3D Shape Sensing of Elongated Objects Using Fibre Bragg Gratings
Navigating in GPS deprived areas can be a challenging task, especially when the environment doesn’t offer sufficient visual clues for stereo camera matching. This paper describes the development of a 3D shape sensor based on optical fibres and the resulting “Sensor Wand”. The intension was to develop a Wand that could be easily deployed in small holes like drill holes for mining or geo-technical applications and determine their 3D shape, which is a vital information for Drill and Blast Engineers in mining, or a geo-technical assessment in civil applications. Initially the expected response of the Wand was modelled for a number of configurations. A Wand was then manufactured to verify the simulated results. The mechanical manufacturing proved itself to be significantly more complex than originally anticipated. As a result, the sensor accuracy was below expectation. Improvements to the manufacturing process were identified to increase the performance of the next generation of the Sensor Wand.
Keywords3D shape sensing Fibre optic sensing Fibre bragg grating FBG
Meaningful navigation requires the knowledge of the current location and pose. In many applications this information can be derived from Global Positioning Systems, Inertial Navigation Units, (stereo) cameras, or a combination of these systems. However, there are applications where it is neither practical nor even possible to utilise these traditional localisation systems. Such examples include medical, underwater and downhole sensing in the oil, gas and mining industries.
The Commonwealth Scientific and Industrial Research Organisation (CSIRO) through its Minerals Resources Business Unit developed a 3D shape sensor based on Fibre Bragg Gratings (FBGs) embedded in optical fibres that can be used in these challenging environments.
2 Sensing Concept
the Luna Fibre Optic Shape Sensor , which has an extremely high spatial resolution as it uses Rayleigh backscatter to determine the strain along the length of the sensor. Because of this sensing principle it has a limited sensor length of 1.5 m and is very expensive; and
the Fraunhofer Fibre Optical 3D Shape Sensor (FibreNavi) , which requires a highly sophisticated optical setup to burn the FBGs into the fibre.
The CSIRO design uses a simple configuration utilising four optical fibres with FBGs embedded in a linear arrangement. These fibres are available off the shelf and then were embedded in a glass-fibre composite tube.
3.1 Static Model and Simulations
This figure shows that the reconstruction fits very well initially, but drifts at the “turning points”. The reconstruction algorithm assumes a constant curvature between sample points, however, this is not a valid assumption for a sinusoidal or helical path.
3.2 Dynamic Model and Simulations
It is worth noting that the above simulations use a static model that can be seen as a “snapshot”. In reality the sensor will progress into the hole and so it is possible to measure the defection at a given depth multiple times, which will reduce all random and not systematic errors. Therefore a dynamic model was developed to simulate the progression of the Sensor Wand through the hole and compare the new readings with the old measurements. Averaging of the repeated deflection angle measurements was used to combine the consecutive readings.
The Sensor Wand measures deflection, which is a relative parameter, therefore the algorithm needs a start point and direction for the absolute 3D shape determination. These values can be assumed to be known at the beginning of the hole. Once fully submerged the algorithm uses its previous estimated path to determine these values.
3.3 Initial Discussion
Depth of hole
Theoretical or design hole shape
Distance between FBG stages
Number of FBGs per stage
The model has been used with various input parameters to identify the influence of particular parameters and their error contribution. We observe that when the interrogator resolution is reduced the error will grow, and that once it reaches 100 pm, the interrogator resolution becomes the dominant error contribution factor. Reducing the Sensor Wand length also increases the error. Reducing the distance between the FBG stages on the other hand reduces the error as demonstrated in Figs. 2 and 3. If the interrogator resolution is increased again to a value of 1 pm, which is achievable with state-of-the-art interrogator systems, the resulting error returns back to the original size of around 5–6 cm.
The heavy oversampling, which happens when a point in the hole is measured again by a consecutive FBG stage, is responsible for the good performance even for a short Sensor Wand.
Unfortunately the fabricated Sensor Wand, which was constructed during this project showed a number of imperfections. Therefore it was not possible to verify the simulated data with the measurements. However, the measurement results show qualitatively the expected behaviour.
4 Sensor Wand Performance
The wavelength and peak level values for each FBG were recorded during the testing and stored in a hierarchical data format grouped by penetration depth. A recording of 18.5 m depth in 25 cm steps resulted in a data file containing roughly 2.5 million values. The data processing was conducted in Matlab. The first task after reading in the data was to apply a filter to remove double peaks and outliers.
Furthermore, the filter verifies that the peaks are within the expected wavelength range. Values which differ by more than ±1 nm from the factory calibration, corresponding to roughly 0.5 mƐ, are tagged to be ignored during processing. Reasons for incorrect wavelength values could be glitches in the interrogator, resulting in some peaks not being recorded, or temporary “over-stretching” of some FBGs during manual handling.
The next step is the data pre-processing. During this step the algorithm searches for the FBGs that are already in the hole and computes the mean values from the recorded data sets. At the same time, the on-the-fly calibration values are generated for the FBGs currently in the calibration jig.
Finally, the deflection algorithm uses the mean FBG wavelength and the calibration values to compute the 3D shape, which accumulates up as the Sensor Wand progresses deeper into the hole.
4.3 Initial Results
To investigate the reason for the deflection of the reconstructed path, the calibration values and the final wavelength values for the fully penetrated Sensor Wand were compared. Theoretically, both values should be equal as no deflection force is applied during the on-the-fly calibration, and when fully submerged in the hole.
All results were heavily influenced by the fibre misalignment and this artefact dominates the plots. Given the limitations of the constructed Sensor Wand these results are very promising nevertheless. The algorithms developed as part of this project managed to reconstruct the 3D shape of the Sensor Wand and reduced some of the errors introduced by the artefacts in the wand. However, the measurement accuracy did not meet the expectations from the simulations due to the wand artefacts.
Future Deflection Sensor Wand developments should take potential residual stresses in the composite material into account; and if possible, optimise the design to reduce these stresses. Furthermore, it is important to characterise the actual location of the FBG along the tube so that the compensation algorithm can use the correct position offsets rather than a first order estimate.
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