The human is covered with soft skin and has tactile receptors inside.The skin deforms along a contact surface.The tactile receptorsdetect the mechanical deformation.The detection of the mechanical deformation is essential for the tactile sensation.We propose amagnetic type tactile sensor which has a soft surface and eight magnetoresistive elements.The soft surface has a permanent magnetinside and the magnetoresistive elements under the soft surface measure the magnetic flux density of the magnet.The tactile sensorestimates the displacement and the rotation on the surface based on the change of the magnetic flux density. Determination ofan estimate equation is difficult because the displacement and the rotation are not geometrically decided based on the magneticflux density. In this paper, a stepwise regression analysis determines the estimate equation. The outputs of the magnetoresistiveelements are used as explanatory variables, and the three-axis displacement and the two-axis rotation are response variables in theregression analysis. We confirm the regression analysis is effective for determining the estimate equations through simulation andexperiment. The results show the tactile sensor measures both the displacement and the rotation generated on the surface by usingthe determined equation.
1. Introduction
The human body is covered with soft skin. We have percep-tions of mechanical and thermal stimulation via the skin. Inregard to the mechanical stimulation, tactile receptors whichare distributed under the skin detect the skin deformation.We recognize the mechanical stimulation based on the tactilereceptors’ detection and use the recognized stimulation todo various tasks. We cannot conduct any tasks well withouttactile sense. The essentiality of the tactile sense indicatesnecessity of tactile sensors. Therefore, the tactile sensors areexpected to have a wide range of application. The tactilesensors provide touch sense to robots, processing machines,intuitive input devices, and texture evaluation and improveintelligence of them.
So as to measure contact states, many tactile sensorshave been developed [1]. They have used various principlesand combinations of a large variety of components. We cancurrently buy several tactile sensors [2, 3]. In particular, most
of them have sheet-like structures. Although the sheet-likestructure is easy to manufacture, the contact state betweenthe sheet-like sensor and an object has a difference from thatbetween human skin and an object. Because the sheet-likesensor has little deformation by contact, the contact surfaceis required to be parallel to the sensor surface in order tomeasure enough. This contact constraints decrease usabilityof the sheet-like sensors. As described above, the humanskin deforms based on contact and recognizes the contactthat includes normal and shear deformations. Therefore, thesoftness and deformation of tactile sensors are essential formultiaxis tactile sensors.
Various tactile sensors which have soft surface and mul-tiaxis sensitivity have been proposed: sensors using a straingauge or a PVDF film, capacitive sensors, optical sensors,magnetic sensors, and sensors using a tomography technique[4]. With regard to optical tactile sensors, the methodswhich capture images of contact surfaces and calculate thedeformation of the surface have been proposed. Ferrier and
Hindawi Publishing CorporationJournal of SensorsVolume 2014, Article ID 459059, 7 pageshttp://dx.doi.org/10.1155/2014/459059
2 Journal of Sensors
Brockett captured inside of thin film by a pinhole cameraand calculated the deformation of the thin film from thepattern of dots on the film [5]. Yussof et al. proposed asensor of a hemisphere face with many elastomer contacts[6]. The pattern of the contacts determined three-axis force.Although these optical tactile sensors have an advantagewhich has no wiring inside the soft surface, downsizing ofcamera devices and high-speed calculation are required. Inaddition, Tactile sensors based on change in capacitance havebeen reported. Hoshi and Shinoda proposed a tactile sensorthat is composed of two urethane forms and three pieces ofconductive fabric [7]. Lipomi et al. proposed a flexible sensorthat was made of an elastomer and carbon nanotubes [8].This sensor measured relative change of capacitance in thecompression of it. Although the elastomer includes electrodesand is flexible, the change of capacitance is too small to reduceexternal noise. As referred to above, soft surface andmultiaxistactile sensors based on variousmeasurement principles havebeen proposed. Their improvement is expected for practicaluse.
In regard to magnetic tactile sensors, Nowlin proposeda tactile sensor with hall elements [9]. To reduce noise, thissensor used a stochastic method based on elaborate calcula-tion. A tactile sensor using induction coils was proposed byTakenawa [10]. The output voltage of the coils was small andhas drift instability. The magnetic tactile sensors need muchcalculation because the magnetic elements have nonlinearcharacteristics. At the same time, an absence of cable betweenmagnet andmagnetic elements is amajor advantage to realizesimple structure of sensor.
In this study, we have proposed a tactile sensor usinga permanent magnet and giant magnetoresistive (GMR)elements [11, 12]. The GMR elements convert change inmagnetic flux density to output voltage. The tactile sensormeasured three-axis displacement applied on the surface.However, the contact surface was limited to being parallelto the tactile sensor in order to use a simple calculation.In the case of being not parallel, the output of the tactilesensor has errors. In this paper, we propose a magnetictype tactile sensor that measures three-axis displacementand two-axis rotation applied on the surface of it. Afterdescribing the structure of the tactile sensor and its problem,we propose a determining method of a regression equation.Explanatory variables in the equation are the output voltagesof the GMR elements, and response variables are values of thedisplacement and the rotation. To confirm the effectivenessof the proposed method, we verify results of both simulationand experiment.
2. Magnetic Type Tactile Sensor
2.1. Structure. The structure of the tactile sensor is shown inFigure 1. The sensor is mainly composed of two layers, thatis, an elastic layer and a substrate layer. The elastic layer ismade of an elastic material, for example, urethane elastomer,and includes a cylindrical permanent magnet inside. Thesubstrate layer is made of a glass epoxy board; its surfaceside is flat and contains no electronic elements. The GMR
Object
External force
MagnetElastic layer
Substrate layer GMR element
Substrate
Urethaneelastomer
Figure 1: Sensor structure.
elements are on the back side. The elastic layer is fixed tothe substrate layer’s surface with an adhesive bond. Becausethese layers are not hard-wired, no wire breakages occur. Ifthe elastic layer is worn away after a long-term usage, it canbe easily replaced with a new one.
2.2. Measurement Principle. When the tactile sensor touchesan object as shown in Figure 1, the contact deforms thesurface of the elastic layer.The magnet inside the elastic layeris also displaced depending on the degree to which the layeris deformed.Thismagnet displacement changes themagneticflux density to the GMR elements on the substrate layer, andthus the outputs of the elements are changed. Based on theoutputs, the sensor estimates three-axis displacement andtwo-axis rotation of the layer surface.
To determine the surface displacement from the outputsof the GMR elements, we proposed an estimate equationof x-axis displacement expressed in (1) [12]. V
𝑖(𝑖 = 1 ⋅ ⋅ ⋅ 4)
indicates the outputs of the four GMR elements:
Δ𝑥 = 𝐶𝑑𝑥1+𝐶𝑑𝑥2
V21
+𝐶𝑑𝑥3
V1
+𝐶𝑑𝑥4
V22
+𝐶𝑑𝑥5
V2
+𝐶𝑑𝑥6
V23
+𝐶𝑑𝑥7
V3
+𝐶𝑑𝑥8
V24
+𝐶𝑑𝑥9
V4
,
(1)
where 𝐶𝑑𝑥𝑗(𝑗 = 1 ⋅ ⋅ ⋅ 9) is a coefficient of each term, and it is
determined by a multiple regression analysis. The equation iseffective in the case that themagnet is displaced parallel to thesubstrate. Therefore, when the magnet rotates in the elasticlayer as shown in Figure 1, Δ𝑥 in (1) includes an error causedby the rotation. To estimate the contact surface correctly,a novel regression equation that estimates both three-axisdisplacement and two-axis rotation is required. In this study,we determine the regression equation by a stepwise regressionanalysis.
3. Method for DeterminingRegression Equation
3.1. Stepwise Regression Analysis. To estimate both displace-ment and rotation based on the outputs of the GMR ele-ments in the tactile sensor, a stepwise method determinesa regression equation. In this method, response variables
Journal of Sensors 3
are five, that is, the three-axis displacement and the two-axis rotation which occurred on the surface of the sensor.Candidates of explanatory variable are the variables basedon the output voltages of the GMR elements. The stepwiseregression analysis selects the explanatory variables from thecandidates to estimate the response variables. This selectionis performed based on Akaike’s information criterion (AIC).The AIC is expressed by
AIC = 𝑛log𝑒𝑆𝑒+ 2𝑝, (2)
where 𝑝 is the number of the explanatory variables usedin the regression equation, 𝑛 is the number of data set ofmeasurement, and 𝑆
𝑒indicates the residual sum of squares
between the measurement data and the output of the regres-sion equation. When the AIC is a small value, the balance ofthe number of the explanatory variables and the accuracy ofthe estimation is in a good condition. Now, the accuracy isdetermined based on the residual sum of squares between themeasurement data and the output of the regression equationand is expressed with the first term in (2). Assuming theregression equation uses many explanatory variables, theaccuracy of the estimation would be high. In that case, theequation has a possibility of including unnecessary explana-tory variables. To estimate both the three-axis displacementand the two-axis rotation in a short time, the less numberof explanatory variables is suitable. Therefore, the regressionequation is determined by minimizing the AIC.
3.2. Determination of Regression Equation. In advance, thedata set, which includes the outputs of the GMR elements,the displacements (Δ𝑥, Δ𝑦, Δ𝑧), and the rotations (𝜃
𝑥, 𝜃𝑦), is
obtained in order to determine the regression equation. Thetactile sensor has eight GMR elements. Their output voltagesare expressed as V
𝑘(𝑘 = 1 ⋅ ⋅ ⋅ 8). We defined the candidates of
the explanatory variables as follows:
V𝑘, V2𝑘, V3𝑘, V4𝑘,1
V𝑘
,1
V2𝑘
,1
V3𝑘
,1
V4𝑘
, V1/2𝑘, V1/3𝑘, V1/4𝑘
.
The stepwise regression selects the explanatory variablesfrom these candidates. The selected explanatory variables areevaluated by the AIC. The algorithm for determining theregression equation is indicated as the following steps.
(1) Use (1) as the initial regression equation, and defineits explanatory variables as the initial variables.
(2) Define the variables in the regression equation as theexplanatory variables and the others as the candidates.
(3) Calculate the AIC by using the regression equationin the case that one of the candidates is added to theexplanatory variables.The calculations are carried outto all the candidates.
(4) Calculate the AIC by using the regression equationin the case that one of the explanatory variablesis removed from the equation. The calculations arecarried out to all the explanatory variables.
(5) In regard to the results of (3) and (4), after determin-ing the regression equation that has the explanatory
variables of the minimal AIC, return to (2). If theminimal AIC is higher than that of the previous trial,proceed to (6).
(6) As the regression equation, determine the equationcomposed of the explanatory variables defined in (2).
The response variables areΔ𝑥,Δ𝑦,Δ𝑧,Δ𝜃𝑥, andΔ𝜃
𝑦. Because
Δ𝜃𝑥and Δ𝜃
𝑦are much affected by Δ𝑥, Δ𝑦, and Δ𝑧, the
candidates of the explanatory variables Δ𝜃𝑥and Δ𝜃
𝑦include
the following variables using Δ𝑥, Δ𝑦, and Δ𝑧:
Δ𝑥, Δ𝑦, Δ𝑧, V𝑘Δ𝑥, V𝑘Δ𝑦, V𝑘Δ𝑧.
The number of the candidates’ variables is 17 kinds in thecase of without counting 𝑘 of V
𝑘. Because the regression
equations of Δ𝜃𝑥and Δ𝜃
𝑦need the estimates of Δ𝑥, Δ𝑦,
and Δ𝑧, first, this determination procedure determines theexplanatory variables of the displacement (Δ𝑥, Δ𝑦, and Δ𝑧).Second, those of the rotation (Δ𝜃
𝑥and Δ𝜃
𝑦) are determined.
4. Simulation and Experiment
4.1. Sensor Design. We designed the substrate of the tactilesensor. To estimate the three-axis displacement and the two-axis rotation on the contact surface, the substrate has theeight GMR elements upon the bottom side. The drawingsare shown in Figure 2. The GMR elements (AA003-02, NVECo.) are arranged on a circular line of 10mm radius not tohave aeolotropy. They have a one-direction sensitivity. Theirdirections are the radial directions of the circle.The substrateis a glass epoxy board. Its thickness is 1.5mm.The position ofthe inside magnet and the size of the elastic layer are shownin Figure 3. The magnet is a cylindrical neodymium magnet.Its size is 6mm in diameter and 1mm in thickness.The spacebetween the bottomof themagnet and the top of the substrateis 11mm. The elastic layer is a circular truncated cone andis made from urethane. The bottom is 20mm in diameter,and the top side is 16mm in diameter. The parameters of thedesign were determined by a finite element method [11].
4.2. Simulation. To confirm the effectiveness of the stepwiseregression analysis, we determined a regression equationbased on simulation data and evaluated the estimationaccuracy of the displacement and rotation of the magnet.Based on the design of the tactile sensor, we calculated themagnetic flux density from the cylindrical magnet at thepositions of theGMRelements. In the calculation, themagnetchanged its displacement and its rotation as follows:
The origin is the center of the top side of the elastic layeras indicated in Figure 3. Each data set is composed of eightmagnetic flux densities, Δ𝑥, Δ𝑦, Δ𝑧, Δ𝜃
𝑥, and Δ𝜃
𝑦. Because
the number of the combinations in the data set is themultiplication of the numbers of Δ𝑥, Δ𝑦, Δ𝑧, Δ𝜃
𝑥, and Δ𝜃
𝑦,
the number of the data set is 1875. The stepwise regression
4 Journal of Sensors
Connector
GMR
10
element
20mm
Elastic layerposition
Figure 2: Design of substrate.
GMR element
Cylindrical magnet
11mm
20mm
16mm
16mm
1mm
6mm
xy
z
Figure 3: Cross-section view of sensor.
analysis determined the regression equations of Δ𝑥, Δ𝑦, Δ𝑧,Δ𝜃𝑥, and Δ𝜃
𝑦based on the data set.
Δ𝑥 and Δ𝑦 have a symmetrical relationship. Δ𝜃𝑥and
Δ𝜃𝑦likewise have a rotational symmetry. Because they have
the same results, the results of Δ𝑥, Δ𝑧, and Δ𝜃𝑥are shown
in Figures 4, 5, and 6, respectively. Each horizontal axisindicates an index of the data set. The indexes betweenthe different charts have no relationship. In the charts, theestimate value and the target value which have the sameindex correspond to each other. The estimate values of Δ𝑥had a good agreement with the target values in Figure 4. Themaximal error of Δ𝑥 was 0.06mm.The estimate values of Δ𝑧coincided approximately with the target values at Δ𝑧 = 0and −1. At Δ𝑧 = −2, the errors were larger than those atΔ𝑧 = 0 and −1. The maximal error of Δ𝑧 was 0.25mm. Theresults indicate the determined regression equation reducedthe influence of the rotation of the magnet for the three-axis displacement. The estimate results of Δ𝜃
𝑥had the same
trend with those of Δ𝑧 and had the large errors at Δ𝜃𝑥= ±5.
The maximal error of Δ𝜃𝑥was 1.23 deg. The resolution of
Δ𝜃𝑥was also evaluated and is shown in Figure 6. Figure 7
−3
−2
−1
0
1
2
3
0 200 400 600 800 1000 1200 1400 1600 1800
Δx
(mm
)
Index number
Target valueEstimate value
Figure 4: Simulation result: displacement in x-axis direction.
−3
−2.5
−2
−1.5
−1
−0.5
0
0.5
1Δz
(mm
)
0 200 400 600 800 1000 1200 1400 1600 1800
Index number
Target valueEstimate value
Figure 5: Simulation result: displacement in z-axis direction.
shows the estimated rotation Δ𝜃𝑥of 0.1 deg per one step.
The other response variables were set at 0. Although theerror at 5 deg was 1 deg, the slope is approximately constant.This result indicates the relative resolution is high. Throughthe simulation, we confirmed that the stepwise regressionanalysis determined the regression equation estimating thedisplacement and the rotation of the magnet.
4.3. Experiment. In the simulation, although the displace-ment and rotation of the magnet are calculated without theelastic layer model, the stepwise regression analysis based onthe AIC determined the regression equation that estimatesthe displacement and the rotation of the magnet. Assumingthe magnet has the displacement and the rotation dependingon the top surface of the elastic layer, the stepwise regressionanalysis is also effective to an actual tactile sensor. Thus,we fabricated a tactile sensor and performed experiments.
Journal of Sensors 5
−10
−5
0
5
10
Δ𝜃x
(deg
)
0 200 400 600 800 1000 1200 1400 1600 1800
Index number
Target valueEstimate value
Figure 6: Simulation result: rotation around x-axis.
0 1 2 3 4 5
0
1
2
3
4
5
Estim
ated
Δ𝜃x
(deg
)
Target Δ𝜃x (deg)
Figure 7: Simulation result: rotation around x-axis of 0.1 deg per onestep.
The tactile sensor is shown in Figure 8. The size or theother parameters of the sensor were along those values inFigures 2 and 3. To generate the displacement and the rotationwith high accuracy, we used a motorized stage (SGSP26-100,Sigma Koki Co.) in the experiments. As shown in Figure 9,The stage has three translation axes and two rotation axesand touches the tactile sensor with a flat plate. The flat platedisplaced and tilted the top surface of the tactile sensor. Theranges of the displacement and rotation are as follows:
(i) Δ𝑥, Δ𝑦: −2, −1, 0, 1, 2mm;
(ii) Δ𝑧: −2, −3mm;
(iii) Δ𝜃𝑥, Δ𝜃𝑦: −5, 0, 5 deg.
Elastic layer
Substrate layer
Figure 8: Fabricated tactile sensor.
x-axis rotation
y-axis rotation
z-axis
y-axis
x-axis
Tactile sensor
Figure 9: Experimental setup.
The number of the combination of the displacement andthe rotation was 450. Since the displacement of Δ𝑧 = −1was too small to rotate the contact surface, we excepted itfrom the combination.The output voltages of the eight GMRelements were measured at each combination. The data setcomposed of the GMRs’ outputs, Δ𝑥, Δ𝑦, Δ𝑧, Δ𝜃
𝑥, and Δ𝜃
𝑦,
was also 450. The stepwise regression analysis determinedthe regression equations based on the data set. Next, theexperimental setup measured another data set. Using theadditional data set, we verified Δ𝑥, Δ𝑦, Δ𝑧, Δ𝜃
𝑥, and Δ𝜃
𝑦
estimated by the determined regression equations.Because the results of Δ𝑦 and Δ𝜃
𝑦had the same trends
with Δ𝑥 and Δ𝜃𝑥, respectively, Figures 10, 11, and 12 show
the results of Δ𝑥, Δ𝑧, and Δ𝜃𝑥, respectively. In contrast to
the simulation result in Figure 4, Figure 10 shows that Δ𝑥had errors. The maximal error was 0.75mm. Although theseresults were improved from the results by (1), the maximalerror was so high that an application of the tactile sensor toa precision measurement is difficult. One of the causes was adecay of the displacement of the magnet by the elastic layer.In that case, the changes of the explanatory variables were notenough for the estimation of the displacement. On the otherhand,Δ𝑧 andΔ𝜃
𝑥had small errors.Themaximal errors ofΔ𝑧
and Δ𝜃𝑥were 0.13mm and 0.95 deg. The stepwise regression
analysis was effective in regards to Δ𝑧 and Δ𝜃𝑥. The numbers
of the explanatory variables of Δ𝑥, Δ𝑧, and Δ𝜃𝑥were 18, 21,
and 39, respectively. The regression equations of Δ𝑥, Δ𝑧, and
6 Journal of Sensors
−3
−2
−1
0
1
2
3
0 50 100 150 200 250 300 350 400 450
Δx
(mm
)
Index number
Target valueEstimate value
Figure 10: Experimental result: displacement in x-axis direction.
0 50 100 150 200 250 300 350 400 450
Index number
−4
−3.5
−3
−2.5
−2
−1.5
−1
Δz
(mm
)
Target valueEstimate value
Figure 11: Experimental result: displacement in z-axis direction.
Δ𝜃𝑥are shown in the Appendix. Because the numbers of the
explanatory variables indicate complexity of estimation, theresults show the estimation of Δ𝜃
𝑥was difficult.
The resolution of Δ𝜃𝑥is shown in Figure 13. Although
the estimated Δ𝜃𝑥had the small variation, the trend was
coincident with the result of the simulation. The estimatedΔ𝜃𝑥has the large difference with the target Δ𝜃
𝑥at the
high value. One of the causes is that the variation of theexplanatory variables is not enough. An addition of otherexplanatory variables is necessary to improve the results.
5. Conclusions
In order to realize a flexible and multiaxis tactile sensor,the stepwise regression analysis determined the regressionequations that estimate the three-axis displacement and thetwo-axis rotation on the tactile sensor with the eight GMR
−10
−5
0
5
10
Δ𝜃x
(deg
)
0 50 100 150 200 250 300 350 400 450
Index number
Target valueEstimate value
Figure 12: Experimental result: rotation around x-axis.
0 1 2 3 4 50
1
2
3
4
5
Estim
ated
Δ𝜃x
(deg
)
Target Δ𝜃x (deg)
Figure 13: Experimental result: rotation around x-axis of 0.1 deg perone step.
elements. The response variables were the values of thedisplacement and the rotation of the sensor surface, and thecandidates of the explanatory variables were composed of theoutputs of the GMR elements. The stepwise regression anal-ysis evaluated the explanatory variables by the AIC. First, theeffectiveness of the method was evaluated in the simulation.Themaximal error was 0.25mm in displacement and 1.23 degin rotation. Second, we conducted the experiments using thetactile sensor. In these results, we confirmed that themaximalerror was 0.75mm in displacement and 0.95 deg in rotation.The stepwise regression analysis determined the regressionequations that estimate the displacement and the rotation ofthe surface of the tactile sensor.
Journal of Sensors 7
The experimental results were not enough to apply thetactile sensor for a precision measurement. So as to improvethe accuracy of the displacement and the rotation, there aretwo ways. The GMR elements were placed on the same planein this study, a three-dimensional configuration of them has apossibility to improve the accuracy. In addition, although theproposed method used the 17 candidates of the explanatoryvariables, they are not enough for expressing the responsevariables with a high accuracy. We need select the candidatesof the explanatory variables based on the physical relationbetween themagnet and theGMR elements.They are a futurework of our study.
Appendix
The regression equations decided on the experiment areshown as follows. Because the equations of Δ𝑦 and Δ𝜃
𝑦had
the same trends with Δ𝑥 and Δ𝜃𝑥, respectively, only the
equations of Δ𝑥, Δ𝑧, and Δ𝜃𝑥are shown:
Δ𝑥 = −6.1 +453.9
V1
−981.1
V3
−195.4
V4
+132.5
V6
+66.0
V7
+49.9
V8
−1006.0
V21
−62.5
V22
+2103.1
V23
+189.1
V24
+33.5
V25
−145.0
V26
−968.5
V28
−2750.0
V43
+1477.2
V41
+975.2
V48
+ 0.024V42,
Δ𝑧 = −32.2 +225.8
V1
+8.3
V2
−105.7
V3
+60.9
V4
−45.7
V5
+123.1
V6
−75.0
V7
−102.5
V8
−422.9
V21
+233.0
V23
−93.1
V24
+77.6
V25
−152.0
V26
+190.2
V27
+153.3
V28
+ 0.41V26− 0.006V4
8+407.3
V41
−319.0
V43
−246.2
V47
,
Δ𝜃𝑥= −13073.9 −
479.3
V2
+292.1
V3
−888.8
V4
−4121.1
V5
+969175.1
V6
+587.4
V7
−15047.9
V8
−630.5
V21
+894.2
V24
−6802.0
V25
−2835023
V26
+1546.1
V28
− 36.1Δ𝑦 + 4.9V8Δ𝑦 + 3.4V
6Δ𝑦 − 4.3V
8Δ𝑥
+ 3.7V7Δ𝑥 − 0.26V4
1+ 487.4V1/4
7− 74.1V4
6+ 5.79V4
4
+ 9.69V48− 58.6V3
8−2130609
V46
− 13.9Δ𝑥
− 106.1Δ𝑧 + 17.4V6Δ𝑧 + 59.6V3
6+ 3.1V
7Δ𝑦
+ 9.1V4Δ𝑧 +3926535
V36
− 8.3V3Δ𝑧 − 3.0V
3Δ𝑦
− 34.7V34+ 19.2V
5Δ𝑧 + 4.9V
1Δ𝑥 −5840.4
V45
+1158.0
V41
.
(A.1)
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper.
Acknowledgment
This work was supported by a research grant of The JGC-SScholarship Foundation.
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