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Abstract
A sliding sensor based on a fiber Bragg grating (FBG) was proposed to enable mechanical fingers to softly grasp an object. FBG strain sensors are embedded in a polymeric material as a sensing element to obtain sliding information. This study expounded the structural design of the sliding sensor and the mechanism of sliding sensation, which were verified using the finite element simulation. The static and dynamic performances of the sliding sensor were studied experimentally. Finally, the sensing signals were processed using fuzzy logic. Results show that the FBG sliding sensor with a simple structure has high sensitivity and can reliably detect the contact state of the target object, thereby providing a design scheme for the study of the sliding sense of mechanical fingers.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Sliding sensing is an important process in the control system of a robot, which can be used for describing the contact status between a mechanical finger and a target object [1]. Data on this status enables the mechanical fingers to exert a minimum force when grasping objects without sliding. At present, sliding sensors are progressing toward integration, miniaturization, and intellectualization; functionalities, such as the ability to determine whether the target is sliding and detect the sliding distance, have also been developed [2]. Different types of tactile sensors were used in this study, which included piezoelectric sensors, capacitive sensors, and optical waveguide sensors [3–5]. For example, a 3 × 1 tactile sensor array embedded in a polydimethylsiloxane was able to detect sliding. The size of the sensing array, which was composed of piezoelectric vibration sensors, was 44 mm × 44 mm × 3 mm [6]. However, there are some disadvantages, such as its complicated design and difficult array scanning, restrict the wide application of this sensor. Another capacitive sliding sensor for intelligent robot bionic skin was proposed by Xu et al., which achieved omnidirectional slip detection [7]. Capacitive sensors have high accuracy and spatial resolution, but they are susceptible to electromagnetic interference. In contrast, the dielectric constant is susceptible to temperature fluctuations. Yuan et al. proposed a fiber-optic sliding sensing method that uses the reflective modulation of a two-dimensional rotating plane-mirror in which an automatically compensated five-fiber sensing probe was adopted to achieve sensing [8]. The fiber-optic sensor has a simple structure and is resistant to electromagnetic interference, but the signal processing methods are complex, which is not conducive to commercialization because of strict production requirements.
The fiber Bragg grating (FBG) sensor has advantages such as its small size, minimal loss, corrosion resistance, immunity to electromagnetic interference, and multiplexing capability [9–11]. Thus, a distributed sliding sensing array consisting of FBGs was proposed. The sensing array was embedded in the packaging material. When there is no relative sliding between an object and the packaging material, the shear force causes internal deformation of the packaging material. In turn, this deformation changes the length and the grating periodicity of the embedded FBG and thus shifts the center wavelength; this shift will eventually stabilize in a particular state. Relatively, when the object slips on the surface of the packaging material, a tiny vibration in the packaging material will be caused owing to the frictional force. This vibration results in the center wavelength shift of FBG sensors embedded in the packaging material within a certain range. For an FBG sliding sensing array arranged in the same plane, the center wavelengths of two adjacent FBGs that detect the sliding reach their peak values and change alternately at different times when sliding occurs between the object and the packaging material. In this paper, first, the theoretical model was presented, followed by an ANSYS finite element simulation to analyze the strain of the sensor. Next, experimental verification and how fuzzy logic was used to process the output signal of the FBGs are discussed.
2. Theory
The center wavelength of an FBG is related to its intrinsic parameters, such as refractive index and grating period, which is sensitive to ambient temperature, axial strain, and radial pressure. When an FBG is subjected only to an axial strain εz, the relative wavelength shift is given by
where ΔλB and λB are the wavelength shift and center wavelength of the FBG, respectively, and Pe is the effective strain-optic coefficient of the fiber.A theoretical model was developed to establish an explicit relationship between the applied shear force and the strain on the FBG. The x-axial shear force (Fx) is applied on the surface of the packaging material and the effective sensor dimensions are length l, width b, and height h. The theoretical model of the shear force [12] applied on the FBG can be built as follows shown in Fig. 1.
The shear strain of the elastic packaging material is given by
where τ is the shear stress and G is the shear modulus of the packaging material.For ease of analysis, it is assumed that no slipping occurred between the packaging material and the FBG sensor, and Δl1 = Δl2 = Δl. Thus,
Equating Eqs. (2) and (3) yieldsThe shear modulus can be written aswhere Em and vm are the Young’s modulus and Poisson’s ratio of the elastic material, respectively.The x-axis elongation of the packaging material can be obtained by solving Eqs. (4) and (5):
whereAlthough the angle between the FBG and the x-axis (θ) changes with the applied shear force, we can assume it as constant because the change in θ is very small; that is, the embedding angle of the FBG remained constant; θ ≈φ. Thus, the elongation of the packaging material along the diagonal can be written as
According to the definition of strain, the applied strain on the FBG is given by
From Eq. (9), to obtain the maximum sensitivity, the value of θ should be 0° for detecting the shear force of the x-axis. Correspondingly, it should be 90° for the y-axis.
3. Design and analysis of sliding sensors
3.1 Structure design of sensing unit
The sliding sensing unit, which consisted of four FBG strain sensors, was embedded in a polymeric material as shown in Fig. 2. To reduce the deviation between the sensor and packaging material, the cladding surface of the FBG was pretreated by a silane coupling agent. Friction-induced micro-vibration, caused by relative sliding between the target object and the surface of the packaging material, could result in the shifting of the FBG center wavelength.
3.2 Simulation results and analysis
The embedded position of the FBG should be determined first to obtain the maximum shear force sensitivity. The material parameters used in the ANSYS simulation were set as follows: 1) a dimensions of 75 mm × 15 mm × 5 mm for the silicone rubber packaging material, 2) a Young’s modulus of 3.7 Gpa, and 3) a Poisson’s ratio of 0.486. Then, a positive x-axis shear force fx = 0.5 N was exerted at the center of its surface, which was evenly applied over an area of 100 mm2 (10 mm × 10 mm). The coordinate origin was set at the center position of the bottom surface of the packaging material, and the x-axis displacement nephogram of the packaging material and different y-axis sections (y1 = 5 mm, y2 = 0 mm) are shown in Figs. 3(a) and 3(b). For the same y-axis section in Fig. 3(b), the closer to the surface of the packaging material, the larger the displacement value can be found. The maximum x-axis displacement value (1.12 × 10−8 m) can be obtained at the coordinated of (0, 0, 5).
Fig. 3 Simulation results of the FBG slip sensor under x-axis positive shear force: (a) 3D view and (b) Sectional drawing of y-axis.
In order to optimize the embedded thickness (z) of the FBG sensor, the length of the FBG sensor was set as 10 mm in the simulation. The relationship between the horizontal positions of fx applied and the length changes of sensor embedded at different thicknesses of z = 2.5 mm, 3 mm, 3.5 mm, 4 mm and 4.5 mm are shown in Fig. 4. By observing Fig. 4, the maximum absolute value of the length change (7.59 × 10−9 m) was reached when the FBG was embedded at z1 = 4.5 mm.
Then, different FBG lengths of l = 4 mm, 6 mm, 8 mm, 10 mm, and 12 mm were used when embedded at z1 = 4.5 mm. Fig. 5 shows that the maximum absolute value of the length change (8.18 × 10−9 m) was reached when l5 = 12 mm. The longer the sensor, the larger the length change of the sensor under the same shear force. Therefore, the FBG shear force sensor should be selected according to the environment and equipment in practical applications.
After optimizing the embedding position and FBG length, different fx values ranging from 0.1 N to 0.5 N were applied based on different embedding angles (θ). The fitting curves in Fig. 6 show that different magnitudes of fx can be perceived by the embedded FBG sensor, and the maximum elongation sensitivity of the x-axis was 1.63 × 10−8 m/N at the angle θ = 0°. This result is the same as that of the theoretical analysis.
4. Experiment and data processing
4.1 Experiment
The experimental setup consisted of a broadband light source, an FBG demodulator (with a resolution of 1 pm), a computer, and the sliding device. A schematic of the experimental setup is given in Fig. 7. The light emitted by the broadband light source is transmitted to the FBG sensor through the isolator and the coupler. Then the information of reflected light is sent to the demodulator through the coupler and finally displayed on the computer. The packaging material used in the experiment is a cuboid-shaped silicone rubber (75 mm × 15 mm × 5 mm). The FBG sensor is embedded in the packaging material after pretreated by a silane coupling agent. When the packaging material was in contact with the target object or relative sliding occurred between them, the center wavelength of the corresponding FBG in the sensing array shifted.
4.2 Output characteristics of sliding sensor
4.2.1 Measurement of shear force
According to the structure of sensing unit in Fig. 2, the four FBG sensors were embedded in the packaging material symmetrically. For the sensing unit, because of its symmetry, a shear force was applied along the positive axis (both x and y), and fx or fy was applied by loading different weights via pulleys in the vertical direction using a connecting device. The maximum ranges of fx and fy were from 0 to 0.348 N, and the resolutions of fx and fy were both 0.058 N. Figures. 8 and 9 indicate the relationship between the center wavelength shifts of four FBGs and the shear force by using the experimental device shown in Fig. 7.
As shown in Fig. 8, since the embedded direction of FBG1 is parallel to fx, the wavelength shift of FBG1 is linearly related to fx. The center wavelength of FBG2 is negatively shifted due to compression, but it is not linearly related to fx. Meanwhile, because FBG3 and FBG4 are perpendicular to the direction of shear force fx, their central wavelength remained unchanged.
The wavelength shifts of four FBGs are shown in Fig. 9 when fy was applied on the surface of the packaging material. In Fig. 9, the wavelength shift of FBG3 is linearly related to fy. FBG2 is compressed and its center wavelength is shifted to the negative direction. Moreover, the center wavelengths of FBG1 and FBG2 remained unchanged.
After linear fitting, the fitting curves of wavelength shifts of FBGi (i = 1, 3) and shear force are y1 = y2 = 0.01x – 2 × 10−10. Therefore, the sensitivities of the FBG sensors are k1 = k2 = 0.01 nm/N. The above sensing results illustrate that the direction and magnitude of the shear force can be recognized by analyzing the wavelength shifts of four FBGs in sensing unit.
4.2.2 Measurement of sliding
In the experiment, the sliding sensing array composed of two sensing units was embedded in the packaging material as shown in Fig. 10. Because the embedded directions were parallel to the x-axis, FBGi, (i = 1, 2, 3) were used to detect the sliding along the x-axis. The lengths of them were all 10 mm with a distance of 15 mm between two successive FBGs. Similarly, FBGi, (i = 4, 5, 6, 7) with the lengths of 3 mm were embedded parallel to the y-axis for sliding detection along the y-axis. The distance between FBG4 and FBG6, as well as between FBG5 and FBG7, was 7 mm. When a sliding sensing array is applied to mechanical finger to grab object, sliding usually occurs only in one direction. Therefore, in the experiment, the object slid along the packaging material in the positive x-axis direction.
The sliding sensing system in Fig. 7 was used to detect the contact state between the packaging material and the object. The center wavelengths of used FBGi, (i = 1, 2, 3) were λB1 = 1556.158 nm, λB2 = 1551.184 nm, and λB3 = 1546.200 nm, with the reflectivities of 79.5%, 77.2%, and 76.8%, and their corresponding 3 dB bandwidths were 0.6944 nm, 0.6754 nm, and 0.6539 nm, respectively.
In order to observe the characteristics of the FBG center wavelength shift in different contact states, slip response curves of FBG1 were derived in three cases: 1) no relative sliding, 2) on the verge of sliding, and 3) relative sliding occurring. As shown in Fig. 11, curve 1 indicates that the object was fully clamped; at this point, the wavelength shift of FBG1 was unchanged. It can be observed from curve 2 that the wavelength shifts fluctuated when sliding was about to occur, and the value was very small. Moreover, curve 3 shows that the object slid on the surface of the packaging material upon the FBG1, and the center wavelength reached its maximum value at t = 0.48 s.
The sensing array shown in Fig. 10 was used for sliding detection to get the sliding direction, speed and distance of the object. A certain friction coefficient was maintained and a relative sliding between the object and packaging material along the positive direction of x-axis was applied by loading different weights via pulleys in the vertical direction using a connecting device. Sliding signals of FBG1, FBG2 and FBG3 were obtained in case of four different sliding conditions as shown in Figs. 12 and 13. As shown in Fig. 12(a), when the friction coefficient was small and the object slides slowly, the wavelength shifts of the three FBGs reached their peak values (ΔλB11 = 0.0338 nm, ΔλB12 = 0.0379 nm, and ΔλB13 = 0.0392 nm) at t11 = 1.02 s, t12 = 1.68 s, and t13 = 2.09 s, respectively. Similarly, when the friction coefficient was constant, as shown in Fig. 12(b), and when the object slides rapidly, the center-wavelength shifts of the three FBGs reached their peak values (ΔλB21 = 0.0316 nm, ΔλB22 = 0.0365 nm, and ΔλB23 = 0.0389 nm) at t21 = 0.35 s, t22 = 0.62 s, and t23 = 0.77 s, respectively.
Fig. 12 Change in wavelength of FBG1–FBG3 for a small friction coefficient: (a) slow slip and (b) fast slip.
Fig. 13 Change in wavelength of FBG1–FBG3 for a large friction coefficient: (a) slow slip and (b) fast slip.
As shown in Fig. 13(a), when the friction coefficient was large and the object slides slowly, the wavelength shifts of the three FBGs reached their peak values (ΔλB31 = 0.0876 nm, ΔλB32 = 0.1101 nm, and ΔλB33 = 0.0948 nm) at t31 = 1.02 s, t32 = 1.46 s, and t33 = 1.78 s, respectively. Similarly, as shown in Fig. 13(b), when the object slides rapidly, the wavelength shifts of the three FBGs reached their peak values (ΔλB41 = 0.0752 nm, ΔλB42 = 0.1047 nm, and ΔλB43 = 0.0950 nm) at t41 = 0.48 s, t42 = 0.75 s, and t43 = 0.90 s, respectively.
In Figs. 12 and 13, the moment when the center wavelength of FBG1 starts to change is defined as t = 0. By calculating the time when the sensing signal reaches its peak value and the distance between two successive FBGs, the averages of the object’s sliding speed shown in Figs. 12 and 13 were are 3.7 cm/s, 9.5 cm/s, 5.2 cm/s, and 9.5 cm/s respectively. The sliding speed is related to factors such as the magnitude of pressure, the different weights loaded on the object along the x-axis using the connecting device, and so on. The wavelength shift of the FBG increased when the grasping force was increased. In contrast, it decreased noticeably when the grasping force was reduced. It can be deduced that if the sliding is in 3D dimension, the sliding information can be obtained by establishing a mathematical model ralating the wavelength shifts of FBGs in sensing unit, the time when the sensing signal of FBG reaches a peak value and the embedded position of FBGs.
4.3 Separation of tactile and slip signal
Variance measures the difference between the source and the expected value; it depicts the degree of discretization of the mathematical expectation of a random variable. Compared to the contact signal, the slip signal is characterized by variability and continuity [13]. Therefore, variance is usually used to indicate sliding, which was the eigenvalue of the discrete data for alternating signals: the larger the variance, the greater the fluctuation.
The contact and sliding variances of four different materials (copper, aluminum, engineering plastic, and a smooth iron tube) are given through the experiment shown in Table 1. It can be observed that the contact variances were extremely small. As for copper and aluminum, the orders of magnitude for sliding variances were four times than those of the contact variance, and for engineering plastic with a smooth iron tube, the orders of magnitude for sliding variances were three times than those of the contact variance. According to the above analysis, it is feasible to separate the contact and slip signal by the variance of FBG center wavelength shift.
Table 1. Contact and Slide Signal Variance of Different Materials
4.4 Fuzzy logic processing of sliding signal
When grasping the target object, the opening or closing angle of the mechanical fingers (θ) is usually determined by the pressure applied on the finger (Fz) and the variance of the sliding signal (V’). The functional relationship θ = f (Fz, V’) cannot be easily described using classical mathematical models. Therefore, fuzzy reasoning can be used for information fusion. Fz (ranges from 0 N to 5 N) and V’ (ranges from 0 to 1.24 × 10−3) are taken as inputs, and θ (range from −15° to 15°) is taken as an output. The fuzzy subsets corresponding to the input (SA, SC) are defined as {S, M, B}, and the fuzzy subset of the output is defined as {N, Z, P}. The domains of S, SC, and U are all defined as {1, 2, 3, 4, 5, 6}. The membership functions of Fz, V’, and θ were established as shown in Figs. 14(a)- 14(c).
Fig. 14 Membership function: (a) pressure (Fz), (b) variance of the sliding signal (V’) and (c) opening or closing angle of mechanical fingers (θ) .
The fuzzy relation can be established as
The fuzzy control rules can then be obtained (Table 2).
Table 2. Rules of Fuzzy Control: Output U
The centroid method [14] is chosen for fuzzy reasoning because of its higher sensitivity compared with other methods, such as the maximum membership function method and the weighted average method [15]. So far, a fuzzy logic system has been designed, and the opening or closing angle of the mechanical fingers can be obtained via a simulation using MATLAB software. For example, when Fz = 0.5 N and V’ = 1 × 10−6, the angle is θ = (2.17 × 10−17)°. When Fz = 4 N, and V’ = 4 × 10−4, the angle is θ = −9.17°.
The control decision of the mechanical finger opening or closing angle can be determined by the integration of pressure and the variance of the slip signal. The information fusion that uses fuzzy inference has advantages of simplicity and timeliness. However, the input and output membership function is difficult to determine in the fuzzy reasoning design process. The precision of control can be enhanced by improving the fuzzy rules according to practical applications.
5. Conclusion
An FBG array was used to monitor the sliding of mechanical fingers. The structural design and sensing principle were expounded to establish an explicit relationship between the sliding sensing and the shifting of the FBG center wavelength. The slip sensing system was constructed after verifying the sensing mechanism by finite element modeling. Experiments on the static output characteristic and slip detection of the fiber grating sliding sensor were performed. The slip sensing system was constructed after verifying the sensing mechanism by finite element modeling. The embedded position, angle and the length of FBG sensor were optimized by simulation. Experiments on the static output characteristic and slip detection of the fiber grating sliding sensor were performed. The experimental results of shear force show that within the operation range of 0 to 0.348 N, the center wavelength of the FBG sensor has a linear relationship with the shear force, and the shear sensitivity k = 0.01 nm/N. The FBG sliding sensor can decide the slip direction according to the characteristics of the wavelength shift of each FBG sensor in the sensor array; thus, sensing is no longer limited to the detection of single direction sliding. Meanwhile, the sliding distance and speed of the object can be obtained by analyzing and calculating the time when the sensing signal of FBG reaches a peak value and the embedded distance of FBGs. To meet the practical application requirements of the mechanical fingers, a different number of sensing units can be embedded in a single package to constitute a sensing array based on different spatial resolutions. The FBG sensing array can achieve large-area and high-resolution slip sensing. Thus, it can provide a possible scheme for secure human–computer interactions and improve the slip detection ability of mechanical fingers.
However, one potential problem is that the FBG sensor is sensitive to both strain and temperature, so temperature compensation for the FBG sliding signal is needed. At the same time, the temperature perception is vital for mechanical fingers. . Research and experimental results show that the temperature detection can be achieved by embedding the FBG temperature sensors that are only sensitive to temperature and are insensitive to strain in the same temperature field of FBG tactile sensors. Further, the influence of temperature change on tactile and sliding measurements can be reduced by analyzing the characteristics of the temperature disturbance of FBGs and using neural networks to establish a mathematical model establishment between temperature and center wavelength shifts of FBGs. Furthermore, adding an FBG temperature sensing function to improve the material recognition of the contact object would widen the application prospects of the mechanical fingers.
References and links
1. M. L. Hammock, A. Chortos, B. C. Tee, J. B. Tok, and Z. Bao, “25th anniversary article: the evolution of electronic skin (E-skin): A brief history, design considerations, and recent progress,” Adv. Mater. 25(42), 5997–6038 (2013). [PubMed]
2. D. Goeger, N. Ecker, and H. Woern, “Tactile sensor and algorithm to detect slip in robot grasping processes,” in IEEE International Conference on Robotics and Biomimetics (IEEE, 2009), pp. 1480–1485.
3. D. P. J. Cotton, P. H. Chappell, A. Cranny, N. M. White, and S. P. Beeby, “A novel thick- film piezoelectric slip sensor for a prosthetic hand,” IEEE Sens. J. 7, 752–761 (2007).
4. K. Xi, Y. Wang, G. Mei, G. Liang, and Z. Chen, “A flexible tactile sensor array based on pressure conductive rubber for three- axis force and slip detection,” in IEEE International Conference on Advanced Intelligent Mechatronics 2015, (IEEE, 2015) pp. 464–469.
5. C. Berger, “Optical sensor for velocity and slip measurement of automobile belt drives,” in Proceeding of IEEE 2002, (IEEE 2002) pp. 823–828.
6. S. Kosaka, M. Nakajima, T. Fukuda, and H. Matsuura, “Slipping detection with integrated piezoelectric vibration tactile sensors,” in IEEE/SICE International Symposium on System Integration (IEEE, 2008), pp. 111–116.
7. D. C. Xu and X. H. Guo, “Design and application of capacitive slip sensor,” Transduc.Microsyst. Technol. 34, 85–88 (2015).
8. L. B. Yuan and Y. J. Liang, “Fiber optic sliding sensing system,” Chinese J. Sci. Instr. 20, 575–577 (1999).
9. H. Wei, C. Tao, Y. Zhu, and S. Krishnaswamy, “Fiber Bragg grating dynamic strain sensor using an adaptive reflective semiconductor optical amplifier source,” Appl. Opt. 55(10), 2752–2759 (2016). [PubMed]
10. D. Ganziy, B. Rose, and O. Bang, “Performance of low-cost few-mode fiber Bragg grating sensor systems: polarization sensitivity and linearity of temperature and strain response,” Appl. Opt. 55(23), 6156–6161 (2016). [PubMed]
11. H. Li, L. Zhu, M. Dong, X. Lou, and Y. Guo, “Analysis on strain transfer of surface-bonding FBG on AI 7075-T6 alloy host,” Optik (Stuttg.) 127, 1233–1236 (2016).
12. S. C. Tjin, R. Suresh, and N. Q. Ngo, “Fiber Bragg grating based shear-force sensor: modeling and testing,” J. Lightwave Technol. 22, 1728–1733 (2004).
13. Z. Z. Luo and J. C. Yang, “The fuzzy processing of slip signal for an artificial- skin,” J. Transcl. Technol (1998).
14. A. W. Zhang, “Statistical analysis of fuzzy linear regression model based on centroid method,” Fuzzy Syst. Math. 7, 579–586 (2016).
15. M. J. Gangeh, M. Hanmandlu, and M. Bister, “A fuzzy-based texture analysis for tissue characterization of diffused liver diseases on B-scan images,” Biomed. Sci. Instrum. 38, 369–374 (2002). [PubMed]
