Abstract
Rotary-laser automatic theodolite (R-LAT) system is a distributed large-scale metrology system, which provides parallel measurement in scalable measurement room without obvious precision loss. Each of R-LAT emits two nonparallel laser planes to scan the measurement space via evenly rotations, while the photoelectric sensors receive these laser plane signals and perform the coordinate calculation based on triangulation. The accurate geometric parameters of the two laser planes play a crucial role in maintaining the measurement precision of R-LAT system. In practice, the geometry of the two laser planes, which is termed as intrinsic parameters, is usually unknown after assembled. Therefore, how to figure out the accurate intrinsic parameter of each R-LAT is a fundamental question for the application of R-LAT system. This paper proposed an easily operated intrinsic parameter calibration method for R-LAT system by adopting coordinate measurement machine. The mathematical model of laser planes and the observing equation group of R-LAT are established. Then, the intrinsic calibration is formulated as a nonlinear least-square problem that minimizes the sum of deviations of target points and laser planes, and the ascertainment of its initial guess is introduced. At last, experience is performed to verify the effectiveness of this method, and simulations are carried out to investigate the influence of the target point configuration in the accuracy of intrinsic parameters.
Highlights
Rotary-laser automatic theodolite (R-LAT) system is a distributed large-scale metrology system with adopting rule of triangulation, which called indoor GPS by Nikon [1] and wMPS [2]
The measurement data for numerical calibration simulations is generated as following steps: (i) sampling desired target points with known coordinate value in CMM coordinate frame; (ii) identifying the truth rotation angles of the two laser planes for each target point according to equation (3) with known truth intrinsic parameters and rotation matrix as well as translation vector; (iii) taking account of the rotation speed fluctuation of the R-LAT, these nominal rotation angles are deliberately distorted by adding zero-mean normally distribute error with known variance (σ=3 arc second)
The main conclusions are summarized as follows: (i) The measurement model of R-LAT system is established as coplanar equations of every R-LAT
Summary
Rotary-laser automatic theodolite (R-LAT) system is a distributed large-scale metrology system with adopting rule of triangulation, which called indoor GPS by Nikon [1] and wMPS [2]. The two rotation angles decide the geometry of the two laser planes for kth R-LAT, while the two planes generate an intersection line goes through the corresponding photoelectric sensor. The measuring mathematic model of R-LAT system has indicated that, for each R-LAT, its two laser plane f1 and f2 formulate two coplanar equations with the rotation angle θ1 and θ2 that go through the target photoelectric sensor P as below: xp [0, cos(. One can figure out that the intrinsic parameters of the R-LAT are the only unknown variables of this coplanar equation group once the coordinate value of these target photoelectric sensors are known. The precise coordinate values of the target photoelectric sensor can be provided by precise coordinate measurement instrument like CMM, laser tracker and so on. In practical, looking forward to improve the accuracy of the solution, the observing equation group is overdefined by measuring plenty of target photoelectric sensor
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