Self-evolution high-precision angle measurement method based on double-grating iterative mutual calibration

Abstract

The present application relates to the technical field of precision measurement of geometric quantities, and in particular to a self-evolution high-precision angle measurement method based on double-grating iterative mutual calibration, which realizes self-evolution and promotion of measurement precision based on the principle of double-grating iterative mutual calibration. The method breaks through the dependence of traditional measurement methods on ultra-high precision standards by mutual calibration of two coaxially installed gratings combined with advanced nonlinear optimization algorithms, and provides a new technical solution for the fields of precision manufacturing, scientific instruments and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of geometric precision measurement, and particularly relates to a self-evolution high-precision angle measurement method based on double-grating iterative mutual calibration. BACKGROUND

[0002] High-precision angle measurement is a key basic technology in the fields of modern precision manufacturing, astronomical observation, inertial navigation and robot technology. As a core angle sensing element, the precision of a circular grating directly determines the performance limit of the entire system.

[0003] The traditional grating calibration method has the following inherent limitations:

[0004] Standard device dependency bottleneck: the calibration precision cannot exceed the precision limit of the reference device relied on;

[0005] Cost constraints: ultra-high precision reference equipment is difficult to manufacture, and is extremely expensive;

[0006] Lack of adaptability: offline calibration cannot compensate for time-varying errors such as temperature drift and stress deformation during use;

[0007] Maintenance complexity: high-precision references require special environmental conditions and regular traceability, and the maintenance cost is high. SUMMARY

[0008] To solve the above technical problems, the present application adopts the following technical solutions:

[0009] A self-evolution high-precision angle measurement method based on double-grating iterative mutual calibration, comprising:

[0010] Differential measurement and error separation: by fixing one A grating and rotating the other B grating for measurement, the reading difference obtained contains the positioning error of the B grating, the error of the A grating and the Abbe error of the system;

[0011] Mutual calibration: by fixing the B grating and rotating the A grating in the opposite direction, another set of measurement data containing different combined errors is obtained;

[0012] Closure principle: the full-circle closure angle is 360 degrees;

[0013] Redundant data and adjustment: through two measurements with different configurations, redundant information about the errors of the A grating and the B grating is obtained, and the error curves of the two gratings are separated by using the closure principle as a constraint and by using the least squares method.

[0014] A further technical solution is that in the differential measurement and error separation, the readings of B relative to A are recorded at n equally spaced positions , j represents the rotation position of B (j=0, 1, 2…, n-1), and the data obtained is: ,in Let J be the ideal angle for grating B at position j. The ideal angle for grating A at position 0. Let be the error of grating B at position j. For grating A at position 0, This is the eccentricity error term during positive rotation. The zero-position deviation between the two gratings, This represents random measurement error.

[0015] A further technical solution is that, in the mutual calibration, the readings of A relative to B are recorded at n equally spaced positions. The data obtained is as follows: ,in For grating A in The ideal angle of the position The ideal angle for the B grating at position 0. For grating A in Positional error, For the error of grating B at position 0, This is the eccentricity error term during reverse rotation. The zero-position deviation between the two gratings, This represents random measurement error.

[0016] A further technical solution is to establish an equation using the aforementioned closure principle: when the grating rotates a full revolution (n points), the increment of the ideal angle is 360°. For each grating, the cumulative sum of its reading errors should equal the closure error, expressed as... definition and To determine the errors of the two gratings at each graduation point, based on the difference in readings from two measurements and the closure condition, a system of equations with the following constraints is constructed: and The obtained observation equation Constraint equations derived from the closure principle Geometric constraints specific to reverse rotation: eccentricity error term and It has a different mathematical form and is an eccentric model unique to counter-rotation, providing additional phase identification information, as shown below: , Write in matrix form Where E is the subset of all The unknown parameter vector, D is a constant vector consisting of measured values ​​and 360° closure error, and A is a coefficient matrix containing a specific pattern introduced by the reverse rotation.

[0017] Further technical solutions are that the error curve is solved by an optimization algorithm: full circumference indexing error of grating A ; full circumference indexing error of grating B ; installation eccentricity parameter , ; zero deviation .

[0018] Compared with the prior art, the present application has the following advantages:

[0019] No need for higher standard devices: this is the most core advantage, without the need for an angle measuring instrument with higher precision than the grating itself to calibrate it, realizing "self-lifting".

[0020] Theoretically infinite precision: through iteration, the "true" error of the grating can be continuously approached.

[0021] System error separation: the systematic indexing errors of the two gratings can be effectively separated, rather than being mixed together.

[0022] Real-time calibration potential: the system can be designed as an online calibration system, periodically performing mutual calibration during the measurement process to compensate for error drift caused by temperature, stress, etc. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical solutions and advantages of the present application clearer, the following embodiments will further illustrate the present application. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0024] Embodiment:

[0025] A self-evolution high-precision angle measuring method based on double-grating iterative mutual calibration in the embodiment specifically comprises:

[0026] Differential measurement and error separation: by fixing one A grating and rotating the other B grating for measurement, the reading difference obtained contains the positioning error of the B grating, the error of the A grating and the Abbe error of the system, etc. A single measurement cannot separate these errors.

[0027] Mutual calibration: by exchanging roles (fixing B and reversing A), another set of measurement data containing different combined errors is obtained. Since the two gratings are coaxial in physics, they face the same "true value" space (360° circumference).

[0028] Closure principle: the full circle closure angle is 360 degrees. The cumulative angle of a circumference must be 360°, and any deviation is a manifestation of grating error. This provides an absolute constraint for error evaluation.

[0029] Redundant data and adjustment: By taking two measurements with different configurations, redundant information about the errors of both gratings is obtained. Using the closure principle as a constraint, the error curves of the two gratings can be separated mathematically (e.g., least squares).

[0030] When the two gratings rotate in the same direction, their systematic errors (e.g., indexing error, eccentricity error) often couple in a similar way in the measurement data, making it challenging for the algorithm to separate the errors of individual gratings. For example, if both gratings have the same periodic error, rotating in the same direction can cause these errors to cancel each other out or enhance each other in the measurement, making it difficult to accurately decouple them through optimization algorithms. Rotating in the same direction is less sensitive to installation errors (e.g., eccentricity), as eccentricity errors may exhibit a common pattern when rotating in the same direction, reducing the identifiability of the error model.

[0031] Counter-rotation can introduce more rich phase information, making the errors of the two gratings combined in different ways in the measurement data. This is equivalent to providing "multi-angle" measurement data, greatly enhancing the ability to separate errors. Specifically, counter-rotation can separate periodic errors such as eccentricity error and indexing error in the frequency domain, making it easier for algorithms (such as nonlinear least squares) to distinguish the contribution of each grating. This directly improves the accuracy and reliability of calibration. From the perspective of information theory, counter-rotation increases the independence of measurement data and reduces the uncertainty of parameter estimation, thereby accelerating algorithm convergence.

[0032] Same direction rotation: The mechanical structure is relatively simple, and the driving system may only need to synchronize the same direction motion of two gratings (A grating and B grating), but strict synchronization needs to be ensured to avoid introducing additional errors. However, in high-speed or high-precision applications, same direction rotation may cause common mode errors due to mechanical coupling (such as torque fluctuations), which are difficult to eliminate.

[0033] Counter-rotation: The mechanical design requires independent driving systems or gear mechanisms to achieve counter-rotation, but modern servo motors and control systems can accurately control counter-rotation. Counter-rotation helps to offset some common mode errors (such as thermal deformation or vibration), because the motion directions of the two gratings are opposite, and some environmental disturbances will appear in differential form, which is easy to filter or compensate.

[0034] The core of the algorithm model is to separate errors through mutual calibration data and nonlinear optimization. Counter-rotation can provide more "orthogonal" measurement data, making the condition number of the Jacobian matrix better, thereby improving the convergence speed and stability of the Levenberg-Marquardt algorithm. In the eccentricity error model, counter-rotation will make the eccentricity terms and have different signs and phases, which helps the algorithm more accurately estimate the eccentricity parameters and .

[0035] Simulation studies show that under reverse rotation, the residuals of error separation are usually smaller and the number of iterations is reduced, which means that the system can reach the "self-evolutionary" convergence state more quickly.

[0036] Reverse rotation directly improves the final calibration accuracy of the system by enhancing error separation capabilities. Under the closure principle, reverse rotation can better expose asymmetric errors (such as odd harmonic errors of the grating), thus allowing for more comprehensive compensation of these errors during the iteration process.

[0037] In the long run, the reverse rotation system is more robust to environmental changes (such as temperature gradients) because the reverse motion can provide differential measurements to compensate for drift in real time.

[0038] This method operates based on a coaxial reverse rotation strategy. In both measurement sequences, the rotation direction of the grating is always opposite, thereby introducing differential measurement information and laying the foundation for high-precision error separation.

[0039] First, assume that the zero points of the two gratings are roughly aligned.

[0040] In the first measurement sequence, grating A is fixed, and grating B is rotated clockwise. The readings of B relative to A are recorded at n equally spaced positions (e.g., one point every 30°). j represents the rotation position of B (j=0,1,2,…,n-1). In practice, A is usually fixed at position 0, and then B is rotated a full circle to obtain the data: ,in Let J be the ideal angle for grating B at position j. The ideal angle for grating A at position 0. Let be the error of grating B at position j. For grating A at position 0, This is the eccentricity error term during positive rotation. The zero-position deviation between the two gratings, This represents random measurement error.

[0041] In the second measurement sequence, grating B is fixed, and grating A is rotated counterclockwise. During the mutual calibration, the readings of A relative to B are recorded at n equally spaced positions. The data obtained is as follows: ,in For grating A in The ideal angle of the position The ideal angle for the B grating at position 0. For grating A in Positional error, Error of B grating at 0 position, Eccentric error term when rotating reversely, Zero position deviation of two gratings, Random measurement error.

[0042] The equation is established by using the closure principle, that is, when the grating rotates a whole circle (n points), the increment of ideal angle is 360°, and for each grating, the cumulative sum of reading error should be equal to the closure error, which is expressed as Definition and Error of two gratings to be solved at each division point, according to the difference between the readings of two measurements and the closure condition, the equation group containing the following constraints is constructed: from and The observation equation obtained ; The constraint equation obtained from the closure principle ; The geometric constraint specific to reverse rotation: eccentric error term and Have different mathematical forms, which are specific eccentric models for reverse rotation, and provide additional phase recognition information, which are expressed as follows: , , written in matrix form , where E is an unknown parameter vector containing all , D is a constant vector composed of measurement values and 360° closure difference, and A is a coefficient matrix containing specific patterns introduced by reverse rotation.

[0043] The error curve is solved by an optimization algorithm: the full circle division error of grating A ; The full circle division error of grating B ; The installation eccentricity parameter , ; The zero position deviation , the solving result of this time is used as prior information, and the above reverse measurement process is repeated in subsequent calibration to realize the iterative evolution of measurement accuracy.

[0044] Although the present application has been described herein with reference to a number of illustrative embodiments, it should be understood that various other modifications and implementations can be devised by those skilled in the art, which will fall within the principles and spirit of the disclosure. More specifically, many variations and modifications of the subject combination arrangement, as well as the arrangement itself, can be made within the scope and spirit of the disclosure and claims. Other uses will also become apparent to those skilled in the art, in addition to modifications and improvements to the constituent elements and / or arrangements of the subject combination arrangement.

Claims

1. A self-evolving high-precision angle measurement method based on dual-grating iterative mutual calibration, characterized in that, include: Differential measurement and error separation: By fixing one grating A and rotating another grating B for measurement, the resulting reading difference includes the positioning error of grating B, the error of grating A, and the Abbe error of the system; Mutual calibration: By fixing grating B and rotating grating A in the opposite direction, another set of measurement data containing different combinations of errors was obtained; Closure principle: The closure angle of a full circle is 360 degrees; Redundant data and adjustment: Redundant information about the errors of grating A and grating B was obtained through two measurements with different configurations. Using the closure principle as a constraint, the error curves of the two gratings were separated by the least squares method. In the differential measurement and error separation process, the reading difference between B and A is recorded at n equally spaced locations. Let j represent the rotation position of B (j=0,1,2…,n-1), and obtain the data: ,in Let J be the ideal angle for grating B at position j. The ideal angle for grating A at position 0. Let be the full-circular indexing error of the B grating at position j. Let A be the full-circular indexing error of grating A at position 0. This is the eccentricity error term during positive rotation. The zero-position deviation between the two gratings, This is due to random measurement error; In the mutual calibration, the reading difference between A and B is recorded at n equally spaced positions. The data obtained is as follows: ,in For grating A in The ideal angle of the position The ideal angle for the B grating at position 0. For grating A in The full-circle indexing error of the position, For the full-circular indexing error of the B grating at position 0, This is the eccentricity error term during reverse rotation. The zero-position deviation between the two gratings, This is due to random measurement error; Using the aforementioned closure principle, an equation is established: after the grating rotates a full revolution (n points), the increment of the ideal angle is 360°. For each grating, the cumulative sum of its reading errors should equal the closure error, expressed as: definition and To determine the errors of the two gratings at each graduation point, based on the difference in readings from two measurements and the closure condition, a system of equations with the following constraints is constructed: and The obtained observation equation Constraint equations derived from the closure principle Geometric constraints specific to reverse rotation: eccentricity error term and It has a different mathematical form and is an eccentric model unique to counter-rotation, providing additional phase identification information, as shown below: , Write in matrix form Where E is the subset of all The unknown parameter vector, where the installation eccentricity parameter , Zero deviation D is a constant vector consisting of the measured values ​​and the 360° closure error, and A is a coefficient matrix containing a specific pattern introduced by the reverse rotation.

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