Sensors and Actuators A: Physical Piezoresistive sensor ﬁber composites based on silicone elastomers for the monitoring of the position of a robot arm

Combining conductive ﬁllers like black with allows the development of elastomer sensors that can reach very large elongations, an important requirement for many robotic applications. However, when the conductive ﬁller is introduced in the polymer, signiﬁcant stiffening occurs, affecting the mechanical properties, e.g. Young’s Modulus, of the soft structure. In this attempt, single piezoresistive ﬁber composites were successfully fabricated, without drastically increasing the stiffness. Two silicone elastomers that are widely used in robotic applications were examined as matrix materials. Furthermore, modeling the stresses exerted on the ﬁber inside the composite was successfully used to predict the detachment of ﬁber inside the matrix, observed by visual inspection. For the PDMS based composite, pre-straining improved sensor properties, which could be conﬁrmed for the monitoring of the movement of the crane robot. The results showed that the pre-strained piezoresistive sensor ﬁber-matrix composites positions of the robot crane can be monitored even at low strains.


Introduction
Robotic systems and automation can be found in many industrial production lines for a wide field of products, performing very demanding tasks that require large forces and high accuracy [1][2][3]. While encoder systems are sufficient for applications involving stiff robots [4,5], when it comes to soft robotics, rigid sensors can't be used. Soft robotic sensors, like strain sensors, are of interest because they allow monitoring the motion of soft robotic systems for better controlling, which helps to improve the functionality of complex robotic systems [6][7][8]. The piezoresistive signal can be used to create a closed-loop control system for the actuator. For this task, the sensor signal must be detectable, reliable and reproducible [9][10][11][12]. Soft sensors based on elastomers can reach large elongations and can conform to complex geometries and structures [13][14][15].
To be able to use strain sensitive elastomer-based sensor materials in practical applications, they are embedded either inside or on the surface of a stretchable structure. Yang et al. and Shintake et al. have integrated sensors in robotic systems like robotic grippers [16,17]. Sensors integrated into a silicone matrix are preferred because of their easy processing and their ability to stretch to large strains [18]. Silicone elastomers are used widely in many soft robotic applications as a structural material [19,20] and besides, silicone rubber is used for the fabrication of soft robotic sensors [9,21]. Silicone rubber-like PDMS (Polydimethylsiloxane) and EcoFlex are known for being lightweight and deformable. An important advantage of liquid silicone elastomers is their compatibility with simple fabrication methods like casting and are easy to work with for the fabrication of robotic systems such as sensors and actuators [22]. PDMS is a popular material option for integrating electronic structures such as sensors for biomedical applications [23][24][25][26]. It is non-toxic, has a low reactivity and can endure very large elongations [26,27].
Soft elastomer strain sensors based on the piezoresistive effect, made of silicone and carbon fillers can lose linearity during release from a certain strain [28][29][30]. Silicone rubber-based sensors will exhibit relaxation in the sensor signal because of the stress reaction of the elastomer [31]. It has been suggested that the application or retraction of a force with some dwell time can cause a distraction and reconstruction of the conductive paths, resulting in resistive recovery, decreasing the impedance and increasing the tunneling current [32]. The stress relaxation in silicone elastomers is a result of the rearrangement of the siloxane bond [33]. Both EcoFlex and PDMS show stress relaxation and this response depends on the shore hardness of the silicone rubber [34][35][36]. Because of the viscoelastic behavior, the material needs a certain time to return to its original shape. Typically, in a cycling test, the unloading phase is required to achieve full relaxation of the elastomer [37]. Due to the viscoelastic behavior, parameters like amplitude and applied strain rate affect the dynamic signal response of strain sensors [38]. Loss of linearity can have serious implications when comes to monitoring and controlling human or robotic movements.
EcoFlex is a popular material for robotic applications [39]. This silicone rubber has a lower elasticity in comparison to PDMS, and it can endure larger elongations than PDMS [40]. Many soft actuators like pneumatic actuators are manufactured using EcoFlex [41]. Giffney et al. developed a pneumatic bending actuator from EcoFlex with an integrated displacement sensor based on carbon nanotubes [42]. Ozel et al. designed a soft-bodied robotic snake from EcoFlex with integrated printed sensors by casting method. The sensor was printed on top of the casted snakeskin [43]. These studies showed the potential of soft silicone rubber in soft robotics and the combination with elastomer sensing. Nonetheless, PDMS as a material for embedding electronic elements provides less relative mobility for the electronic structures compared to the softer EcoFlex [44]. The effect of integrating an elastomer-based sensor like a sensor film or fiber in these materials has not yet been investigated. Soft strain sensor elements are not only integrated in soft robots, but they can also be attached on hinges and joints of hard robot arms and human bodies for the evaluation of the arm position and movement [26]. Cases of elastomer sensors were the whole volume of the structure was based on composites with carbon fillers had good sensitivity. However, these sensors had a limited strain range and it has not been reported that they can reach large elongations (>50 %) [29,[45][46][47].
In this study, a piezoresistive sensor fiber that has been developed in a previous study [48] will be integrated into two popular silicone rubber matrix materials (PDMS and EcoFlex) to investigate the behavior in robotic applications. Fiber composites have a significant advantage that they do not increase significantly the stiffness of the composite compared with cases where the entire volume of the soft material is enhanced filled with the particles. However, it has been proven in the past that embedding the fiber in an elastomer matrix, can affect the sensor properties [30]. This work is extended in this study, to the two most common commercial silicones: PDMS and EcoFlex. For better understanding the effect of fiber-matrix combination on strain sensor signal properties. For the first time, the effect of pre-straining the piezoresistive sensor fiber composite on the sensor behavior is being studied and the concept of pre-straining the strain sensor fiber-matrix composite is also applied for monitoring the movement of a crane robot.

Sensor Fiber preparation
The detailed description of the preparation of the sensor fibers has been published by Melnykowycz et al. [15]. In brief, 50 wt. % of ENSACO 250 carbon black (TIMCAL, Bodio, Switzerland) was mixed with 50 vol. % of a styrene-ethylene/butylene-styrene triblock copolymer thermoplastic elastomer (Kraiburg TPE, Waldkraiburg, Germany). After extrusion of fibers with a diameter of 0.3 mm using a capillary rheometer (NETZSCH-Gerätebau, Selb, Germany), the fibers were cut in the desired length. Electrical connections were made with silver wires, using conductive silver epoxy glue.

Sensor Fiber composite preparation
Custom-made 3D printed molds were designed and 3D printed using a Carftbot 2 Fused Deposition Modelling 3D printer (Craftunique, Budapest, Hungary) and using PLA filament from Fiberology (Fiberlab, Brezie, Poland). The dimensions of the molds were chosen to produce monofilament sensor composites with 130 mm length x10 mm width x3 mm thickness. The fiber with the attached silver wires was carefully attached to the mold and fixed properly with special metallic crimps. For the casting procedure, two, in robotic applications frequently used, commercial liquid silicone matrix materials were used. PDMS Dow Corning 3140 (Dow Corning, Midland, USA) and EcoFlex 00-30 (Smooth-on, Macungie, USA). In the case of the PDMS, the one component silicone was casted in the mold after fixing the sensor fibers. The liquid silicone nicely enclosed the fiber and curing time of 16 h at room temperature was used. In the case of the EcoFlex, casting was performed after mixing monomer and hardener 1:1 with a plastic syringe. Similar to PDMS it enclosed the fiber. After molding, the samples were cured for 40 h at room temperature.
Fixing electrical connections between the fiber and the silver wires inside the matrix during the casting improved mechanical robustness. The samples were visually examined with the multifocal optical microscope Zeiss Stereomicroscope (Carl Zeiss Microscopy, Jena, Germany) under magnification x44 ( Fig. 1c and d) in order to exclude fabrication defects.

Measuring the shore hardness
The shore hardness was measured using an HBA handheld analog durometer (Sauter, Balingen, Germany). According to DIN 53,505 the fiber composites were folded to 6 mm thick samples for measuring the shore hardness with the durometer.

Tensile testing
To examine the mechanical properties and the electrical performance of the piezoresistive fiber composites, tensile testing was performed. The tensile test was performed with a universal testing machine Zwick Roell Z005, (Zwick Roell, Ulm, Germany). The nominal tensile stress was calculated using the measured force divided by the initial cross-section of the samples. Pneumatic clamps were used to fix the sensor fiber composites. 4 bar pneumatic pressure was applied to minimize the slipping of the samples.
For the electrical resistance measurement, a source meter Keithley 2450 (Keithley Instruments, Solon, USA) was used in combination with the KickStart software from the same company. A two-terminal sensing mode was used to measure the electrical resistance by measuring the current, while the voltage was held constant at 1 V. From the resistance measurements the relative resistance R rel was calculated as shown in Eq. 1, where R is the measured resistance and R 0 the value of the resistance measured after the sensor was fixed in the clamps, e.g. without any straining being applied on the sensor.
The tensile experiments consisted of three different tests: Tensile test up the point of fracture, cycling straining test and quasistatic test. The tensile test up to failure (loading rate of 200 mm/min.) was performed, in order to assess the operational range and the sensitivity of the sensor system. The sensitivity was estimated using the gauge factor, as defined in Eq. 2: Where ε is the strain and R rel the relative resistance, measured at strain ε. Additionally, dynamic testing was performed by loading and releasing fiber composites in subsequent cycles between specified values of strain. The loading rate for the dynamic tensile test was 50 mm/sec and ten cycles were performed in each test.
Finally, in order to investigate the electrical and mechanical relaxation of the sensor fiber composites, the casted samples were strained to a value of strain and remained at this value of strain for 30 s. Afterward, the strain was released to the initial value of strain and holding for 30 s before repeating the same cycle. The loading rate applied to this quasi-static test was 50 mm/sec and up to five cycles were investigated.

Modeling of the stresses exerted on the fiber inside the composite
According to the general rule of mixtures, in the case of a composite assuming equal strain in the matrix and the fiber, the stress in the composite can be calculated by the equation: Where tot is the true stress exerted on the fiber composite, F is the true stress in the fiber inside the composite and M is the true stress in the matrix, A F is the cross-section area of the fiber, A M is the cross-section area of the matrix of the composite, and A tot is the cross-section area of the fiber composite.
In order to calculate the real stress, Eq. 4 was used: Where v is the Poisson's ratio.
The values used for the calculation were obtained from the tensile test at each strain value up to fracture for the pure fiber and the fiber composites. The real stress of the fiber inside the composite can therefore be calculated, using Eq. 5.

Crane robot fabrication and assembly
To investigate the soft sensor fiber composite for robotic applications under controlled conditions, the fiber composites were mounted on the hinge of a robotic arm. For this study, an opensource design, calledcrane robot, was printed with the Craftbot 2 printer and PLA. For the actuation of the crane robot, servomotors Dynamixel AX-12A (Robotis, Lake Forest, USA) and Arduino microcontroller were used. Fig. 2 shows the setup of the experiment.

Tensile testing of sensor fiber composites to the point of fracture
In order to assess the mechanical and electrical sensor behavior, the stress-strain curves determined with specimens made from matrix material only and specimens of sensor fiber composites were investigated as shown in Fig. 3.
As shown in Fig. 3, the composite based on PDMS matrix reaches higher strains in comparison the EcoFlex composite. In the case of the soft sensor fiber inside the EcoFlex matrix (Fig. 3a), the composite system was able to reach elongation up to 120 %. After reaching a strain of 10 %, the fiber composite based on EcoFlex is stiffer than the pure elastomer matrix. After casting, a shore hardness of 4A and 45A could be observed for the EcoFlex and PDMS materials, respectively. Comparing the two systems, the addition of the fiber in the composite stiffens the system much more for the EcoFlex based composite than for the PDMS. Additionally, the PDMS based fiber composite was able to reach much larger elongations.
During the tensile tests, the electrical resistance was measured in situ, in order to assess the piezoresistive sensor response (Fig. 4). In the case of the pure fiber, the Gauge Factor was very high: 28 and 47 for a strain below and above 110 %, respectively. However, in the case of the pure fiber, noise was observed, especially at strains higher than 60 %. Surprisingly, for both sensor fiber composites, the sensitivity dropped significantly compared to the pure sensor fiber. For the PDMS-based fiber composite, a Gauge Factor of 5 and 10 could be observed at strains below and above 120 %, respectively. The fiber composite based on PDMS could endure higher strains than the pure soft sensor fiber. This can be explained by a more homogeneous longitudinal stress being induced into the fiber. The EcoFlex-based composite had a Gauge Factor of 2.9. For the EcoFlex based composite, fracture occurred at lower strain and. Therefore,  the stress introduced into the fiber was not homogeneous which resulted in a lower strain to rupture.

Dynamic testing
The dynamic tensile testing was performed to investigate the sensor behavior under repeated loading and releasing. All experiments have been made with fibers, after the pre-straining procedure as explained in the experimental part. Looking at the mechanical response for the three sensor systems (Fig. 5), it was seen that there was a large hysteresis for the stress in all three fiber composites.
For the case of the pure sensor fiber (Fig. 5a), it was seen that the hysteresis for the mechanical stress (Table 1) was larger but no stress plateau can be observed. Interestingly, the hysteresis of both sensor fiber composites is smaller. The fiber composite with PDMS as a matrix material had the lowest hysteresis (51 %) but it was quite a large amount of hysteresis. Stress value of zero indicates the irreversible deformation behavior of the material. The stiffness of the soft sensor changes at 19 % strain, whereas the PDMS and EcoFlex-based composites show an irreversible deformation at 30 % and 16 % strain, respectively, after the first cycle. Table 1 shows the strain where the irreversible deformation appeared in the fifth cycle.
Looking at Fig. 6 and the response of the sensor signal during the dynamic test, in the case of the pure sensor fiber (Fig. 6a), the relative resistance followed loading and the unloading of the dynamic test. Fig. 6 shows, that the best sensor performance can be achieved by the pure sensor fiber. However, in the unloading part of the cycling, a decrease in the slope of the relative resistance (change in sensitivity) can be observed. This decrease corresponds with the strain range of the mechanical properties, where change in stiffness appeared (Table 1). After the first cycle, a good reproducibility of the electrical signal between the different cycles can be achieved with a very small drift of only 0.4 %.
In the case of the soft sensor fiber embedded in the silicone matrix, the response of the sensor fiber in the composite changed and the stiffness of the matrix seems to affect the piezoresistive behavior. Similar results have been already reported by Georgopoulou et al. in a previous study [30]. Unexpectedly, in the case of PDMS-based composite (Fig. 6b), a secondary peak appeared at a strain of 22 % and a lagging phase can be observed until 14 % strain for unloading and loading, respectively. The term lagging phase is used, when the relative resistance does not follow the change in

Table 1
Values of the initial resistance (Ro), the drift of the electrical signal between the second cycle and the last, the mechanical hysteresis, the strain range were buckling appears and the uncertainty in sensor signal expressed by the loss of linearity because of the appearance of a secondary peak or a plateau for the sensor fiber and the sensor fiber composites with PDMS and EcoFlex as a matrix material.  strain and remains almost constant. However, the drift of the signal at high strain is only 0.5 % between the second and the tenth cycle.
For the EcoFlex-based composite (Fig. 6c), the sensor behavior is completely different. In this case, the relative resistance decreased during the loading, when the strain increased and increased during the unloading when the strain decreased. This type of reversed piezoresistive response has been seen before in the case of conductive elastomer strain sensors [49]. However, the EcoFlex-based composite does not show a secondary peak, lagging phase or plateau as discussed earlier for the PDMS-based composite. The drift of the maximum relative resistance between each cycle is significant (20 %) and is a problem for robotic applications without an additional intelligent algorithm [50].

Model of the stresses in the fiber composite
Due to the three different sensor behaviors, the stresses exerted on the fiber, inside the composite was calculated by subtracting the stress values of the pure elastomer matrix from the stress value of the fiber composite at a given strain.
Looking at Fig. 7, it can be seen that the correlation between calculated and measured stress-strain behavior of the sensor fiber, using Eq. 5.
In the case of the PDMS-based fiber composite (Fig. 7a), the calculated stress exerted on the fiber inside the composite fit quite well with the one measured for the pure sensor fiber. From this observation, it can be concluded that the assumption of the model, e.g. stress over the surface area of the composite is constant, good adhesion between fiber and matrix, no slipping effect, was fulfilled. Therefore, a good mechanical load transfer between the PDMS matrix and the fiber can be assumed. Nonetheless, it can be observed that there is a strain range, where a deviation from the model can be observed around a strain of 18-22 % (Fig. 7b). This is the level of strain, where the appearance of a secondary peak in the relative electrical resistance was observed. This deviation can be a result of a detachment of the fiber inside the matrix at this strain. It is proposed, that the shear stress at the inter- face between the fiber and the matrix will be not transferred ideally.
In the case of the EcoFlex (Fig. 7c), it can be seen that calculated and measured stress-strain properties of the fiber did not fit. Based on these results and the analysis reported by Georgopoulou et al. [30], it can be assumed, that the mismatch of the mechanical properties between the sensor fiber and the elastomer matrix affects the bonding between the fiber and the matrix. A lower mechanical bonding, caused by a low shore hardness of the elastomer matrix, will result in a detachment of the fiber from the matrix and the model is not valid any longer. Finally, this results in a reverse piezoresistivity behavior of the sensor signal.

Dynamic testing with pre-straining conditions
According to the prediction of the model, difference in the mechanical properties between 10 and 30 % strain could be observed for the PDMS based composite. In this area (at 22 % strain, a secondary peak in the electrical signal of the sensor could be observed. Moreover, the PDMS-based composite revealed in lower strain hysteresis and the appearance of a secondary peak at 22 % strain. To ensure a good load and strain transfer from the matrix to the fiber, dynamic test was performed with a pre-strain of 30 %. The dynamic tests were cycled between 30-70 % strain. From the response of the stress (Fig. 8a), it can be seen that the hysteresis of the stress significantly decreased from 51 % to 10 % in the prestraining conditions and irreversible deformation during cycling could be avoided.
For the electrical signal (Fig. 8b), the resistance followed the change in strain both in loading and the unloading. No secondary peak can be observed under pre-straining conditions. At higher strains, the sensor had good linearity, reproducibility and low drift (1%) and all these elements can be important for applications where reliability and the ability to distinguish between different strains are important, like position monitoring of a robotic arm in the field of robotics.

Quasi-static testing
It is well known, that elastomers typically show mechanical relaxation under static strain conditions. Quasi-static cycling testing has been used for the characterization of soft sensor materials in literature to investigate the relaxation effects of the sensor signal [26,51]. Following the previous experiment for PDMS-based composite, the quasi-static testing was performed between 30-70 % strains. (Fig. 9).
For the case of the PDMS, the mechanical relaxation was 14 % at a strain level of 30 % and 11 % at a strain level of 70 % ( Table 2). For   the EcoFlex, the mechanical relaxation was 18 % for the strain level of 30 % and 13 % for the strain level of 70 %. Therefore, the EcoFlex exhibited higher mechanical relaxation than the PDMS. In situ, the electrical signal was recorded to investigate the effect of the relaxation on the electrical signal (Fig. 10).
As expected, for the PDMS-based composite the relative electrical resistance followed the change in strain. The relaxation of the relative resistance during the dwell time was 15 % for the strain level of 30 % and 4% for the strain level of 70 %, respectively. For the Ecoflex-based composite, the relative resistance decreased when the strain increased and increased when the strain decreased. Therefore, the sensor fiber composites showed the same results as already discussed for the dynamic testing. However, the static strain at 30 % resulted in a relaxation of 138 %, as can be seen from Fig. 9, with each cycle the relaxation increase for the EcoFlex-based composite.

Application: Sensor fiber composite for monitoring the position of the crane robot arm
To prove the applicability of the sensor fiber composite in robotic applications, the composite was mounted on the hinge of the crane robot to create a sensorized robotic arm. To prove the sensor fiber composite application, the PDMS-based composite was mechanically fixed on the crane robot with and without pre-straining (Fig. 11).
In order to be able to compare the results of the sensor signal on the robotic arm with the tensile tests, the hinge of the robot arm was flexed and extended to achieve 0-22 % strain in the fiber composite. The relative resistance value at 22 % was used to predict the strain of 28 % during tensile cycling (Table 3). This small difference in the values can be explained by the fact that the strain exerted on the robot is a non-uniform bending, while in the case of the ten-   sile testing, a uniaxial mechanical deformation occurs. The relative resistance followed the change in strain and the response of the sensor signal was reproducible over the ten cycles (Fig. 11 f). As expected, a secondary peak appeared (6% strain) for the unstrained fiber composite. The uncertainty in the sensor response is smaller in comparison to the dynamic tensile tests. One reason can be the different load transfer. The same experiment was repeated with a pre-strained sensor fiber composite. In this case, the fiber composite was mounted with a pre-strain of 30 % on the hinge of the robot arm. As expected, the secondary peak disappeared and the response of the sensor fiber composite was linear even at low strains. In this case, it was possible to distinguish the position of the robot from the position of the sensor signal for strains lower than 6%. For the pre-strained sensor fiber composite, during the releasing of the strain, when the robot arm was moving upwards, a lower value of the relative resistance could be assigned to every position of the robot arm (Fig. 11 a-e). Looking at the sensor signal and the value of the relative resistance, it was possible to determine the position of the robot arm and if the actuation was working properly.

Conclusions
In this study, sensor fiber composites based on silicone elastomers were developed and their performance was assessed for their potential to be used as piezoresistive strain sensors in robotic applications. By introducing elastomer-based piezoresistive fibers in an elastomer matrix using casting method, it was possible to produce a fiber composite for robotic applications. Two silicone elastomers, namely PDMS and EcoFlex, that are widely used in robotic applications were evaluated as matrix materials. The EcoFlex had ten times lower shore hardness in comparison to PDMS. An increase of the stiffness could be observed by the integration of a single piezoresistive fiber. For the EcoFlex based composite, the increase in stiffness was significantly higher. The sensor fiber composite based on PDMS could reach higher elongations than the single fiber, however the sensor signal sensitivity decreased.
Looking at the dynamic response, for the PDMS based composite the relative resistance followed the change in strain. In the case of the EcoFlex based composite, the relative resistance decreased, when the strain increased and vice versa (negative piezoresistive behavior). In order to explain the difference in the response of the two sensor fiber composites, a model based on the general rule of mixtures was used to calculate the stress exerted on the sensor fiber inside the composite. The model showed that in the case of the EcoFlex-based composite, the modelled stress-strain behavior of the sensor fiber inside the composite did not match with the measured stress-strain curve of the pure sensor fiber. This was caused by the detachment of the fiber inside the matrix. It is assumed that this was caused by the strong mismatch of the mechanical properties between the sensor fiber and he EcoFlex matrix.
For the PDMS-based fiber composite, the modelled stress-strain behavior of the fiber inside the composite, and the measured one were in congruity. However, at a strain between 16 % and 26 %, a deviation between the two stress-strain curves was observed. In this range, the secondary peak in the piezoresistive signal appeared during the tensile testing. By pre-straining the PDMS-based sensor fiber composite to 30 % strain, the secondary peak could be removed and the hysteresis of the sensor signal was significantly reduced. The same strategy, of pre-straining was applied to senorize the hinge of the crane robot and the results showed that the position of the robot arm could be detected, even at low strains after pre-straining of the fiber composite.
Overall, piezoresistive sensor fiber composites are an option for applications where it is desired that the stiffness of the structure does not increase significantly. Nevertheless, embedding the sensor fiber in an elastomer matrix affects the sensor properties. With the strategy of pre-straining the sensor fiber composite during mounting on the robotic structure, the sensor fiber composite can be used for detecting the position of the robot arm even at low strains.

Funding
This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 828,818 (SHERO Project).