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Advances in Mechanical Engineering

Volume 2013 (2013), Article ID 629385, 8 pages

http://dx.doi.org/10.1155/2013/629385

## Automatic Measurement in Large-Scale Space with the Laser Theodolite and Vision Guiding Technology

State Key Laboratory of Precision Measuring Technology & Instrument, Tianjin University, Tianjin 300072, China

Received 28 June 2013; Accepted 3 September 2013

Academic Editor: Fuqiang Zhou

Copyright © 2013 Bin Wu and Bing Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The multitheodolite intersection measurement is a traditional approach to the coordinate measurement in large-scale space. However, the procedure of manual labeling and aiming results in the low automation level and the low measuring efficiency, and the measurement accuracy is affected easily by the manual aiming error. Based on the traditional theodolite measuring methods, this paper introduces the mechanism of vision measurement principle and presents a novel automatic measurement method for large-scale space and large workpieces (equipment) combined with the laser theodolite measuring and vision guiding technologies. The measuring mark is established on the surface of the measured workpiece by the collimating laser which is coaxial with the sight-axis of theodolite, so the cooperation targets or manual marks are no longer needed. With the theoretical model data and the multiresolution visual imaging and tracking technology, it can realize the automatic, quick, and accurate measurement of large workpieces in large-scale space. Meanwhile, the impact of artificial error is reduced and the measuring efficiency is improved. Therefore, this method has significant ramification for the measurement of large workpieces, such as the geometry appearance characteristics measuring of ships, large aircraft, and spacecraft, and deformation monitoring for large building, dams.

#### 1. Introduction

With the development of the large-scale equipment manufacturing, the precise measurement of point, length, and surface characteristics in large-scale space becomes a hot and knotty issue for industrial production. Due to the wide measuring range and high accuracy, the theodolite, total station, and laser tracker have been the mainstream measuring systems in the field of precise industrial measurement [1–5]. Both total station and laser tracker need cooperation targets in the measurement process; therefore the realization and application of such contact measurement methods are greatly limited by measuring range and conditions in the field of industrial measurement. The theodolite measurement system needs two or more high precision electronic theodolites to realize the spatial angle intersection measurement without cooperation targets and also has high measurement accuracy and flexibility in application. However, traditional theodolites measurement needs the human eye to collimate measured features, which inevitably brings about the obvious artificial error and low measurement efficiency.

With the development of electronic technology, information processing technology, and measurement theory, the industrial photogrammetry system represented by V-STARS of Geodetic Services Inc. and indoor space positioning measurement system represented by iGPS of the Nikon Inc. are developed for largescale space measurement [6–10]. Based on multidirectional imaging for the coding and non-coding marks by high-precision digital camera and the image processing algorithms, the photogrammetry system achieves the coordinates’ measurement of the space characteristics (the light reflecting symbols attached on the surface of the measured object or optical projection marks) [11–15]. This method requires the measured object to be imaged at different positions and directions. Simultaneously, it also needs to paste marks on the object surface or carry on regional optical projections with projector. In addition, aerial platform or other auxiliary lifting device is required in the measurement of large-scale objects. With the complicated process and low efficiency, this method tends to be adopted in the measurement of the single sample. Similar with the operation model of the Global Positioning System (GPS), several transmitters as the positioning satellites in GPS are placed in the measuring space and their relationships are calibrated accurately to build the global measurement and control network of the iGPS. Then the receivers similar to the positioning terminals in GPS, handheld or fixed on a workpiece, can be located [16]. With the advantage of extended measuring range without loss of accuracy, the ability of multiobjective real-time measurement, iGPS has been used in the precise assembly and adjustment of large aircraft, antenna, and so on [10]. However, it is not suitable for the automatic measurement of the large-scale workpieces with quantities of characteristic points or geometric dimensions.

Based on the traditional forward intersection measuring principle of theodolite, this paper presents a novel automatic measurement method with laser theodolites which can project a collimated laser beam along its sight-axis, as the Leica DL2 laser pointer, and the vision tracking technology for volume workpiece (equipment) in large space. Supported by the theoretical model data and the multiresolution vision imaging and guiding technology, it can realize the automatic, quick, and accurate measurement of large workpiece. In the measuring system, the measured marks on the surface of the workpieces are spotted by the collimating laser, and cooperation targets or artificial markers are not required. In addition, the collimated laser beam is coaxial with the sight-axis of the theodolite, so the projected light spot on the object indicates the aiming direction of the theodolite. The projected light spot can be captured by camera and used to evaluate the intersection of multitheodolite. And then automatic tracking the light spot instead of aiming with human eye and guiding the exact intersection of multitheodolite can be achieved. Obviously, it can reduce the artificial error and improve the measuring efficiency. Therefore, this method is of great significance for the measurement of large-scale space and large workpieces (equipment), such as the geometry appearance characteristics measuring of ships, large aircraft, spacecraft, and high-speed trains and deformation monitoring for large buildings or dams and so on.

#### 2. Operating Principle and Its Workflow

The automatic measurement system based on vision tracking and guiding laser theodolite consists of the laser theodolite measurement subsystem and the vision tracking and guiding subsystem, which is shown as in Figure 1. The laser theodolite measurement subsystem is composed of two Leica TM5100A (or TM6100A) electric theodolites with DL2 laser pointer and servomotor. After precise orientation, the subsystem obtains three-dimensional (3D) coordinates of target point by the spatial forward angular intersection method or the sophisticated bundle adjustment method. The vision tracking and guiding subsystem contains a two-dimensional (2D) precise turntable and a CCD camera with 30x optical zoom lens. The CCD camera rotates with the precise turntable to track the measured characteristics and the projected spot of laser pointer, and then guides two theodolites to intersect automatically and accurately.

The laser beam from the laser pointer, coaxial with the theodolite sight-axis, not only provides measuring marks on the measured workpiece but also supports the vision tracking and guiding by realizing visualization of theodolite aiming direction. When initially searching and tracking the measured characteristics, the tracking camera, with the ability of multilevel zoom and multiresolution imaging, works on the mode of short focal length, large field of view, and low resolution to track the measured characteristic in specific areas. Then the focal length is increased and the field of view is decreased to increase the imaging resolution. The camera guides two theodolites to intersect accurately and identifies the result, thus ensuring the automatic precise coordinate measurement.

Referring to the schematic diagram shown as in Figure 1, the workflow of the measurement system is as follows. Establish the coordinates system of double-theodolite measurement system (DMS) and the mathematical model of multiresolution vision tracking measurement system (MMS). Measure the designed or machining datum points on the measured workpiece, and establish the relationship between the real workpiece and DMS. Input the theoretical designed data of the workpiece, and transform theoretical designed data into the coordinate system of DMS. With the guidance of transformed designed data and MMS, the CCD camera rotates with the precise turntable to track the characteristic area. Drive the primary (left) theodolite to aim at the measured characteristics of the workpiece according to MMS and certain control strategy, and then guide the secondary (right) theodolite to intersect with the primary theodolite accurately, and obtain the 3D coordinates of the measured characteristic. Repeat step 4 and step 5 until all the characteristics are measured.

In the measuring process above, the key technologies mentioned such as the theodolite precise mutual aiming, measurement model of forward intersection, sophisticated bundle adjustment method, and the control strategy of theodolite and precise turntable are comparatively mature. However, there are few researches on the technologies of vision tracking and guiding measurement based on theodolite system.

#### 3. Mathematical Model of Vision Tracking and Guiding System

Automatic tracking and superposition recognition of laser marks (equivalent to the intersection of two theodolites) are crucial steps in theodolite automatic measurement, which can be achieved by multiresolution camera with the cooperation of precise turntable. Firstly, the DMS should be orientated precisely and the coordinate transformation relationship between the real workpiece and DMS is established. Then, the camera tracks the measured characteristic according to the model data of workpiece. Synchronously, the theodolites are automatically guided to the nearby area of theoretical measured characteristics via the model data of workpiece and the inverse model of theodolite intersection measurement. The guidance of mathematical model data to the theodolite can be realized by the relationship between the measured workpiece and DMS. However, the guidance of mathematical model data to the tracking camera and the tracking outcome of camera to theodolites are achieved by the relationship above and the calibration of the relationship of DMS and the vision tracking subsystem in advance, namely, the establishment of MMS.

MMS and relationships between coordinate systems are shown in Figure 2. The 2D precise turntable is composed of the horizontal turntable and the vertical rotating end platform. The end platform, which the tracking camera is mounted on, is fixed on the horizontal turntable and rotates with the horizontal turntable. The relative position relationship between the camera coordinate system and the end platform coordinate system remains unchanged during the guidance. Three steps are required to establish the transformed relation from double-theodolite coordinate system (DCS) to the camera coordinate system. Build the initial precise turntable coordinate system under DCS. Set up the real-time precise turntable coordinate system. Establish the relationship between the real-time precise turntable coordinate system and the camera coordinate system.

Define DCS as , the initial precise turntable coordinate system as , and the real-time precise turntable coordinate system as .

##### 3.1. Initial Precise Turntable Coordinate System under the Double-Theodolite Coordinate System

Fix ZrO_{2} ceramic balls (2 mm in diameter, precision class G10, GB308-2002/ISO3290-1998) on the end platform of the precise turntable. The precise turntable rotates horizontally several steps, and then the center coordinates of ceramic balls in each position can be measured and recorded via DMS. Since the trajectory of ceramic ball is an arc, which can be fitted by the center coordinates of the ceramic balls, the coordinates of arc center and the normal vector of fitting arc plane can be obtained to determine the vertical rotation axis of the precise turntable, that is the -axis. Similarly, keep the horizontal rotating position of the turntable unchanged while it rotates vertically; the horizontal rotation axis, the -axis, is obtained.

Due to the turntable machining and assembling error, the horizontal rotation axis and the vertical rotation axis are not intersecting but are vertical in different planes. The relative offset Δ between -axis and -axis can be calculated via the parameters of the -axis and -axis. Build -axis, parallel with -axis and intersecting with *-*axis, and the initial precise turntable coordinate system in DCS can be constructed according to the right-hand rule.

##### 3.2. Real-Time Precise Turntable Coordinate System

Assume that the real-time precise turntable coordinate system is and the angles of the precise turntable rotating around the vertical and horizontal axes are and , respectively. Then, the relationship between the initial precise turntable coordinate system and the real-time precise turntable coordinate system can be written as Thereinto,

Set the coordinate of a spatial point in DCS as and that in initial precise turntable coordinate system as . So the relationship between two coordinates can be expressed as with where and are the direction vectors of horizontal axis and vertical axis, respectively; is the initial orientation parameter of the horizontal axis and vertical axis. can be obtained according to the calibration algorithm in Section 3.1. Combining (1) and (3), the relationship between DCS and real-time precise turntable coordinate system is as follows:

##### 3.3. Relationship between the Real-Time Precise Turntable Coordinate System and Camera Coordinate System

Place a planar target ( dots matrix, and 30 mm distance between adjacent features in row and column, as shown in Figure 3) in several positions, and lock the pose and focal length of tracking camera. Capture images of planar target and use calibration algorithm of Zhang [17] to obtain the external parameters of the tracking camera, which indicates the relationship between the camera coordinate system and the target coordinate system. Meanwhile, with the “+” features measurement of the planar target via double theodolites, the relationship between DCS and the target coordinate system can be established. Take DCS as a medium and obtain the relationship between DCS and the camera coordinate system. Then, combined with the aforementioned relationship between the DCS and the precise turntable coordinate system, it realizes the calibration of the relationship between the precise turntable coordinate system and the camera coordinate system.

Assume that a feature point of the planner target in the target coordinate system is and in the camera coordinate in DCS respectively. Define the transformation matrix from the camera coordinate system to the target coordinate system to be ; then we can get

Set the transformation matrix from DCS to the target coordinate system as ; then we get

From (6) and (8), the transforming relationship between the camera coordinate system and DCS can be expressed as

From (5) and (9), the relationship of precise turntable coordinate system and camera coordinate system can be written as

The camera is fixed on the end platform of the precise turntable, so can be calibrated in advance.

Combining (5) with (10), we can get the transforming relationship between DCS and the real-time camera coordinate system, namely, the MMS as

The camera detects the measured characteristic; then the camera optical axis points to the characteristic automatically. Therefore, from (12) and the angles of precise turntable’s horizontal and vertical rotation, the horizontal and vertical angles when both the theodolites point to the same measured characteristic can be obtained. Conversely, if the coordinates of measured characteristics in DCS are known, the tracking camera can also be guided to the measured area.

#### 4. Realization of the Vision Tracking and Guiding Measurement

According to the analysis above, the process of vision tracking and guiding measurement can be realized by two procedures. On the basis of the relationship between real workpiece and the DMS, theodolites and tracking camera are initially guided by the theoretical designed data of workpiece (the mathematical model data of workpiece). The tracking camera guides theodolites to complete the intersecting measurement.

##### 4.1. Initial Guidance of the Theodolites and Tracking Camera Based on Theoretical Designed Data

After orientation of DMS and construction of MMS, the designed or machining reference points are measured via DMS. Then, the theoretical designed data of workpiece is transformed to the coordinate system of DMS. According to the MMS, the camera rotates with the precise turntable to track the characteristic area. After that, the horizontal and vertical angles at which theodolites point to the theoretical characteristic can be determined, respectively, and thus the initial guidance to the tracking camera and theodolites is realized.

##### 4.2. Guidance of Tracking Camera to the Scanning Measurement of Theodolite

After the initial guidance of the designed model data, the sight-axis of theodolite and the optical axis of tracking camera have already pointed to the neighboring area of measured characteristic, with the visible laser mark located in the field of view of camera. Adjust the pose of tracking camera and ensure that the camera can detect the theoretical characteristic mark. Theoretically, when combining the image processing technologies like feature recognition and positioning, with MMS, the tracking camera can guide the theodolites to intersect precisely in the area of measured characteristic, and the precise measurement can be realized. Since the theodolite is driven by stepping motors, a scanning step angle exists in the automatic measurement. Take Leica TM5100A theodolite as an example. Figure 4 shows the changing curve of horizontal angles that the theodolite continuously receives 200 instructions of 0.0005° () horizontal rotation. According to the changing curve, there is no valid movement in the horizontal direction of theodolite besides the stochastic disturbance, and further tests confirmed that the minimum scanning step angle is . Therefore, the collimation of theodolite sight-axis to the measured characteristic and the precise intersection of double theodolites cannot be truly realized in the strict sense. Aimed at the realization of the automatic and high-precision vision guiding measurement, neighborhood scanning of measured characteristic and discrete linear interpolation is necessary.

###### 4.2.1. Neighborhood Scanning of Measured Characteristic

In order to realize the measurement of the characteristic points, the theodolites are controlled to complete the ergodic neighborhood scanning. The scanning process involves the horizontal linear scanning and vertical linear scanning of theodolite. Take the horizontal linear scanning as an example; the horizontal dial plate of theodolite rotates at a small angle while the vertical dial plate is fixed. The neighborhood of measured characteristic is small enough to be regarded as a local plane approximately, named . When theodolite scans horizontally, the trajectory of laser beam coaxial with the sight-axis of theodolite on plane is approximatly a line segment, named and shown us in Figure 5. Lets set as the image plane of tracking camera and as the optical center of the camera. Referring to the ideal pin-hole imaging model of camera, the line segments and have two intersection points with plane , respectively, named and , which are the corresponding image points of and on plane . Then the line segment is the trajectory of laser mark on the image plane. According to the analysis, if the pose of tracking camera is fixed and the theodolite carries out a horizontal or vertical uniaxial scanning only, there is little change on the trajectory slope of laser mark in neighborhood area, and those trajectories on image plane can be approximately regarded as a parallel grid, shown in Figure 6.

Generally, the distance between the theodolite and characteristic points ranges from several meters to tens of meters, while the range of scanning neighborhood is a few centimeters, so . When the theodolite carries out a neighborhood scanning of measured characteristic, an approximate linear relationship can be indicated from the shift distance of laser mark on and the scanning angle of theodolite, namely, . In addition, the distance between tracking camera and measured point is far outweigh the scanning range of laser mark, and can be obtained approximately, and thus .

###### 4.2.2. Discrete Linear Interpolation Model of Laser Mark

Since the relationship between the DCS and the coordinate system of tracking camera is not just translation, the small-scope and uniaxial rotation of the theodolite may cause the image position changes of laser mark in both and directions simultaneously. According to the analysis above, the translational distance of laser mark on image plane and the scanning angle of theodolite have an approximate linear relationship. Set the image plane position of laser mark as and the horizontal angle and vertical angle as and , respectively; then we can get Thereinto, and are coefficients of two linear equations. Slightly drive the theodolite at least three times positions in the range of neighborhood, and take the corresponding value of and as control points; then the coefficients of equations can be calculated via the least square method as

In the above equations,

Thus, (14) can be rewritten in matrix form as

Then (16) can be further transformed as

Substitute the centroid coordinate of measured characteristic into (17), and then the angle when the theodolite aims at the measured characteristic can be obtained. Furthermore, the space coordinate of measured characteristic can be calculated referring to the measurement model of forward intersection.

#### 5. Equipment Setup and Experiment Procedure

In this experiment system, the laser theodolite measurement subsystem is composed of two Leica TM5100A electric theodolites (with DL2 laser pointer), and the vision tracking and guiding measurement subsystem contains a precise turntable, a Toshiba CS8620Ci camera and a Tokina TM33Z1540NPN zoom lens, which are shown as in Figure 7.

Based on the above-mentioned method of vision tracking and guiding measurement, experiments of coordinate measurement of spatial points were conducted to verify the accuracy of the system. As regards small quantity of measured points, the accuracy of manual aiming measurement ranges from 0.01 mm to 0.05 mm. Due to the high precision, the result of manual aiming measurement was regarded as the true value and was compared with the results of automatic measurement.

11 points were measured automatically, and their three-dimensional coordinates can be calculated, respectively. Compared with the results of manual aiming measurement, the deviations of , and coordinate at each point are shown in Table 1 and Figure 8.

The errors of automatic measurement are within 0.3 mm and meet the requirement of large-scale measurement. The factors that affect the accuracy of the automatic measurement involve the extraction accuracy of laser mark, position accuracy of measured characteristic, and the coaxiality of laser beam and the sight-axis of theodolite. On the basis of further optimization of extraction algorithm and improvement of the measuring conditions, the measurement accuracy can still be improved largely.

#### 6. Conclusions and Future Work

Based on traditional theodolite measurement principle of forward intersection, this paper presents a new kind of laser theodolite automatic measurement method for large space and large workpiece (equipment), through the integration of collimating laser coaxial with the sight-axis of new type electronic theodolite and the vision tracking and guiding technology. This method needs no cooperation targets and avoids pasting manual marks on the large workpiece, thus realizing the automatic, quick, and accurate measurement. Therefore, it has significant ramification for the measurement of large-scale space and large workpiece (equipment), such as the geometry appearance characteristics measuring of ships, large aircraft, spacecraft, and high-speed trains and deformation monitoring for large building, dams. In the experiments the measurement errors are within 0.3 mm, and satisfy the requirement of large-scale measurement. By further optimization of extraction algorithm, the measurement accuracy can be improved to the scale of 10 *μ*m, and the measurement system can apply to more measurement occasions and more complicated industrial environment.

#### Conflict of Interests

The authors declared that they have no conflict of interests in this work.

#### Acknowledgments

This work was funded by the National Natural Science Funds of China (61172120, 61372143) and the Natural Science Foundation of Tianjin in China (12JCQNJC02200, 13JCZDJC34800).

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