Conversion matrix resolving method based on 321 rule

Abstract

The invention discloses a conversion matrix resolving method based on a 321 rule, which comprises the following steps of: selecting a plurality of monitoring measuring points in advance based on the 321 rule, obtaining all feasible surfaces, feasible lines and original points by using the monitoring measuring points, representing a coordinate system by using the feasible surfaces, the feasible lines and the original points, resolving all possible conversion matrixes, calculating a residual matrix by utilizing each conversion relationship M', the actual measurement coordinates of the system establishment and point selection and the theoretical coordinates, searching for the residual matrix with the minimum non-monitoring direction value in the plurality of residual matrixes, and recording the corresponding conversion relationship M' as a final conversion matrix. According to the method, the problem that an existing solving method is not convergent is avoided, and a more reasonable and accurate conversion matrix can be obtained; and thus, the stability and the measurement precision of the whole measurement system are ensured.

Description

technical field [0001] The invention relates to the field of conversion relationship calculation, in particular to a conversion matrix calculation method based on the 321 rule. Background technique [0002] The 321 system establishment rule is a common system establishment method in the field of surveying. "3" means that three points that are not on the same straight line can establish a plane, and the direction of a coordinate axis is determined by the normal vector of the plane; "2" means that two points are determined A straight line, which is perpendicular to the normal vector of the plane, establishes the second axis; "1" refers to a point to determine the origin position of the coordinate system; in practical applications, use this system establishment rule to select measuring points, and monitor the workpiece in XYZ three In order to evaluate the overall performance of the measurement system, it is necessary to align the measurement coordinates with the theoretical co...

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Problems solved by technology

[0002] The 321 system establishment rule is a common system establishment method in the field of surveying. "3" means that three points that are not on the same straight line can establish a plane, and the direction of a coordinate axis is determined by the normal vector of the plane; "2" means that two points are determined A straight line, which is perpendicular to the normal vector of the plane, establishes the second axis; "1" refers to a point to determine the origin position of the coordinate system; in practical applications, use this system establishment rule to select measuring points, and monitor the workpiece in XYZ three In order to evaluate the overall performance of the measurement system, it is necessary to align the measurement coordinates with the theoretical coordinates in the same coordinate system, and then compare the offsets. This requires correct calculation of the relationship between the measurement system and the theoretical system. The conversion relationship between them; the existing common conversion relationship solution methods are the Bursa-wolf model and the seven-parameter model iterative method. In the actual process, the optimal solution obtained may not necessarily be the conversion relationship with the smallest residual error, that is, using the 321 rule to establish a system, there should be multiple conversion relationships between the theoretical coordinate system and the actual coordinate system, among which the residual The transformation relationship with the smallest difference is the best transformation matrix finally obtained, but the existing solution method is only based on mathematical iteration, and there will be cases where the calculation does not converge. Even if the calculation converges, the optimal solution it provides may not be the same as the actual one. The optimal transformation matrices required are different, which leads to errors in the calculation of the transformation matrix and affects the stability and measurement accuracy of the overall measurement system.

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