Modelling and optimization of a modified sequential multilateration method for three-dimensional coordinate collection

Zhenjiu Zhang,Linzhong Xia,Wei Zhang,Zhenyu Zhao,Xiaomei Xu,Jiaji Jiang,Mingjun Liu

doi:10.1177/1687814019889790

Zhenjiu Zhang, Linzhong Xia + Show 5 more

Open Access

https://doi.org/10.1177/1687814019889790

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Abstract

This article proposes a modified sequential multilateration method for measuring three-dimensional coordinates. The measuring system consists of a single laser tracker and four relay targets whose relative positions have been pre-calibrated by the multilateration method. The laser tracker is fixed on three prescribed positions successively, and these positions can be calibrated by using the distances between the laser tracker and the four relay targets based on the multilateration principle. Subsequently, the three-dimensional coordinates of each under-test point can be determined by the three laser trackers’ positions based on the trilateration principle. This method is more flexible than previous multilateration methods for three-dimensional coordinate collection, especially if the measurement space is partially covered by other objects. The mathematical model of this method is established. Based on the Monte Carlo method, a series of computer simulations are performed to optimize the system arrangement by investigating the performances of the measuring system with different system arrangement, and an optimal system arrangement is finally obtained. Practical measurement is also conducted to demonstrate the validity of the proposed method by comparing with a reference coordinate measuring machine.

Highlights

Three-dimensional (3D) coordinate measurement is widely used in industrial production and scientific research, such as quality inspection of work piece, surface reconstruction from point clouds and measurement of geometric error of machine tools.[1,2,3] The coordinate measuring machine (CMM) is one of the most typical instruments for 3D coordinate measurement, and it is of high measuring accuracy
Its measuring volume is restricted by the measuring range, and the samples to be measured must be fixed on the table of the CMM, so CMM is not suitable for geometric error measurement of machine tool and large-scale metrology
A modified sequential multilateration method based on the laser tracker is proposed to measure coordinates of spatial points

Summary

Introduction

Three-dimensional (3D) coordinate measurement is widely used in industrial production and scientific research, such as quality inspection of work piece, surface reconstruction from point clouds and measurement of geometric error of machine tools.[1,2,3] The coordinate measuring machine (CMM) is one of the most typical instruments for 3D coordinate measurement, and it is of high measuring accuracy. The verification is realized by comparing the laser tracker with a high precision reference CMM of which maximum permissible error, according to the manufacturer’s catalogue, is (0.9 + l/333) mm, where l is CMM’s displacement in the measurement procedure In this verification, eight target points are arranged to form a circle with diameter being 300 mm, and the distance between these points and the laser tracker is approximately 1 m. The selfcalibration is applied to obtain the coordinate of laser tracker’s position and the absolute distances between all the target points and the laser tracker This experiment is repeated 20 times, and the maximum deviation and the repeatability are found to be 0.807 and 0.334 mm, respectively. The first step is to simulate the position error of the four relay targets P0, O, Q and K, and the second step is to simulate the 3D coordinate measurement uncertainty of the modified sequential multilateration method

The computer simulation of the position errors of the relay targets

Experiments and analysis

Conclusion