Optimization Method for Solution Model of Laser Tracker Multilateration Measurement

Chen, Hongfang; Tao, Zhi; Shi, Zhaoyao; Song, Huixu; Yan, Hao

doi:10.1515/msr-2016-0025

Cited by 10 publications

(8 citation statements)

References 12 publications

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“…Such a choreography can be achieved in less than 20 s. It is then possible to move the target to another position. After at least nine target positions, 11,12 a multilateration algorithm can be applied for three-dimensional position determination from the set of distance measurements (4 × 9 distances).…”

Section: Multilateration Systemmentioning

confidence: 99%

“…However, for multilateration application, its value does not need to be known since it can be determined online using an algorithm with self-calibration. 11,12…”

Section: Review Of Scientific Instrumentsmentioning

confidence: 99%

“…8 Therefore, the multilateration coordinate measurement technique appears as a good alternative since it eliminates the angular contribution, although it requires a large number of distance meters distributed throughout the space. 9 Indeed, the distances between four measuring stations and one target, associated with different target locations, provide sufficient information to establish the spatial locations of the target and that of the measuring heads themselves (using the self-calibration technique [10][11][12][13] ). Such multilateration systems based on interferometry were already demonstrated and commercialized, using fringe counting interferometry with commercial laser tracer devices 14 or more recently using Frequency Scanning Interferometry.…”

Section: Introductionmentioning

confidence: 99%

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Assessment of the mechanical errors of a prototype of an optical multilateration system

Guillory

Truong

Wallerand

2020

Review of Scientific Instruments

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We are developing a multilateration system at a reasonable cost that aims at an accuracy better than 50 µm determined with a consistent metrological approach. In this context, an absolute distance meter, developed in-house, is used as a unique telemetric system to feed the different measurement heads of the multilateration system through a network of optical fibers. The uncertainty contribution for a distance measurement of the telemetric system itself, in a controlled environment, is from 2 µm up to 100 m (k = 1). In this paper, the uncertainty contribution due to mechanical designs of the measurement heads and the target is estimated: the gimbal mechanisms we have designed are presented and their sources of error are identified, experimentally quantified, and minimized. At the end, we demonstrate that the current design of the measurement head does not induce errors higher than 2 µm on the measured distances and the design of the target does not induce errors higher than 9 µm.

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Section: Multilateration Systemmentioning

confidence: 99%

“…However, for multilateration application, its value does not need to be known since it can be determined online using an algorithm with self-calibration. 11,12…”

Section: Review Of Scientific Instrumentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Assessment of the mechanical errors of a prototype of an optical multilateration system

Guillory

Truong

Wallerand

2020

Review of Scientific Instruments

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“…To minimize the cost function described in formula ( 6) correctly, at least nine target positions have to be measured [26,28]. This is the minimum of points required to have an equation system with more observations than unknowns.…”

Section: Data Processingmentioning

confidence: 99%

Uncertainty assessment of a prototype of multilateration coordinate measurement system

Guillory

Truong

Wallerand

2020

Precision Engineering

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Large Volume Metrology is essential to many high value industries to go towards the factory of the future, but also to many science facilities for fine alignment of large structures. In this context, we have developed a multilateration coordinate measurement system, traceable to SI metre, and suitable for outdoor measurements or industrial environments. It is based on a high accuracy absolute distance meter developed in-house and shared between several measurement heads by fibre-optic links. Thus, from these measurement stations, multiple distance measurements of several positions of a target can be performed. At the end, coordinates of the heads and of the different target locations are determined using a multilateration algorithm with self-calibration. In this paper, the uncertainty of this multilateration coordinate measurement system is determined with a consistent metrological approach. First, 13 different sources of errors are listed and quantified. Then, thanks to Monte Carlo simulations, the standard uncertainty on a single absolute distance measurement is assessed to 4.7 µm. This includes the uncertainty contribution of the telemetric system itself, but also the contributions of the mechanical designs of the measurement heads and the target. Lastly, measurements of three-dimensional coordinates of target positions are performed in a control environment, then in a large workshop without temperature control: these measurements validate the uncertainty assessment of the system.

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“…Gao et al [9] summarized the multi-axis coordinate measurement methods such as triangulation and multilateration. To determine the TI position coordinates, Chen et al [10] proposed a calibration procedure based on additional measurements comparatively to the classic multilateration procedure. Camboulives et al [11] presented a calibration procedure of a 3D working space based on multilateration using only one TI.…”

Section: Introductionmentioning

confidence: 99%

Effects of number of digits in large-scale multilateration

Linares

Arroyave-Tobón

Pires³

et al. 2020

Precision Engineering

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Since many years ago, multilateration has been used in precision engineering notably in machine tool and coordinate measuring machine calibration. This technique needs, first, the use of laser trackers or tracking interferometers, and second, the use of nonlinear optimization algorithms to determine point coordinates. Research works have shown the influence of the experimental configuration on measure precision in multilateration. However, the impact of floating-point precision in computations on largescale multilateration precision has not been addressed. In this work, the effects of numerical errors (rounding and cancellation effects) due to floating-point precision (number of digits) were studied. In order to evaluate these effects in large-scale multilateration, a multilateration measurement system was simulated. This protocol is illustrated with a case study where large distances (≤20 m) between pairs of target points were simulated. The results show that the use of multi-precision libraries is recommended to control the propagation of uncertainties during the multilateration computation.

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Optimization Method for Solution Model of Laser Tracker Multilateration Measurement

Cited by 10 publications

References 12 publications

Assessment of the mechanical errors of a prototype of an optical multilateration system

Assessment of the mechanical errors of a prototype of an optical multilateration system

Uncertainty assessment of a prototype of multilateration coordinate measurement system

Effects of number of digits in large-scale multilateration

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