Static Tactile Sensing for a Robotic Electronic Skin Via an Electromechanical Impedance-Based Approach

sensors

Article Static Tactile Sensing for a Robotic Electronic Skin via an Electromechanical Impedance-Based Approach

Cheng Liu 1,*, Yitao Zhuang 2, Amir Nasrollahi 3 , Lingling Lu 4, Mohammad Faisal Haider 3 and Fu-Kuo Chang 3

1 Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA 2 Zenith Aerospace, Redwood City, CA 94063, USA; [email protected] 3 Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA; [email protected] (A.N.); [email protected] (M.F.H.); [email protected] (F.-K.C.) 4 Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Science, Beijing 100190, China; [email protected] * Correspondence: [email protected]

Received: 31 March 2020; Accepted: 14 May 2020; Published: 16 May 2020

Abstract: Tactile sensing is paramount for robots operating in human-centered environments to help in understanding interaction with objects. To enable robots to have sophisticated tactile sensing capability, researchers have developed different kinds of electronic skins for robotic hands and arms in order to realize the ‘sense of touch’. Recently, Stanford Structures and Composites Laboratory developed a robotic electronic skin based on a network of multi-modal micro-sensors. This skin was able to identify temperature profiles and detect arm strikes through embedded sensors. However, sensing for the static pressure load is yet to be investigated. In this work, an electromechanical impedance-based method is proposed to investigate the response of piezoelectric sensors under static normal pressure loads. The smart skin sample was firstly fabricated by embedding a piezoelectric sensor into the soft silicone. Then, a series of static pressure tests to the skin were conducted. Test results showed that the first peak of the real part impedance signal was sensitive to static pressure load, and by using the proposed diagnostic method, this test setup could detect a resolution of 0.5 N force. Numerical simulation methods were then performed to validate the experimental results. The results of the numerical simulation prove the validity of the experiments, as well as the robustness of the proposed method in detecting static pressure loads using the smart skin.

Keywords: robotic tactile sensing; electronic skin; piezoelectric sensors; static pressure load sensing; electromechanical impedance-based method

1. Introduction Tactile sensing in human and animal skins enables them to touch, sense temperature, etc. The haptic perception, if added to robots, can signiﬁcantly enhance their performance through better human-robot and robot-environment interactions. In comparison, even the most sophisticated robots have at most a few dozen tactile sensors. Regardless of over thirty years of research, tactile sensing still falls behind progress in computer vision methods. The reason for this discrepancy is that compared to cameras, tactile sensors must be compliant, tough and ﬂexible enough to coat the surfaces of robotic limbs and hands. In addition, as the number of sensors increases, wiring and signal transfer become a major issue [1–5]. To overcome the aforementioned challenges for robotic tactile sensing, Stanford Structures and Composites Laboratory (SACL) developed a smart skin shown in Figure1 by embedding a multi-modal stretchable sensor network [6] into a soft silicone. Guo [7] has documented in detail the fabrication and

Sensors 2020, 20, 2830; doi:10.3390/s20102830 www.mdpi.com/journal/sensors SensorsSensors 20202020, ,2020, ,x 2830 FOR PEER REVIEW 22 of of 14 14 fabrication and material selection process of this skin. This artificial skin has been added to a robotic armmaterial for realizing selection autonomous process of this control skin.,This which artiﬁcial leverages skin advanced has beenadded sampling to a- roboticbased motion arm for planning realizing techniquesautonomous [7]. control, Utilizing which the signals leverages of the advanced multi-modal sampling-based sensors, which motion are embedded planning techniquesin the skin [in7]. stateUtilizing awareness the signals algorithms of the as multi-modal input parameters, sensors, the which robotic are arm embedded can sense in and the skinreact into stateenvironmental awareness changalgorithmses such as as input temperature parameters, variance the robotic and armlocal can dynamic sense and impacts react toonto environmental the skin [7]. changesHowever, such one as criticaltemperature aspect variancein tactile andsensing local has dynamic not been impacts well studied, onto the which skin [ 7is]. how However, to detect one static critical pressure aspect in in thetactile smart sensing skin using has not lead been zirconate well studied, titanate which (PZT) is howelements to detect, also static known pressure as piezoelectric in the smart sensors. skin using lead zirconate titanate (PZT) elements, also known as piezoelectric sensors.

Figure 1. Robotic electronic skin (a.k.a. smart skin) with embedded multi-modal sensor network. Figure 1. Robotic electronic skin (a.k.a. smart skin) with embedded multi-modal sensor network. There exist different tactile sensors for measuring static pressure and contact conditions using differentThere transduction exist different mechanisms tactile sensors [8–11 for]. Resistive-basedmeasuring static tactile pressure sensors and cancontact reach conditions high sensitivity, using differentbut have transduction high power consumptionmechanisms [8 and–11] lack. Resistive the measurement-based tactile of sensors contact can forces reach [12 high]. Optical sensitivity, tactile butsensors have arehigh also power capable consumption of reaching and high lack sensitivity, the measurement although of they contact will force shows [ loss12]. ofOptical light duetactile to sensorsmicro bending are also chirping.capable of Meanwhile, reaching high power sensitivity, consumption although is also they abig will challenge show loss [12 of]. light Triboelectric due to microtactile bending sensors havechirping. the advantageMeanwhile, of power being self-powering,consumption is although also a big their challenge long-term [12]. unreliability Triboelectric is tactilestill an sensors issue [ 13have]. One the ofadvantage the most of common being self tactile-powering sensors, although are capacitive their long tactile-term sensors, unreliability which can is stillachieve an issue high [13 sensitivity]. One of [the4]. most However, common noises tactile coming sensors from are temperature capacitive tactile and humidity sensors, which variations, can achieveand even high electrical sensitivity noise [4] introduced. However, bynoises unshielded coming from power temperature supplies, may and significantlyhumidity variations decrease, and the evencapacitive electrical signal-to-noise noise introduced ratio. This by issue unshielded imposes powera signal supplies conditioning, may stage significantly in order to decrease obtain a high the capacitivesignal-to-noise signal ratio,-to-noise which ratio. results This in issue complex imposes circuitry a signal [4]. In conditioning addition, under stage highly in order repetitive to obtain loads, a highthe capacitive signal-to-noise sensors ratio, are pronewhich toresults failure in due complex to mechanical circuitry fatigue,[4]. In addition, which undermines under highly the repetitive reliability loads,of the the method capacitive [14]. sensors are prone to failure due to mechanical fatigue, which undermines the reliabilityCompared of the method with capacitive [14]. sensors, PZT sensors are excellent in terms of mechanical robustness andCompared their simplicity with ofcapacitive use and noisesensors, resistance. PZT sensors Piezoelectricity are excellent in in PZT terms is a of well-known mechanical transduction robustness andmechanism their simplicity for dynamic of use forceand noise measurement resistance. byPiezoelectricity using the direct in PZT piezoelectric is a well-known effect. transduction However, a mechanismdifferent mechanism for dynamic is required force measurement to sense static by loads using using the PZTdirect sensors. piezoelectric One promising effect. However, method ais differentto use PZT mechanism sensors in is a required resonant to piezoelectric sense static loads sensing using mode. PZT Safour sensors. and One Bernard promising [15] demonstrated method is to usethat PZT the sensors measured in a electric resonant admittance piezoelectric spectrum sensing of mode. a PZT Safour sensor and can Bernard be correlated [15] demonstrated to the static forces that theapplied measured to the PZT electric sensor. admittance Although spectrum their study of was a PZT focused sensor on can the beapplied correlated force in to the the order static of forces 100 N, appliedwhich is to relatively the PZT high,sensor. and Although applied their directly study on thewas PZT focused sensor, on theirthe applied results showedforce in the possibilityorder of 100 of N,this which method is forrelatively tactile sensing. high, and In applied general, directly tactile sensing on the requires PZT sensor, a higher their resolution, results showed and sensors the possibilitymust be embedded of this method in a skin for material.tactile sensing. Suchinclusion In general, of tactile the sensors sensing inside requires skin materiala higher likeresolution silicone, andrubber sensors or fiberglass must be canembedded prevent in sensors a skin frommaterial. direct Suc contacth inclusion with externalof the sensors environments, inside skin which material may likedamage silicone the rubber sensors. or fiberglass Shin [14] can also prevent investigated sensors the from effect direct of staticcontact load with on external PZT sensors environments, by using whichimpedance may damage measurement. the sensors. Their Shin results [14 showed] also investigated a decrease the in theeffect impedance of static load value on at PZT anti-resonance sensors by usifrequencies,ng impedance with increasing measurement. applied Their load. results However, showed their a work decrease demonstrated in the impedance a force resolution value at of anti 10 N,- resonanceand has not frequencies been proven, with theoretically increasing or applied numerically. load. However, Ozeri [16 ]their also work experimentally demonstrated investigated a force resolution of 10 N, and has not been proven theoretically or numerically. Ozeri [16] also experimentally investigated the static force measurement by PZT sensors. However, the minimum

SensorsSensors2020 2020,,20 20,, 2830x FOR PEER REVIEW 33 ofof 1414

detectable load in their work was still very large, at about 17.67 N (25 kPa on a circular area of 30 mm thein diamete static forcer). In measurement this paper, byan PZT electromechanical sensors. However, impedance the minimum (EMI)-based detectable method load is in used their as work the wasdiagnostic still very approach large, atto investigate about 17.67 the N ability (25 kPa of onthe a proposed circular areasmart of skin 30 mmfor sensing in diameter). static pressure In this paper,loads. Different an electromechanically than other studies, impedance however, (EMI)-based we especially method focus is used on the as detection the diagnostic for small approach amount tos investigateof normal load thes ability (0.5 N of as the the proposed resolution) smart. Furthermore, skin for sensing such active static pressuresensing method loads. Dis arefferently considered than otherto be studies,more simplified however, than we especiallypassive sensing, focus on as thethey detection eliminate for the small required amounts power of normal supply loadsthroughout (0.5 N asthe the operation resolution). time. Furthermore, such active sensing methods are considered to be more simplified than passive sensing, as they eliminate the required power supply throughout the operation time. 2. Problem Statement 2. Problem Statement As the shortcomings of the current sensing approaches in robotic smart skin application impede As the shortcomings of the current sensing approaches in robotic smart skin application impede high-resolution and robust tactile sensing, in this study an electromechanical impedance (EMI)-based high-resolution and robust tactile sensing, in this study an electromechanical impedance (EMI)-based approach is proposed to be implemented. The hypothesis is that the amplitude of the impedance approach is proposed to be implemented. The hypothesis is that the amplitude of the impedance response of lead zirconate titanate (PZT) sensors, as the sensing elements, depends on the contact response of lead zirconate titanate (PZT) sensors, as the sensing elements, depends on the contact properties of the skin. Considering the PZT sensor’s mechanical robustness and simplicity to use, the properties of the skin. Considering the PZT sensor’s mechanical robustness and simplicity to use, objective of this work is to study the capability of the PZT sensor in the smart skin to detect static the objective of this work is to study the capability of the PZT sensor in the smart skin to detect static pressure loads, which is a critical portion of robotic tactile sensing. The EMI-based approach is used pressure loads, which is a critical portion of robotic tactile sensing. The EMI-based approach is used by by correlating the impedance signal directly to static pressure load. The resolution and sensitivity of correlating the impedance signal directly to static pressure load. The resolution and sensitivity of this this method are then evaluated. A special effort is emphasized on the numerical simulation method are then evaluated. A special effort is emphasized on the numerical simulation investigation investigation to physically validate the relationship between the impedance signal variation and the to physically validate the relationship between the impedance signal variation and the applied static applied static pressure load. pressure load. 3. Method of Approach 3. Method of Approach The goal of this work is to study the feasibility of detecting static pressure loads using lead The goal of this work is to study the feasibility of detecting static pressure loads using lead zirconate titanate (PZT) sensors embedded in the smart skin by an electromechanical impedance zirconate titanate (PZT) sensors embedded in the smart skin by an electromechanical impedance (EMI)-based approach. In order to achieve this objective, as shown in Figure 2, the method of (EMI)-based approach. In order to achieve this objective, as shown in Figure2, the method of approach approach can be divided into the following tasks: (1) developing the smart skin sample with sensors can be divided into the following tasks: (1) developing the smart skin sample with sensors and and silicone rubber, emulating the skin material; (2) measuring the electromechanical impedance of silicone rubber, emulating the skin material; (2) measuring the electromechanical impedance of the the sensors under various static pressure loads applied to the sample; (3) signal processing to sensors under various static pressure loads applied to the sample; (3) signal processing to correlate the correlate the impedance response to the applied static pressure loads; and (4) validating the impedance response to the applied static pressure loads; and (4) validating the resonance behavior of resonance behavior of the sensor embedded in the skin by numerical and analytical methods. the sensor embedded in the skin by numerical and analytical methods.

Figure 2. The framework of using the EMI-based method to detect static pressure loads for application onFigure smart 2. skinThe framework with an embedded of using PZTthe EMI sensor.-based method to detect static pressure loads for application on smart skin with an embedded PZT sensor.

4. Experiment and Results

4.1. Smart Skin Sample Development

Sensors 2020, 20, 2830 4 of 14

Sensors 2020, 20, x FOR PEER REVIEW 4 of 14 4. Experiment and Results The development of the smart skin sample is presented in this section. The 3D schematic of a Sensors4.1.smart Smart20 20skin, 20 Skin,sample x FOR Sample PEER with REVIEW Development an embedded lead zirconate titanate (PZT) sensor is shown in Figure 3a4 of. This 14 sensor,The whose development dimensions of the were smart 2skin mm sample × 2 mm is presented× 0.254 mm, in this was section. fabricated The 3Dby schematicAPC ceramics. of a smart The The development of the smart skin sample is presented in this section. The 3D schematic of a skinmaterial sample properties with an of embedded this PZT sensor lead zirconate can be found titanate in (PZT)Table sensor1. The iswired shown sensor in Figure was then3a. This embedded sensor, smart skin sample with an embedded lead zirconate titanate (PZT) sensor is shown in Figure 3a. This whosein the skin dimensions-like soft weresilicone 2 mm rubber2 mmmaterial0.254 (Smooth mm, was-On fabricatedEcoflex 00- by30 APC[17]), ceramics.as illustrated The in material Figure sensor, whose dimensions were ×2 mm × ×2 mm × 0.254 mm, was fabricated by APC ceramics. The 3b, to form a smart skin sample. This sample was 50.8 mm by 50.8 mm, with a thickness of 1.5 mm. materialproperties properties of this PZTof this sensor PZT sensor can be can found be found in Table in1 Table. The 1. wired The wired sensor sensor was then was embeddedthen embedded in the inskin-like the skin soft-like silicone soft silicone rubber rubber material material (Smooth-On (Smooth Ecoﬂex-On Ecoflex 00-30 [17 00]),-30 as illustrated[17]), as illustrated in Figure 3inb, Figure to form 3ba, smartto form skin a smart sample. skin This sample. sample This was sample 50.8 mm was by 50.8 50.8 mm mm, by with50.8 m am thickness, with a ofthickness 1.5 mm. of 1.5 mm.

(a) (b) Figure 3. (a) Schematic of smart skin sample with a PZT sensor embedded in soft silicone; (b) the real sample with wiring and connectors.(a) (b)

FigureFigure 3. 3.(a)( aSchematic) Schematic of ofsmart smart skin skin sample sample with with a PZT a PZT sensor sensor embedded embedded in in soft soft silicone; silicone; (b ()b t)he the real real Table 1. The properties of the piezoelectric material in APC plate sensor. samplesample with with wiring wiring and and connectors. connectors. Relative Young’sTable 1. The propertiesYoung’s of the piezoelectric material inPiezo APC plate Charge sensor. Piezo Voltage Density Table 1. The properties of the piezoelectricDielectric material in APC plate sensor. Modulus E11 Modulus E33 Constant d33 Constant g33 Young’s Young’s ConstantRelative DielectricKT Piezo Charge Piezo Voltage Density Relative 7.6 Young’sModulus E11 Young’sModulus E33 Constant KT Piezo ChargeConstant d33 PiezoConstant Voltage g33 Density 3 63 GPa 54 GPa Dielectric1700 400 pC/N 24.8 mV-m/N g/cm7.63 g /cmModulus 63E11 GPa Modulus 54 E GPa33 1700Constant 400 d pC33 /NConstant 24.8 mV-m g33/N Constant KT 7.6 4.2. Test Procedure63 GPa 54 GPa 1700 400 pC/N 24.8 mV-m/N g/cm3 To applyapply thethe staticstatic pressurepressure load,load, inin eacheach instanceinstance aa 5050 gg calibrationcalibration weightweight waswas gentlygently placedplaced 4.2.on Test top Procedure of the embedded PZT sensor,sensor, as shownshown in Figure4 4.. ToTo guaranteeguarantee aa uniformuniform pressure,pressure, aa rigidrigid thin compositecomposite plate with dimensionsdimensions of 20 mm by 20 mm was placed between the skin and the To apply the static pressure load, in each instance a 50 g calibration weight was gently placed calibration weight.weight. Two wires (AWG 40)40) ofof 80 µµmm in diameter embedded in the silicone skin extended on top of the embedded PZT sensor, as shown in Figure 4. To guarantee a uniform pressure, a rigid the top and bottom electrodes of the PZT sensor sensor,, respectively,respectively, toto thethe outsideoutside ofof thethe skin,skin, whichwhich were thin composite plate with dimensions of 20 mm by 20 mm was placed between the skin and the then connectedconnected toto aa PC-connectedPC-connected impedanceimpedance analyzeranalyzer (SinePhase(SinePhase ImpedanceImpedance AnalyzerAnalyzer 167,7716777 k). calibration weight. Two wires (AWG 40) of 80 µm in diameter embedded in the silicone skin extended This impedance analyzer analyzer then then actuates actuates the the PZT PZT sensor sensor over over a designated a designated range range of frequencies of frequencies,, and the top and bottom electrodes of the PZT sensor, respectively, to the outside of the skin, which were andcollect collectss the impedance the impedance response response accordingly accordingly over over this this frequency frequency range. range. In the In expethe experiment,riment, the then connected to a PC-connected impedance analyzer (SinePhase Impedance Analyzer 16777 k). theimpedance impedance signal signal was was recorded recorded at ateach each load load increment. increment. One One of of the the collected collected impedance impedance signals signals for This impedance analyzer then actuates the PZT sensor over a designated range of frequencies, and 100100 kHzkHz toto 3 3 MHz, MHz with, with an an increment increment of of 1 kHz, 1 kHz is, shown is shown in Figure in Figure5. Both 5. Both the real the and real imaginary and imaginary parts collects the impedance response accordingly over this frequency range. In the experiment, the ofparts the of recorded the recorded data are data shown are shown in Figure in 5 Figure; however, 5; however, only the only real part the real was part used was for laterused analysis.for later impedance signal was recorded at each load increment. One of the collected impedance signals for Theanalysis. ﬁrst resonantThe first resonant peak is around peak is 900around kHz, 900 which kHz, corresponds which corresponds to the radial to the vibrationradial vibration modes modes of the 100 kHz to 3 MHz, with an increment of 1 kHz, is shown in Figure 5. Both the real and imaginary PZTof the sensor. PZT sensor. parts of the recorded data are shown in Figure 5; however, only the real part was used for later analysis. The first resonant peak is around 900 kHz, which corresponds to the radial vibration modes of the PZT sensor.

Figure 4. Schematic of the experimental test setup.

Sensors 2020, 20, x FOR PEER REVIEW 5 of 14 SensorsSensors2020 2020, 20, 20, 2830, x FOR PEER REVIEW 55 of of 14 14

Figure 5. The electromechanical impedance behavior from the PZT sensor at zero static pressure load. FigureFigure 5. 5.The The electromechanical electromechanical impedance impedance behavior behavior from from the the PZT PZT sensor sensor at at zero zero static static pressure pressure load. load. 4.3.4.3. Results Results of of Impedance Impedance Response Response to to Static Static Pressure Pressure Loads Loads 4.3. Results of Impedance Response to Static Pressure Loads InIn this this study, study, we we focused focused on on the the real real part part of of the the impedance impedance response. response. As As illustrated illustrated in in Figure Figure6 a,6a, In this study, we focused on the real part of the impedance response. As illustrated in Figure 6a, inin general, general, a a gradual gradual decrease decrease in in the the amplitude amplitude at at the the ﬁrst first peak peak frequency frequency happens happens with with the the increment increment in general, a gradual decrease in the amplitude at the first peak frequency happens with the increment ofof the the static static pressure pressure load. load. The The maximum maximum amplitude amplitude value value at at each each load load was was extracted. extracted. The The percentage percentage of the static pressure load. The maximum amplitude value at each load was extracted. The percentage changechange of of these these values values at eachat each load, load with, with respect respect to the to maximum the maximum amplitude amplitude value at value 0.5 N, at were 0.5 plottedN, were change of these values at each load, with respect to the maximum amplitude value at 0.5 N, were inplotted Figure 6inb. Figure Directly 6b. comparing Directly comparing the maximum the maximum amplitude amplitude under each under load each is the load traditional is the traditional method plotted in Figure 6b. Directly comparing the maximum amplitude under each load is the traditional thatmethod has been that previouslyhas been previously investigated investigated and applied and at applied large load at large levels load [14, 15level]. Ins our[14,15 case,]. In however, our case, method that has been previously investigated and applied at large load levels [14,15]. In our case, sincehowever the load, since level the is load as small level asis as 0.5 small N, this as direct0.5 N, comparisonthis direct comparison of maximum of maximum amplitude amplitude does not work does however, since the load level is as small as 0.5 N, this direct comparison of maximum amplitude does well.not work It can well. be observed It can be that observed although that there although is a decreasing there is a trend,decreasing there trend, exists inconsistencythere exists inconsistency at the load not work well. It can be observed that although there is a decreasing trend, there exists inconsistency ofat 2 the N. Thisload is of due 2 N. to theThis mismatch is due to between the mismatch this high-resolution between this load high and-resolution the limited load sampling and the rates limited of at the load of 2 N. This is due to the mismatch between this high-resolution load and the limited thesampling data acquisition rates of the system. data acquisition system. sampling rates of the data acquisition system.

(a) (b) (a) (b) FigureFigure 6. 6.( a()a) Real Real part part of of the the impedance impedance response response under under di differentﬀerent static static pressure pressure load; load; (b ()b maximum) maximum impedanceFigureimpedance 6. ( amplitudea )amplitude Real part change ofchange the atimpedance at each each static static response load load with with under respect respect different to to the the static value value pressure at at 0.5 0.5 N. N load;. (b) maximum impedance amplitude change at each static load with respect to the value at 0.5 N. ToTo overcome overcome this this challenge, challenge, a a novel novel diagnostic diagnostic method method was was proposed proposed by by using using the the root root mean mean squaresquareTo deviation deviation overcome (RMSD) (RMSD) this challenge, [18 [1] of8] Equationof Equationa novel (1) diagnostic as(1) the as tactilethe tactilemethod index index (TI)was to (TI)proposed evaluate to evaluate by the using static the pressurestaticthe root pressure load:mean square deviation (RMSD) [18] of Equation (1) as the tactile index (TI) to evaluate the static pressure load: tv load: Pn 2 i=1 [Re(Zh(ωi)) Re(Zu(ωi))] TI = ∑푛 [푅푒(푍 (휔−))−푅푒(푍 (휔 ))]2, (1) 𝑖P=1n ℎ 𝑖 2 푢 𝑖 푇퐼 = √ 푛 2, (1) ∑ i[=푅푒([푛Re푍ℎ(휔Z𝑖h)()ω−i푅푒))](푍푢2(휔𝑖))] 𝑖=1 1∑𝑖=1[푅푒(푍ℎ(휔𝑖))] 푇퐼 = √ 푛 2 , (1) ∑𝑖=1[푅푒(푍ℎ(휔𝑖))] InIn this this equation, equation,Z h푍(ℎω(휔i)푖) denotes denotes the the baseline baseline impedance; impedance;Z 푍u(uω(휔i)푖) is is added added weight weight impedance; impedance; and andω 휔i 푖 denotesIdenotesn this frequencyequation, frequency 푍 interval. ℎinterval.(휔푖) denotes the baseline impedance; 푍u(휔푖) is added weight impedance; and 휔푖 denotesToTo apply frequencyapply this this TI, interval.TI, baseline baseline data data were were selected selected as the as impedance the impedance response response at 0 static at 0 loads, static as load showns, as inshown FigureTo in 7applya. Figure Note this 7a that TI,. Note there baseline that is a there perceivabledata iswere a perceivable selected di ﬀerence as difference the between impedance between the baseline response the signalbaseline at 0 and staticsignal the load signalsands, the as shown in Figure 7a. Note that there is a perceivable difference between the baseline signal and the

Sensors 2020, 20, 2830 6 of 14 Sensors 2020, 20, x FOR PEER REVIEW 6 of 14 undersignals static under loads. static This loads. is due This to theis due diff toerent the forcedifferent boundary force boundary conditions conditions in these two in dithesefferent two scenarios. different Thisscenarios. tactile This index tactile is essentially index is essentially describing describing the average the impedance average impedance change from change the baseline from the signal baseline at eachsignal corresponding at each corresponding load. By using load. this By definition,using this thedefinition applied, the frequency appliedrange frequency is centered range inis thecentered first peakin the frequency first peak within frequency a range within of 50 a range kHz, asof shown50 kHz in, as Figure shown7a. in Note Figure that 7a to. Note collect that data to collect over this data 50over kHz thi frequencys 50 kHz range, frequency the response range, the time response was about time 600 wasµ abouts. The 600 TI valuesµs. The were TI values then calculated were then undercalculated each staticunder load each and static plotted load and in Figure plotted7b in with Figure error 7b bars, with which error wasbars based, which on was five based individual on five tests.individual It is observed tests. It that is with observed the increment that with of thestatic increment pressure load, of static the TI pre valuesssure consistently load, the TI increase, values andconsistently are highly increase distinguishable, and are highly for each distinguishable force increment for ofeach 0.5 force N, which increment was the of 0.5 minimal N, which detectable was the forceminimal in this detectable current setup, force with in this a sensitivity current setup of 1.8%, with/N. This a sensitivity resolution of is 1.8%/N. comparable This to resolution capacitive is sensors,comparable and proves to capacitive its great sensors sensitivity, and in terms proves of its detecting great sensitivity the static pressure in terms load of using detecting the proposed the static diagnosticpressure load method. using the proposed diagnostic method.

(a) (b)

FigureFigure 7. 7.( a(a)) Real Real part part of of the the impedance impedance response response under under di differentﬀerent static static pressure pressure loads, loads, including including baselinebaseline data; data (; b(b)) tactile tactile index index at at di differentﬀerent static static loads. loads.

5.5. Finite Finite Element Element Simulation Simulation Study Study ToTo model model the the electromechanical electromechanical impedance impedance (EMI) (EMI) response response of of the the embedded embedded lead lead zirconate zirconate titanatetitanate (PZT) (PZT) sensors, sensors, a a finite finite element element model model (FEM) (FEM) was was created created using using the the commercial commercial software software AbaqusAbaqus 6.12. 6.12. The The objective objective of of the the simulation simulation was was to to obtain obtain qualitative qualitative insights insights into into the the resonant resonant behaviorsbehaviors of of the the embedded embedded PZT PZT sensors sensors under under the the applied applied static static pressure pressure loads. loads. The The dimensions dimensions of of thethe model model were were identical identical to to what what is is shown shown in in Figure Figure3 ,3 and, and the the mechanical mechanical material material properties properties of of this this piezoelectricpiezoelectric material material are are shown shown in in Table Table2. 2. The The direct direct piezoelectric piezoelectric matrix matrix [d] [d] and and permittivity permittivity [e] [e] areare shown shown in in matrix matrix (2) (2) and and (3) (3) respectively. respectively. The The C3D8E C3D8E elements, elements, which which stand stand for for solid solid elements elements withwith built-in built-in piezoelectric piezoelectric properties, properties, were were applied applied to to model model the the PZT PZT sensor. sensor. The The mesh mesh size size of of the the PZTPZT sensor sensor was was set set to to 100 100µ µmm, based, based on on the the previous previous convergence convergence study study [ 18[1].8]. The The EMI EMI of of the the PZT PZT sensorsensor was was calculated calculated over over the the frequency frequency domain domain from from 0.5 MHz0.5 MHz to 1.5 to MHz, 1.5 MHz with, with an interval an interval of 10 kHz.of 10 ConsideringkHz. Considering this frequency this frequency range and range the and typical the mechanicaltypical mechanical wave speed wave in siliconespeed in rubber, silicone which rubber, is aroundwhich is1000 around m/s [100019], them/s wavelength [19], the wavelength of acoustic of acoustic waves in waves the silicone in the silicone rubber rubber material material varies fromvaries 0.67from mm 0.67 to mm 2 mm. to 2 Therefore, mm. Therefore, the mesh the size mesh of size the siliconeof the silicone was chosen was chosen as 0.5 mm as 0.5 to ensuremm to thatensure it was that fineit was enough fine enough to capture to thecapture response the response over the desiredover the frequencies. desired frequencies. The FEM The model FEM and model mesh and sizes mesh are shownsizes are in Figureshown8 .in The Figure interaction 8. The interaction between the between PZT sensor the PZT and siliconesensor and was silicone defined was in both defined tangential in both andtangential normal and direction: normal the direction: tangential the behavior tangential was behavior defined withwas defined a friction with coeffi a cientfriction of 0.9coefficient [20], and of the 0.9 normal[20], and behavior the normal was setbehavior as “Hard” was contact.set as “Hard” contact.    0 0 0 0 584 0    12 1 d =  0 0 0 584 0 0  10− CN− , (2)   ×  171 171 374 0 0 0  − −

Sensors 2020, 20, 2830 7 of 14

   1730 0 0    εσ =  0 1730 0  ε0, (3)   ×  0 0 1700 

Table 2. The mechanical material properties used in the numerical simulation.

Property Unit Piezo PZT-5A

E11 GPa 60.97 E22 GPa 60.97 E33 GPa 53.19 G23 GPa 21.05 G31 GPa 21.05 G12 GPa 22.57 v23 0.4402 v13 0.4402 v12 0.3500 Sensors 2020, 20, x FOR PEER REVIEWρ kg/m3 7750 7 of 14

FigureFigure 8. 8.The The FEM FEM model model and and mesh mesh of of the the smart smart skin skin sample sample with with an an embedded embedded PZT PZT sensor. sensor.

5.1. Hyperelastic Material Property of Silicone Rubber Table 2. The mechanical material properties used in the numerical simulation. One key factor dominating the impedance behavior of the embedded PZT sensor is the hyperelastic Property Unit Piezo PZT-5A material property of the silicone rubber material. The stress-strain relationship of hyperelastic E11 GPa 60.97 materials such as silicone rubber is normally defined as nonlinear elastic and incompressible [17,21]. E22 GPa 60.97 Sparks et al. [17] demonstrated the stress and strain relationship shown in Figure9 under a static E33 GPa 53.19 compressive load for the Smooth-On Ecoflex 00-30, which is the silicone rubber used in our experiment. G23 GPa 21.05 It shows a clear nonlinear behavior, which indicates that the stiffness of this silicone material increases G31 GPa 21.05 with the applied load. G12 GPa 22.57 v23 0.4402 v13 0.4402 v12 0.3500 ρ kg/m3 7750

0 0 0 0 584 0 푑 = [ 0 0 0 584 0 0] × 10−12퐶푁−1, (2) −171 −171 374 0 0 0 1730 0 0 휀𝜎 = [ 0 1730 0 ] × 휀0, (3) 0 0 1700

5.1. Hyperelastic Material Property of Silicone Rubber One key factor dominating the impedance behavior of the embedded PZT sensor is the hyperelastic material property of the silicone rubber material. The stress-strain relationship of hyperelastic materials such as silicone rubber is normally defined as nonlinear elastic and incompressible [17,21]. Sparks et al. [17] demonstrated the stress and strain relationship shown in Figure 9 under a static compressive load for the Smooth-On Ecoflex 00-30, which is the silicone rubber used in our experiment. It shows a clear nonlinear behavior, which indicates that the stiffness of this silicone material increases with the applied load. Therefore, to correlate the stress level to the silicone’s stiffness change, the stress and strain relationship from Sparks’ experiment result was fitted into a quadratic curve, which is also plotted in Figure 9. This quadratic curve is presented explicitly in Equation (4), where S denotes stress and ε denotes strain. The stresses at each load increment in the experiment were used to calculate the corresponding strains using Equation (4). These strain values were then used to obtain the corresponding stiffness as the slope of the quadratic curve at each stress level. Table 3 shows the values of stress, strain and stiffness at each load increment. Note that the weight of the rigid

Sensors 2020, 20, x FOR PEER REVIEW 8 of 14

composite plate, which is 1.5 g and used for even pressure distribution, was also taken into Sensorsconsideration.2020, 20, 2830 8 of 14

FigureFigure 9. 9.Nonlinear Nonlinear stress-strain stress-strain relationship relationship for for Smooth-On Smooth-On Ecoflex Ecoflex 00-30 00 under-30 under static static compressive compressive load. load. Therefore, to correlate the stress level to the silicone’s stiffness change, the stress and strain relationship from Sparks’ experiment result was fitted into a quadratic curve, which is also plotted 2 in Figure9. This quadratic curve 푆 = is147 presented.7휀 + explicitly57.14휀 + in0. Equation3583 푘푃푎 (4),, where S denotes stress(4) and ε denotes strain. The stresses at each load increment in the experiment were used to calculate the correspondingTable strains3. Stress, using strain Equationand stiffness (4). of the These silicone strain rubber values at eac wereh load then increment. used to obtain the corresponding stiffness as the slope of the quadratic curve at each stress level. Table3 shows the values Static Load (N) Stress (kPa) Strain Stiffness (kPa) of stress, strain and stiffness at each load increment. Note that the weight of the rigid composite plate, 0.5 1.2875 0.01563 61.757 which is 1.5 g and used for even pressure distribution, was also taken into consideration. 1.0 2.5375 0.03498 67.473 1.5 S = 147.73.7875ε2 + 57.14ε +0.052810.3583 kPa ,72.740 (4) 2.0 5.0375 0.06943 77.650 2.5 6.2875 0.08506 82.267 Table 3. Stress, strain and stiffness of the silicone rubber at each load increment. 5.2. Dynamic Compressive Behavior of Silicone Rubber Material Static Load (N) Stress (kPa) Strain Stiffness (kPa) The stress-strain0.5 relationship in 1.2875 Figure 9 was measured 0.01563 under a static compressive 61.757 load. In our simulation, however1.0, the interaction 2.5375between the PZT sensor 0.03498 and silicone rubber 67.473was highly dynamic at the frequency1.5 level of megahertz. 3.7875 Therefore, the silicone 0.05281 rubber was driven 72.740 by the PZT sensor under dynamic 2.0strains. This means 5.0375that this stress-strain 0.06943 curve for the silicone 77.650 rubber needs to be 2.5 6.2875 0.08506 82.267 modified, considering this load rate effect. In highly viscous materials such as silicone rubber, the stress-strain curve is greatly dependent on the applied strain rates. Song et al. [22] experimentally 5.2.determined Dynamic Compressivethe dynamic Behavior compressive of Silicone stress Rubber-strain Material relationships of an ethylene propylene-diene monomerThe stress-strain copolymer relationship(EPDM) rubber in Figure at various9 was strain measured rates. underTheir test a static results compressive showed that load. at the In ourtrue simulation,strain of 0.1, however, as the strain the interaction rate increases between from the 653 PZT Hz sensor to 4730 and Hz, silicone the true rubber stress was increases highly dynamicfrom 1.0 atMPa the frequencyto 7.0 MPa level, which of megahertz. is seven times Therefore, higher the in silicone stiffness. rubber It is was also driven observed by the that PZT the sensor nonlinear under dynamicbehavior strains.of the hy Thisperelastic means thatmaterials this stress-strain still holds, curveregardless for the of siliconethe increase rubber of needsthe strain to be rate. modified, Based consideringon the fact from this loadthis study rate e ffthatect. with In highly the 7.24 viscous times materials increase suchof the as strain silicone rate, rubber, the stiffness the stress-strain increased curveby seven is greatly times. dependent Therefore, on in theour applied simulation, strain the rates. stiffness Song etval al.ues [22 in] experimentallyTable 3 were amplified determined by thethe dynamicsame amount compressive. This amplification stress-strain factor relationships is already of anquite ethylene conservative propylene-diene, considering monomer that the copolymer frequency (EPDM)range in rubberour simulation at various is strainon the rates.orders Their of 10 test6 Hz. results Again, showed the objective that at of the this true simulation strain of 0.1,study as was the strainto obtain rate qualit increasesative from insights 653 Hz into to 4730the impedance Hz, the true behavior stress increases of the embedded from 1.0 MPa PZT to sensor. 7.0 MPa, Therefore, which is sevenby amplifying times higher seven in times stiffness., the stiffness It is also was observed good enough that the to nonlinear capture the behavior change of of the the hyperelastic impedance materialsbehavior. still holds, regardless of the increase of the strain rate. Based on the fact from this study that with theTaking 7.24 into times account increase both of the the strain hyperelastic rate, the property stiffness increasedand dynamic by seven effec times.t on the Therefore, silicone rubber in our simulation,stiffness, in the order stiff toness simulate values the in Table static3 pressurewere amplified load effect by the onto same the amount. smart skin This sample, amplification the following factor isstiffness already values quite conservative,were used to consideringrepresent each that corresponding the frequency loading range in status our simulation, as shown isin on Table the orders4. of 106 Hz. Again, the objective of this simulation study was to obtain qualitative insights into the

Sensors 2020, 20, 2830 9 of 14 impedance behavior of the embedded PZT sensor. Therefore, by amplifying seven times, the stiffness was good enough to capture the change of the impedance behavior. Taking into account both the hyperelastic property and dynamic effect on the silicone rubber stiffness, in order to simulate the static pressure load effect onto the smart skin sample, the following stiSensorsffness 20 values20, 20, x were FOR PEER used REVIEW to represent each corresponding loading status, as shown in Table4. 9 of 14

TableTable 4. 4.Dynamic Dynamic sti stiffnessﬀness of of the the silicone silicone rubber rubber at at each each load load increment. increment. Static Load (N) Dynamic Stiffness (kPa) Static Load (N) Dynamic Stiﬀness (kPa) 0.5 431.27 0.5 431.27 1.01.0 472.25 472.25 1.51.5 509.12 509.12 2.02.0 543.46 543.46 2.52.5 575.78 575.78

5.3.5.3. A A Direct Direct Steady-State Steady-state Dynamic Dynamic Analysis Analysis for for Simulating Simulating Impedance Impedance Behavior Behavior AA direct direct steady-state steady-state dynamic dynamic analysis analysis was was performed performed using using Abaqus Abaqus 6.12. 6.12. A zero A zero displacement displacement in thein xthe, y x,and y andz directions z directions on theon the bottom bottom surface surface of theof the skin skin was was considered considered as as mechanical mechanical boundary boundary conditions.conditions The. The following following electrical electrical boundary boundary conditions conditions were applied were applied to the sensor: to the a sensor: constant a voltage constant ofvoltage 1 V in magnitudeof 1 V in magnitude and 0 in phaseand 0 atin thephase top at surface the top electrode surface electrode of the PZT of sensor,the PZT while sensor the, while bottom the surfacebottom electrode surface was electrode ﬁxed as was the fixed ground as ofthe 0 groundV. For each of 0 simulation, V. For each the simulation, nodal electric the charges nodal atelectric the topcharges surface at electrodethe top surfac weree extractedelectrode andwere summed extracted to and compute summed the totalto compute electrical the charge total electrical (Q). Figure charge 10 shows(Q). Figure the simulation 10 shows result the simulation of the nodal result electric of the charge nodal at electric one node charge at the at top one surface. node at Again, the top the surface. total electricAgain, charge the total (Q) electric is the summation charge (Q) ofis thesethe summation nodal electric of these charges nodal over electr all theic charges nodes at over the all top the surface nodes ofat the the PZT top sensor.surface of the PZT sensor.

FigureFigure 10. 10.Simulation Simulation result result of of the the nodal nodal electric electric charge charge at one at one node node at the at topthe surfacetop surface of the of PZT the sensor.PZT sensor. AfterAfter obtaining obtaining the the total total electric electric charge charge (Q), (Q) the, the current current in in the the transducer transducer can can be be determined determined by by thethe following following equation equation I = iωQ, (5) 퐼 = 푖휔푄, (5) where ω is the angular frequency of the applied actuation voltage. whereThe ω impedance is the angular was frequency then calculated of the using applied Equation actuation (6) voltage. The impedance was then calculated using Equation (6)

V 푉 Z =푍 =, (6)(6) I 퐼 , wherewhere V V is is the the voltage voltage di ﬀdifferenceerence across across the the PZT PZT sensor, sensor, which which was was 1 V. Note1 V. Note that thethat impedance the impedance is in a is complexin a complex form. form. Figure 11 illustrates the simulation results, including both real and imaginary parts of the impedance response at baseline state (0 pressure load). For comparison, the experimental results were also plotted in the figure, and show good agreement with the simulation results. Here, in order to match the amplitude of the first resonant peak in the experiment, a structural damping coefficient of 0.04 for the PZT sensor was used in the simulation. Although the damping coefficient is very difficult to be accurately determined by experiments [18], its value used in this simulation was assumed to be the closest estimation towards our experiment. Again, the purpose of this numerical study was to

Sensors 2020, 20, 2830 10 of 14

Figure 11 illustrates the simulation results, including both real and imaginary parts of the impedance response at baseline state (0 pressure load). For comparison, the experimental results were also plotted in the figure, and show good agreement with the simulation results. Here, in order to match the amplitude of the first resonant peak in the experiment, a structural damping coefficient of 0.04 for the PZT sensor was used in the simulation. Although the damping coefficient is very difficult toSensors be accurately 2020, 20, x FOR determined PEER REVIEW by experiments [18], its value used in this simulation was assumed to10 of be 14 the closest estimation towards our experiment. Again, the purpose of this numerical study was to gain gain a qualitative understanding about the effect of normal pressure loads to the impedance behavior a qualitative understanding about the effect of normal pressure loads to the impedance behavior of the of the PZT sensors embedded in the silicone rubber. PZT sensors embedded in the silicone rubber.

(a) (b)

FigureFigure 11. 11Comparison. Comparison of of the the experiment experiment and and simulation simulation results results on on the the impedance impedance behavior behavior of of a a PZT PZT sensorsensor embedded embedded in in the the silicone silicone rubber: rubber: (a ()a real) real part; part; (b ()b imaginary) imaginary part. part.

5.4.5.4. The The E Effectffect of of the the Silicone Silicone Rubber Rubber Sti Stiffnessffness to to the the Impedance Impedance Response Response ToTo study study the the e ffeffecectsts of of changing changing the the sti stiffnessffness of of the the silicone silicone rubber, rubber, di differentfferent dynamic dynamic sti stiffnessffness valuesvalues at at each each static static normal normal pressure pressure level level were were used used in in the the numerical numerical model, model, and and the the corresponding corresponding impedanceimpedance response response was was then then obtained obtained for for each each sti stiffnessffness state. state. Figure Figure 12 1a2a shows shows the the real real part part of of the the impedanceimpedance responses responses at at each each normal normal pressure pressure state. state. The The impedance impedance peak peak decreases decreases with with the the increase increase of theof static the static normal normal pressure. pressure. As shown As fromshown Figure from 12 Figureb, a similar 12b, trenda similar was observed trend was in observedthe experiment in the resultsexperiment in Figure results6b. Thisin Figure verified 6b. ourThis assumption verified our that assumption the static normalthat the pressurestatic normal load changedpressure theload stichangedffness of the hyperelastic stiffness of silicone the hyperelastic material, which silicone eventually material contributes, which eventually to the impedance contributes behavior to the changeimpedance of the behavior embedded change PZT sensor.of the embedded PZT sensor.

(a) (b)

Figure 12. (a) Simulation results of the static normal pressure load effect to the smart skin sample with a PZT sensor embedded in the silicone rubber; (b) simulated maximum amplitude change at each static load, with respect to the value at 0.5 N.

6. Discussions Based on the Theoretical Model

6.1. Analytical Model: Dynamic Interaction between the PZT Sensor and Structure

Sensors 2020, 20, x FOR PEER REVIEW 10 of 14 gain a qualitative understanding about the effect of normal pressure loads to the impedance behavior of the PZT sensors embedded in the silicone rubber.

(a) (b)

Figure 11. Comparison of the experiment and simulation results on the impedance behavior of a PZT sensor embedded in the silicone rubber: (a) real part; (b) imaginary part.

5.4. The Effect of the Silicone Rubber Stiffness to the Impedance Response To study the effects of changing the stiffness of the silicone rubber, different dynamic stiffness values at each static normal pressure level were used in the numerical model, and the corresponding impedance response was then obtained for each stiffness state. Figure 12a shows the real part of the impedance responses at each normal pressure state. The impedance peak decreases with the increase of the static normal pressure. As shown from Figure 12b, a similar trend was observed in the experiment results in Figure 6b. This verified our assumption that the static normal pressure load changed the stiffness of the hyperelastic silicone material, which eventually contributes to the Sensorsimpedance2020, 20 ,behavior 2830 change of the embedded PZT sensor. 11 of 14

(a) (b)

FigureFigure 12. 12.( (aa)) SimulationSimulation resultsresults ofof thethe staticstatic normalnormal pressurepressure load load e effectﬀect to to the the smart smart skin skin sample sample with with aa PZT PZT sensor sensor embedded embedded in in the the silicone silicone rubber; rubber; (b) simulated(b) simulated maximum maximum amplitude amplitude change change at each at static each load,static with load respect, with respect to the valueto the atvalue 0.5 N. at 0.5 N.

6. Discussions Based on the Theoretical Model 6.1. Analytical Model: Dynamic Interaction between the PZT Sensor and Structure Sensors6. Discussions 2020, 20, x FOR Based PEER on REVIEW the Theoretical Model 11 of 14 Liang et al. [23] developed a 1D model to describe the interaction between a lead zirconate Liang et al. [23] developed a 1D model to describe the interaction between a lead zirconate titanate6.1. Analytical (PZT) sensorModel: Dynamic and a structure. Interaction The between essence the ofPZT this Sensor impedance-based and Structure model is illustrated in titanate (PZT) sensor and a structure. The essence of this impedance-based model is illustrated in Figure 13. Their results show that the complex electromechanical admittance Y, which is the inverse of Figure 13. Their results show that the complex electromechanical admittance Y, which is the inverse electromechanical impedance, can be represented by Equation (7), in which ω is the angular frequency; of electromechanical impedance, can be represented by Equation (7), in which ω is the angular w, l and h are the width, length and thickness of the PZT sensor, respectively; d31 is the piezoelectric frequency; w, l and h are the width, length and thicknessE of the PZT sensor, respectively; d31 is the strain coeﬃcient; ε33 is the dielectric permittivity; and Y is the Young’s Modulus of the PZT sensor. piezoelectric strain coefficient; ε33 is the dielectric permittivity; and YE is the Young’s Modulus of the The structural mechanical impedance ZS is shown in Equation (8), where c is the damping coeﬃcient PZT sensor. The structural mechanical impedance ZS is shown in Equation (8), where c is the damping and the mechanical impedance of the PZT sensor Za is represented in Equation (9) coefficient and the mechanical impedance of the PZT sensor Za is represented in Equation (9) " !# wl푤푙 2 E2 퐸 Za 푍푎 2 E2 tan퐸 kltan 휅푙 푌Y==22ω휔푖i ε[33휀33 d−31 Y푑31+푌 + ( d31) Y푑31푌 ( ,)], (7)(7) hℎ − Zs + Z푍푠a+푍푎 kl 휅푙   ω2 휔2  R  푅 (8) 푍Z푠s = c푐++ω im휔푖푚1 (1 −,2), (8)  − ω2  휔

kwhY휅푤Eℎ푌퐸 Za푍=푎 = ,, (9)(9) ωi tan휔𝑖 tankl 휅푙 q q k 푘 ρ 𝜌 wherewhereω 휔R == √and andk = 휅ω= 휔E .√ 푅 m 푚 Y 푌퐸

Figure 13. Electro-mechanical coupling between the PZT sensor and the structures.

6.2. The Effect of Stress on PZT Material Properties to Impedance Response Since in Equation (7), Y is a function of the PZT properties, it is necessary to investigate the stress effects to these parameters to evaluate its influence on the impedance response. Zhang et al. [24] studied the effect of mechanical stresses on the responses of PZT sensors. Both the soft-type PZT and hard-type PZT were selected in their study. Their results show that for the hard PZT ceramics under compressive uniaxial stress T3, with the increase of T3 from 0 MPa to 75 MPa, the piezoelectric strain coefficient d31 increased proportionally by around 50%, and the dielectric permittivity ε33 also increased almost linearly by 60%. However, considering that the compressive stress level in our study is in the order of 10−2 MPa, the stress effect to the coefficient of d31 and ε33 is negligible. In addition, in both studies of Zhang et al. [24] and Safour et al. [15], the Young’s Modulus YE has even less change under the uniaxial compressive stress compared with d31 and ε33, so that its change can also be ignorable. Therefore, in this study, the effect of stress on PZT material properties to impedance response is insignificant.

6.3. The Effect of Stress on PZT Geometry Change to Impedance Response Since in Equation (7), Y is also a function of PZT geometry, it is necessary to investigate the stress effects to variations of PZT geometry to evaluate its influence on the impedance response. More specifically, geometry parameters of w, l and h—which are the width, length and thickness of the PZT sensor—were taken into consideration. Finite element model (FEM) simulation analysis of the

Sensors 2020, 20, 2830 12 of 14

6.2. The Effect of Stress on PZT Material Properties to Impedance Response Since in Equation (7), Y is a function of the PZT properties, it is necessary to investigate the stress effects to these parameters to evaluate its influence on the impedance response. Zhang et al. [24] studied the effect of mechanical stresses on the responses of PZT sensors. Both the soft-type PZT and hard-type PZT were selected in their study. Their results show that for the hard PZT ceramics under compressive uniaxial stress T3, with the increase of T3 from 0 MPa to 75 MPa, the piezoelectric strain coefficient d31 increased proportionally by around 50%, and the dielectric permittivity ε33 also increased almost linearly by 60%. However, considering that the compressive stress level in our study is in the order of 2 10− MPa, the stress effect to the coefficient of d31 and ε33 is negligible. In addition, in both studies of Zhang et al. [24] and Safour et al. [15], the Young’s Modulus YE has even less change under the uniaxial compressive stress compared with d31 and ε33, so that its change can also be ignorable. Therefore, in this study, the effect of stress on PZT material properties to impedance response is insignificant.

6.3. The Effect of Stress on PZT Geometry Change to Impedance Response Since in Equation (7), Y is also a function of PZT geometry, it is necessary to investigate the stress effects to variations of PZT geometry to evaluate its influence on the impedance response. More specifically, geometry parameters of w, l and h—which are the width, length and thickness of the Sensors 2020, 20, x FOR PEER REVIEW 12 of 14 PZT sensor—were taken into consideration. Finite element model (FEM) simulation analysis of the PZT sensorPZT sensor under under static static normal normal pressure pressure was performed. was performed. The material The material properties, properties, element element type and type mesh and sizemesh were size thewere same the assame described as described in the in impedance the impedance simulation simulation section. section. The bottom The bottom surface surface of the of PZT the sensorPZT sensor was applied was applied a mechanical a mechanical boundary boundary condition condition with fixed with displacement fixed displacement in all three in directions. all three Thedirections. top surface The top of thesurface PZT of sensor the PZT was sensor applied was a staticapplied normal a static pressure normal loadpressure of 6.29 load kPa, of which6.29 kPa is, thewhich maximum is the maximum load shown load in shown Table3. in Figure Table 14 3. showsFigure the14 shows displacement the displacement distribution distribution in the thickness in the 11 direction.thickness direction. The maximum The maximum displacement displacement in the thickness in the thickness direction isdirection2.457 is 10-2.457− m. × 10 For−11 m. the For width the 11 − × 11 and length direction, the maximum displacements are 1.621 10 m and 1.885−11 10 m, respectively.−11 width and length direction, the maximum displacements× are− 1.621 × 10 m× and− 1.885 × 10 m, Byrespectively. plugging theseBy plugging changes these into changes Equation into (7), Equation we found (7 that), we the found overall that changes the overall to the changes impedance to the responseimpedance are response at the level are at of the 0.0002%. level of This 0.0002%. change This is essentiallychange is essentially extremely extremely small compared small compared with the experimentwith the experiment results, which results have, which a change have a ofchange 5% in of the 5% amplitude in the amplitude decrease. decrease. Therefore, Therefore,in this studyin this, thestudy, effect the of effect stress of on stress PZT on geometry PZT geometry changes changes to impedance to impedance response response can be neglected. can be neglected.

FigureFigure 14.14. DisplacementDisplacement distribution of a PZTPZT sensorsensor inin thicknessthickness directiondirection underunder aa staticstatic pressurepressure loadload ofof 6.296.29 kPa.kPa. (U(U andand U3U3 areare displacementdisplacement inin m.).m.).

7.7. Conclusions andand FutureFuture WorkWork BasedBased on on the the robotic robotic electronic electronic skin technology skin technology developed developed by Stanford by Structures Stanford and Structures Composites and Laboratory,Composites Laboratory, this work isthis focused work is on focused the study on the of study tactile of tactile sensing sensing for static for static pressure pressure using using an electromechanicalan electromechanical impedance-based impedance-based method. method. A smart A skinsmart sample skin samplewith an embeddedwith an embedded lead zirconate lead titanatezirconate (PZT) titanate sensor (PZT) was fabricated,sensor was and fabricated, a set of static and pressurea set of static load experimentspressure load were experiments performed. were The collectedperformed. impedance The collected data from impedance the embedded data PZT from sensor the embedded showed a consistent PZT sensor decrease showed in the a amplitude consistent ofdecrease ﬁrst peak in inthe the amplitude real part impedance, of first peak with in thethe increasereal part of impedance the applied, staticwith pressurethe increase load. of A the diagnostic applied static pressure load. A diagnostic method was proposed, which can successfully distinguish a force resolution of 0.5 N. A numerical simulation was performed to verify the change of the impedance response in the experiment, which is closely related to the stiffness change of the silicone rubber due to load effects. Finally, based on the theoretical model, different effects for the impedance response were discussed. Again, the stiffness change of the silicone rubber skin due to applied static pressure was proven to be the dominant factor for the impedance change in this study. Future work includes: (a) applying this transduction mechanism to a real robotic gripper to realize the dexterous manipulation of pick and drop; (b) investigating higher static pressure load range, where not only the silicone material property will change, but so too will the piezoelectric material property; and (c) studying the impedance response to other load conditions, such as non- uniform stress.

Funding: This work was supported in part by the National Science Foundation, and in part by the National Robotics Initiative under Grant 1528145.

Acknowledgments: The authors would like to thank Fotis Kopsaftopoulos at Rensselaer Polytechnic Institute and Raphael Nardari at Zenith Aerospace for their insights and guidance through scientific discussions to initiate this project.

Sensors 2020, 20, 2830 13 of 14 method was proposed, which can successfully distinguish a force resolution of 0.5 N. A numerical simulation was performed to verify the change of the impedance response in the experiment, which is closely related to the stiffness change of the silicone rubber due to load effects. Finally, based on the theoretical model, different effects for the impedance response were discussed. Again, the stiffness change of the silicone rubber skin due to applied static pressure was proven to be the dominant factor for the impedance change in this study. Future work includes: (a) applying this transduction mechanism to a real robotic gripper to realize the dexterous manipulation of pick and drop; (b) investigating higher static pressure load range, where not only the silicone material property will change, but so too will the piezoelectric material property; and (c) studying the impedance response to other load conditions, such as non-uniform stress.

Author Contributions: Methodology, C.L.; software, C.L., Y.Z. and A.N; validation, C.L., A.N. and M.F.H.; formal analysis, C.L., A.N., Y.Z. and L.L.; investigation, C.L. and L.L.; writing—original draft preparation, C.L.; writing—review and editing, Y.Z. and A.N.; supervision, F.-K.C.; and funding acquisition, F.-K.C. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported in part by the National Science Foundation, and in part by the National Robotics Initiative under Grant 1528145. Acknowledgments: The authors would like to thank Fotis Kopsaftopoulos at Rensselaer Polytechnic Institute and Raphael Nardari at Zenith Aerospace for their insights and guidance through scientific discussions to initiate this project. Conflicts of Interest: The authors declare no conflict of interest.

References

1. Jacobsen, S.C.; Wood, J.E.; Knutti, D.; Biggers, K.B. The UTAH/MIT dextrous hand: Work in progress. Int. J. Robot. Res. 1984, 3, 21–50. [CrossRef] 2. Dahiya, R.S.; Metta, G.; Valle, M.; Sandini, G. Tactile sensing—From humans to humanoids. IEEE Trans. Robot. 2009, 26, 1–20. [CrossRef] 3. Lee, M.H. Tactile sensing: New directions, new challenges. Int. J. Robot. Res. 2000, 19, 636–643. [CrossRef] 4. Cutkosky, M.R.; Howe, R.D.; Provancher, W.R. Force and Tactile Sensors. Springer Handb. Robot. 2008, 100, 455–476. 5. Howe, R.D. Tactile sensing and control of robotic manipulation. Adv. Robot. 1993, 8, 245–261. [CrossRef] 6. Chen, X.; Topac, T.; Smith, W.; Ladpli, P.; Liu, C.; Chang, F.-K. Characterization of Distributed Microfabricated Strain Gauges on Stretchable Sensor Networks for Structural Applications. Sensors 2018, 18, 3260. [CrossRef] [PubMed] 7. Guo, Z. Robust Design and Fabrication of Highly Stretchable Sensor Networks for the Creation of Intelligent Materials; Stanford University: Stanford, CA, USA, 2014. 8. Stassi, S.; Cauda, V.; Canavese, G.; Pirri, C.F. Flexible tactile sensing based on piezoresistive composites: A review. Sensors 2014, 14, 5296–5332. [CrossRef][PubMed] 9. Zou, L.; Ge, C.; Wang, Z.J.; Cretu, E.; Li, X. Novel tactile sensor technology and smart tactile sensing systems: A review. Sensors 2017, 17, 2653. [CrossRef][PubMed] 10. Chi, C.; Sun, X.; Xue, N.; Li, T.; Liu, C. Recent progress in technologies for tactile sensors. Sensors 2018, 18, 948. [CrossRef] 11. Huh, T.M.; Liu, C.; Hashizume, J.; Chen, T.G.; Suresh, S.A.; Chang, F.-K.; Cutkosky, M.R. Active sensing for measuring contact of thin ﬁlm gecko-inspired adhesives. IEEE Robot. Autom. Lett. 2018, 3, 3263–3270. [CrossRef] 12. Almassri, A.M.; Wan Hasan, W.; Ahmad, S.A.; Ishak, A.J.; Ghazali, A.; Talib, D.; Wada, C. Pressure sensor: State of the art, design, and application for robotic hand. J. Sens. 2015, 2015. [CrossRef] 13. Cheng, Y.; Wu, D.; Hao, S.; Jie, Y.; Cao, X.; Wang, N.; Wang, Z.L. Highly stretchable triboelectric tactile sensor for electronic skin. Nano Energy 2019, 64, 103907. [CrossRef] 14. Shin, K.; Lee, S.; Min, K.; Ko, D.; Mun, J.H. Methodology for Force Measurement Using Piezoelectric Ceramic; World Congress on Medical Physics and Biomedical Engineering 2006, 2007; Springer: Berlin/Heidelberg, Germany, 2007; pp. 853–856. Sensors 2020, 20, 2830 14 of 14

15. Safour, S.; Bernard, Y. Static force transducer based on resonant piezoelectric structure: Root cause investigation. Smart Mater. Struct. 2017, 26, 055012. [CrossRef] 16. Ozeri, S.; Shmilovitz, D. Static Force Measurement by Piezoelectric Sensors, 2006 IEEE International Symposium on Circuits and Systems, 2006; IEEE: Island of Kos, Greece, 2006; p. 4. 17. Sparks, J.L.; Vavalle, N.A.; Kasting, K.E.; Long, B.; Tanaka, M.L.; Sanger, P.A.; Schnell, K.; Conner-Kerr, T.A. Use of silicone materials to simulate tissue biomechanics as related to deep tissue injury. Adv. Skin Wound Care 2015, 28, 59–68. [CrossRef] 18. Zhuang, Y.; Kopsaftopoulos, F.; Dugnani, R.; Chang, F.-K. Integrity monitoring of adhesively bonded joints via an electromechanical impedance-based approach. Struct. Health Monit. 2018, 17, 1031–1045. [CrossRef] 19. Folds, D. Speed of sound and transmission loss in silicone rubbers at ultrasonic frequencies. J. Acoust. Soc. Am. 1974, 56, 1295–1296. [CrossRef] 20. Mohamed, M.; Samy, A.; Ali, W. Friction coefficient of rubber shoes sliding against ceramic flooring. KGK-Kautsch. Gummi Kunstst. 2012, 65, 52. 21. Elsayed, Y.; Vincensi, A.; Lekakou, C.; Geng, T.; Saaj, C.; Ranzani, T.; Cianchetti, M.; Menciassi, A. Finite element analysis and design optimization of a pneumatically actuating silicone module for robotic surgery applications. Soft Robot. 2014, 1, 255–262. [CrossRef] 22. Song, B.; Chen, W. One-Dimensional dynamic compressive behavior of EPDM rubber. J. Eng. Mater. Technol. 2003, 125, 294–301. [CrossRef] 23. Liang, C.; Sun, F.P.; Rogers, C.A. Coupled electro-mechanical analysis of adaptive material systems-determination of the actuator power consumption and system energy transfer. J. Intell. Mater. Syst. Struct. 1997, 8, 335–343. [CrossRef] 24. Zhang, Q.M.; Zhao, J. Electromechanical properties of lead zirconate titanate piezoceramics under the influence of mechanical stresses. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 1999, 46, 1518–1526. [CrossRef][PubMed]

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).