阅读说明：本技术 一种基于平面约束的多边法激光跟踪三维坐标测量方法 (Multilateral laser tracking three-dimensional coordinate measuring method based on plane constraint ) 是由 张福民 张画迪 曲兴华 周伦彬 于 2020-06-11 设计创作，主要内容包括：本发明公开了一种基于平面约束的多边法激光跟踪三维坐标测量方法：(1)选定第一测站位置并布置光学面包板；(2)选定采样点,在第一测站位置对每一个采样点进行测量,获得每一个采样点在球坐标系下的三维坐标数据和每一个采样点与绝对测量式激光跟踪仪的测量中心之间的距离；(3)根据步骤(2)完成其他测站位置的数据测量；(4)根据步骤(2)得到的三维坐标数据,获得每块光学面包板的标准平面；(5)系统参数解算；(6)采用系统参数对待测物体的待测点坐标依照激光跟踪多边法进行解算。本发明通过在传统多边系统中引入平面约束,为系统提供优化方程,提高多边系统的系统参数解算精度,进而提高多边系统对空间点三维坐标测量的精度。(The invention discloses a multilateral laser tracking three-dimensional coordinate measuring method based on plane constraint, which comprises the following steps: (1) selecting a first station position and arranging an optical bread board; (2) selecting sampling points, and measuring each sampling point at the position of a first measuring station to obtain three-dimensional coordinate data of each sampling point under a spherical coordinate system and the distance between each sampling point and the measuring center of an absolute measuring type laser tracker; (3) completing data measurement of other station positions according to the step (2); (4) obtaining a standard plane of each optical bread board according to the three-dimensional coordinate data obtained in the step (2); (5) resolving system parameters; (6) and resolving the coordinates of the points to be measured of the object to be measured by adopting the system parameters according to a laser tracking multi-edge method. According to the method, plane constraint is introduced into a traditional multilateral system, an optimization equation is provided for the system, the system parameter resolving precision of the multilateral system is improved, and the precision of the multilateral system for measuring the three-dimensional coordinates of the space points is further improved.)

1. A multilateral laser tracking three-dimensional coordinate measuring method based on plane constraint, the measuring device adopted comprises an absolute measurement type laser tracker (1) and a tracker target ball, and the measuring method is characterized by comprising the following steps:

step 1, constructing a measuring field: selecting a certain position capable of measuring an object to be measured as a first station position; arranging p optical bread boards (2) within a set range of the first station position;

step 2, data measurement: selecting p multiplied by q points which are the same as q hole sites on each optical bread board (2) as sampling points, matching the tracker target ball at a first measuring station position by adopting the absolute measurement type laser tracker (1), measuring each sampling point, obtaining three-dimensional coordinate data of each sampling point under a ball coordinate system and the distance between each sampling point and the measuring center of the absolute measurement type laser tracker (1), and completing the measurement of the first measuring station position;

step 3, station transfer measurement: selecting three positions which can measure the object to be measured except the first measuring station position as a second measuring station position, a third measuring station position and a fourth measuring station position, keeping a distance among all measuring stations, and respectively finishing the measurement of the second measuring station position, the third measuring station position and the fourth measuring station position according to the step 2;

step 4, standard plane acquisition: according to the three-dimensional coordinate data of the q hole sites on each optical bread board (2) at the first station measurement position obtained in the step 2, for each optical bread board (2), 6 hole sites are selected from the q hole sites on each optical bread board (2) to carry out standard plane fitting, in all plane results, a plane with the minimum flatness error is selected to serve as a standard plane of the optical bread board (2), and the 6 hole sites corresponding to the standard plane are target points on the standard plane;

and 5, resolving system parameters: in a system consisting of p optical bread boards (2) and 4 station measuring stations, the measuring coordinate system of the first measuring station position is taken as a system coordinate system, and the coordinates of the second measuring station position, the third measuring station position and the fourth measuring station position under the system coordinate system are obtained according to a laser tracking multi-edge method;

step 6, measuring an object to be measured: and 5, calculating the coordinates of the points to be measured of the object to be measured according to a laser tracking multi-edge method by adopting the system parameters obtained in the step 5.

2. The multilateral laser tracking three-dimensional coordinate measuring method based on plane constraint according to claim 1, wherein in step 5, the system parameter calculation specifically includes:

the laser tracking multilateral method uses a distance equation under plane constraint as a basis for solving three-dimensional coordinates of space points, and the distance equation under the known plane constraint is as follows:

(x_i-x_j)²+(y_i-y_j)²+(z_i-z_j)²＝l_ij ²(1)

in the formula (x)_i,y_i,z_i) The coordinates of the ith target point on the standard plane are i ═ 1,2, …, and p × 6; (x)_j,y_j,z_j) Coordinates of the jth station position, j being 1,2,3, 4; l_ijThe distance from the ith target point to the jth measuring station position;

writing equation (1) as a function as follows:

in the formula (f)_ijRepresents the squared difference of the measured distances, i.e. the difference of the square of the ideal distance and the square of the actual distance.

Taylor expansion is performed on the formula (2), and the result after high-order terms are omitted is as follows:

in the formula (I), the compound is shown in the specification,

is f_ijThe expression is shown below:

in the formula (I), the compound is shown in the specification,

for points on the standard plane constraint, there is a plane equation:

Ax_i+By_i+Cz_i+D＝0 (5)

in the formula, A, B, C and D are plane parameters;

writing equation (5) as a function:

f_pi＝Ax_i+By_i+Cz_i+D (6)

in the formula (f)_piEvaluating the adjustment when the coordinates of the measurement target points are substituted into the plane equation;

writing equation (6) as a differential form:

in the formula (I), the compound is shown in the specification,

writing equations (3) and (7) in matrix form as follows:

in the formula, F_qIs f in the formula (3)_ijArray of compositionsA matrix; a. the_qIs the coefficient a of the unknown number in the formula (3)_ij、b_ij、c_ijThe formed matrix; dX is the matrix formed by the measurement error of the system parameter, and is the difference between the measured value and the actual value in the spherical coordinate system, where dX is [ dX ]_i,dy_i,dz_i,…dx_j,dy_j,dz_i,…]^TWherein (dx)_i,dy_i,dz_i) Is composed of(dx_j,dy_j,dz_j) Is composed of

co-writing equations (8) and (9) as:

F＝AdX+f⁰(10)

wherein F is F_piAnd f_ijA column matrix of the composition; a is a parameter coefficient matrix in the equation set, f⁰In order to be a flat matrix, the flat matrix,

and correcting the approximate coordinates of the position of the measuring station by adopting the system parameter measurement error:

3. the multilateral laser tracking three-dimensional coordinate measuring method based on plane constraint according to claim 1, wherein in step 6, the measurement of the object to be measured specifically includes:

after system parameters are measured, calculating coordinates of points to be measured of the object to be measured according to an equation set formed by the formula (12):

(x_k-x_j)²+(y_k-y_j)²+(z_k-z_j)²＝r_kj ²(12)

in the formula (x)_k,y_k,z_k) Coordinates of points to be measured on the object to be measured are obtained; (x)_j,y_j,z_j) Coordinates of each station position obtained in the step 5 in a system coordinate system; r is_kjThe distance from the kth point to be measured to the jth station is obtained through measurement.

Technical Field

The invention relates to a three-dimensional coordinate measuring technology, in particular to a multilateral laser tracking three-dimensional coordinate measuring method based on plane constraint.

Background

Industrial measurement is a subject that provides measurement technical support for product design, simulation, measurement, lofting, imitation, simulation, product quality control, product motion state, and the like in each link of industrial production and scientific research. Laser light has important applications in the field of industrial measurements due to its good directionality and energy concentration.

The laser tracker is a measuring device established on a spherical coordinate, and an absolute measurement type laser tracker performs distance measurement in a mode of combining TOF (time of flight) and laser interference principle and performs angle measurement by using a high-precision angle encoder. The method has the characteristics of high precision, good portability and the like, and is widely used in industrial measurement. However, in some measurement occasions with higher requirements on accuracy, especially in large-size measurement, the disadvantage of lower accuracy of the angle measurement relative to the distance measurement of the laser tracker appears. The multilateration system can perform spatial three-dimensional coordinate calculation only by using distance measurement data, thereby avoiding errors caused by angle measurement.

Disclosure of Invention

The invention aims to overcome the defects in the prior art and provide a multilateral laser tracking three-dimensional coordinate measuring method based on plane constraint.

The technical scheme adopted by the invention is as follows: a multilateral laser tracking three-dimensional coordinate measuring method based on plane constraint adopts a measuring device comprising an absolute measurement type laser tracker and a tracker target ball, and comprises the following steps:

step 1, constructing a measuring field: selecting a certain position capable of measuring an object to be measured as a first station position; arranging p optical bread boards in a set range of the first station position;

step 2, data measurement: selecting p multiplied by q points in total at q hole sites on each optical bread board as sampling points, matching a tracker target ball at a first measuring station position by adopting the absolute measurement type laser tracker, measuring each sampling point, obtaining three-dimensional coordinate data of each sampling point under a ball coordinate system and a distance between each sampling point and a measurement center of the absolute measurement type laser tracker, and finishing measurement of the first measuring station position;

step 3, station transfer measurement: selecting three positions which can measure the object to be measured except the first measuring station position as a second measuring station position, a third measuring station position and a fourth measuring station position, keeping a distance among all measuring stations, and respectively finishing the measurement of the second measuring station position, the third measuring station position and the fourth measuring station position according to the step 2;

step 4, standard plane acquisition: according to the three-dimensional coordinate data of the q hole sites on each optical bread board at the first station measurement position obtained in the step 2, for each optical bread board, 6 hole sites are selected from the q hole sites on each optical bread board to carry out standard plane fitting, in all plane results, a plane with the minimum flatness error is selected to serve as a standard plane of the optical bread board, and the 6 hole sites corresponding to the standard plane are target points on the standard plane;

and 5, resolving system parameters: in a system consisting of p optical bread boards and 4 station measuring station positions, the measuring coordinate system of the first measuring station position is taken as a system coordinate system, and the coordinates of the second measuring station position, the third measuring station position and the fourth measuring station position under the system coordinate system are obtained according to a laser tracking multi-edge method;

step 6, measuring an object to be measured: and 5, calculating the coordinates of the points to be measured of the object to be measured according to a laser tracking multi-edge method by adopting the system parameters obtained in the step 5.

Further, in step 5, the system parameter calculation specifically includes:

the laser tracking multilateral method uses a distance equation under plane constraint as a basis for solving three-dimensional coordinates of space points, and the distance equation under the known plane constraint is as follows:

(x_i-x_j)²+(y_i-y_j)²+(z_i-z_j)²＝l_ij ²(1)

in the formula (x)_i,y_i,z_i) The coordinates of the ith target point on the standard plane are i ═ 1,2, …, and p × 6; (x)_j,y_j,z_j) Coordinates of the jth station position, j being 1,2,3, 4; l_ijThe distance from the ith target point to the jth measuring station position;

writing equation (1) as a function as follows:

in the formula (f)_ijRepresents the squared difference of the measured distances, i.e. the difference of the square of the ideal distance and the square of the actual distance.

Taylor expansion is performed on the formula (2), and the result after high-order terms are omitted is as follows:

in the formula (I), the compound is shown in the specification,the approximate coordinates of the ith target point on the standard plane are measured by an absolute measurement type laser tracker at the position of the first measuring station;the approximate coordinates of the jth measuring station position are obtained by using backward intersection calculation of the distance measurement values of the measuring station positions to the target point;

is f_ijThe expression is shown below:

in the formula (I), the compound is shown in the specification,measuring the distance between the jth measuring station position and the ith target point, namely measuring the ith target point by an absolute measurement type laser tracker at the jth measuring station position;

for points on the standard plane constraint, there is a plane equation:

Ax_i+By_i+Cz_i+D＝0 (5)

in the formula, A, B, C and D are plane parameters;

writing equation (5) as a function:

f_pi＝Ax_i+By_i+Cz_i+D (6)

in the formula (f)_piEvaluating the adjustment when the coordinates of the measurement target points are substituted into the plane equation;

writing equation (6) as a differential form:

in the formula (I), the compound is shown in the specification,

is f_piIn the approximation of (a) to (b),the approximate coordinates of the ith target point on the standard plane are measured by an absolute measurement type laser tracker at the position of the first measuring station; wherein m is a standard plane serial number, and m is 1,2, …, p; i is the target point number, 6 target points are on each standard plane, p × 6 target points are counted, and for the mth standard plane, i is 6 × (m-1) +1,6 × (m-1) +2, …,6 × (m-1) + 6;

writing equations (3) and (7) in matrix form as follows:

in the formula, F_qIs f in the formula (3)_ijA column matrix of the composition; a. the_qIs the coefficient a of the unknown number in the formula (3)_ij、b_ij、c_ijThe formed matrix; dX is the matrix formed by the measurement error of the system parameter, and is the difference between the measured value and the actual value in the spherical coordinate system, where dX is [ dX ]_i,dy_i,dz_i,…dx_j,dy_j,dz_i,…]^TWherein (dx)_i,dy_i,dz_i) Is composed of(dx_j,dy_j,dz_j) Is composed of

Is shown in formula (3)A column matrix of the composition; f_pIs f in the formula (7)_piA column matrix of the composition; a. the_pIs the coefficient A of the unknown number in the formula (7)_m、B_m、C_mThe formed matrix;is as in formula (7)A column matrix of the composition;

co-writing equations (8) and (9) as:

F＝AdX+f⁰(10)

wherein F is F_piAnd f_ijA column matrix of the composition; a is a parameter system in the equation setNumber matrix, f⁰In order to be a flat matrix, the flat matrix,

and correcting the approximate coordinates of the position of the measuring station by adopting the system parameter measurement error:

further, in step 6, the measuring of the object to be measured specifically includes:

after system parameters are measured, calculating coordinates of points to be measured of the object to be measured according to an equation set formed by the formula (12):

(x_k-x_j)²+(y_k-y_j)²+(z_k-z_j)²＝r_kj ²(12)

in the formula (x)_k,y_k,z_k) Coordinates of points to be measured on the object to be measured are obtained; (x)_j,y_j,z_j) Coordinates of each station position obtained in the step 5 in a system coordinate system; r is_kjThe distance from the kth point to be measured to the jth station is obtained through measurement.

The invention has the beneficial effects that: the invention adopts standard plane constraint, and effectively improves the measurement precision of the laser tracker to the point to be measured. The standard plane constraint provides an optimization equation for the system under the condition of not increasing the number of unknown numbers, so that the multilateral measurement system can be constructed under the condition of only three laser trackers, and the cost is reduced. A method for obtaining standard plane constraint is provided, which can realize that the standard plane constraint is obtained through an optical bread board on a measurement site.

Drawings

FIG. 1: the invention relates to a multilateral laser tracking three-dimensional coordinate measuring method flow and a chart based on plane constraint;

FIG. 2: a layout of a measuring apparatus according to the present invention;

the attached drawings are marked as follows: 1-absolute measurement type laser tracker, 2-optical bread board, 3-target holder and 4-length standard ruler.

Detailed Description

In order to further understand the contents, features and effects of the present invention, the following embodiments are illustrated and described in detail with reference to the accompanying drawings:

as shown in fig. 2, the measuring apparatus according to the present invention includes: the device comprises an absolute measurement type laser tracker 1, a tracker target ball, an optical bread board 2, a target seat 3 for fixing the tracker target ball and a tripod for fixing the optical bread board 2 and the absolute measurement type laser tracker 1.

The absolute measurement type laser tracker 1 is a laser tracker which has absolute distance measurement capability and further obtains three-dimensional coordinates of space measurement points, in the measurement method provided by the invention, four stations of absolute measurement type laser trackers 1 are needed, four absolute measurement type laser trackers 1 can be used at the same time, and one absolute measurement type laser tracker 1 can be used for station moving operation among a plurality of positions.

The target ball of the tracker generally has a right-angle triangular pyramid prism structure, and the structure can reflect laser along the incident direction and ensure the parallelism of incident light and reflected light. The good sphericity ensures that the centre of the sphere remains as constant as possible when the target ball of the tracker faces different directions on the target holder 3. The manufacturing precision is good, and the cone top of the prism structure is ensured to be coincident with the sphere center as much as possible.

The target holder 3 provides three support points and has adsorption capacity, and a target ball of the tracker can be fixed on the target holder.

An optical bread board 2, providing an array of holes for assisting in the positioning of the tracker target balls thereon. The substrate has certain flatness and provides standard plane constraint required by the measurement method provided by the invention.

The tripod is used for fixing the absolute measurement type laser tracker 1 and the optical bread board 2.

In the invention, the absolute measurement type laser tracker 1 is LEICA AT 960; the tracker target ball adopts a matched LEICA 1.5' tracker target ball; selecting three common optical bread boards 2; the three standard rulers have the nominal lengths of 969.045mm, 970.108mm and 1000.943mm respectively. Several tripods are additionally used for arranging the absolute measuring laser tracker 1 and the optical bread board 2 in the measuring field.

As shown in fig. 1, a method for measuring three-dimensional coordinates by multilateral laser tracking based on plane constraint provides an optimization equation for a system by introducing plane constraint into a conventional multilateral system, improves the system parameter calculation accuracy of the multilateral system, and further improves the accuracy of the multilateral system in measuring three-dimensional coordinates of space points. The method comprises the following steps:

step 1, constructing a measuring field: selecting a certain position capable of measuring an object to be measured as a first station position; p optical bread boards 2 are arranged within the set range of the first station position.

In this embodiment, the absolute measurement type laser tracker 1 is placed at an appropriate position in the measurement field as a first station position. Three optical bread boards 2 are arranged in the range of 15 m multiplied by 5m of the absolute measurement type laser tracker, wherein two optical bread boards are supported by a tripod, one optical bread board is placed on the ground, the fixing of the optical bread board is guaranteed without shaking, and errors caused by shaking can be effectively avoided on the tripod. 9 target seats 3 are arranged in the range of an absolute measurement type laser tracker of 110 m multiplied by 10m and used as 9 orientation point positions of the system, the orientation points can be used in the traditional multilateral method system parameter calculation and can also be used in the plane constraint multilateral method system parameter calculation, and the target seats 3 are not required to be arranged in practical application. In order to verify the accuracy of the measuring method of the present invention, three length standard rulers 4 are used as the measured object, the three length standard rulers 4 are respectively placed at positions about 25m, 30m and 38m away from the first station position, and the three length standard rulers 4 have nominal lengths of 969.045mm, 970.108mm and 1000.943mm, respectively.

Step 2, data measurement: selecting p multiplied by q points in total at the q hole sites on each optical bread board 2 as sampling points, matching the absolute measurement type laser tracker 1 with the tracker target ball at the first measuring station position, measuring each sampling point, obtaining three-dimensional coordinate data of each sampling point under a ball coordinate system and the distance between each sampling point and the measuring center of the absolute measurement type laser tracker 1, and completing the measurement of the first measuring station position.

In this embodiment, the absolute measurement type laser tracker 1 is used to match the tracker target ball at the first station, and the hole site, the orientation point and the two end points of the length standard ruler 4 on the optical bread board 2 are measured respectively, and three-coordinate data and distance data of all points are stored respectively. Wherein 36 points are measured on each optical bread board 2, and the total of 108 points, 9 orientation points and 6 length standard ruler 4 endpoints and the total of 123 points are measured on three optical bread boards 2.

Step 3, station transfer measurement: selecting three positions which can measure the object to be measured except the first measuring station position as a second measuring station position, a third measuring station position and a fourth measuring station position, keeping a certain distance among all measuring stations, and respectively finishing the measurement of the second measuring station position, the third measuring station position and the fourth measuring station position according to the step 2;

in this embodiment, a station transfer operation is performed between a plurality of positions using one absolute measurement type laser tracker 1. After the measurement of the position of the first station measuring station is finished, the position of the absolute measurement type laser tracker 1 is moved, the height of a tripod of the tracker is changed to be used as the position of the second station measuring station, and all point positions are measured again. And carrying out three station shifting operations totally, and carrying out 4 measurements on all point positions totally.

Step 4, standard plane acquisition: according to the three-dimensional coordinate data of the q hole sites on each optical bread board 2 of the first station measurement position obtained in the step 2, 6 hole sites are selected from the q hole sites on each optical bread board 2 for each optical bread board 2 to carry out standard plane fitting, in all plane results, a plane with the minimum flatness error is selected as a standard plane of the optical bread board 2, and the 6 hole sites corresponding to the standard plane are target points on the standard plane.

The measuring method of the invention requires to provide a standard plane for constraint use, and if a plane with larger flatness error is used, the measuring result is greatly influenced, so the invention provides a method capable of obtaining a plane with better flatness on a measuring site. Is divided intoThe flatness of the optical bread board 2 itself and the large number of hole sites provided thereon are not utilized. The flatness of the optical bread board 2 provides a substrate for searching a high-flatness plane; the holes can help to position the tracker ball on the optical bread board 2. Taking a bread board with 121 hole sites, selecting 6 points for plane fitting as an example, selecting 36 hole sites according to a certain rule, covering the whole bread board range as much as possible, calculating the flatness error of the plane formed by all the selected 6 points, and sharing

And (4) carrying out the following steps. And selecting the group of hole sites with the smallest flatness error as a point group forming the standard plane.

In this embodiment, the coordinates of 108 points of 36 points and 3 points on each optical bread board 2 are obtained in the data measurement, 6 points are selected from the 36 points on each optical bread board 2 for standard plane fitting, and it is known that

And selecting the plane with the minimum flatness error from the total 1947792 plane results, and using the plane as a standard plane constraint. The result of comprehensively considering the flatness requirement and the measurement point number requirement is obtained by selecting 6 points for plane fitting. Experiments have shown that the three minimum flatness errors obtained using a 6-point fit are 7.37 × 10, respectively^-5mm、1.91×10^-4mm、2.33×10^-4mm, mean 1.66X 10^{- 4}mm in the hundred nm scale. It is considered to be usable as a standard planar constraint.

And 5, resolving system parameters: and after standard plane constraint is obtained and coordinates and distance measurement values of all sampling points are obtained, system parameter calculation can be carried out. In a system consisting of p optical bread boards 2 and 4 station measuring station positions, the measuring coordinate system of the first station position is taken as a system coordinate system, and the coordinates of the second station position, the third station position and the fourth station position under the system coordinate system are obtained according to a laser tracking multi-edge method.

And taking the position of the first measuring station as an origin, wherein the measuring coordinate system of the position of the first measuring station is a system coordinate system. If there are m stations, nTarget point. This allows the introduction of m x n distance equations, n plane equations. Introducing 3m-3 unknowns into m stations, introducing 3n unknowns into n target points, and if the equation set has a solution, the condition that m multiplied by n + n is more than or equal to 3m +3n-3 is required, namely

When m and n are both positive integers, m is 3 at minimum, and n is 6 at minimum.

The laser tracking multilateral method uses a distance equation under plane constraint as a basis for solving three-dimensional coordinates of space points, and the distance equation under the known plane constraint can be written as follows:

(x_i-x_j)²+(y_i-y_j)²+(z_i-z_j)²＝l_ij ²(1)

in the formula (x)_i,y_i,z_i) The coordinates of the ith target point on the standard plane are i ═ 1,2, …, and p × 6; (x)_j,y_j,z_j) Coordinates of the jth station position, j being 1,2,3, 4; l_ijIs the distance from the ith target point to the jth station position.

It can be easily found that to measure the three-dimensional coordinates of the space by using the multilateration method, the position relationship between the stations, that is, the system parameters, needs to be known. The traditional multilateral method adopts a method of setting directional points, and solves system parameters by utilizing the characteristic that the number of the introduced equations is larger than the number of unknown numbers when the directional points are introduced. The plane constraint scheme provided by the invention enables the orientation point to additionally introduce a plane equation, thereby achieving the purpose of optimizing the system. In addition, the equation number is further larger than the unknown number, so that the number of the measuring stations can be reduced. After the absolute measurement type laser tracker 1 finishes measuring all measuring points at one measuring station position, the position needs to be moved to be used as the next measuring station until the required number of measuring stations is measured. Therefore, the scheme of reducing the stations can greatly reduce the workload of multilateration measurement.

Writing equation (1) as a function as follows:

in the formula (f)_ijRepresents the squared difference of the measured distances, i.e. the difference of the square of the ideal distance and the square of the actual distance.

Taylor expansion is performed on the formula (2), and the result after high-order terms are omitted is as follows:

in the formula (I), the compound is shown in the specification,the approximate coordinates of the ith target point on the standard plane are measured by an absolute measurement type laser tracker 1 at the position of the first measuring station;

the approximate coordinates of the jth measuring station position are obtained by using backward intersection calculation of the distance measurement values of the measuring station positions to the target point;

is f_ijThe expression is shown below:

in the formula (I), the compound is shown in the specification,

measuring the distance between the jth measuring station position and the ith target point, namely measuring the ith target point by an absolute measurement type laser tracker at the jth measuring station position;

for points on the standard plane constraint, there is a plane equation:

Ax_i+By_i+Cz_i+D＝0 (5)

in the formula, A, B, C and D are plane parameters;

writing equation (5) as a function:

f_pi＝Ax_i+By_i+Cz_i+D (6)

in the formula (f)_piIs the adjustment when evaluating the coordinates of the measurement target points and substituting the coordinates into the plane equation.

Writing equation (6) as a differential form:

in the formula (I), the compound is shown in the specification,is f_piIn the approximation of (a) to (b),the approximate coordinates of the ith target point on the standard plane are measured by an absolute measurement type laser tracker 1 at the position of the first measuring station; wherein m is the serial number of the standard plane, and the value of m is 1,2, … and p; i is the target point number, 6 target points are arranged on each standard plane, p × 6 target points are counted, and for the mth standard plane, the value of i is 6 × (m-1) +1,6 × (m-1) +2, …,6 × (m-1) +6 in sequence.

Approximate coordinates of all target points in the above expressionIs directly measured by an absolute measuring laser tracker 1 at the position of a first measuring station, and the approximate coordinates of all measuring stations

And the distance measurement values of the target points of all the stations are calculated by using back intersection.

Writing equations (3) and (7) in matrix form as follows:

in the formula, F_qIs f in the formula (3)_ijA column matrix of the composition; a. the_qIs the coefficient a of the unknown number in the formula (3)_ij、b_ij、c_ijThe formed matrix; dX is the matrix formed by the measurement error of the system parameter, and is the difference between the measured value and the actual value in the spherical coordinate system, where dX is [ dX ]_i,dy_i,dz_i,…dx_j,dy_j,dz_i,…]^TWherein (dx)_i,dy_i,dz_i) Is composed of(dx_j,dy_j,dz_j) Is composed of

Is shown in formula (3)A column matrix of the composition; f_pIs f in the formula (7)_piA column matrix of the composition; a. the_pIs the coefficient A of the unknown number in the formula (7)_m、B_m、C_mThe formed matrix;is as in formula (7)

A column matrix of the composition;

the equations (3) and (7) are combined to obtain a linear equation system, and the matrix form is to write the equations (8) and (9) together:

F＝AdX+f⁰(10)

wherein F is F_piAnd f_ijA column matrix of the composition; a is a parameter coefficient matrix in the equation set, f⁰In order to be a flat matrix, the flat matrix,

in this embodiment, taking 4 survey stations, 3 standard planes for constraint, and 33 target points (including 9 orientation points and 6 length standard rulers 4 end points) which are another 15 target points on each standard plane as an example, the results are as follows:

dX＝dX_111×1＝[dx_i,dy_i,dz_i,…dx_j,dy_j,dz_i,…]^T

the matrix form is utilized to solve the least square solution of the over-determined equation set to obtain system parameters, namely the position relation among the measuring stations, and then the multilateral method can be used for calculating the three-dimensional coordinates of the space points to be measured.

And correcting the approximate values of the system parameters by the system parameter errors obtained in the steps to obtain more accurate system parameters, and then resolving the coordinates of the target to be measured according to the basic principle of the multilateral method by using the system parameters, namely the accurate position relation between the measuring stations.

Step 6, measuring and evaluating progress of the object to be measured: and 5, calculating the coordinates of the object to be measured according to a laser tracking multi-edge method by adopting the system parameters obtained in the step 5.

After system parameters, namely the position relation among the stations, are measured, the coordinates of the points to be measured of the object to be measured can be calculated according to an equation set formed by the formula (12):

(x_k-x_j)²+(y_k-y_j)²+(z_k-z_j)²＝r_kj ²(12)

in the formula (x)_k,y_k,z_k) Coordinates of points to be measured on the object to be measured are obtained; (x)_j,y_j,z_j) Coordinates of each station position obtained in the step 5 in a system coordinate system; r is_kjThe distance from the kth point to be measured to the jth station is obtained through measurement.

In this embodiment, to verify the accuracy of the system, three standard rulers with nominal lengths of 969.045mm, 970.108mm and 1000.943mm are used as the measured objects and are respectively placed at distances of about 25m, 30m and 38m, so as to verify the accuracy performance of the system at different measuring distances. After obtaining the coordinates of the two end points of the length standard ruler 4, the length of the length standard ruler 4 can be calculated, and the measured lengths of the three length standard rulers 4 with the nominal lengths of 969.045mm, 970.108mm and 1000.943mm are respectively 969.035mm, 970.081mm and 1000.894mm by calculation in the case of the invention. The obtained measuring errors of the multilateral laser tracking measuring method based on plane constraint are respectively 0.01mm, 0.027mm and 0.049mm, and the average value is 0.029 mm. When the traditional four-station multilateral method is used for measurement, the obtained average error is 0.056mm, and when the single-station measurement is used, the average error is 0.085 mm. The plane constraint can effectively improve the measurement accuracy of the system.

In summary, the invention provides a multilateral laser tracking three-dimensional coordinate measuring method based on plane constraint, and simultaneously provides a method for obtaining standard plane constraint on a measuring site, thereby providing possibility for realizing the measuring method. The measuring device adopted by the measuring method comprises absolute measuring type laser tracker 1, 1.5' tracker target balls, an optical bread board 2, a length standard ruler 4, a tripod and the like. The multilateral laser tracking three-dimensional coordinate measuring system can avoid errors caused by angle measurement of the absolute measurement type laser tracker 1, and only uses distance measurement data to calculate three-dimensional coordinates of space points. The accurate calibration of the parameters of the multilateral system is the key for improving the measurement precision of the space three-dimensional coordinate. In order to improve the accuracy of a multilateral method measurement system, the invention provides a multilateral method laser tracking three-dimensional coordinate measurement method based on plane constraint, which adopts standard plane constraint to provide an optimization equation for the system under the condition of not increasing the number of unknowns. In order to obtain standard plane constraint on a measurement site, a method for obtaining the standard plane constraint is also provided.

Although the preferred embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and those skilled in the art can make many modifications without departing from the spirit and scope of the present invention as defined in the appended claims.