaft parts, which greatly improves the benchmark accuracy and operational efficiency of precision testing.

[0027] Based on the above reasons, this invention can be widely applied in fields such as precision measurement. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a schematic diagram of the calibration reference system of the present invention.

[0030] Figure 2 This is a schematic diagram illustrating two scenarios (large ball scenario and small ball scenario) in this invention. Detailed Implementation

[0031] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. 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.

[0032] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification and claims of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products, or devices.

[0033] like Figure 1 As shown, the present invention provides an adaptive calibration method for the orbital sphere of a rotating scanning system, comprising the following steps: S0. Establish a world coordinate system with the rotation center as the origin and the rotation axis as the axis; align the original point cloud of the side-mounted sensor with the attitude through a preset transformation matrix, so that the direction of the aligned sensor coordinate axis is consistent with the world coordinate system, and the main axis of the sensor coordinate axis points to the Y-axis direction (radial) of the world coordinate system.

[0034] Figure 1 and Figure 2 middle, (World Coordinate System / Rotated Coordinate System): A global coordinate system established with the rotation center as the reference reference, used to describe the actual distribution of point clouds in three-dimensional space. (Sensor coordinate system): A local coordinate system established with the measurement center of the line laser sensor as the origin. (Depth Offset): Refers to the installation position deviation of the sensor measurement reference surface in the direction of the rotation axis (Z-axis), used to correct the vertical distance of the sensor relative to the rotary table reference plane. (Horizontal offset): refers to the lateral offset distance of the sensor scanning center line relative to the geometric rotation center axis of the rotating mechanism. (Radius of revolution): The physical radius of the trajectory of a fixed sphere when its center moves in a circle around its axis of rotation. (Calibration sphere radius): The known precise physical radius of the calibration sphere, which serves as the absolute reference for system size calibration. (Rotation angle): refers to the instantaneous physical azimuth angle of the calibration ball driven by the rotary table. (Rotational angular velocity): Describes the dynamic speed at which the rotary table drives the calibration ball to rotate. (Calibrating the center of the sphere): The position of the sphere's center is relative to the sensor coordinate system. origin Overlap. P: The position where the laser hits the calibration ball. : Axial correction component. (Depth measurement dimension): refers to the measurement dimension obtained by the laser beam hitting the calibration ball.

[0035] S1. Install the calibration ball in the rotary table fixture, control the rotary table to rotate at a constant angular velocity, and collect the original point cloud dataset. The original point cloud dataset includes sensor axial displacement, encoder angle readings, and sensor ranging data.

[0036] The present invention is implemented in an environment based on a non-contact rotary scanning measurement system, the hardware of which includes: 1) High-precision rotary table: used to drive the workpiece to rotate circumferentially, equipped with a circular grating encoder with superior angular resolution; 2) Linear motion axis: Drives the sensor to move along the workpiece axis, with a positioning accuracy of [insert accuracy here]. Laser displacement sensor: Employs a triangular reflection type or confocal microscope sensor, with linearity superior to FS; 3) Standard calibration ball: High-roundness ceramic ball is used, with a ball diameter deviation grade better than G5; 4) Line laser sensor: Based on the principle of triangulation, a laser line is projected onto the surface of the object being measured by a line laser scanner, and the laser line contour on the object surface is captured by a built-in camera to collect point cloud data of the object surface.

[0037] When performing calibration, firstly, the known radius is... A standard ball is mounted in the rotary table fixture. The rotary table is controlled to rotate at a constant angular velocity, while the sensor performs stepping or scanning data acquisition along the axial direction.

[0038] The original point cloud dataset is ,in, Sensor axial displacement; For readings from a precision rotary encoder; This is sensor ranging data.

[0039] As a preferred embodiment of the present invention, the original data point set is further filtered, including iterative elimination based on the absolute deviation of the median and spatial consistency check based on K nearest neighbors.

[0040] Iterative elimination based on median absolute deviation (MAD) includes: A spatial circular model is constructed, the residuals from each observation point to the circumference are calculated, and the MAD value is calculated. Points whose absolute residual value is greater than 2.5 × 1.4826 × MAD are marked as outliers. This process is repeated multiple times (3 times in this embodiment) until the original point cloud dataset is stable. The value of M ranges from 2.5 to 4.

[0041] K-nearest neighbor-based spatial consistency checks include: Calculate the average k-nearest neighbor distance for each data point, remove isolated noise points with abnormal density, and ensure the purity of the underlying dataset.

[0042] S2. Normalize the encoder angle readings and calculate the angle mapping coefficient based on the normalized angle readings.

[0043] The formula for calculating the angle mapping coefficient is:

[0044] in, k est For angle mapping coefficients, This is the normalized angle reading.

[0045] The encoder's gap ratio is calculated. When the gap ratio is less than a preset threshold, it is determined that the diameter of the calibration ball is greater than the revolution diameter. When the gap ratio is greater than or equal to the preset threshold, it is determined that the diameter of the calibration ball is less than the revolution diameter.

[0046] The formula for calculating the gap ratio is:

[0047] in, ρ The gap ratio, g i This represents the difference in encoder values ​​between two adjacent samples.

[0048] In a preferred embodiment of the present invention, when the preset threshold is 5, if the gap ratio is less than 5, it is determined that the standard sphere "encloses" the center of rotation. At this time, the sensor obtains circumferential data, and the diameter of the calibration sphere is larger than the revolution diameter, referred to as the large sphere case. In this case, a lower regularization coefficient is adaptively configured. This is done to fully utilize redundant data to improve fitting accuracy. When the gap ratio is greater than or equal to 5, the sphere is determined to be outside the center. In this case, the sensor obtains segmented data, and the diameter of the calibration sphere is smaller than the revolution diameter, which is called the small sphere case. In this case, a higher regularization coefficient is adaptively configured. This strengthens the prior constraint on the installation angle and prevents the parameters from drifting in the data-free range.

[0049] like Figure 2As shown, this illustrates two geometric coupling states between the size of the calibration ball and its trajectory in a rotating scanning system: In the case of the small ball on the left, the scanning field of view is limited and exhibits a circumferentially discontinuous point cloud distribution because the radius of the calibration ball is smaller than the revolution radius. In this case, the algorithm compensates for the lack of information through a high-intensity regularization term to maintain the stability of the solution. In the case of the large ball on the right, the geometric arrangement of the calibration ball covering the center of rotation achieves 360° full-range continuous sampling, enabling the system to adaptively reduce the regularization constraint, make full use of the redundant data information under the full-circle constraint, and significantly improve the identification accuracy of the sensor's three-axis mounting angle and motion parameters.

[0050] S3. Establish the corrected physical coordinate system. The sensor axial displacement and sensor ranging data should be set in the corrected physical coordinate system to obtain the tangential offset components and the corrected physical coordinate system conforms to the ZYX Euler angle rotation matrix of the right-hand coordinate system.

[0051] The formula for calculating the ZYX Euler angle rotation matrix is:

[0052] in, Let ZYX be the Euler angle rotation matrix. The pitch angle, This is the roll angle. Yaw angle This is the fundamental rotation operator about the z-axis of the world coordinate system. For the fundamental rotation operator about the y-axis of the world coordinate system, This is the fundamental rotation operator about the x-axis of the world coordinate system. The formula for calculating the fundamental rotation operator about the x-axis of the world coordinate system is: , The formula for calculating the fundamental rotation operator about the y-axis of the world coordinate system is: , The formula for calculating the fundamental rotation operator about the z-axis of the world coordinate system is: .

[0053] The mapping specifically involves mapping the original laser point cloud into components parallel to the axes of the world coordinate system:

[0054] in, , and These are the correction components for the x-axis, y-axis, and z-axis, which are parallel to the axes of the world coordinate system.

[0055] S4. Calculate the angle offset increment using the correction component parallel to the x-axis, and calculate the composite rotation angle trajectory in the world coordinate system using the normalized angle reading, angle mapping coefficient, and angle offset increment.

[0056] The formula for calculating the angular offset increment is:

[0057] in, This is the increment of the angle offset. The correction component is parallel to the x-axis (tangential). r Let be the radius of rotation.

[0058] The formula for calculating the composite rotation angle trajectory is:

[0059] in, k For angle mapping coefficients, To synthesize the rotation angle trajectory, This is the normalized angle reading.

[0060] The formula for calculating the radius of rotation is:

[0061] in, Let be the radius of rotation. This is a correction component parallel to the y-axis (radial). For the sensor measurement center in the world coordinate system Horizontal offset in the axial direction For the sensor measurement center in the world coordinate system Radial offset in the axial direction, For the sensor in the world coordinate system The reference value for distance measurement along the axial direction.

[0062] S5. Establish the objective function. Based on the objective function, use a variable parameter regularization optimization strategy to iteratively solve the calibration parameter set to obtain the optimal calibration parameters. The objective function is established based on the sum of squared residuals between the Euclidean distance from the measurement point to the center of the calibration sphere and the radius of the calibration sphere.

[0063] The formula for calculating the objective function is:

[0064] in, Let be the objective function. The x-axis coordinate component of the i-th measurement point after being mapped to the world coordinate system by the synthesized rotation angle. The y-axis coordinate component of the i-th measurement point after being mapped to the world coordinate system by the synthesized rotation angle. The z-axis coordinate component of the i-th measurement point after being mapped to the world coordinate system by the synthesized rotation angle. C x To calibrate the x-axis coordinate components of the sphere's center in the world coordinate system, C y To calibrate the y-axis coordinate components of the sphere's center in the world coordinate system, C z To calibrate the z-axis coordinate components of the sphere's center in the world coordinate system, The total number of measurement points. These are the regularization weight coefficients. Install pose vectors on the three axes of the sensor. Let be the prior expectation vector. To calibrate the radius of the sphere, the formulas for calculating the coordinate components of the x, y, and z axes of the measurement point after mapping to the world coordinate system via a composite rotation angle are as follows:

[0065] in, The x-axis coordinate components of the measurement point after being mapped to the world coordinate system by the synthesized rotation angle. The y-axis coordinate component of the measurement point after being mapped to the world coordinate system by the synthesized rotation angle. The z-axis coordinate component of the measurement point after being mapped to the world coordinate system by the synthesized rotation angle. To synthesize the rotation angle trajectory, The correction component is parallel to the y-axis. For the sensor measurement center in the world coordinate system Horizontal offset in the axial direction For the sensor measurement center in the world coordinate system Radial offset in the axial direction, For the sensor in the world coordinate system Distance reference value in the axial direction, The correction component is parallel to the x-axis. The correction component is parallel to the z-axis. This represents the axial height of the laser line.

[0066] The steps for adjusting the regularization weight coefficients include: The gap ratio of the encoder is calculated. When the gap ratio is less than a preset threshold, the data is determined to have circumferential continuity, and the regularization weight coefficient in the objective function is reduced. When the gap ratio is greater than or equal to the preset threshold, the data is determined to have circumferential discontinuity, and the regularization weight coefficient is increased.

[0067] Two-stage variable parameter regularization strategies include: The first phase performs global coarse localization, employing high-strength regularization constraints. Introducing a feature for the initial phase and angle mapping coefficient The hierarchical sampling multi-starting-point strategy locks in the parameter magnitude; The second stage involves local fine-tuning, reducing the regularization strength to... The process iterates on the clean point cloud after outlier removal, and the final output includes radial depth offset. Horizontal offset Three-axis mounting angle Orbital radius Initial phase Angle mapping coefficient and the height of the fitted sphere center The optimal parameters include those found in the text.

[0068] Example 1 This embodiment provides a calibration method for the case of a large sphere, aiming to verify that the system can operate with a standard sphere radius larger than its orbital radius (where the sphere's radius is larger than its orbital radius). The calibration performance at that time. In this configuration, the standard sphere "wraps" the center of rotation, enabling the sensor to achieve continuous observation in the entire circumference. The steps are as follows: S1. Select nominal radius A precision ceramic standard sphere of mm is used. The sensor is mounted laterally so that its ranging axis points radially (Y-axis) in the world coordinate system. The sensor's reference distance is... Set to 245mm. Control the rotary table to move the standard ball. Rotational scanning was used to acquire approximately 15,000 raw point cloud data points.

[0069] First, an iterative elimination algorithm based on MAD is applied, and a threshold is set. This process eliminates random noise caused by laser pulse jumps. Approximately 12,000 high-quality interior points are retained after preprocessing.

[0070] S2. Normalize the encoder angle readings. Based on the normalized angle readings, calculate the angle mapping coefficients as the search benchmark for subsequent nonlinear optimization.

[0071] S3. Calculate the encoder gap between adjacent sampling points and obtain the gap ratio. .because (Set threshold) The system automatically determines the geometric configuration as "large sphere".

[0072] S4. Establish an attitude correction model based on the ZYX Euler angle rotation matrix, mapping the ranging data into three-dimensional correction components parallel to the axes of the world coordinate system. , and .in, World coordinate system Tangential correction component in the axial direction. for Radial correction component in the axial direction.

[0073] S5. Utilizing tangential correction components Calculate the angle offset increment Phase compensation is performed on the normalized encoder angle readings to obtain the synthetic rotation angle trajectory in the world coordinate system. .

[0074] The angular offset increment is calculated using the tangential offset component, and the normalized angle reading is corrected based on the angular offset increment. S6. A two-stage variable parameter regularization strategy is used for the corrected angle readings to output the optimal calibration parameters.

[0075] Because the data has full circumferential continuity, the system automatically reduces the regularization strength to [value missing]. And set the revolution radius The search range is [3,25] mm.

[0076] A smart multi-starting-point strategy was initiated to generate 50 hierarchically distributed initial points. A global search was performed using the Levenberg-Marquardt algorithm, and the initial fitting error RMSE was determined to be 0.045 mm. The rough positioning is around 9.12 mm.

[0077] Based on the results of the first stage, a complete three-axis rotational correction model is applied. This model calculates the tangential displacement components. Real-time correction of rotation angle: This correction eliminates the pitch angle. phase angle Interference.

[0078] (6) The final calibration parameters converge to: radial depth offset mm, pitch angle Roll angle revolution radius mm. The final fitting residual RMSE reached 0.032 mm.

[0079] Example 2 This embodiment provides a calibration method for a small ball scenario, simulating a standard ball located outside the center of rotation. In such scenarios, the sensor's observation angle is limited, resulting in significant data discontinuities. The steps are as follows: S1. Install the calibration ball in the rotary table fixture, control the rotary table to rotate at a constant angular velocity, and collect the original point cloud dataset. The original point cloud dataset includes sensor axial displacement, encoder angle readings, and sensor ranging data.

[0080] Select radius A standard sphere of mm is installed approximately 12 mm from the axis. The sensor is mounted laterally so that its ranging spindle points radially (Y-axis) in the world coordinate system. During scanning, the data in the encoder direction exhibits significant discontinuity, with approximately [missing information - likely a missing section]. The blind spot in observation.

[0081] S2. Normalize the encoder angle readings and calculate the angle mapping coefficient based on the normalized angle readings.

[0082] S3. Calculate the gap characteristics to obtain the gap ratio. Much greater than the threshold The system identified it as a "small ball situation".

[0083] S4. Based on the pre-aligned sensor pose model, obtain the corrected components for each axis of the world coordinate system. In this scenario, due to the short effective observation segment, the system enhances the accuracy of the sensor mounting angle. Constraints approaching zero prior.

[0084] S5. Utilizing tangential components Correcting phase deviations within a limited angular range ensures the correct physical correspondence between the angular trajectory and the geometric surface under discontinuous sampling conditions.

[0085] S6. A two-stage variable parameter regularization strategy is adopted. To address the risk of parameter divergence that may result from data discontinuities, the algorithm adaptively increases the regularization strength. .

[0086] For the case of small balls, add key dimensions ( and The sampling density was [value missing]. After the first stage, the RMSE was 0.062 mm.

[0087] Execution based on Outlier removal criteria to preserve clean datasets Perform local fine-tuning.

[0088] Final calibration output: Radial depth offset mm, pitch angle revolution radius mm. The final fitting residual RMSE was 0.048 mm. Although the accuracy was slightly lower than in the case of large spheres, it still maintained high robustness under the extreme condition of incomplete data.

[0089] The above embodiments demonstrate that the "adaptive calibration method for a revolving sphere" proposed in this invention overcomes the physical limitation that the calibration sphere must be centered, achieving adaptive processing of the calibration sphere at any installation position. The large sphere case provides a better upper limit of accuracy, while the small sphere case verifies the survivability of the framework under extreme conditions, together constituting a complete solution for high-precision calibration of a rotating scanning system.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive calibration method for a revolution sphere in a rotating scanning system, characterized in that, Includes the following steps: The calibration ball is installed in the rotary table fixture, and the rotary table is controlled to rotate at a constant angular velocity to collect the original point cloud dataset, which includes sensor axial displacement, encoder angle reading and sensor ranging data. The encoder angle readings are normalized, and the angle mapping coefficient is calculated based on the normalized angle readings. A sensor mounting pose model based on the ZYX Euler angle rotation matrix is ​​established, and the sensor ranging data is mapped into correction components parallel to each axis of the world coordinate system based on the sensor mounting pose model. The angle offset increment is calculated using the correction component parallel to the x-axis, and the composite rotation angle trajectory in the world coordinate system is calculated using the normalized angle reading, the angle mapping coefficient, and the angle offset increment. An objective function is established, and based on the objective function, a variable parameter regularization optimization strategy is used to iteratively solve the calibration parameter set to obtain the optimal calibration parameters. The objective function is established based on the sum of squared residuals between the Euclidean distance from the measurement point to the center of the calibration sphere and the radius of the calibration sphere.

2. The adaptive calibration method for the orbital sphere of the rotating scanning system according to claim 1, characterized in that, The formula for calculating the ZYX Euler angle rotation matrix is ​​as follows: in, Let ZYX be the Euler angle rotation matrix. The pitch angle, This is the roll angle. Yaw angle This is the fundamental rotation operator about the z-axis of the world coordinate system. For the fundamental rotation operator about the y-axis of the world coordinate system, This is the fundamental rotation operator about the x-axis of the world coordinate system. The formula for calculating the fundamental rotation operator about the x-axis of the world coordinate system is: ， The formula for calculating the fundamental rotation operator about the y-axis of the world coordinate system is: ， The formula for calculating the fundamental rotation operator about the z-axis of the world coordinate system is: 。 3. The adaptive calibration method for the orbital sphere of the rotating scanning system according to claim 1, characterized in that, The formula for calculating the gap ratio is: in, ρ The gap ratio, g i The angle offset increment is calculated as the difference in encoder values ​​between two adjacent samples, using the following formula: in, This is the increment of the angle offset. The correction component is parallel to the x-axis. r Let be the radius of rotation. The formula for calculating the synthetic rotation angle trajectory is: in, k For angle mapping coefficients, To synthesize the rotation angle trajectory, This is the normalized angle reading. The formula for calculating the radius of rotation is: in, Let be the radius of rotation. The correction component is parallel to the y-axis. For the sensor measurement center in the world coordinate system Horizontal offset in the axial direction For the sensor measurement center in the world coordinate system Radial offset in the axial direction, For the sensor in the world coordinate system The reference value for distance measurement along the axial direction.

4. The adaptive calibration method for the orbital sphere of the rotating scanning system according to claim 1, characterized in that, The variable parameter regularization optimization strategy includes: The first phase performs global coarse localization, employing high regularization strength. A hierarchical sampling multi-starting-point strategy is introduced to lock the parameter magnitude; The second phase involves local fine-tuning, reducing the regularization strength based on the first phase. The outlier removal mechanism is used to perform iterative solutions and output the optimal calibration parameters.

5. The adaptive calibration method for the orbital sphere of the rotating scanning system according to claim 1, characterized in that, Also includes: The original data point set is filtered, and the filtering includes: iterative elimination based on the absolute deviation of the median and spatial consistency check based on K nearest neighbors. The iterative elimination based on the absolute deviation of the median includes: Construct a spatial circle model, calculate the residuals from each observation point to the circumference, calculate the MAD value, and mark the points whose absolute residual value is greater than M×MAD as outliers. Repeat this process multiple times until the original point cloud dataset is stable, where M is an empirical coefficient. The K-nearest neighbor-based spatial consistency check includes: Calculate the average k-nearest neighbor distance for each data point and remove isolated noise points with abnormal density.

6. The adaptive calibration method for the orbital sphere of the rotating scanning system according to claim 1, characterized in that, The formula for calculating the angle mapping coefficient is: in, k est For angle mapping coefficients, This is the normalized angle reading.

7. The adaptive calibration method for the orbital sphere of the rotating scanning system according to claim 1, characterized in that, The formula for calculating the objective function is as follows: in, Let be the objective function. The x-axis coordinate component of the i-th measurement point after being mapped to the world coordinate system by the synthesized rotation angle. The y-axis coordinate component of the i-th measurement point after being mapped to the world coordinate system by the synthesized rotation angle. The z-axis coordinate component of the i-th measurement point after being mapped to the world coordinate system by the synthesized rotation angle. C x To calibrate the x-axis coordinate components of the sphere's center in the world coordinate system, C y To calibrate the y-axis coordinate components of the sphere's center in the world coordinate system, C z To calibrate the z-axis coordinate components of the sphere's center in the world coordinate system, The total number of measurement points. These are the regularization weight coefficients. Install pose vectors on the three axes of the sensor. Let be the prior expectation vector. To calibrate the radius of the sphere, the formulas for calculating the coordinate components of the x, y, and z axes of the measurement point after mapping to the world coordinate system via a composite rotation angle are as follows: in, The x-axis coordinate components of the measurement point after being mapped to the world coordinate system by the synthesized rotation angle. The y-axis coordinate component of the measurement point after being mapped to the world coordinate system by the synthesized rotation angle. The z-axis coordinate component of the measurement point after being mapped to the world coordinate system by the synthesized rotation angle. To synthesize the rotation angle trajectory, The correction component is parallel to the y-axis. For the sensor measurement center in the world coordinate system Horizontal offset in the axial direction For the sensor measurement center in the world coordinate system Radial offset in the axial direction, For the sensor in the world coordinate system Distance reference value in the axial direction, The correction component is parallel to the x-axis. The correction component is parallel to the z-axis. This represents the axial height of the laser line.

8. The adaptive calibration method for the orbital sphere of the rotating scanning system according to claim 7, characterized in that, The adjustment steps for the regularization weight coefficients include: The gap ratio of the encoder is calculated. When the gap ratio is less than a preset threshold, the data is determined to have circumferential continuity, and the regularization weight coefficient in the objective function is reduced. When the gap ratio is greater than or equal to the preset threshold, the data is determined to have circumferential discontinuity, and the regularization weight coefficient is increased.

9. The adaptive calibration method for the orbital sphere of the rotating scanning system according to claim 1, characterized in that, The calibration parameter set includes: radial depth offset, horizontal offset, pitch angle, roll angle, yaw angle, calibration sphere revolution radius, initial phase, angle mapping coefficient, and fitted sphere center height.

10. The adaptive calibration method for the orbital sphere of the rotating scanning system according to claim 1, characterized in that, The method further includes: Establish a world coordinate system with the rotation center as the origin and the rotation axis as the axis; use a preset transformation matrix to align the original point cloud of the side-mounted sensor in attitude, so that the direction of the aligned sensor coordinate axis is consistent with the world coordinate system, and the main axis of the sensor coordinate axis points to the axis direction of the world coordinate system.

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