This work describes the development of a quasi-distributed real-time tactile sensing system with a reduced number of fiber Bragg grating-based sensors and reports its use with a reconstruction method based on differential evolution. The sensing system is comprised of six fiber Bragg gratings encapsulated in silicone elastomer to form a tactile sensor array with total dimensions of 60 × 80 mm, divided into eight sensing cells with dimensions of 20 × 30 mm. Forces applied at the central position of the sensor array resulted in linear response curves for the gratings, highlighting their coupled responses and allowing the application of compressive sensing. The reduced number of sensors regarding the number of sensing cells results in an undetermined inverse problem, solved with a compressive sensing algorithm with the aid of differential evolution method. The system is capable of identifying and quantifying up to four different loads at four different cells with relative errors lower than 10.5% and signal-to-noise ratio better than 12 dB.
Some works have pointed to the use of arrays of fiber Bragg grating- (FBG-) based transducers in tactile sensing systems (TSS) applied to the mapping of forces in robotic systems [
Different approaches have been proposed for the development of sensor arrays. Such strategies include gluing grating-based transducers directly under the surface of a steel or polymethyl methacrylate (PMMA) plate [
The embedding of many FBG in a single thin sheet of a host material makes the tactile sensor array (TSA) flexible, so that it can be adapted to surfaces with different forms. Among the manufacturing methods, molding is a low-cost process that allows an easy encapsulation of a set of FBG sensors [
Some tactile sensing systems use one sensor element dedicated to each point of sensing, requiring an increased number of elements if the area of monitoring is wide. Under these conditions, the cost and complexity of the sensing system also increase. Nevertheless, this number can be reduced if the responses of the sensor elements in the TSS are coupled, making such a system less expensive and more robust [
Computational methods as artificial neural networks [
In 2017, Negri et al
Devices based on different principles of operation as resistive strain gauges [
In this work, the SDE method was used to reconstruct up to four loads applied on the surface of a TSA composed of six FBGs embedded in a single thin and flat sheet of silicone elastomer. The paper is an extended version of a previous work that describe the details of the sensor array manufacture [
Fiber Bragg gratings were used in this work owing to their unique advantageous characteristics and the capacity to detect mechanical deformations [
Longitudinal deformations and temperature variations produce changes in the effective refractive index (
As the FBG shows cross-sensitivity to deformation and temperature, it is necessary to compensate such effect in order to measure only mechanical deformations. If the temperature is kept constant, the response of the FBG to longitudinal deformation is given by the following:
In this work, all FBGs were written in standard single mode fiber (SSMF, DRAKTEL, G-652) by the exposition to laser light diffracted by a phase mask [
The first stage of the TSA production starts with the adequate choice of the host material used to embed the FBG. A room temperature vulcanizing (RTV) silicone (Down Corning, BX3-8001) was chosen as embedding material considering its suitable properties [
To shape the tactile sensor array and also to dispose the six FBGs in the middle of the silicone sheet thickness, it used a 3D-printed mold produced from a model created by a computer-aided-design (CAD) software. This fabrication method allows the production of narrow slits at the mold walls, which are used for positioning the segment of the optical fiber containing the FBG in the desired place. In addition, with the use of acrylonitrile butadiene styrene (ABS) filament (1.75 mm) to print the mold, there is nonadhesion with the RTV silicone, resulting in an easy process of demolding.
The mold is a rectangular box with internal dimensions of 75 × 105 mm and walls 5 mm high. The slits in the opposite walls are 2.5 mm deep and 15 mm apart from each other, as shown in Figure
Schematic representation of the FBGs at the 3D-printed mold and a detail of the slits in the mold walls.
The six optical fiber segments, each one containing a single FBG, are positioned at the mold using the slits. FBGs are distributed in order to keep the gratings approximately 25 mm apart. After this process, the mold was fixed on a flat and stiff surface. Then, the fiber segments were stretched one by one and the loose tips were fixed on the flat surface with adhesive tape. Finally, the silicone mixture with quartz was carefully spread out in the mold forming a homogeneous layer embedded with the FBGs.
The vulcanization process occurs at room temperature along 24 hours; after this period, the TSA is easily removed from the mold. The TSA surface kept in contact with the mold is free from irregularities and is used as the sensing surface. Afterwards, the tips of the optical fiber segments were connected generating a set of six in-series FBGs (Figure
Tactile sensing system (TSS) and the interrogation unit.
For the TSA interrogation, one of the free fiber tips is connected to a superluminescent LED (Superlum PILOT-2, centered at 1558.2 nm, spectral bandwidth of 73.8 nm) via an optical coupler. The reflected spectra of the FBG sensors are measured by an optical interrogation monitor (Ibsen, I-MON 512E, 970 Hz maximum sampling rate) with resolution smaller than 0.5 pm. All spectral data are sent to a computer that records the Bragg wavelengths and their relative shifts. Figure
Spectrum of the six FBGs in the TSA recorded with an optical spectrum analyzer (Anritsu, OSA MS9710b, 1001 samples, 0.1 nm resolution).
For the TSA assessment by means of the FBGs’ repeatability and linearity, loads up to 250 g were applied at the central position of the array, in steps of 25 g with delay of approximately 5 s, using the
Schematic representation of the
The same previously described methodology was applied to a single FBG of the TSA, and the complete metrological characteristics were determined, including hysteresis, sensitivity, resolution, and linearity [
The TSA linearity was evaluated in three tests in which loads were applied both individually and simultaneously on the sensor array to verify the additivity property. It is expected for a linear system that the summation of the individual responses matches the response obtained with the simultaneous application of those loads [
The TSA was divided into eight rectangular regions (sensing cells labeled from A to H) with dimensions of 20 × 30 mm, as shown in Figure
Schematic representation of the TSA divided into eight sensing cells.
As sensitivity depends on the distance between the load application and the sensor element, the size of the sensing area was defined in order to guarantee the coupling between the six FBG responses [
The optimization method used to solve the problem in (
First, a set of validation tests, containing 22 values measured with the application of up to three loads (200 g, 100 g, and 50 g) on the TSA, was used to determine the parameters
The metallic cylindrical loads with different masses have also different cross-sections. Therefore, circular-shaped elements with 20 mm of diameter were positioned on the TSA surface in order to create a unique contact area.
After all tests, the signal-to-noise ratio (SNR) was used as a metric to evaluate the matching between the reconstructed signals and the actual applied loads [
The sparse differential evolution (SDE) depends on the knowledge of the sensing matrix
The application of loads at the central position of the TSA resulted in wavelength shifts of all FBGs. This behavior indicates a coupled response among the FBGs, allowing its application in a quasi-distributed sensing system. An important feature is the linearity of the FBG responses that allows the use of the optimization method described in (
As shown in Table
FBG sensitivities for loads applied at the central position of the TSA.
Sensor | Sensitivity (pm/g) | Distance of the load application (mm) | |
---|---|---|---|
1 | 0.0327 ± 0.0004 | 39.53 | 0.999 |
2 | 0.0661 ± 0.0004 | 25.74 | 0.999 |
3 | 14.58 | 0.999 | |
4 | 14.58 | 0.997 | |
5 | 0.0455 ± 0.0007 | 25.74 | 0.998 |
6 | 0.0183 ± 0.0003 | 39.53 | 0.998 |
FBGs 3 and 4, the FBGs closest to the position of the load application, showed the highest sensitivities, as can be seen in Table
As the positioning of the segments of fiber containing the FBGs in the mold is manually controlled, small differences in the distance of the gratings with respect to the point of load application result in different sensitivities for these gratings. Furthermore, the 3D printer has 0.10 mm of resolution, which results in slits with 0.25 ± 0.10 mm.
It is well known that a nonuniform distribution of mechanical deformation along the length of an FBG leads to a chirping, which deforms the spectrum of the fiber Bragg grating [
An overall understanding of the behavior presented by the FBGs embedded in the silicone elastomer is necessary to optimize the sensor. Therefore, for a complete characterization, the previous test was replicated; however, the loads were applied directly at the position of one of the FBGs in the TSA. The complete metrological characteristics are shown in Table
Metrological characteristics of one FBG in the TSA.
Metrological characteristics | Encapsulated FBG |
---|---|
Measuring interval (g) | 0–250 |
0.99 | |
Sensitivity (pm/g) | 0.371 ± 0.003 |
Resolution (g) | 1.35 ± 0.39 |
Linearity (%) | ± 2.42 |
Hysteresis (%) | ± 4.33 |
Linearity and hysteresis were calculated with respect to the difference between the upper and lower limits (
Searching for a complete assessment of the TSA linearity, tests of additivity were carried out and the results are shown in Figures
Sensor responses to loads applied individually (stack columns) and simultaneously (square symbols) on cells B and G. The inset indicates the position of the loads in a diagram of the TSA.
Sensor responses to loads applied individually (stack columns) and simultaneously (square symbols) on cells E and F. The inset indicates the position of the loads in a diagram of the TSA.
Sensor responses to loads applied individually (stack columns) and simultaneously (square symbols) on cells A, D, and H. The inset indicates the position of the loads in a diagram of the TSA.
Tests of additivity resulted in errors lower than 31.5% for FBGs close to the applied loads. For the FBGs far away from the point of the load application, errors of up to 92% were obtained. Hysteresis and thermal expansion were the main sources of error. Figure
The TSA performance was assessed with the reconstruction tests carried out with 1, 2, 3, and 4 loads. As previously stated, the TSA was divided into eight sensing cells, each one with 30 × 20 mm, and different configurations of load application were tested.
The ulimit for the SDE method was 0.250 (250 g); in other words, the reconstruction algorithm only recognizes applied loads from 0 to 250 g. This approach is used to limit the search space and optimize the results. Negri et al
Figure
Reconstruction results for loads simultaneously applied to the TSA: (a) the worst and (b) best configurations for three loads; (c) the worst and (d) best configurations for four loads. One of the cases where the SNR was lower than 12 dB is indicated by arrows in (c).
For the tests with four loads, Figures
Table
Average SNR, relative error, and reconstruction ratio for the reconstruction tests with application of up to four loads.
Number of loads | SNR (dB) | SEM (dB) | Error (%) | RR (%) |
---|---|---|---|---|
1 | 25.440 | 0.998 | 8.775 | 100 |
2 | 25.170 | 0.854 | 7.363 | 100 |
3 | 23.279 | 0.573 | 8.117 | 100 |
4 |
The results in Table
Considering the sensing area of 60 × 80 mm divided in 8 cells, the spatial resolution is 30 × 20 mm.
The TSS metrological characteristics shown in Table
Metrological characteristics of the tactile sensing system.
Metrological characteristics | TSS |
---|---|
Measuring interval (g) | 25–250 |
Size (mm) | 60 × 80 |
Spatial resolution (mm) | 30 × 20 |
Error (%) | <10.5 |
The circular-shaped contact elements produce small wavelength shifts in the Bragg wavelengths that are compensated with a reference spectrum. Figures and tables of this section show results obtained with experiments realized at 22.0 ± 0.5°C. Nevertheless, the capability of reconstruction was also tested with the TSA and the loads in thermal equilibrium at 17.5 ± 0.5°C and 27.0 ± 0.5°C without impairing the system performance.
The ability of detecting four loads simultaneously applied to the TSA opens the possibility of mapping forces produced by the touch of the hand. Figure
Picture showing a real-time reconstruction resulting from the touch of four fingers at the TSA.
As the body skin and the silicone have low thermal conductivity and the silicone shows slow thermal expansion, the TSA performance is not impaired by heat transfer when the contact with the fingers occurs during a short-time interval of a few seconds.
This application shows that the TSS of this work could be used for rehabilitation of the hand or any other real-time application that requires recognizing the touch of the fingers.
The FBG encapsulation with silicone allows manufacturing a flexible TSA that can be directly attached to surfaces with different shapes. Furthermore, the silicone encapsulation is economically attractive and the production takes 24 hours without the need for special cure processes.
The FBG-coupled responses, allied to the linearity of the system, allow the TSA application in quasi-distributed sensing with a reduced number of the sensors.
The TSA operation is based on the measurement of the induced wavelength shifts of the six FBGs with respect to the reference wavelength values measured just before the force application. Therefore, as the system recognizes a pattern in the wavelength shifts experienced by the set of FBGs, the reconstruction performance is not affected by the temperature of operation if all system is in thermal equilibrium with the environment. Localized changes of temperature can negatively affect the TSA performance; however, the influence of temperature changes in the sensor responses is reduced by the encapsulation due to the low value of thermal conductivity [
Reconstruction of up to four simultaneous loads in real time with an average SNR of 19.66 dB and relative error lower than 10.5% was demonstrated with the SDE method developed by Negri et al
The method of encapsulation allows the production of a flexible and robust array of sensors embedded in a unique block of silicone that represent a considerable improvement compared to the rigid steel plate used in [
The advantages of the silicone elastomer combined with the 3D printing technology and the outstanding characteristics of the FBGs result in tactile sensor array that can be used in a large number of applications, including biomedical and medical areas, mainly in the rehabilitation of the hand.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
This work was supported by the Brazilian agencies CAPES, CNPq, FINEP, and Fundação Araucária.
Examples of the tactile system operation are shown in two videos. One of them shows the spatial mapping of four loads and, in the other one, the TSA realizing real-time touch sensing can be seen.