Inconsistency Calibrating Algorithms for Large Scale Piezoresistive Electronic Skin

micromachines

Article Inconsistency Calibrating Algorithms for Large Scale Piezoresistive Electronic Skin

Jinhua Ye , Zhengkang Lin, Jinyan You , Shuheng Huang and Haibin Wu *

School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China; [email protected] (J.Y.); [email protected] (Z.L.); [email protected] (J.Y.); [email protected] (S.H.) * Correspondence: [email protected]

Received: 17 November 2019; Accepted: 18 January 2020; Published: 3 February 2020

Abstract: In the field of safety and communication of human-robot interaction (HRI), using large-scale electronic skin will be the tendency in the future. The force-sensitive piezoresistive material is the key for piezoresistive electronic skin. In this paper, a non-array large scale piezoresistive tactile sensor and its corresponding calibration methods were presented. Because of the creep inconsistency of large scale piezoresistive material, a creep tracking compensation method based on K-means clustering and fuzzy pattern recognition was proposed to improve the detection accuracy. With the compensated data, the inconsistency and nonlinearity of the sensor was calibrated. The calibration process was divided into two parts. The hierarchical clustering algorithm was utilized firstly to classify and fuse piezoresistive property of different regions over the whole sensor. Then, combining the position information, the force detection model was constructed by Back-Propagation (BP) neural network. At last, a novel flexible tactile sensor for detecting contact position and force was designed as an example and tested after being calibrated. The experimental results showed that the calibration methods proposed were effective in detecting force, and the detection accuracy was improved.

Keywords: calibration; electronic skin; inconsistency; large scale; piezoresistive

1. Introduction Tactility is an essential perception for intelligent robots to acquire external information [1]. It plays an important role in safe human-robot interaction [2,3]. Electronic skin can simulate the human tactile nervous system and sense information such as pressure [4], position [5], temperature [6], and texture [7] and so on for subsequent motion control in real time. With the growing demand of whole-body sensing, people have begun to focus on the study of large-scale electronic skin which is often called tactile sensor. A series of research on tactile sensing technology have already been carried out. It has made great breakthroughs in piezoresistive tactile sensors, whose structure can be divided into array and non-array style. By splicing small pieces of high precision sensing units or integrating them into a large substrate in a certain order, array sensors can achieve large area tactile detection. Luo et al. [8] presented a flexible 6 6 pressure-sensitive array based on the porous substrate. The graphene-coated foams × (GCF) were integrated in it as sensing units for pressure perception. Wang et al. [9] designed a novel skin-like tactile sensor array to measure the contact pressure of curved surfaces. It used nickel powder filled polymer and Silver-Nanowires/Polydimethylsiloxane (AgNWs/PDMS) forming stretchable interconnects. Cheng et al. [10] proposed an approach to realize a large-area highly-twistable artificial skin, and each tactile sensing element was formed by attaching conductive polymer on the spiral electrodes. The sensor can detect force through the relationship of electrical resistance and pressure on every tactile sensing element.

Micromachines 2020, 11, 162; doi:10.3390/mi11020162 www.mdpi.com/journal/micromachines Micromachines 2020, 11, 162 2 of 20

However, the detection area of array sensors is incontinuous, and the sensing information is acquired by unit-to-unit scanning. By comparison, non-array tactile sensors are integrative in structure without detection blind spots. It doesn’t need flexible complicated array electrodes, and is easy to be fabricated. That’s why non-array structure is more suitable for large area force detection. Yao, A., et al. [11] designed an based Electrical Impedance Tomography fabric sensor that can provide a pressure map using some current carrying and voltage sensing electrodes attached to the boundary of the fabric patch. Lee et al. [12] proposed a multi-point and multi-directional strain mapping sensor based on multiwall carbon nanotube (MWCNT)-silicone elastomer nanocomposites and anisotropic electrical impedance tomography (aEIT). It can successfully estimate surface normal forces. For these sensors, the amount of data to be collected and calculated in each detecting cycle is large, which requires a higher detection system to improve real-time performance. Moreover, the imaging algorithms are relatively complicated. Although piezoresistive composite is a good force-sensing element for flexible tactile sensor, it is viscoelastic and has great time-dependent character, i.e., the creep. It influences precision of sensors seriously and must be improved before sensor calibration. At present, there are many studies on creep property of the composites. The numerous viscoelastic creep models [13] have been constructed through experimental analysis, but few studies on how to compensate the creep. In general, there are two ways to solve the problem. On the one hand, creep can be reduced through the selection of matrix materials and manufacturing process. Huang, Y., et al. [14] found the creep resistance of the conductive rubber composites can be improved by doping certain nano-SiO2. Wang, P., et al. [15] studied the variation of electrical resistance under uniaxial pressure for carbon black-silicone rubber composite, and developed a novel way to mitigate resistance creep in rubber composites by the inclusion of white silica fillers. But not every piezoresistive material could match a suitable doping dose material to alleviate the creep character. Even the method of doping has been adopted, it is difficult to thoroughly eliminate the creep. On the other hand, we can compensate the creep through the signal processing algorithm or electronic circuit of the sensors. Ahmed, M.M. et al. [16] built a Levenberg-Marquard BackPropagation (LMBP) neural network model of self-calibration for a pressure sensor, which successfully predicted the desired pressure over time and reduced the impact of creep. Wang, L., et al. [17] used a linear combination of two negative exponential functions to fit the data of creep. Kim [18] described the creep as a superposition of exponential functions. Because of difference of creep character under different contact conditions and regions, it is hard to be compensated by fitting a unified function model. In this paper, we presented the creep compensation method to ensure the accuracy of data used for calibration. Then, the calibration method was used to alleviate inconsistency and nonlinearity of large scale piezoresistive tactile sensors. Combining with our previous researches, a novel large scale tactile sensor for detecting contact position and force was designed as a test example to verify these methods.

2. Principle of the Large Scale Piezoresistive Tactile Sensor The piezoresistive film is mostly used in tactile sensor for contact force detection. In this paper, a large scale of piezoresistive film as a whole non-array structure is adopted to design a sensor shown in Figure1a. The sensor can be easily attached to the robot surface, as shown in Figure1b. It has three layers including upper electrode layer, piezoresistive film layer and lower electrode layer, and each of them closes to each other tightly. The electrode layers are both good conductors. When anywhere of the sensor is pressed, the resistance between the upper and lower electrode layer at the contact position of the piezoresistive film will decrease. It is just like an electric leakage channel at the pressed position when an excitation is applied to the two electrodes, but the resistance of the unpressed region remains large. With the characteristics of piezoresistive film, there is a negative correlation between the applied pressure and the equivalent resistance. Therefore, the resistance change of the piezoresistive film between the upper and lower electrode layers can reflect the external force. Micromachines 2020, 11, 3 of 21

For the piezoresistive tactile sensor as shown in Figure 1a, the equivalent resistance RF between upper and lower electrode layer can be measured using a detection circuit. As long as the resistance of the film under external pressure is measured, it is possible to deduce the pressure F depending on the relationship of F and RF . The detection circuit of the contact force can realize the conversion from resistance to voltage by a simple circuit, as shown in Figure 1d. The sensor is connected with a constant current source (CCS). The CCS can provide constant current. The voltage at the connection point is buffered by a voltage follower, and can be transmitted to the microcontroller for the A/D conversion. Finally, the output resistance RF can be calculated by Equation (1). =⋅ VIRFF (1) Micromachines 2020, 11, 162 3 of 20

Leakage channel

The tactile sensor

Electrode UR5 robot

Piezoresistive film

Electrode

(a) (b)

I V F ADC MCU RF C

FigureFigure 1. 1. TheThe structure structure and detection principleprinciple of of the the tactile tactile sensor: sensor: (a )(a The) The sandwich sandwich structure; structure; (b) ( Theb) Thesensor sensor covered covered on UR5 on robot;UR5 robot; (c) The ( equivalentc) The equivalent resistance resistance in the pressed in the position; pressed ( dposition;) The contact (d) forceThe contactdetection force circuit. detection circuit.

But,For the piezoresistive tactilefilm is sensor normally as shown fabricated in Figure by mixing1a, the some equivalent conductive resistance particlesRF between into a viscoelasticupper and lowerinsulating electrode substrate. layer canThis be kind measured of piezoresistive using a detection film has circuit. the creep As long characteristics, as the resistance and of thethe creep film under is inconsistent external pressure for different is measured, region over it is possiblethe whole to deducefilm. The the piezoresistive pressure F depending characteristics on the ofrelationship the film are of alsoF and nonlinearRF. and inconsistent. In order to get consistent force measurements over the fullThe film, detection the problems circuit of theof creep contact inconsistency, force can realize piezoresistive the conversion inconsistency from resistance andto nonlinearity voltage bya shouldsimple be circuit, resolved. as shown A new in data Figure processing1d. The sensor algorithm is connected was proposed with a includ constanting currentcreep compensation source (CCS). andThe force CCS cancalibration provide as constant shown current.in Figure The 2. The voltage whole at theprocession connection includes point two is bu algorithms.ffered by a voltageOne is creepfollower, compensation and can be transmittedalgorithm, toand the the microcontroller other is force for thecalibration A/D conversion. algorithm Finally, calibrating the output for piezoresistiveresistance RF caninconsistence be calculated and by nonlinearity. Equation (1). The creep of the sensor should be compensated before the subsequent calibration. VF = I RF (1) · But, the piezoresistive film is normally fabricated by mixing some conductive particles into a

viscoelastic insulating substrate. This kind of piezoresistive film has the creep characteristics, and the creep is inconsistent for different region over the whole film. The piezoresistive characteristics of the film are also nonlinear and inconsistent. In order to get consistent force measurements over the full film, the problems of creep inconsistency, piezoresistive inconsistency and nonlinearity should be resolved. A new data processing algorithm was proposed including creep compensation and force calibration as shown in Figure2. The whole procession includes two algorithms. One is creep compensation algorithm, and the other is force calibration algorithm calibrating for piezoresistive inconsistence and nonlinearity. The creep of the sensor should be compensated before the subsequent calibration. MicromachinesMicromachines2020 2020, ,11 11,, 162 4 ofof 2021 Micromachines 2020, 11, 4 of 21

Figure 2. The sensor data processing. Figure 2. The sensor data processing. 3.3. CreepCreep CompensationCompensation beforebefore SensorSensor CalibrationCalibration 3. Creep Compensation before Sensor Calibration 3.1.3.1. CreepCreep ProcessProcess AnalysisAnalysis 3.1. Creep Process Analysis It’sIt’s knownknown thatthat thethe piezoresistivepiezoresistive ﬁlmfilm existsexists creepcreep andand creepcreep inconsistency.inconsistency. TwoTwo teststests werewere conductedconductedIt’s known onon thethe that sensor.sensor. the piezoresistive OneOne isis thatthat 11 NfilmN forceforce exists waswas creep pressedpressed and at atcreep aa position,position, inconsistency. andand waswas Two unloadedunloaded tests were afterafter keepingconductedkeeping aboutabout on the 3030 s.sensor.s. AfterAfter One aa while,while, is that 33 N,N, 1 5N5 NNforce ofof forceforc wase werewerepressed pressedpressed at a position, atat thethe samesame and positionposition was unloaded inin sequence.sequence. after ThekeepingThe creepcreep about characteristiccharacteristic 30 s. After waswas a while, shownshown 3 in N,in Figure Figure5 N of3 a.3a.forc The Thee were other other pressed is is that that anat an incrementalthe incremental same position stepper stepper in forcesequence. force was was pressedThepressed creep atat characteristic a a position position of of the thewas sensor, sensor, shown as as in shown shown Figure in in3a. Figure Figure The 3otherb. 3b. is that an incremental stepper force was pressed at a position of the sensor, as shown in Figure 3b.

(a) (b) (a) (b) FigureFigure 3.3. CreepCreep ofof thethe sensorsensor underunder didifferefferentnt forceforce imposing imposing situations:situations: ((aa)) ImposingImposing didifferentfferent forceforce independent;Figureindependent; 3. Creep ( b(b )of) Imposing Imposing the sensor force force under incremental incremental different step forcestep by by imposing step. step. situations: (a) Imposing different force independent; (b) Imposing force incremental step by step. AsAs shownshown inin FigureFigure3 ,3, the the resistance resistance is is still still getting getting smaller smaller under under a a constant constant force, force, but but the the downwarddownwardAs shown trendtrend in slowsslowsFigure downdown 3, the asas resistance timetime goesgoes is by.by. still AsAs getting thethe pressurepressure smaller increases,increases, under a theconstantthe resistanceresistance force, variationvariation but the causeddownwardcaused byby creep creeptrend also alsoslows decreases.decreases. down as InIn time summary,summary, goes by. thethe As workingworking the pressure processprocess increases, ofof thethe sensorsensor the resistance cancan bebe divideddivided variation intointo threecausedthree stages,stages, by creep as as shown shown also decreases. in in Figure Figure 4In a,b.4a,b. summary, the working process of the sensor can be divided into three stages, as shown in Figure 4a,b. (1)(1) Loading Loading/unloading/unloading stage:stage: the resistance increasesincreases oror decreasesdecreases significantly.significantly. (1) Loading/unloading stage: the resistance increases or decreases significantly. (2)(2) Creep Creep stage:stage: when the loading force remains constant,constant, thethe resistanceresistance decreasesdecreases slowly.slowly. (2) Creep stage: when the loading force remains constant, the resistance decreases slowly. (3)(3) Transitional Transitional stage: stage: it closesit closes to the to junction the junction of loading of /unloadingloading/unloading and creep and stage, creep and representedstage, and (3) Transitional stage: it closes to the junction of loading/unloading and creep stage, and byrepresented the circle inby thethe followingcircle in the figure. following figure. represented by the circle in the following figure. Actually, once the sensor is compressed, the creep occurs. To study the creep of the sensor in loading stage, the central position of the sensor was compressed for a test. A maximal 3 N force was applied to the sensor at different loading speed of 1, 2, 3, 4, 5 and 6 mm/min respectively. When loading to 3 N, the force was maintained for 30 s. The results were shown in Figure5.

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RF Creep RF Recovery ΔRε Loading Creep Recovery Micromachines 2020, 11, 162 Creep Recovery Stage I1 5 of 20 ΔR Micromachines 2020, 11, εt Stage D1 RF0 5 of 21 Creep ΔRε1 R Unloading Stage D Loading Unloading Stage F1 Stage I0 D0 Transitional RF Transitional Loading Creep R Stage F Stage Stage I2 Recovery

Creep ΔRεt ΔRε RF2 Loading CreepCreep Recovery Stage I1 Creep ΔRε2 Creep Recovery RF3 Stage I1 ΔR εt Stage D1 RF0 Creep ΔRε1 Time R Unloading Stage D Loading Unloading Stage F1 Time Stage I0 D0 Transitional (a) Transitional Loading (b) Stage Stage Stage I2

Creep ΔRεt Figure 4. The sensor output resistance under different RworkingF2 stages: (a) Loading force once; (b) Creep Stage I1 Creep ΔRε2 Loading force many times. RF3 Time Actually, once the sensor is compressed, the creep occurs. To study the creep of Timethe sensor in loading stage, the central( aposition) of the sensor was compressed for a test.(b) A maximal 3 N force was applied to the sensor at different loading speed of 1, 2, 3, 4, 5 and 6 mm/min respectively. When loadingFigure to 34. N, TheThe the sensor sensorforce output was output maintained resistance resistance under for under 30 different s. di Theﬀerent results working working were stages: stages: shown (a) ( Loadingain) LoadingFigure force 5. force once; once; (b) (Loadingb) Loading force force many many times. times.

Actually, once the sensor is compressed, the creep occurs. To study the creep of the sensor in loading stage, the central position of the sensor was compressed for a test. A maximal 3 N force was applied to the sensor at different loading speed of 1, 2, 3, 4, 5 and 6 mm/min respectively. When loading to 3 N, the force was maintained for 30 s. The results were shown in Figure 5.

Figure 5. Sensor output resistance at different loading speed. Figure 5. Sensor output resistance at different loading speed. Curves above the dotted line in Figure5 is the loading stage, and curves below the dotted line is Curves above the dotted line in Figure 5 is the loading stage, and curves below the dotted line the creep stage. In the case of different loading speeds, the resistances at the full load point are still is the creep stage. In the case of different loading speeds, the resistances at the full load point are approximately equal. That means the creep during loading stage can be neglected. After entering into still approximately equal. That means the creep during loading stage can be neglected. After creep stage, the faster the loading speed is, the more obvious the creep is. We have to compensate entering into creep stage, the faster the loading speed is, the more obvious the creep is. We have to creep after loading stage compensate creep afterFigure loading 5. Sensor stage output resistance at different loading speed. In summary, the sensor is difficult to provide accurate force feedback, and using a simple function In summary, the sensor is difficult to provide accurate force feedback, and using a simple fitting method can’t cope with such different contact situations. A new creep tracking compensation functionCurves fitting above method the dotted can’t line cope in withFigure such 5 is dithefferent loading contact stage, situations. and curves A below new thecreep dotted tracking line method was proposed to compensate the creep. firstly, the resistance variation during the creep stage iscompensation the creep stage. method In the was case proposed of different to loadincompensateg speeds, the the creep. resistances firstly, atthe the resistance full load pointvariation are was sampled, based on the known critical point between loading and creep stage. Then, the resistance stillduring approximately the creep stage equal. was Thatsampled, means based the oncreep the knownduring criticalloading point stage between can be loading neglected. and Aftercreep corresponding to the actual contact force can be obtained by subtracting creep-induced resistance enteringstage. Then, into thecreep resistance stage, the corresponding faster the loading to the speed actual is, contact the more force obvious can be theobtained creep is.by Wesubtracting have to variations. The specific formula is as follows: compensatecreep-induced creep resistance after loading variations. stage The specific formula is as follows: In summary, the sensor is difficult to provide accurate force feedback, and using a simple  (n) (n) (n 1) function fitting method can’t cope R with such= Rdifferent∆R εcontact− situations. A new creep tracking  fload/unload f t −  (n) (n) (n 1) (n) (2) compensation method was proposed R to= compensateR ∆R − the ∆creep.R firstly, the resistance variation  fcreep f t ε εt during the creep stage was sampled, based on th−e known− critical0 point between loading and creep stage. Then, the resistance corresponding to the actual contact force can be obtained by subtracting creep-induced resistance variations. The specific formula is as follows:

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()nnn () (-1 ) RRR=−Δε  fftload/ unload (2)  ()nnn () (-1 ) () n RRR=−Δ−Δε R′  fftcreep εt

()n ()n where n is the number of contact force change. R f and R f are the sensor output Micromachines 2020, 11, 162 load/ unload creep 6 of 20 resistances corresponding to actual contact force in the loading/unloading and creep stage, ()n Δ ()n respectively. R is the resistance at time t . ( ) R ′ is the( resistance) variation caused by the ft n εt n where n is the number of contact force change. R f and R f are the sensor output resistances ′ ()nload-1 /unload creep creep at time t of n -th creep stage. ΔRε is the resistance variation caused by(n ) creep corresponding to actual contact force in the loading/unloading and creep stage, respectively. R f t is the accumulation during previous(n) ()n −1 creep stages. resistance at time t. ∆R is the resistance variation caused by the creep at time t0 of n-th creep stage. εt0 (n 1) ∆R −Accordingis the resistance to Equation variation (2), it caused is important by creep to accumulation determine whether during the previous current(n working1) creep stage stages. of ε − the sensorAccording is in toloading Equation stage (2), or it iscreep important stage. toAs determine shown in whetherFigure 5, the the current output working resistance stage curve of the is sensorsteep on is inthe loading left of the stage critical or creep point, stage. but Asgentle shown on inthe Figure right.5 ,Relative the output variation resistance of the curve resistance is steep is onused the to left describe of the degree critical of point, change but and gentle expressed on the right. as follows: Relative variation of the resistance is used to describe degree of change and expressedΔ− as follows: RRRfff110 δ == (3) ∆R f 1 R f 1 R f 0 δ =RRff11= − (3) R f 1 R f 1

where Rf 0 is the sensor output resistance at the previous period. Rf 1 is the sensor output where R f 0 is the sensor output resistance at the previous period. R f 1 is the sensor output resistance at theresistance current at period. the current period. TheThe creepcreep at at di differentﬀerent positions positions and and forces forces was furtherwas further studied studied by relative by relative variation. variation. Four corners Four (ABCD)corners and(ABCD) the central and the position central (E) ofposition the sensor (E) wereof the chosen sensor as testedwere areas.chosen An as incremental tested areas. stepper An forceincremental was applied stepper to them force from was 1applied N to 10 to N (atthem an intervalfrom 1 N of to 1 N).10 N After (at eachan interval change, of the 1 N). force After was kepteach forchange, 10 s. Wethe collectedforce was the kept sensor for output10 s. We resistance collected and the calculated sensor output the relative resistance variation and by calculated Equation the (3). Therelative results variation were shown by Equation in Figure (3).6 .The results were shown in Figure 6.

Figure 6. Relative variation of sensor output resistance at diﬀerent positions.

Based on the analysis of the Figure6, the relative variations of resistance in the loading stage and creep stage are obviouslyFigure 6. Relative different. variation The peaks of sensor belong output to loading resistance stage, at different and the positions. troughs belong to creep stage. In other word, the resistance changes more greatly in the loading stage. It is an important basis for determiningBased on the the analysis working of state the ofFigure the sensor. 6, the relative variations of resistance in the loading stage and creep stage are obviously different. The peaks belong to loading stage, and the troughs belong 3.2.to creep Creep stage. Tracking In Compensationother word, the resistance changes more greatly in the loading stage. It is an important basis for determining the working state of the sensor. In this paper, the sample data in Figure6 were used as a data space. The K-means clustering algorithm was adopted to find out the boundaries among different working stages of sensor. The specific algorithm is as follows: Micromachines 2020, 11, 162 7 of 20

(1) The pressing process of the sensor can be divided into loading stage, transitional stage and creep stage, so 3 set of sample data in the data space were selected as the initial cluster centers. (2) The absolute distance between the remaining sample data and the current three cluster centers were calculated. According to the K-means clustering algorithm, the nearest distance criterion is defined. Because the samples clustered in this paper is one-dimensional data and the type of samples data is resistance value, we use the absolute distance which is simplest and most direct to define the nearest distance criterion. These sample data were classified into corresponding categories and can be expressed as:

Ck = n : k = argmin δn µk (4) k − where Ck is the set of sample date belonging to cluster k. µk is the cluster center of cluster k. (3) The averages of all sample data in each category were calculated and taken as the new cluster centers of the category. The update of cluster centers can be expressed as:

1 X µ = δ (5) k N n k n C ∈ k

(4) The sum of weighted mean absolute distance GJ used as clustering criterion functions can be expressed as:  3  = P  GJ pksk∗  k=1  P P s = 2 (6)  k∗ N (N 1) δi δj  k k− i C j C −  ∈ k ∈ k  Nk pk = N where pk is the priori probability, which can be calculated by the total number of sample data N and the number of sample data Nk of each category. sk∗ is the average of absolute distance between sample data of cluster k. After updating the cluster centers each time, GJ was calculated. When GJ converged to a minimum value or cluster centers no longer changed, it was judged as the end of clustering. Then, the ﬁnal clustering center and boundary can be obtained. Otherwise, return to step (2). After K-means clustering, the results were shown in Figure7. The boundaries of loading stage, creepMicromachines stage and2020, transitional11, stage can be seen clearly. 8 of 21

Figure 7.7. The results of K-means clustering.

To verify the rationality of clustering results, the silhouette coefficient was introduced as the evaluation index of cluster density and dispersion. It can be calculated by the following formula: ai()− bi ()  ()= si {}() ()  maxai , bi  (  N  si() (7)  S = i=1  N

Where ai() is the average of the distance between sample i and the other sample of the same

cluster. bi() is the minimum of the average distance between sample i and the samples in other categories. The range of silhouette coefficient is from −1 to 1. The closer its value is to 1, the more reasonable the clustering is. The silhouette of each category was shown in Figure 8. The silhouette coefficient of the final clustering results is 0.931 by Equation (7). That is, the clustering in this paper is reasonable.

Figure 8. The silhouette of categories.

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Figure 7. The results of K-means clustering.

To verify the rationality of clustering results, the silhouette coefficient was introduced as the Micromachinesevaluation index2020, 11 of, 162 cluster density and dispersion. It can be calculated by the following formula:8 of 20  ai()− bi () si()= To verify the rationality of clustering results, the{} silhouette() () coefficient was introduced as the  maxai , bi evaluation index of cluster density and dispersion. It can be calculated by the following formula: (  N (7)  a(i)si()b(i)  s(i) =  −  maxi=1 a(i),b(i)  S N=  P { } (7)  s(i) N  i=1 S = N Where ai() is the average of the distance between sample i and the other sample of the same Where a(i) is the average of the distance between sample i and the other sample of the same cluster. bcluster.(i) is the bi() minimum is the minimum of the average of the distance average betweendistance samplebetweeni andsample the samplesi and the in samples other categories. in other The range of silhouette coefficient is from 1 to 1. The closer its value is to 1, the more reasonable the categories. The range of silhouette coefficient− is from −1 to 1. The closer its value is to 1, the more clusteringreasonable is. the clustering is. The silhouette of each category was shown in FigureFigure8 8.. TheThe silhouettesilhouette coecoefficientfficient of the finalfinal clustering results is 0.931 by Equation (7).(7). That is, the clustering in this paper is reasonable.

Figure 8. The silhouette of categories.

Due to the fuzziness of transitional stage, it is difficult to identify the critical point accurately between loading and creep stages. In this paper, the concept of fuzzy mathematics was introduced to solve it. The relative variation of resistance was taken as the discourse domain V. T1 and T2 were the fuzzy subsets({loading stage} and {creep stage}) of V. Based on the boundary of different categories obtained from the clustering result, the membership functions of loading stage and creep stage can be defined by fuzzy distribution of semi-trapezoidal type as follows:   0 δ 0.00612  ≤ T (δ) =  δ 0.00612 0.00612 0.02374 (8) 1  −0.01762 < δ  ≤ 1 δ > 0.02374

  0 δ > 0.02374  T (δ) =  0.02374 δ 0.00612 0.02374 (9) 2  0.01762− < δ  ≤ 1 δ 0.00612 ≤ With the help of the maximum membership principle, the current working stage of the sensor was recognized by fuzzy recognition. Comparing T1(δ) with T2(δ) at the current moment, if T1(δ) is greater than T2(δ), the sensor is in loading stage. Otherwise, it is in creep stage. Then, the formula Equation (2) of creep compensation was chosen according to the current working state of sensor. Micromachines 2020, 11, 9 of 21

Due to the fuzziness of transitional stage, it is difficult to identify the critical point accurately between loading and creep stages. In this paper, the concept of fuzzy mathematics was introduced to solve it. The relative variation of resistance was taken as the discourse domain V . T1 and T2 were the fuzzy subsets({loading stage} and {creep stage}) of V . Based on the boundary of different categories obtained from the clustering result, the membership functions of loading stage and creep stage can be defined by fuzzy distribution of semi-trapezoidal type as follows:

 0δ ≤ 0.00612 δ − ()δδ=<≤ 0.00612 T1  0.00612 0.02374 (8)  0.01762 δ >  1 0.02374

 0δ > 0.02374  − δ ()δδ=<≤ 0.02374 T2  0.00612 0.02374 (9)  0.01762 δ ≤  1 0.00612 With the help of the maximum membership principle, the current working stage of the sensor ()δ ()δ was recognized by fuzzy recognition. Comparing T1 with T2 at the current moment, if ()δ ()δ T1 is greater than T2 , the sensor is in loading stage. Otherwise, it is in creep stage. Then, the formula Equation (2) of creep compensation was chosen according to the current working state ofMicromachines sensor. 2020, 11, 162 9 of 20 Four experiments were used to verify the feasibility of the method as follows: (1) AnFour incremental experiments stepper were usedforce toof verify 1 N to the 7 feasibilityN (at 1 N of intervals) the method was as applied follows: to three random positions of the sensor. After each increase, the force was maintained for 10 s. (1) An incremental stepper force of 1 N to 7 N (at 1 N intervals) was applied to three random positions (2) The sensor central position was selected to be applied a force of 6 N firstly at a loading speed of the sensor. After each increase, the force was maintained for 10 s. of a. When reaching to 6 N, the force remained constant for 5 s. Then, the force was increased (2) The sensor central position was selected to be applied a force of 6 N ﬁrstly at a loading speed continuously to 9 N at a loading speed of b, and remained it for a period of time. of a. When reaching to 6 N, the force remained constant for 5 s. Then, the force was increased (3) 5 N single loading was applied to a random position of the sensor. continuously to 9 N at a loading speed of b, and remained it for a period of time. (4) An incremental stepper force of 1 N to 10 N (at 1 N intervals) was applied to the position (3) 5 N single loading was applied to a random position of the sensor. which is same as the position of experiment (3). After each increase, the force was maintained (4) forAn 10 incremental s. stepper force of 1 N to 10 N (at 1 N intervals) was applied to the position which is same as the position of experiment (3). After each increase, the force was maintained for 10 s. The results of the first two experiments (Experiment (1), Experiment (2)) were shown in Figure 9a,b. TheThe results results of thethe ﬁrstlast twotwo experimentsexperiments (Experiment (Experiment (1), (3), Experiment Experiment (2)) (4)) were were shown shown in Figurein Figure9a,b. 10a,b.The results of the last two experiments (Experiment (3), Experiment (4)) were shown in Figure 10a,b.

(a) (b)

FigureFigure 9. 9. TheThe sensor sensor output output resistance resistance after after creep creep compensation: compensation: (a ()a Different) Diﬀerent positions; positions; (b (b) Different) Diﬀerent Micromachinesloadingloading 2020speeds. speeds., 11, 10 of 21

(a) (b)

FigureFigure 10. 10. ResultsResults of of creep creep compensation compensation at at the the same same position: position: (a ()a Result) Result of of 5 5N N single single loading loading creep creep compensation;compensation; (b (b) )Result Result of of multiple multiple loading loading creep creep compensation. compensation.

AsAs shown shown in in Figures Figures 9 andand 1010,, afterafter K-meansK-means clusteringclustering analysis and definingdefining appropriate membershipmembership function, function, the sensorsensor workingworking stagestage can can be be identified identified eff effectively.ectively. Meanwhile, Meanwhile, the the creep creep was wasalso also compensated compensated by Equation by Equation (2), no (2), matter no matter what force, what position force, position and loading and speedloading were. speed In particular,were. In particular,it ensures theit ensures accuracy the and accuracy stability and of thestability collected of the sensor collected data forsensor force data calibration for force to calibration a certain extent. to a certain extent.

4. Fusion and Calibration for Piezoresistive Units

4.1. Clustering Analysis of Sensing Units Because of the piezoresistive inconsistency over the full film, when calculating the force loaded on the sensor, it is not enough to only consider the mapping between the force and the sensor output resistance. The different pressed position must be taken into account. In this paper, the whole sensor was regarded as a combination of several units, and the mapping relationship of each unit between the force and the resistance is established. Because the data detected in different units have a certain degree of redundancy and the boundaries between different sensing units have force detection error which is caused by positional error (the maximum positional error is 3 mm in the paper), before fitting the mathematical model, it is necessary to cluster and fuse the data after creep compensation for different positions. It can classify the positions with similar piezoresistive properties into the same categories, so as to reduce the computational complexity of subsequent fitting and reduce error of borders by reducing number of borders. However, it is hard to determine where the piezoresistive characteristics of the sensor are similar at first. This paper used agglomerative nesting (AGNES) algorithm to find how many sensing units should be divided. The specific algorithm is as follows: (1) The sensor was evenly divided into N independent sensing units, and a force of 1 N~15 N, at intervals of 1 N, was applied to them respectively. The obtained output resistances of the units were used as initial categories. They can be expressed as follows: ==[ ] () RrrrrFi i123; i ; i ;...; i 15 i 1,2,3,..., N (10)

2 dij is defined as the Euclidean square distance of sample i and j. The formula is as follows:

15 2 =−()2 dRRij Fik Fjk (11) k=1

(2) The distance between two clusters of the initial clusters was calculated to obtain the initial distance matrix, and Ward’s method was used as the basis of clustering in this paper. To describe

Micromachines 2020, 11, 162 10 of 20

4. Fusion and Calibration for Piezoresistive Units

4.1. Clustering Analysis of Sensing Units Because of the piezoresistive inconsistency over the full film, when calculating the force loaded on the sensor, it is not enough to only consider the mapping between the force and the sensor output resistance. The different pressed position must be taken into account. In this paper, the whole sensor was regarded as a combination of several units, and the mapping relationship of each unit between the force and the resistance is established. Because the data detected in different units have a certain degree of redundancy and the boundaries between different sensing units have force detection error which is caused by positional error (the maximum positional error is 3 mm in the paper), before fitting the mathematical model, it is necessary to cluster and fuse the data after creep compensation for different positions. It can classify the positions with similar piezoresistive properties into the same categories, so as to reduce the computational complexity of subsequent fitting and reduce error of borders by reducing number of borders. However, it is hard to determine where the piezoresistive characteristics of the sensor are similar at first. This paper used agglomerative nesting (AGNES) algorithm to find how many sensing units should be divided. The specific algorithm is as follows: (1) The sensor was evenly divided into N independent sensing units, and a force of 1 N~15 N, at intervals of 1 N, was applied to them respectively. The obtained output resistances of the units were used as initial categories. They can be expressed as follows:

RFi = [ri1; ri2; ri3; ...; ri15](i = 1, 2, 3, ..., N) (10)

2 dij is deﬁned as the Euclidean square distance of sample i and j. The formula is as follows:

15 X 2 d2 = R R (11) ij Fik − Fjk k=1

(2) The distance between two clusters of the initial clusters was calculated to obtain the initial distance matrix, and Ward’s method was used as the basis of clustering in this paper. To describe similarity of piezoresistive characteristics of two sensing units, the distance between clusters was deﬁned as follows: npnq ( ) = 2 Dist p, q dpq (12) np + nq where np and nq is the number of samples of cluster p and q respectively. p and q are the centroids of cluster p and q respectively. (3) The two clusters with the smallest distance between clusters were merged. For example, if the distance between cluster p and cluster q is the smallest, they can be merged as a new cluster k for the basis of the next clustering. The distance between cluster k and the rest cluster r can be calculated by the following formula:

np + nr nq + nr n Dist(k, r) = Dist(p, r) + Dist(q, r) r Dist(p, q) (13) nk + nr nk + nr − nk + nr where nk and nr is the number of samples of cluster k and r respectively. (4) Step (3) was repeated until all categories were merged into a category. The clustering analysis was done with AGNES algorithm for the sensor data. In order to find the appropriate number of classification, the dendrogram was generated, as shown in Figure 10. The clustering coefficient of the clustering process was shown in Figure 11. As shown in Figure 11, the sensing units in different categories and the distance between categories can be seen intuitively. In Figure 12, with the number of categories increasing, the clustering coefficient Micromachines 2020, 11, 11 of 21

similarity of piezoresistive characteristics of two sensing units, the distance between clusters was defined as follows:

nnpq Dist() p, q= d 2 + pq (12) nnpq

where np and nq is the number of samples of cluster p and q respectively. p and q are the centroids of cluster p and q respectively. (3) The two clusters with the smallest distance between clusters were merged. For example, if p q the distance between cluster and cluster is the smallest, they can be merged as a new cluster k for the basis of the next clustering. The distance between cluster k and the rest cluster r can be calculated by the following formula: nn++ nn n Dist() k,,,, r=+−pr Dist() p r qr Dist() q rr Dist() p q +++ (13) nnkr nn kr nn kr Micromachines 2020, 11, 162 11 of 20

where nk and nr is the number of samples of cluster k and r respectively. decreases.(4) Step When (3) the was number repeated of categoriesuntil all cate reachedgories were about merged 5, the downward into a category. trend slows down. Therefore, after clusteringThe clustering and fusion,analysis the was sensor done waswith mergedAGNES intoalgorithm 5 sets fromfor the 36 sensor initial data. sensing In order units. to Similarfind sensingthe appropriate units were number represented of classification, by the same the color, dend androgram the piezoresistive was generated, curves as shown of them in Figure were drawn, 10. asThe shown clustering in Figure coefficient 13a,b. of the clustering process was shown in Figure 11.

Rescaled distance cluster combine 020305 10 15 4 17 5 8 30 3 9 23 29 14 20 2 1 13 7 16 22 10 15 Cluster 21 28 24 34 35 31 11 27 33 26 32 11 19 6 18 12 25 Micromachines 2020, 11, 12 of 21 Figure 11. Dendrogram of clustering’s result. Figure 11. Dendrogram of clustering’s result.

Micromachines 2020, 11, 12 of 21 As shown in Figure 11, the sensing units in different categories and the distance between categories can be seen intuitively. In Figure 12, with the number of categories increasing, the clustering coefficient decreases. When the number of categories reached about 5, the downward trend slows down. Therefore, after clustering and fusion, the sensor was merged into 5 sets from 36 initial sensing units. Similar sensing units were represented by the same color, and the piezoresistive curves of them were drawn, as shown in Figure 13a,b.

Figure 12. Clustering’s coefficient of different categories. FigureFigure 12. 12.Clustering’s Clustering’s coecoefficientﬃcient of different diﬀerent categories. categories.

(a) (b)

Figure 13. FigurePiezoresistive 13. Piezoresistive fusion fusion results: results: (a) Initial (a) Initial units units and and clustering clusteringresults; results; ( b)) Piezoresistive Piezoresistive curves curves of each unit after clustering. of each unit after clustering. (a) (b) 4.2. Force Calibration Figure 13.Because Piezoresistive the mapping fusion between results: resistance (a) Initial and forc unitse was and not clustering obtained, aresults; contact (forceb) Piezoresistive detection curvesmodel of eachneeds unit to be after constructed clustering. through BP neural network training compensated samples data. The reason why the neural network is selected is that the piezoresistive characteristics of the sensor 4.2. Forceitself Calibration are nonlinear and inconsistent, and the BP neural network has good stability and robustness and is very suitable for nonlinear fitting. So BP neural network is more suitable than other Becausealgorithms. the mapping between resistance and force was not obtained, a contact force detection model needsAfter to be clustering, constructed the sample through data BP of neuraleach sensing network units trainingwill be used compensated for force calibration. samples As data. The reason whyshown the in Figureneural 13a,b, network the sensor is selected output resistance is that isthe non-linear, piezoresistive which is charac relatedteristics to contact of force the sensor itself areand nonlinear the sensing and units. inconsistent, So the force detec andtion the model BP neural can be networkexpressed ashas follows: good stability and robustness = () and is very suitable for nonlinear fitting. RfUnitFSoF BP neural, network is more suitable (14)than other algorithms. Afterwhere clustering, Unit and the F sample is the sensingdata of unit each and sensingcontact force units respectively. will be used RF isfor the force sensor calibration. output As shown inresistance. Figure To13a,b, eliminate the sensor the influence output of resistancenon-target parametersis non-linear, on the which sensor is output, related the to reverse contact force and the sensing units. So the force detection model can be expressed as follows: = () RfUnitFF , (14)

where Unit and F is the sensing unit and contact force respectively. RF is the sensor output resistance. To eliminate the influence of non-target parameters on the sensor output, the reverse

Micromachines 2020, 11, 162 12 of 20

4.2. Force Calibration Because the mapping between resistance and force was not obtained, a contact force detection model needs to be constructed through BP neural network training compensated samples data. The reason why the neural network is selected is that the piezoresistive characteristics of the sensor itself are nonlinear and inconsistent, and the BP neural network has good stability and robustness and is very suitable for nonlinear ﬁtting. So BP neural network is more suitable than other algorithms. After clustering, the sample data of each sensing units will be used for force calibration. As shown in Figure 13a,b, the sensor output resistance is non-linear, which is related to contact force and the sensing units. So the force detection model can be expressed as follows:

RF = f (Unit, F) (14)

Micromachines 2020, 11, 13 of 21 where Unit and F is the sensing unit and contact force respectively. RF is the sensor output resistance. To eliminatemodeling the method inﬂuence is generally of non-target adopted. parameters The mathematical on the sensor model output, of force the detection reverse of modeling the sensor method in is generallythis paper adopted. can be expressed The mathematical as follows: model of force detection of the sensor in this paper can be expressed as follows: −1 FfUnitR=1 (), (15) F = f − (Unit, RF) F (15) BP neuralBP neural network network is a multi-layeris a multi-layer feed feed forward forward network network with with highly highly non-linear non-linear mapping mapping ability and one-wayability and transmission. one-way transmission. A continuous A function continuous in any function closed intervalin any canclosed be approximatedinterval can bybe a BP approximated by a BP network with an implicit layer. It is also called the universal approximation network with an implicit layer. It is also called the universal approximation theorem [19]. In this paper, theorem [19]. In this paper, BP neural network algorithm was adopted to build the mathematical BP neural network algorithm was adopted to build the mathematical model for detecting contact force. model for detecting contact force. The typicalThe typical structure structure of of BP BP neural neural network network containscontains input input layer, layer, hidden hidden layer layer and andoutput output layer, layer, as shownas shown in Figure in Figure 14 .14. In In this this paper, paper, twotwo neuron neuron nodes nodes were were set setin the in input the input layer, layer, corresponding corresponding to to sensingsensing unit unit and and its its outputoutput resistanceresistance respectively. respectively. A Aneuron neuron node node was was set in set the in output the output layer, layer, correspondingcorresponding to contactto contact force. force. The learning learning process process is mainly is mainly composed composed of forward of forward and error and back error back propagation.

FigureFigure 14. 14.The The structure structure of of BackPropagation BackPropagation (BP) (BP) neural neural network network model. model.

BP neuralBP neural network network construction construction process process is is asas follows:follows: (1) Input(1) Input samples samples and and output output samples samples were were set:set: TwoTwo neuron neuron nodes nodes were were arranged arranged in in the the input input layer layer to to correspond correspond toto sensingsensing unit unit Unitat at stress position and output voltage RF. one neuron node was arranged in the output layer to correspond to stress position and output voltage RF. one neuron node was arranged in the output layer to the standard pressure value F. correspond to the standard pressure value F . (2) Selection of the number of hidden layer nodes: (2) Selection of the number of hidden layer nodes: The appropriate designing hidden layer can reduce the error and improve BP neural network training accuracy. In practice, it usually takes several experiments and a combination of artificial control to determine the final number of hidden layer nodes, and there is not absolute ideal analytic formula to calculate the number of hidden layer nodes. If the number of nodes is too little, the learning ability is limited, which is not enough to reflect all the characteristics of training samples. If the number of nodes is too many, the training time will be increased and it will reduce generalization ability, which results in overfitting. This paper adopts the following empirical formula Equation (16) to determine the approximate range of the number of nodes in the hidden layer first, and to find the best number of nodes by the method of trial.

hmna=++ (16)

Micromachines 2020, 11, 162 13 of 20

The appropriate designing hidden layer can reduce the error and improve BP neural network training accuracy. In practice, it usually takes several experiments and a combination of artificial control to determine the final number of hidden layer nodes, and there is not absolute ideal analytic formula to calculate the number of hidden layer nodes. If the number of nodes is too little, the learning ability is limited, which is not enough to reflect all the characteristics of training samples. If the number of nodes is too many, the training time will be increased and it will reduce generalization ability, which results in overfitting. This paper adopts the following empirical formula Equation (16) to determine the approximate range of the number of nodes in the hidden layer first, and to find the best number of nodes by the method of trial. h = √m + n + a (16) where h is the number of hidden layer nodes, m is the number of input layer nodes, n is the number of nodes in the output layer, a is the adjustment constant of which the range is from 1 to 10. So, it can be calculated that the reference range of the number of hidden layer nodes in this network is 3 to 12. (3) The connection weights ωij from the input layer to the hidden layer and the connection weights νj from the hidden layer to the output layer were initialized. And the threshold of the hidden layer neuron θj and threshold of output layer neurons θ were initialized. (4) The hidden layer used Sigmoid as an activation function, such as Equation (17). Since the value of the Sigmoid range from 0 to 1, the values which are imported output layer needed to be scaled in any range to facilitate comparison with the values of the pressure applied to the actual calibration. Hence, the output layer used a Purelin function such as Equation (18).

1 S(x) = (17) 1 + exp( x) − P(x) = x (18)

The output of each unit of the hidden layer is as follows: ! P2 Hj = S ωijxi θj (j = 1, 2, ..., l) (19) i=1 − where ωij is the connection weight from the i-th node of the input layer to the j-th node of the hidden layer. θj is the threshold of the j-th neuron node of the hidden layer. l represents the number of hidden layer neuron nodes. The output of the output layer is as follows:   Xl  Xl   f = P νjHj θ = νjHj θ (20)  −  − j=1 j=1 where νj is the connection weight from the j node of the hidden layer to the output layer. θ is the threshold of the output layer neuron. (5) The mean square error which is of the output values and the expected output values was calculated, as follows: 1 E = (F f )2 (21) 2 − In order to minimize the error, the most rapid gradient descent method was adopted, and the BP network weights and thresholds were updated along the negative gradient of the error function. The weights and threshold correction formulas for each neuron of the output layer and the hidden layer are as follows: Micromachines 2020, 11, 162 14 of 20

 ∂E ∆νj = η = ηHj(F f )  ∂νj  − −  ν (n + 1) = ν (n) ∆ν (n)  j j j (22)  ∂E −  ∆θ = η = η( f F)  − ∂θ −  θ(n + 1) = θ(n) ∆θ(n) − The weights and threshold correction formulas for the neurons in the hidden layer and the input layer are as follows:  2 l  ∂E P P  ∆ωij = η = η (F f )νjHj 1 Hj xi  ∂ωij  − i=1 j=1 − −   ω (n + 1) = ω (n) ∆ω (n)  ij ij − ij (23)  l  = ∂E = P ( )  ∆θj η ∂θ η f F νjHj 1 Hj  − j j=1 − −   θ (n + 1) = θ (n) ∆θ (n) j j − j where η (0, 1) is the learning rate which controls the update step length of each iteration. n is the ∈ number of iterations. (6) The two processes of forward propagation and error back propagation were repeated until the error reaches the set value. Since the hidden layer of this network used Sigmoid as the activation function, the following formula should be used to normalize the sample data at ﬁrst in order to improve the training speed and should be sensitivity and made the input data value fall in its saturation region which is from 0 and 1.

Dat(i) Dat Dat(i) = − min (24) Datmax Dat − min where Dat(i) is the processed sample data, Dat(i) is the original sample data, Datmax and Datmin is the maximum and minimum values corresponding to the sample data respectively. The BP neural network model was constructed by MATLAB. The output resistance of each sensing units after clustering and fusion were taken as training samples. The learning rate was set to 0.01. Adam training function combined with Mini-batch gradient descent method was used to optimize the network model and accelerate the convergence speed. The number of hidden layer nodes was adjusted to achieve the optimum training eﬀect. After about 500 iterations, the Root Mean Squared Error (RMSE) of training set is reduced to less than 1, and the RMSE of testing set is less than 2. The ﬁnal weight matrix ωij, υj and threshold matrix θj, θ were obtained. The results of the training were shown in FigureMicromachines 15. 2020, 11, 16 of 21

FigureFigure 15.15. The results of BP training.

5. Experiments

5.1. Design and Fabrication of Sensor The contact force detection model mentioned above needs the position information of sensing units. Based on the principle of electric field potential uniqueness, our team have already developed four-wire [20] and five-wire [21] tactile sensors in recent years. These sensors can detect the contact position by extracting the potential value distributed over the sensor film. The sensor shapes were also designed for different style, such as rectangle, sector [22] and irregular planes [23]. According to the previous research works, we improved the upper and lower electrode layers of the original structure proposed in Figure 1. Then, a novel large scale tactile sensor was designed for detecting contact position and force. As shown in Figure 16, the position detection layer is divided into uniform electric field layers in X and Y directions. Two groups of strip line electrodes (X+, X− and Y+, Y−) are set vertically to each other on the conductive films, which are used to introduce excitation source and extract the sensor signals. The force detection layer is a piezoresistive film. The protective layers are used for collision buffering and the protection of the interior sensing materials.

Figure 16. Structure of the presented sensor.

According to the electrical and physical characteristics of the tactile sensor, the sensing materials should be as light and flexible as possible. For position detection, Indium-tinoxide based on polyethylene terthalate (PET-ITO) conductive film was chosen as the layer of uniform electric field, whose thickness is only 0.125 mm. It’s uniform in conductivity, soft in flexibility and stable in chemistry. Silkscreen was adopted to print the conductive silver paste on both ends of ITO film directly as the electrodes. It can keep the sensor’s structural strength and electrical characteristics

Micromachines 2020, 11, 16 of 21

Micromachines 2020, 11, 162 15 of 20 Figure 15. The results of BP training. 5. Experiments 5. Experiments 5.1. Design and Fabrication of Sensor 5.1. Design and Fabrication of Sensor The contact force detection model mentioned above needs the position information of sensing The contact force detection model mentioned above needs the position information of sensing units. Based on the principle of electric field potential uniqueness, our team have already developed units. Based on the principle of electric field potential uniqueness, our team have already developed four-wire [20] and five-wire [21] tactile sensors in recent years. These sensors can detect the contact four-wire [20] and five-wire [21] tactile sensors in recent years. These sensors can detect the contact position by extracting the potential value distributed over the sensor film. The sensor shapes were also position by extracting the potential value distributed over the sensor film. The sensor shapes were designedalso designed for diff forerent different style, suchstyle, assuch rectangle, as rectangle, sector sector [22] and[22] irregularand irregular planes planes [23 ].[23]. AccordingAccording to to the the previous previous research research works, works, we we improved improved the the upper upper andand lowerlower electrodeelectrode layerslayers of theof original the original structure structure proposed proposed in Figure in Figure1. Then, 1. Th aen, novel a novel large large scale scale tactile tactile sensor sensor was was designed designed for detectingfor detecting contact contact position position and force.and force. AsAs shown shown in in Figure Figure 16 16,, the the position position detection detection layer layer is is divided divided into into uniformuniform electricelectric fieldfield layerslayers in X andin XY and directions. Y directions. Two Two groups groups of strip of strip line electrodesline electrodes (X+,X (X+, andX− and Y+ ,YY+, )Y are−) are set set vertically vertically to eachto − − othereach on other the conductiveon the conductive films, whichfilms, which are used are to used introduce to introduce excitation excitation source source and extractand extract the sensor the signals.sensor The signals. force The detection force detection layer is alayer piezoresistive is a piezoresistive film. The film. protective The protective layers arelayers used are for used collision for bucollisionffering and buffering the protection and the protection of the interior of the sensing interior materials. sensing materials.

Figure 16. Structure of the presented sensor. Figure 16. Structure of the presented sensor. According to the electrical and physical characteristics of the tactile sensor, the sensing materials should beAccording as light andto flexiblethe electrical as possible. and Forphysical position char detection,acteristics Indium-tinoxide of the tactile sensor, based on the polyethylene sensing terthalatematerials (PET-ITO) should be conductive as light and film flexible was chosen as possible. as the For layer position of uniform detection, electric Indium-tinoxide field, whose thickness based is onlyon polyethylene 0.125 mm. It’sterthalate uniform (PET-ITO) in conductivity, conductive soft fi inlm flexibilitywas chosen and as stablethe layer in chemistry. of uniform Silkscreen electric field, whose thickness is only 0.125 mm. It’s uniform in conductivity, soft in flexibility and stable in was adopted to print the conductive silver paste on both ends of ITO film directly as the electrodes. chemistry. Silkscreen was adopted to print the conductive silver paste on both ends of ITO film It can keep the sensor’s structural strength and electrical characteristics when bent. The Velostat directly asMicromachines the electrodes. 2020, 11, It can keep the sensor’s structural strength and electrical17 ofcharacteristics 21 piezoresistive film was used for the layer of force detection. A double-sided tape was used to bond when bent. The Velostat piezoresistive film was used for the layer of force detection. A the outer edge of all the layers. Finally, a dimension of 120 120 mm tactile sensor was successfully double-sided tape was used to bond the outer edge of all the ×layers. Finally, a dimension of 120 × fabricated, as120 shown mm tactile in sensor Figure was 17 successfullya,b. fabricated, as shown in Figure 17a,b.

(a) (b)

Figure 17.FigureThe sensor17. The sensor sample: sample: (a )Before(a)Before sensor sensor packaging; packaging; (b) Sensor (b) detection Sensor layers. detection layers.

5.2. the Creep and Inconsistence Test for Piezoresistive Film Velostat is an anisotropic piezoresistive film made of polyolefins foil impregnated with carbon black, produced by the 3M Co. (Minnesota Mining and Manufacturing Company in America, Shanghai, China), limited. Its piezoresistive effect is obvious. In this paper, a 120 mm × 120 mm Velostat film was cut out to fabricate the large scale tactile sensor as a tested example. A force of 3 N by step-by-step was loaded using a compression testing machine of type ZQ-990B (Dongguan Zhihui Precision Instrument Ltd., Dongguan, China). The resistance variation caused by creep can be calculated by the formula as follows: Δ= − RRFF01 R F (25)

where RF0 and RF1 are the sensor output resistance at initial and time t under constant force respectively. The result indicates that creeps at different positions are inconsistent under a same force, as shown in Figure 18.

Figure 18. Creep at different positions under the constant force of 3 N.

Micromachines 2020, 11, 17 of 21

when bent. The Velostat piezoresistive film was used for the layer of force detection. A double-sided tape was used to bond the outer edge of all the layers. Finally, a dimension of 120 × 120 mm tactile sensor was successfully fabricated, as shown in Figure 17a,b.

(a) (b)

Micromachines 2020Figure, 11, 16217. The sensor sample: (a)Before sensor packaging; (b) Sensor detection layers. 16 of 20

5.2. the Creep and Inconsistence Test for Piezoresistive Film 5.2. the Creep and Inconsistence Test for Piezoresistive Film Velostat is an anisotropic piezoresistive film made of polyolefins foil impregnated with carbon black,Velostat produced is an anisotropicby the 3M piezoresistiveCo. (Minnesota film Mining made and of polyolefinsManufacturing foil impregnatedCompany in withAmerica, carbon black,Shanghai, produced China), by thelimited. 3M Co. Its (Minnesota piezoresistive Mining effect and is Manufacturingobvious. In this Companypaper, a 120 in America, mm × 120 Shanghai, mm China),Velostat limited. film was Its piezoresistivecut out to fabricate effect the is obvious.large scale In tactile this paper, sensor a as 120 a tested mm example.120 mm VelostatA force of film 3 N was × cutby out step-by-step to fabricate was the largeloaded scale using tactile a compression sensor as a tested testing example. machine A of force type of 3ZQ-990B N by step-by-step (Dongguan was loadedZhihui using Precision a compression Instrument testing Ltd., Dongguan, machine of China). type ZQ-990B The resistance (Dongguan variation Zhihui caused Precision by creep Instrument can Ltd.,be calculated Dongguan, by China).the formula The as resistance follows: variation caused by creep can be calculated by the formula as follows: Δ= − RRFF01 R F (25) ∆RF = RF R (25) 0 − F1 wherewhereRF 0RandF0 RandF1 areRF the1 are sensor the outputsensor resistanceoutput resistance at initial at and initial time and t under time constant t under forceconstant respectively. force Therespectively. result indicates The result that creeps indicates at di thatfferent creeps positions at different are inconsistent positions are under inconsistent a same force, under as a shown same in Figureforce, 18 as. shown in Figure 18.

Micromachines 2020Figure, Figure11, 18.18. CreepCreep at different diﬀerent positions positions under under the the constant constant force force of of3 N. 3 N. 18 of 21

The sensorThe sensor was was divided divided into into 36 units.36 units. The The forces forces of of 1 N1 N to to 15 15 N N were were loaded loaded on on the the di differentﬀerent units. The resistancesunits. The resistances of the sensor of the during sensor loadingduring loading were recorded were recorded and drawnand drawn as a as three-dimensional a three-dimensional graph. The relationshipgraph. The relationship among force, among units force, and units resistance and resi ofstance the of sensor the sensor was shownwas shown in Figure in Figure 19. 19. It canIt be seencan that be the seen curve that is the not curve completely is not smoothcompletely and smooth exists wrinkles.and exists Itwrinkles. means thatIt means the piezoresistive that the characteristicpiezoresistive is inconsistent. characteristic is inconsistent.

FigureFigure 19. 19.The The result of of surface surface fitting. ﬁtting.

5.3. Detection Circuit We built a detection circuit for the sensor, which can be powered by a 5 V battery. The whole framework is shown in Figure 20, including exciting source, analog switch, signal processing circuit, A/D conversion, reference voltage circuit, communication circuit and main controller. Among them, the exciting source consists of three constant current sources. The former two were used to constructing the uniform electric field in both X and Y directions, and the latter for contact force detection. The process of detection is as follows: (1) The sensor’s lead wires are connected with corresponding analog switch. The controller controls the analog switch to connect different detection channels and exciting sources cyclically. (2) The sensor’s output signals are amplified and filtered by the signal processing circuit. Then, they are input into corresponding A/D conversion ports respectively. (3) The controller uploads the quantized data to the host computer for the algorithm calibration through the serial port. Ultimately, the contact position and force can be calculated and shown on PC.

Figure 20. Detection system of the tactile sensor.

Micromachines 2020, 11, 18 of 21

The sensor was divided into 36 units. The forces of 1 N to 15 N were loaded on the different units. The resistances of the sensor during loading were recorded and drawn as a three-dimensional graph. The relationship among force, units and resistance of the sensor was shown in Figure 19. It can be seen that the curve is not completely smooth and exists wrinkles. It means that the piezoresistive characteristic is inconsistent.

Micromachines 2020, 11, 162 17 of 20 Figure 19. The result of surface fitting.

5.3. Detection Circuit We builtbuilt aa detectiondetection circuitcircuit forfor thethe sensor,sensor, whichwhich cancan bebe poweredpowered byby aa 55 VV battery.battery. TheThe wholewhole framework is shownshown inin FigureFigure 2020,, includingincluding excitingexciting source,source, analoganalog switch,switch, signalsignal processingprocessing circuit,circuit, AA/D/D conversion,conversion, reference reference voltage voltage circuit, circuit, communication communication circuit circuit and and main main controller. controller. Among Among them, them, the excitingthe exciting source source consists consists of three of constant three currentconstant sources. current The sources. former twoThe wereformer used two to constructing were used theto uniformconstructing electric the ﬁeld uniform in both electric X and field Y directions, in both andX and the Y latter directions, for contact and forcethe latter detection. for contact The process force ofdetection. detection The is asprocess follows: of detection is as follows:

(1)(1) TheThe sensor’ssensor’s leadlead wires wires are are connected connected with with corresponding corresponding analog analog switch. switch. The controller The controller controls controlsthe analog the switch analog to connectswitch ditoff erentconnect detection differ channelsent detection and excitingchannels sources and cyclically.exciting sources cyclically. (2) The sensor’s output signals are amplified and filtered by the signal processing circuit. Then, they (2) The sensor’s output signals are amplified and filtered by the signal processing circuit. Then, are input into corresponding A/D conversion ports respectively. they are input into corresponding A/D conversion ports respectively. (3) The controller uploads the quantized data to the host computer for the algorithm calibration (3) The controller uploads the quantized data to the host computer for the algorithm calibration through the serial port. Ultimately, the contact position and force can be calculated and shown through the serial port. Ultimately, the contact position and force can be calculated and shown on PC. on PC.

Micromachines 2020, 11, 19 of 21 Figure 20. Detection system of the tactile sensor. 5.4. Pressing Experiment after Calibration

In orderorder to to verify verify the the eﬀ ecteffect of creep of creep compensation compensation and force and calibration, force calibration, the sensor the was sensor calibrated was calibratedearly by theearly methods by the proposed. methods Threeproposed. pressing Three tests pressing were carriedtests were out withcarried the out compression with the compressiontesting machine testing ZQ-20B-1 machine (Dongguan ZQ-20B-1 Zhihui (Dongguan Precision Zhihui Instrument Precision Ltd., Instrument Dongguan, Ltd., China), Dongguan, and the China),experimental and the platform experimental is shown platform in Figure is shown 21. in Figure 21.

Spring testing machine

Force bar

Force/Position Touch position sensor

Figure 21. Experimental platform of compression testing machine.

Firstly, an incremental stepper force was applied on it and kept for 5 s after each increase. Then, a force of 3 N was applied to three positions of the sensor sample in turn. The results were shown in Figure 22a,b.

. (a) (b)

Figure 22. Sensor output before and after creep compensation: (a) Imposing force incremental step by step; (b) Different positions.

As shown in Figure 22, the results of force detection are quite different between before creep compensation and after creep compensation. Without compensation, the maximum error is up to 5 N after loading to 7 N. The error will continue to increase as time goes on. By contrast, the compensated sensor output is more stable, which can provide more accurate feedback information of force. Above all, the effect of compensation is not affected by the pressed position and force basically. It extends application range of the sensor, such as stabilizing grasping operation of dexterous hands and plantar pressure distribution testing. Finally, four corners (A, B, C, D) and center (E) of the sensor sample were selected as the contact positions, and a force of 1 N to 15 N was applied to them individually. As shown in

Micromachines 2020, 11, 19 of 21

5.4. Pressing Experiment after Calibration In order to verify the effect of creep compensation and force calibration, the sensor was calibrated early by the methods proposed. Three pressing tests were carried out with the compression testing machine ZQ-20B-1 (Dongguan Zhihui Precision Instrument Ltd., Dongguan, China), and the experimental platform is shown in Figure 21.

Spring testing machine

Force bar

Force/Position Touch position sensor

Micromachines 2020, 11, 162 18 of 20 Figure 21. Experimental platform of compression testing machine.

Firstly,Firstly, an incremental stepper force was applied on it and kept for 5 s after each increase. Then, aa force force of 3 N N was applied to three positions of the sensor sample in turn. The The results results were were shown shown in in FigureFigure 22a,b.22a,b.

. (a) (b)

FigureFigure 22. Sensor output beforebefore andand afterafter creep creep compensation: compensation: (a ()a Imposing) Imposing force force incremental incremental step step by bystep; step; (b) ( Dib) ﬀDifferenterent positions. positions.

AsAs shown shown in in Figure Figure 22,22, the the results results of of force force detection detection are are quite quite different different between between before before creep creep compensationcompensation and after creepcreep compensation.compensation. WithoutWithout compensation, compensation, the the maximum maximum error error is is up up to to 5 N5 Nafter after loading loading to 7 to N. 7 The N. error The willerror continue will continue to increase to asincrease time goes as on.time By goes contrast, on. By the contrast, compensated the compensatedsensor output sensor is more output stable, is which more canstable, provide which more can accurateprovide feedbackmore accurate information feedback of force.information Above ofall, force. the e ffAboveect of compensationall, the effect isof notcompensation affected by theis not pressed affected position by the and pressed force basically.position and It extends force basically.application It rangeextends of theapplication sensor, such range as stabilizing of the sensor, grasping such operation as stabilizing of dexterous grasping hands operation and plantar of dexterouspressure distribution hands and plantar testing. pressure distribution testing. MicromachinesFinally,Finally, 2020 fourfour, 11 corners,corners (A, (A, B, B, C, C, D) D) and and center center (E) of(E) the of sensorthe sensor sample sample were selectedwere selected as the contact20as ofthe 21 contactpositions, positions, and a force and ofa 1force N to of 15 1 N N was to applied15 N was to themapplied individually. to them individually. As shown in As Figure shown 23 a,b,in Figurethe maximum 23a,b, the error maximum of force detectionerror of force is less detection than 2 N, is and less most than of 2 the N, error and canmost be of maintained the error can within be maintained1 N. within 1 N.

(a) (b)

Figure 23. The results of force contact experiment: ( (aa)) The The result result of of contact contact force force detection; ( (b)) Error distribution of contact force detection.

6. Conclusions Based on K-means clustering and fuzzy recognition, a creep tracking compensation method was proposed in this paper for creep inconsistency of large scale piezoresistive film. It guarantees the data collected for calibration more accurate and stable. Then, the sensor was calibrated for piezoresistive inconsistency and nonlinearity of the large scale tactile sensor. Firstly, different sensing units were classified and fused by hierarchical clustering algorithm. The fusion can reduce the complexity of subsequent neural network fitting and reduce boundaries between different sensing units, and prevent overfitting. Secondly, introducing the position information of sensing units, the BP neural network was used to build the contact force detection model. The BP neural network can solve problem which is the nonlinear and inconsistent characteristics of the piezoresistive sensor. Finally, the sensor sample was fabricated, and the experiments were carried out by the calibrated sensor detection system. The results demonstrate that the methods proposed can compensate the creep effectively. Besides, the computation in large-scale sensor calibration is reduced to a certain extent by decreasing redundant calibration data through the hierarchical clustering. In summary, these methods are valuable for designing large-scale piezoresistive tactile sensor with force detection.

Author Contributions: conceptualization, H.W. and J.Y. (Jinhua Ye); methodology, Z.L.; software, J.Y. (Jinyan You); validation, H.W., Z.L., J.Y. (Jinyan You) and S.H.; formal analysis, Z.L., J.Y. (Jinhua Ye); investigation, S.H.; resources, H.W. and J.Y. (Jinhua Ye); data curation, J.Y. (Jinyan You); writing—original draft preparation, Z.L.; writing—review and editing, J.Y. (Jinyan You); visualization, J.Y. (Jinhua Ye); supervision, H.W.; project administration, H.W.; funding acquisition, H.W.

Funding: This research was funded by the National Key Research and Development Project of China, grant number 2018YFB1308603, and the National Natural Science Foundation of China, grant number 51575111.

Conflicts of Interest: The authors declare no conflict of interest.

References

Micromachines 2020, 11, 162 19 of 20

6. Conclusions Based on K-means clustering and fuzzy recognition, a creep tracking compensation method was proposed in this paper for creep inconsistency of large scale piezoresistive film. It guarantees the data collected for calibration more accurate and stable. Then, the sensor was calibrated for piezoresistive inconsistency and nonlinearity of the large scale tactile sensor. Firstly, different sensing units were classified and fused by hierarchical clustering algorithm. The fusion can reduce the complexity of subsequent neural network fitting and reduce boundaries between different sensing units, and prevent overfitting. Secondly, introducing the position information of sensing units, the BP neural network was used to build the contact force detection model. The BP neural network can solve problem which is the nonlinear and inconsistent characteristics of the piezoresistive sensor. Finally, the sensor sample was fabricated, and the experiments were carried out by the calibrated sensor detection system. The results demonstrate that the methods proposed can compensate the creep effectively. Besides, the computation in large-scale sensor calibration is reduced to a certain extent by decreasing redundant calibration data through the hierarchical clustering. In summary, these methods are valuable for designing large-scale piezoresistive tactile sensor with force detection.

Author Contributions: Conceptualization, H.W. and J.Y. (Jinhua Ye); methodology, Z.L.; software, J.Y. (Jinyan You); validation, H.W., Z.L., J.Y. (Jinyan You) and S.H.; formal analysis, Z.L., J.Y. (Jinhua Ye); investigation, S.H.; resources, H.W. and J.Y. (Jinhua Ye); data curation, J.Y. (Jinyan You); writing—original draft preparation, Z.L.; writing—review and editing, J.Y. (Jinyan You); visualization, J.Y. (Jinhua Ye); supervision, H.W.; project administration, H.W.; funding acquisition, H.W. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Key Research and Development Project of China, grant number 2018YFB1308603, and the National Natural Science Foundation of China, grant number 51575111. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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