Development of three-coordinate measurement system and its application in spacecraft inspection

In recent years, the research and application of large-size three-coordinate measurement systems of theodolites have gradually been carried out in the aviation, aerospace, antenna, automobile, water conservancy, machinery and surveying and mapping industries. With the technological transformation of enterprises in my country's aviation and aerospace sectors in recent years, nearly 100 mature large-size three-coordinate measurement systems have been introduced from abroad, among which the theodolite measurement systems ECDS3, MANCAT and Axyz STM/MTM of Leica of Switzerland are the most. With the rapid expansion of application scale and field, domestic research and development is relatively backward. In addition, previous research and applications were mainly aimed at two sensors. Due to the limitation of hardware conditions, there is relatively little research and implementation on systems consisting of multiple sensors and hybrid sensors with both angle and distance. The problem that this paper focuses on is the research and development of a hybrid measurement system composed of multiple instruments. Based on the principle of relying on existing equipment, absorbing advanced technologies at home and abroad, and optimizing the performance-price ratio of the entire system, after sufficient investigation, selection, comparison and testing, a large-scale flexible three-coordinate measurement system MetroIn has been developed. The system has been successfully applied in projects such as roundness detection of spacecraft propulsion modules, antenna surface measurement, seat ring detection of the Three Gorges Dam unit, and installation and detection of large gates.

1 Basic Idea of ​​System Design

MetroIn, a large-scale three-dimensional coordinate measurement system for theodolites, is a hybrid measurement system composed of multiple electronic theodolites or total stations. The system uses theodolites or total stations as sensors to ultimately obtain the three-dimensional coordinates of the target point, manages the measurement data using a database, and can perform geometric calculations such as length and angle and measurement and analysis of form and position errors on the measurement data. The basic flow of the system is shown in Figure 1.

2 Basic system configuration

The basic configuration of MetroIn mainly consists of two or more electronic theodolites or total stations (Leica, Topcon, Zeiss, Sokkia, etc.), a desktop or portable computer with a 486 or higher operating system (operating system is Win95/98/2000), a multi-channel serial port conversion card, a LINK2, a reference ruler, a laser eyepiece and aiming mark, a high-stability tripod that matches the electronic theodolite, and an online cable.

3 System Software

3.1 Function Introduction

The system software functions mainly include the following contents:

(1) Equipment connection

Equipment connection includes the connection between computer and theodolite and the initialization of the built-in parameters of theodolite. Using keyboard simulation technology, the computer controls theodolite to complete the setting of various initialization parameters.

(2) System orientation (establishing theodolite measurement coordinate system)

To measure the three-dimensional coordinates of a point in space, we must first establish a system coordinate system, that is, to determine the relative position (relative orientation) and absolute scale (absolute orientation) between sensors, which we call system orientation.

System orientation is to establish a unified measurement coordinate system by mutual aiming between measuring stations (instruments) or observing a certain number of object points and reference scales and performing adjustment calculations. After the system orientation is completed, the relative position relationship between the measuring stations has been determined, and the visible points in space can be measured online and their three-dimensional coordinates can be solved in real time.

System orientation is the most critical step, and the quality of orientation directly affects the quality of subsequent point coordinate measurement.

(3) Online coordinate measurement

After the system is oriented, real-time three-dimensional coordinate measurement can be performed. For general workpieces, the points to be measured can be marked with special markers in advance, and then the spatial coordinates of each point can be determined by observing point by point. For workpieces that cannot be touched or it is difficult to stick markers, a laser beam can be projected onto the workpiece to form a laser point, and the laser point can be used as a measurement mark. After the orientation of a system with multiple theodolites is completed, two or more theodolites can form multiple measurement systems to carry out measurement work at the same time. The measurement coordinates are all in a unified measurement coordinate system, and the measurement data are displayed in different windows on the screen. In the combined measurement system of the total station and theodolite, the total station can collect coordinate data alone, or it can intersect with the theodolite to collect coordinates.

(4) Data management and editing

The interface of the internal data manager window is similar to the Windows Explorer. On the left is a tree structure, which is the main list of the database, such as workpieces, station settings, benchmarks, reflectors and reference libraries, coordinate systems, etc. On the right are the database tables and their contents of the specific database selected on the left, such as point coordinates, observation values, etc. You can edit each data record, add a new record (such as 3D point coordinates), delete records, and sort records. You can select or compound select certain rows in the data in the database table for editing. The operation is performed directly on the database, and each operation changes the content in the database, which is equivalent to automatic saving in time. Each record can be edited, but all original observations can only be read and cannot be changed.

(5) Generation and transformation of coordinate system

A new coordinate system can be generated by translation, rotation and scaling. In addition, there are two other methods, namely axis alignment method and least squares transformation method. For example, a coordinate system is generated by axis alignment of three points that are not in a straight line. Among them, the first point determines the origin of the coordinate system, the second point determines the x-axis, and the third point determines the z-axis. The common point least squares transformation method can be used to transform the measured data and the design data of the workpiece into the same coordinate system for comparison. With the generation and transformation function of the coordinate system, it is very convenient to analyze and process the data in different coordinate systems.

(6) Measurement data analysis and calculation

Based on the coordinate measurement results, various point, line and surface analyses and calculations can be performed, such as the distance between points, lines and surfaces; the angle calculation between lines and lines, lines and surfaces, the analysis and calculation of the parallel, perpendicular and bisection relationships between points and lines, points and surfaces, lines and lines, lines and surfaces, etc.; the standard shapes can be generated by fitting the measurement data, and the shape errors of lines, planes and circles can be detected; the various geometric shapes generated by fitting can be stored in the shape library of the data manager.

(7) Stakeout and measurement of reference data

The theoretical design data is input into the reference library. After the design coordinate system is restored through measurement, the design data is converted into corresponding angle information and indicated in the field.

(8) Data input and output

MetroIn system not only uses its own data, but also is compatible with external data. External data can be directly input into a specified workpiece and converted into a specific coordinate system; point coordinates and their observed values ​​can be output into files of corresponding formats; and the results of orientation can be printed out.

(9) 3D graphics display

Online or offline measurement data can be displayed in three-dimensional visualization, including discrete single point display, basic geometric shapes (such as straight lines, planes, cylinders, spheres, etc.) calculated by fitting, and the view can be observed from any angle, giving us an intuitive feeling of the measurement results.

4 Main mathematical principles of the system

4.1 System Orientation

The three-dimensional coordinate measurement of the theodolite is based on the triangulation principle of the intersection of angles. For the measurement system composed of multiple instruments, due to the existence of "redundant" data, there are two methods for orientation and coordinate solution algorithms: one is the three-dimensional network adjustment method of the station based on the precise leveling of the instrument; the other is the bundle adjustment method based on the collinear equation of photogrammetry. The following mainly introduces the mathematical principle of the former method. The system orientation of multiple instruments is to determine the relative position relationship of each station of the instrument, which is actually the solution of the three-dimensional control network of the station. The observation values ​​in the three-dimensional control network of the three-dimensional coordinate measurement system of the theodolite are only the horizontal direction value and the zenith distance (or vertical angle), and the necessary relative control conditions (such as the length of the reference ruler) can complete the adjustment solution of the network.

In the three-dimensional control network of the measuring station, the measurement of the reference ruler is added to provide a scale control condition for the network. The length between the two ends of the reference ruler is known, and the measurement of the reference ruler constitutes the distance condition.

The coefficients and constants of the above error equations can be found in reference 6. After the relative control (distance) condition is introduced into the three-dimensional control network of the measuring station, the adjustment processing can be divided into two types. One is to regard the relative control as a determined value, and use it as a conditional equation and the angle observation equation to form an indirect adjustment model with conditions for processing; the other is to regard the relative control as an observation value, transform the conditional equation into a virtual observation value error equation, and assign a certain weight to it, and process it together with the angle observation value according to the indirect adjustment.

If the relative control is regarded as a virtual observation value, the indirect adjustment model can be obtained:

4.2 Online Measurement

After the system orientation is completed, the relative position relationship between the measuring stations has been determined, and the visible points in space can be measured online. The so-called hybrid measurement system refers to a measurement system composed of both theodolite and total station. The measurement of the object point has both angle observation information and distance observation information.

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Each object point has three unknowns, so each point needs at least two theodolites to observe the horizontal angle and zenith distance, or a total station to measure angles and distances, so that online measurement can be carried out, and the measured coordinates are all in a unified measurement coordinate system.

It should be noted that for the error equation that has both angle observation values ​​and distance observation values, due to the different accuracy of angle and distance observations, it is necessary to select a suitable weight matrix P. The weights of the observation values ​​can be selected based on the prior observation accuracy of the instrument.

5 System Accuracy Test and Application

5.1 System Accuracy Test

In the laboratory, we used 4 instruments (3 T3000s and 1 T2000S) to set up a quadrilateral station network. In order to test the system's error in length measurement, the reference ruler (calibrated length is 900.706±0.008 mm) was placed in 10 positions in the front, back, left, right, top and bottom of the station network (6m×5m×2m). Each point was measured by three instruments with relatively good intersection patterns; then, the actual measured length of the reference ruler was calculated based on the coordinates of the two end points of the reference ruler. The results are shown in Table 1.

From the data in the table above, it can be calculated that the average length of the measured reference ruler is 900.739mm, and the difference with the calibrated length is 0.033mm. There are many factors that affect the uncertainty of system coordinate measurement, mainly including instrument angle measurement error, baseline length between theodolites, intersection figure quality, and human eye aiming error. Therefore, there has been no accurate error evaluation model. Literature [2,3,8] believes that within a range of 5 meters, the most accurate point measurement accuracy can reach 0.05mm.

5.2 Practical Application

We have successfully applied the theodolite/total station three-dimensional coordinate measurement system MetroIn in projects such as roundness detection of spacecraft propulsion modules, antenna surface measurement, seat ring detection of Unit 1 of the Three Gorges Dam, and installation and detection of large gates [2]. The following is the measurement result of a spacecraft propulsion module.

We used 6 T3000 electronic theodolites to form a three-coordinate measurement system to measure the roundness of the rear end frame of a spacecraft propulsion module (about 3m in diameter). A measurement mark was pasted every 10°, and a total of 36 points were measured in the whole circle. The circle was fitted using the least squares method using the coordinates of the 36 points, and then the values ​​of 18 diameters in the radial direction were calculated. The values ​​were measured twice at temperatures of 20℃ and 34℃, respectively, and compared with the measurement results of the traditional CNC boring and milling machine table method. The statistical results of the 18 diameters are listed in Table 2. From the data in the above table, it can be seen that the repeated measurement accuracy of the theodolite three-coordinate measurement system is very good, with a repeated measurement difference of 0.05mm, while the traditional CNC boring and milling machine table method is 0.43mm.

6 Conclusion

The non-contact large-size flexible three-dimensional coordinate measurement system MetroIn is a domestically developed theodolite/total station three-dimensional coordinate measurement system based on multiple sensors. Its measurement range is from several meters to tens of meters, and its measurement accuracy is from 0.05 mm to sub-millimeter level. Compared with traditional three-dimensional coordinate measuring machines, it does not require a workbench and guide rails, is easy to carry and install, and can perform non-contact measurements during the processing of the object being measured or at the installation site. The system has been successfully applied to projects such as roundness detection of spacecraft propulsion modules, antenna surface measurement, seat ring detection of Unit 1 of the Three Gorges Dam, and installation and detection of large gates.

References

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2 Li Guangyun. The Latest Progress of Industrial Measurement Systems. Beijing: PLA Press, 2000

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